JP4693555B2 - Two-dimensional image generation method and generation apparatus based on a three-dimensional virtual object with a fiber sheet attached to the surface - Google Patents

Description

  The present invention relates to a technique for creating a two-dimensional image when a three-dimensional virtual object with a fiber sheet attached to the surface is observed from a predetermined direction, and more particularly to a technique for rendering processing using a computer.

  Due to the improvement in computer performance, CG images are being used in various fields of industry. For example, in the design stage of buildings, furniture, automobiles, etc., many CG images are usually used. Also, various CG images of articles are indispensable for various video expressions such as product presentations and movies using computers. Furthermore, recently, there are many examples in which CG images are used instead of actual product photos in product catalogs and the like. In general, in the case of a product that has been commercialized through a design stage using CAD, it is possible to create a CG image using the CAD data used in the design. It becomes possible to create.

CAD data such as buildings, furniture, and automobile interior parts is three-dimensional data of a virtual object, whereas a CG image for presentation is usually prepared as a two-dimensional image. Therefore, when creating a CG image using CAD data, the 3D data of the virtual object is taken into the computer, the illumination condition, the viewpoint position, and the projection plane are set, and then the 2D of the 3D virtual object is set. A rendering process for obtaining a dimensional projection image on the projection plane is performed. This process basically simulates the phenomenon in which the illumination light from the light source determined by the illumination conditions is reflected at each part of the virtual object and travels to the viewpoint position on the computer. It can be said that the light intensity is calculated. When a sheet material with some pattern is pasted on the surface of the virtual object, prepare the pattern of the sheet material as texture data, map this pattern on the surface of the virtual object, and then reflect the reflectance. An operation is performed. For example, Patent Document 1 below discloses a technique of mapping a two-dimensional texture onto the surface of a three-dimensional object and then performing a rendering process to generate a two-dimensional image.
Japanese Patent Laying-Open No. 2005-63041

  For furniture such as chairs and sofas, car interiors, doormats and carpets, apparel products such as clothes, bags and shoes, sheets made of fibrous materials such as cloth (hereinafter referred to as fiber sheets) There are a lot of things that are attached. Thus, when generating a two-dimensional image obtained when a three-dimensional virtual object with a fiber sheet attached to the surface is observed from a predetermined viewpoint position under a predetermined illumination condition, the surface of the fiber sheet is usually used. The texture data for expressing is prepared, and the rendering process is performed after mapping the texture to the three-dimensional virtual object.

  However, when the conventional general texture mapping method is used, there is a problem that the characteristics of the material of the actual fiber sheet cannot be expressed sufficiently. In particular, the texture of fiber sheets such as denim, iridescent weave, towels, and velvet piles is very delicate, and conventional rendering methods cannot sufficiently express the texture on a two-dimensional image.

  Accordingly, the present invention provides a two-dimensional image in which the texture of the fiber is sufficiently expressed when generating two-dimensional data indicating a state in which a fiber sheet is attached to the surface of the virtual object based on the three-dimensional data of the virtual object. It is an object of the present invention to provide a two-dimensional image generation method and a generation apparatus capable of generating the image.

(1) The first aspect of the present invention is a two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of the object based on the three-dimensional data of the object and observed from a predetermined viewpoint. In a two-dimensional image generation method based on a three-dimensional virtual object that generates
A layer data input stage in which the computer inputs m layer data indicating reflection characteristics for each of a plurality of m layers constituting a virtual fiber sheet to be pasted;
A visual ratio information input stage in which a computer inputs visible ratio information indicating a visible ratio for each layer in a state where the fiber sheet is bent with various curvatures;
An object data input stage in which a computer inputs three-dimensional data indicating a three-dimensional shape of a virtual object;
A projection condition setting stage in which a computer sets illumination conditions, a viewpoint position, and a projection plane;
A curvature calculating step for calculating a curvature of the surface of the virtual object for a position of a predetermined sample point defined on the surface of the virtual object;
When the computer pastes the fiber sheet on the surface of the virtual object, the reflected light intensity calculation stage for calculating the intensity of the reflected light from each sample point toward the viewpoint position;
A pixel defining stage in which a computer defines a pixel having a pixel value corresponding to the intensity of the reflected light at the intersection of the reflected light from the sample point and the projection plane;
A projection data generation stage in which a computer generates two-dimensional projection data representing a projection image of a virtual object by a set of a large number of pixels defined for a large number of sample points;
And run
In the reflected light intensity calculation stage, when calculating the reflected light intensity from one sample point,
A first step of determining a visible ratio for each layer corresponding to the curvature at the sample point position with reference to the visible ratio information;
A second step of obtaining the reflection characteristic at the sample point position by combining the reflection characteristics of the m kinds of layer data according to the visible ratio obtained in the first step;
A third step for determining the intensity of the reflected light from the sample point based on the reflection characteristics obtained in the second step;
Is to do.

(2) According to a second aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first aspect described above, the fiber sheet is attached to the surface.
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, find the curvature with a factor of direction,
In the first step of the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the curvature having the orientation factor is obtained.

(3) According to a third aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the second aspect described above, the fiber sheet is attached to the surface.
In the visible ratio information input stage, the visible ratio for each layer in a state where the fiber sheet is stuck to the cylinder side in a predetermined direction is defined, the curvature σ is defined using the reciprocal of the radius of the cylinder, and the central axis of the cylinder is defined. The angle ξ formed by the projection line obtained by projecting in the radial direction on the side surface of the cylinder and the reference direction line of the fiber sheet is defined as a curvature angle with respect to the curvature σ, and each curvature σ and each curvature angle ξ Enter visibility ratio information that indicates the visibility ratio for each layer corresponding to each combination,
In the object data input stage, information on the direction of the reference direction line of the fiber sheet attached on the virtual object is input,
In the curvature calculation stage, the curvature angle ξ indicating the deviation between the curvature direction and the reference direction line according to the curvature σ and the curvature direction σ is obtained by referring to the information on the direction of the reference direction line for the position of the predetermined sample point. Seeking
In the first step of the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the combination of the curvature σ and the curvature angle ξ is obtained.

(4) According to a fourth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first to third aspects described above, the fiber sheet is attached to the surface.
In the layer data input stage, a two-dimensional image having reflection characteristics indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system is input as layer data for each individual layer,
In the second step of the reflected light intensity calculation stage, the value of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the sample point position is determined by the visible ratio obtained in the first step. By combining in accordance with the weighting, the reflection coefficient k at the sample point position is obtained,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflected light intensity I is calculated using the reflection coefficient k,
I = k · Ii
It is obtained by the following formula.

(5) According to a fifth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object having a fiber sheet attached to the surface according to the first to third aspects described above,
At the layer data input stage, the diffuse reflection coefficient for each layer is input as layer data.
In the second step of the reflected light intensity calculation stage, the diffuse reflection coefficient kd at the sample point position is obtained by synthesizing the diffuse reflection coefficient for each layer according to the weighting by the visible ratio obtained in the first step. Seeking
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, and the angle between the normal line n set at the sample point position on the virtual object surface and the incident illumination light is α And the reflected light intensity I,
I = kd ・ Ii ・ cos α
It is obtained by the following formula.

(6) According to a sixth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the fifth aspect, the fiber sheet is attached to the surface.
In the layer data input stage, a two-dimensional image having a diffuse reflection coefficient indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system is input as layer data for each individual layer,
In the second step of the reflected light intensity calculation stage, the value of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the sample point position is determined by the visible ratio obtained in the first step. The diffuse reflection coefficient kd at the sample point position is obtained by combining in accordance with the weighting.

(7) According to a seventh aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first to third aspects described above, the fiber sheet is attached to the surface.
In the layer data input stage, the reflection coefficient k (α) depending on the angle α formed by the normal n standing on the layer surface and the illumination light, and the parameter β indicating the sharpness of specular reflection are input as layer data. ,
In the second step of the reflected light intensity calculation stage, the angle formed between the normal n set at the sample point position on the virtual object surface and the incident illumination light is α, the emission direction of the specular reflection light at the sample point and the viewpoint direction When the angle formed by γ is γ, refer to the layer data for the reflection coefficient for each layer,
k (α) ・ cos ^β γ
The reflection coefficient k at each sample point is obtained by combining the obtained reflection coefficient for each layer according to the weighting by the visible ratio obtained in the first step,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflected light intensity I is calculated using the reflection coefficient k,
I = k · Ii
It is obtained by the following formula.

(8) According to an eighth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the seventh aspect described above, a fiber sheet attached to the surface.
Instead of k (α), the reflection coefficient depending on the angle α is a coefficient ks that does not depend on the angle α.
ks ・ cos ^β γ
It is obtained by the following formula.

(9) According to a ninth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first to third aspects described above, the fiber sheet is attached to the surface.
In the layer data input stage, the angle between the normal line n set at a predetermined point on the layer surface and the illumination light is θL, the projected image of the illumination light on the layer surface and the reference line passing through the predetermined point on the layer surface When the angle between the normal line n and the reflected light is θV, and the angle between the projected image of the reflected light on the layer surface and the reference line is φV, “θL, φL, θV, The reflection coefficient kb (θL, φL, θV, φV) given as a function of “φV” is input as layer data for each layer,
In the visible ratio information input stage, for each of various combinations of “curvature, θL, φL, θV, φV”, the visible ratio information indicating the visible ratio for each layer is input.
In the reflected light intensity calculation stage, the angle between the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and the projected image of the incident illumination light on the orthogonal plane orthogonal to the normal line n The angle formed by the reference line passing through the sample point on the orthogonal plane is φL, the angle formed by the normal line n and the reflected light is θV, and the angle formed by the projected image of the reflected light on the orthogonal plane and the reference line is φV. Define
In the first step of the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the combination of “curvature, θL, φL, θV, φV” at the sample point position is obtained by referring to the visible ratio information,
In the second step of the reflected light intensity calculation stage, the reflection coefficient kb (θL, φL, θV, φV) corresponding to the combination of “θL, φL, θV, φV” at the sample point position is referred to by referring to the layer data. For each layer, and by combining the obtained reflection coefficients kb according to the weighting by the visible ratio obtained in the first step, the reflection coefficient kb at the sample point position is obtained,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflection from the sample point is performed using the reflection coefficient kb at the sample point position obtained in the second step. The light intensity I,
I = kb · Ii
It is obtained by the following formula.

(10) According to a tenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first to third aspects described above, the fiber sheet is attached to the surface.
In the layer data input stage, the angle between the normal line n set at a predetermined point on the layer surface and the illumination light is θL, and the projection image of the illumination light on the layer surface and the reference line passing through the predetermined point on the layer surface The angle formed by φL, the angle formed by the normal n and the reflected light is θV, the angle formed by the projected image of the reflected light on the layer surface and the reference line is φV, and the uv two-dimensional coordinate system defined on the layer surface Is the reflection coefficient kb (θL, φL, θV, φV, u, v) given as a function of “θL, φL, θV, φV, u, v” ) As the layer data for each layer,
In the visible ratio information input stage, for each of various combinations of “curvature, θL, φL, θV, φV, u, v”, the visible ratio information indicating the visible ratio for each layer is input.
In the reflected light intensity calculation stage, the angle between the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and the projected image of the incident illumination light on the orthogonal plane orthogonal to the normal line n The angle formed by the reference line passing through the sample point on the orthogonal plane is φL, the angle formed by the normal line n and the reflected light is θV, the angle formed by the projected image of the reflected light on the orthogonal plane and the reference line is φV, Define the coordinate value of the sample point as (u, v),
In the first step of the reflected light intensity calculation stage, by referring to the visible ratio information, the visible for each layer corresponding to the combination of “curvature, θL, φL, θV, φV, u, v” of the sample point position is obtained. Find the percentage,
In the second step of the reflected light intensity calculation stage, the reflection coefficient kb (θL, φL, corresponding to the combination of “θL, φL, θV, φV, u, v” at the sample point position is referred to by referring to the layer data. θV, φV, u, v) is obtained for each layer, and the obtained reflection coefficients kb are synthesized in accordance with the weighting by the visible ratio obtained in the first step, thereby obtaining the reflection coefficient at the sample point position. Find kb,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflection from the sample point is performed using the reflection coefficient kb at the sample point position obtained in the second step. The light intensity I,
I = kb · Ii
It is obtained by the following formula.

(11) In an eleventh aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above-described first to tenth aspects, a fiber sheet is attached to the surface.
In the curvature calculation stage, as the curvature for a specific sample point Q, the curvature in the vicinity of the sample point Q of the contour line of the virtual object appearing on the cut surface obtained by cutting the virtual object by a predetermined plane including the sample point Q is obtained. Is.

(12) According to a twelfth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the eleventh aspect, the fiber sheet is attached to the surface.
Two points QL and QR that are equidistant from the sample point Q along the contour line are defined on both sides of the sample point Q on the contour line of the virtual object that appears on the cut surface, and the contour line at the point QL is defined on the cut surface. An intersection point QQ between a line perpendicular to the tangent line TL and a line perpendicular to the tangent line TR of the contour line at the point QR is obtained, and the reciprocal of the distance r between the sample point Q and the intersection point QQ is defined as the curvature σ of the sample point Q. It is what I did.

(13) According to a thirteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above-described first to tenth aspects, the fiber sheet is attached to the surface.
In the object data input stage, the solid shape of the virtual object is input as a polygonal aggregate,
When obtaining the curvature for a specific sample point Q in the curvature calculation stage, for the target polygon having J sides including the specific sample point, the target polygon and a plurality of J adjacent to the target polygon are adjacent to the target polygon. The formation angles ω1 to ωJ about the inside of the virtual object between the polygon and the polygon are obtained, respectively, and the jth formation is used as the curvature with respect to the jth side forming the boundary with the jth adjacent polygon. The j-th forming angle ωj has an absolute value that decreases as the angle ωj approaches 180 ° and decreases as the size of the target polygon and the j-th adjacent polygon increases. And a curvature σj having a sign corresponding to the magnitude relationship between and 180 °, and the curvatures σ1 to σJ are defined for the first side to the Jth side, respectively, and a specific sample point and the jth side Short if the distance to is short More, so that the influence of the j-th curvature σj increases, by synthesizing the J curvature Shiguma1～shigumaJ, is obtained so as to obtain a curvature σQ for sample point Q.

(14) According to a fourteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the thirteenth aspect, the fiber sheet is attached to the surface.
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the reference direction line indicating the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, angles ξ1 to ξJ formed by the reference direction line and each of the first side to the Jth side of the target polygon are obtained as curvature angles for each side, and the sample point Q and The curvature angle ξQ for the sample point Q is synthesized by combining the J curvature angles ξ1 to ξJ so that the influence of the jth curvature angle ξj increases as the distance to the jth side becomes shorter. Seeking
In the first step of the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the curvature having the orientation factor indicated by the curvature angle ξQ is obtained.

(15) According to a fifteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the first to tenth aspects, the fiber sheet is attached to the surface.
In the object data input stage, the three-dimensional shape of the virtual object is input as a collection of triangles,
When calculating the curvature for a specific sample point Q in the curvature calculation stage, the target triangle Tq including the specific sample point is adjacent to the target triangle Tq and sides A, B, and C as boundaries. The formation angles ωa, ωb, and ωc about the inside of the virtual object between the adjacent triangles Ta, Tb, and Tc are respectively obtained, and the curvature with respect to the side A becomes smaller as the formation angle ωa approaches 180 °, In addition, a curvature σa having an absolute value that decreases as the size of the target triangle Tq and the adjacent triangle Ta increases, and having a sign corresponding to the magnitude relationship between the formation angle ωa and 180 °, is defined as side B As for the curvature, the smaller the formation angle ωb is closer to 180 °, the smaller the curvature is, and the smaller the size of the target triangle Tq and the adjacent triangle Tb is. And the curvature σb having a sign corresponding to the magnitude relationship between the forming angle ωb and 180 ° is defined, and the curvature with respect to the side C becomes smaller as the forming angle ωc approaches 180 °, And defining a curvature σc having an absolute value that decreases as the size of the target triangle Tq and the adjacent triangle Tc increases, and having a sign corresponding to the magnitude relationship between the formation angle ωc and 180 °, The shorter the distance between Q and side A, the greater the effect of curvature σa, and the shorter the distance between sample point Q and side B, the greater the effect of curvature σb. The curvature σQ for the sample point Q is obtained by combining the curvatures σa, σb, and σc so that the influence of the curvature σc increases as the distance becomes shorter.

(16) According to a sixteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the fifteenth aspect, the fiber sheet is attached to the surface.
When defining the curvature with respect to the side A, the length hqa of the perpendicular line from the diagonal to the side A of the triangle Tq of interest to the side A and the length of the perpendicular line from the diagonal to the side A of the adjacent triangle Ta to the side A And a line segment having a length hqa and a line segment having a length ha are connected to each other at a connection point Ja, and a connection point is obtained. The angle between both line segments in Ja is arranged to be the formation angle ωa, and the vertical bisector of “line segment with length hqa” and the vertical bisector of “line segment with length ha” The reciprocal of the distance Ra between the intersection Oa and the connection point Ja with the dividing line is defined as the absolute value of the curvature σa with respect to the side A,
When defining the curvature with respect to the side B, the length hqb of the perpendicular line from the diagonal of the triangle Tq to the side B to the side B and the length of the perpendicular line from the diagonal to the side B of the adjacent triangle Tb to the side B Hb, and “on a plane, a line segment having a length hqb” and “a line segment having a length hb” are connected to each other at a connection point Jb. Arranged so that the angle formed by both line segments in Jb is the forming angle ωb, the vertical bisector of “line segment having length hqb” and the vertical bisector of “line segment having length hb” The reciprocal of the distance Rb between the intersection Ob with the segment and the connection point Jb is defined as the absolute value of the curvature σb with respect to the side B,
When defining the curvature with respect to the side C, the length hqc of the perpendicular line from the diagonal to the side C of the triangle Tq of interest to the side C and the length of the perpendicular line from the diagonal to the side C of the adjacent triangle Tc to the side C The length hc is obtained, and one end of each of the “line segment having the length hqc” and the “line segment having the length hc” is connected at the connection point Jc on the plane, and the connection point Arranged so that the angle formed by both line segments in Jc is the formation angle ωc, the vertical bisector of “line segment having length hqc” and the vertical bisector of “line segment having length hc” The reciprocal of the distance Rc between the intersection Oc with the segment and the connection point Jc is defined as the absolute value of the curvature σc with respect to the side C.

(17) According to a seventeenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the fifteenth or sixteenth aspect, a fiber sheet is attached to the surface.
When obtaining the curvature σQ for the sample point Q, the distance between the diagonal of the target triangle Tq with respect to the side A and the sample point Q is La, the distance between the diagonal of the target triangle Tq with respect to the side B and the sample point Q is Lb, When the distance between the diagonal to the side C of the triangle of interest Tq and the sample point Q is Lc,
σQ = (La · σa + Lb · σb + Lc · σc) / (La + Lb + Lc)
The operation is performed as follows.

(18) According to an eighteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the fifteenth or sixteenth aspect, a fiber sheet is attached to the surface.
In determining the curvature σQ for the sample point Q, a perpendicular line from the sample point Q to the side A, a perpendicular line from the sample point Q to the side B, and a perpendicular line from the sample point Q to the side C, The target triangle Tq is divided into three regions, the area of the region including the diagonal to the side A is Ua, the area of the region including the diagonal to the side B is Ub, and the area of the region including the diagonal to the side C is Uc. When
σQ = (Ua · σa + Ub · σb + Uc · σc) / (Ua + Ub + Uc)
The operation is performed as follows.

(19) According to a nineteenth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above-described fifteenth to eighteenth aspects, a fiber sheet is attached to the surface.
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the reference direction line indicating the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, angles ξa, ξb, and ξc formed by the reference direction line and each of the sides A, B, and C of the target triangle are respectively obtained as the curvature angles for the respective sides, and the sample point Q, side A, and The shorter the distance, the greater the influence of the curvature angle ξa, and the shorter the distance between the sample point Q and the side B, the greater the influence of the curvature angle ξb, and the shorter the distance between the sample point Q and the side C. The curvature angle ξQ for the sample point Q is obtained by synthesizing the curvature angles ξa, ξb, and ξc so that the influence of the curvature angle ξc becomes larger as the length becomes shorter.
In the first step of the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the curvature having the orientation factor indicated by the curvature angle ξQ is obtained.

(20) According to a twentieth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the nineteenth aspect, the fiber sheet is attached to the surface.
When obtaining the curvature angle ξQ for the sample point Q, the distance between the diagonal of the target triangle Tq with respect to the side A and the sample point Q is La, and the distance between the diagonal of the target triangle Tq with respect to the side B and the sample point Q is Lb. When the distance between the diagonal to the side C of the triangle Tq of interest and the sample point Q is Lc,
ξQ = (La · ξa + Lb · ξb + Lc · ξc) / (La + Lb + Lc)
The operation is performed as follows.

(21) According to a twenty-first aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the nineteenth aspect, the fiber sheet is attached to the surface.
When determining the curvature angle ξQ for the sample point Q, a perpendicular line from the sample point Q to the side A, a perpendicular line from the sample point Q to the side B, and a perpendicular line from the sample point Q to the side C The target triangle Tq is divided into three regions, the area of the region including the diagonal to the side A is Ua, the area of the region including the diagonal to the side B is Ub, and the area of the region including the diagonal to the side C is Uc And when
σQ = (Ua · ξa + Ub · ξb + Uc · ξc) / (Ua + Ub + Uc)
The operation is performed as follows.

(22) According to a twenty-second aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above-described first to tenth aspects, a fiber sheet is attached to the surface.
In the object data input stage, the three-dimensional shape of the virtual object is input as a parametric curved surface expressed by a mathematical formula and the parameter value used in the mathematical formula,
In the curvature calculation stage, the curvature for a specific sample point Q is obtained by calculation using mathematical formulas and parameter values.

(23) According to a twenty-third aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above first to twenty-second aspects, a fiber sheet is attached to the surface.
The computer inputs the shape data of the fiber sheet structure, and based on this shape data, simulates the state where the fiber sheet is bent with various curvatures, and shows the visible ratio of each layer for various curvatures. A visible ratio information creation stage for creating ratio information is further provided, and the created visible ratio information is input at the visible ratio information input stage.

(24) According to a twenty-fourth aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the twenty-third aspect, the fiber sheet is attached to the surface.
When the fiber sheet structure is projected vertically upward with respect to the layer surface and the hidden surface treatment is performed, the visible ratio is determined based on the area ratio of each layer appearing on the projection surface.

(25) According to a 25th aspect of the present invention, in the two-dimensional image generation method based on the three-dimensional virtual object according to the above first to twenty-fourth aspects, a fiber sheet is attached to the surface.
In the visual ratio information input stage, enter the visual ratio information for each of a plurality of discretely defined curvatures.
In the first step of the reflected light intensity calculation stage, the visible ratio corresponding to the curvature for the specific sample point obtained in the curvature calculation stage is interpolated with the visible ratio defined for the discrete curvature by the visible ratio information. It is what you ask for by doing.

  (26) According to a twenty-sixth aspect of the present invention, the computer executes each step in the two-dimensional image generation method based on the three-dimensional virtual object having a fiber sheet attached to the surface according to the first to the twenty-fifth aspects. A program for this purpose is prepared.

(27) According to a twenty-seventh aspect of the present invention, two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of the object based on the three-dimensional data of the object and observed from a predetermined viewpoint In a two-dimensional image generation device based on a three-dimensional virtual object that generates
A data input unit for inputting various data given from the outside;
A three-dimensional data storage unit that stores three-dimensional data that is input from the data input unit and indicates the three-dimensional shape of the virtual object;
A layer data storage unit that stores m layers of data indicating the reflection characteristics of each of a plurality of m layers constituting a virtual fiber sheet to be pasted, input from the data input unit;
Visible rate information storage unit that stores the visible rate information indicating the visible rate for each layer in a state where the fiber sheet is bent with various curvatures, which is input from the data input unit;
A projection condition setting unit for setting illumination conditions, a viewpoint position, and a projection plane based on data input from the data input unit;
A curvature calculator that calculates the curvature of the surface of the virtual object with respect to the position of the predetermined sample point defined on the surface of the virtual object based on the three-dimensional data;
When the fiber sheet is attached to the surface of the virtual object, a reflected light intensity calculation unit that calculates the intensity of reflected light from each sample point toward the viewpoint position;
A pixel definition unit that defines a pixel having a pixel value corresponding to the intensity of the reflected light at the intersection of the reflected light from the sample point and the projection plane;
A projection data storage unit that stores a set of a large number of pixels defined for a large number of sample points as two-dimensional projection data indicating a projection image of a virtual object;
Provided,
The reflected light intensity calculation unit
A first functional unit that obtains a visible ratio for each layer corresponding to the curvature at one sample point position with reference to the visible ratio information;
A second functional unit that obtains the reflection characteristic at the sample point position by combining the reflection characteristics of m layer data according to the visible ratio obtained by the first functional unit;
Based on the reflection characteristics obtained by the second functional unit, a third functional unit for obtaining the intensity of the reflected light from the sample point;
It is constituted by.

(28) According to a twenty-eighth aspect of the present invention, in the two-dimensional image generation device based on the three-dimensional virtual object according to the twenty-seventh aspect, a fiber sheet is attached to the surface.
The data input unit has a function of inputting information regarding the orientation of the reference direction line defined on the fiber sheet when the fiber sheet is attached to the virtual object,
The visible ratio information storage unit has a function of inputting visible ratio information indicating the visible ratio of each layer for each curvature having a direction factor,
The curvature calculator has a function to calculate the curvature with the orientation factor,
The reflected light intensity calculation unit has a function of obtaining the reflected light intensity using the visible ratio for each layer corresponding to the curvature having the orientation factor.

  According to the two-dimensional image generation method and the generation apparatus according to the present invention, the reflection characteristics of the fiber sheet are handled separately for each of a plurality of layers, and the reflected light intensity from each part of the virtual object to which the fiber sheet is attached is calculated. In addition, since the reflection characteristics of each layer are synthesized at a predetermined ratio determined according to the curvature of each part, it is possible to generate a two-dimensional image in which the texture of the fiber is sufficiently expressed.

  Hereinafter, the present invention will be described based on the illustrated embodiments.

<<< §1. Basic concept of rendering processing >>
The present invention relates to a rendering process using a computer, and particularly relates to a rendering process for a three-dimensional virtual object in which a fiber sheet (a sheet made of a fibrous material such as cloth) is attached to the surface. Here, a basic concept of a conventional general rendering process, its problems, and a basic concept of the present invention for solving the problems will be described.

  First, let us consider a process of generating a two-dimensional image obtained when a three-dimensional virtual object 10 as shown in FIG. 1A is observed from a predetermined viewpoint position. The virtual object 10 is a rectangular parallelepiped solid and actually has all six surfaces. However, on the obtained two-dimensional image, three surfaces of an upper surface 11, a front surface 12, and a side surface 13 as illustrated. Only appears. The rendering process is a process of generating a two-dimensional image as shown in the figure based on the three-dimensional data of the virtual object 10, and the three-dimensional data of the virtual object 10 is input to the computer, and the illumination condition (the type and position of the light source) ), A process of simulating an optical phenomenon in which the illumination light from the light source is reflected from each part of the surface of the virtual object 10 toward the viewpoint position after setting the viewpoint position and the projection plane. By calculating the reflected light intensity distribution from each part of the surface of the virtual object 10 on a predetermined projection plane, a two-dimensional image can be obtained on the projection plane.

  On the other hand, the virtual object 20 shown in FIG. 1B is obtained by attaching a fiber sheet to the surface of the virtual object 10 shown in FIG. As shown in the figure, on the obtained two-dimensional image, three surfaces of an upper surface 21, a front surface 22, and a side surface 23 appear, and all are surfaces to which a fiber sheet is attached. As described above, rendering processing that indicates a state in which a two-dimensional sheet is pasted on the surface of a three-dimensional virtual object is usually performed using a texture mapping technique. That is, the pattern information of a two-dimensional sheet is prepared as two-dimensional texture data (data indicating a two-dimensional reflection characteristic distribution), and the reflectance of each part is set with the texture data pasted on the surface of a virtual object. Processing to calculate is performed. If pattern data representing the density of each fiber is prepared as texture data, the texture of the fiber is also expressed on the obtained two-dimensional image.

  However, as described above, when the conventional general texture mapping method is used, it is difficult to sufficiently express the characteristics of the material of the actual fiber sheet. For this reason, the two-dimensional image generated by CG looks unnatural in the texture of the fiber compared to a real photographic image, resulting in poor realism.

  Therefore, the inventor of the present application has searched for the cause of the inability to perform sufficient fiber expression when a two-dimensional image of an object with a fiber sheet attached thereto is generated by CG. As a result, it was found that the unnaturalness of fiber expression tends to be particularly noticeable for furniture such as sofas and automobile seats. Through further technical verification and consideration, I noticed the following two facts.

  The first fact is that unnaturalness is more conspicuous when the fiber sheet is attached to a curved surface than when the fiber sheet is attached to the plane of the virtual object. For example, the virtual object 30 including a curved surface as shown in FIG. 2 (a) is more unnatural than the virtual object 10 consisting only of a plane as shown in FIG. 1 (a). An upper surface 31 and a side surface 32 appear on the virtual object 30, and the upper surface 31 of these has a curved surface. Here, as shown in FIG. 2 (b), when a virtual object 40 with a fiber sheet attached to the surface is prepared and rendering processing is performed by a conventional general method, the fiber on the side surface 42 formed of a plane is obtained. It was found that the fiber representation of the upper surface 41 made of a curved surface tends to look unnatural rather than the representation.

  The second fact is that the fiber expression becomes unnatural particularly when a fiber sheet such as a pile fabric such as denim, iridescent weave, towel or velvet is attached. Common to these fabrics is that the surface has a flocked structure, or the area ratio between the warp and weft projected onto the field of view is not fixed. It occurs.

  For example, in the example shown in FIG. 2 (b), when the fabric is attached to the side surface 42 (plane) as a reference state, when the fabric is attached to the upper surface 41 (curved surface), the fabric is curved in a convex shape. Will do. For this reason, in the case of a fabric having a large number of flocking structures on the surface, the distance between the tips of each hair is further increased. For example, towel fabric has a structure in which a large number of piles are planted on the base material, but if the fabric is curved in a convex shape, the distance between the tips of the individual piles increases, and the base This increases the area where the material is observed. Conversely, when the dough is curved in a concave shape, the distance between the tips of the individual piles is narrowed, and the area where the base material is observed is reduced. As a result, the observation mode of the fabric changes depending on the curvature of the surface on which the fabric is pasted.

  In the case of iridescent weaving, the area ratio between the warp and weft projected onto the field of view has a great influence on the observation mode of the fabric. In this case, the area ratio between the warp and the weft projected on the field of view changes. In this case, the observation mode of the cloth changes depending on the bending direction. Or in felt ground, the phenomenon that the specular reflection component increases by bending in a convex shape is also seen. This is considered because the direction of the fibers is aligned in one direction by the tension generated by the curvature of the fabric. The same phenomenon seems to occur not only in felt but also in various fiber sheets.

  From these two facts, in the two-dimensional image of the virtual object pasted with the fiber sheet, one of the factors causing unnaturalness in the texture of the fiber is the change in the surface structure of the fiber sheet pasted on the curved surface. Can be considered. Therefore, the inventor of the present application thought that when creating a two-dimensional image with CG, unnaturalness could be eliminated by performing a rendering process in consideration of changes in the surface structure of the fiber sheet. It is. For this purpose, in the rendering process, the curvature of the virtual object surface may be taken into account when quantitatively evaluating the reflection characteristics on the virtual object surface. Hereinafter, this concept will be described in more detail.

  FIG. 3 is a perspective view showing the principle of general rendering processing. This example shows a shading model for obtaining a projection image 55 on the projection plane M when the virtual object 50 is observed from the viewpoint E. At this time, a projection image with the virtual fiber sheet 60 attached to the surface of the virtual object 50 is obtained. In order to perform such rendering processing, first, three-dimensional data indicating the virtual object 50 is prepared. For example, in the illustrated example, the virtual object 50 is expressed as a set of a large number of polygons (polygons) defined on an XYZ three-dimensional coordinate system, and each part of the surface of the virtual object 50 is configured by a polygon. Has been.

  On the other hand, the virtual fiber sheet 60 is prepared as two-dimensional texture data. In the example shown in the figure, a heart-shaped picture is expressed on the base of the lattice pattern by image data defined on the uv two-dimensional coordinate system on the virtual fiber sheet 60. After all, this pattern data can be referred to as reflection characteristic data indicating the distribution of reflection characteristics of the virtual fiber sheet 60. When rendering processing is performed, the pattern data defined on the uv coordinate system is mapped to the surface of the virtual object defined on the XYZ coordinate system, and the reflection characteristics of each part of the virtual object surface are determined. Become.

  In the rendering process, it is necessary to set the illumination conditions, the viewpoint position, and the projection plane. As illumination conditions, the type (for example, shape, size, wavelength characteristics, etc.) and position of the light source are set. In the case of the illustrated example, the light source G, the viewpoint E, and the projection plane M are set at the illustrated positions. In addition, an xy two-dimensional coordinate system is defined on the projection plane M, and a projection image 55 (a two-dimensional image obtained as an object of rendering processing) is obtained as image data on the xy coordinate system. become.

  Now, as illustrated, a sample point Q is defined on the virtual object 50, and the reflected light V traveling from the sample point Q toward the viewpoint E is considered. The reflected light V is light obtained by reflecting the illumination light L from the light source G at the sample point Q, and is light that is observed at the position of the viewpoint E. However, “reflection” here is a broad concept that includes not only “specular reflection” but also “diffuse reflection”, and illumination light incident on the sample point Q at various angles is reflected as viewpoint E. Will head to. Accordingly, the reflected light V shown in the figure is a collection of reflected light obtained from illumination light incident from various angles.

  On the surface of the virtual object 50, a pixel P having a pixel value corresponding to the intensity of the reflected light V is defined at the intersection of the reflected light V from the sample point Q toward the viewpoint E and the projection plane M. Similarly, if pixels are defined on the projection plane M with respect to each reflected light directed from the large number of sample points to the viewpoint E, the projection image of the virtual object 50 is obtained by the collection of the large number of pixels defined for the large number of sample points. Is obtained on the projection plane M. In practice, a pixel array is defined in advance on the projection plane M at a desired resolution, and a line connecting the viewpoint E and the representative point (for example, the center position) of each pixel P is extended onto the virtual object 50. If the sample point Q is defined at the intersection position with the virtual object surface and the pixel value of each pixel P is calculated by the above-described method, two-dimensional data having the necessary resolution can be obtained.

  As described above, in order to obtain the pixel value of the pixel P on the projection plane M, it is necessary to obtain the intensity of the reflected light V from the sample point Q through the pixel P toward the viewpoint E. The intensity of V can be basically obtained by calculation in consideration of the intensity of the illumination light L incident on the sample point Q and the light reflectance (specular reflectance or diffuse reflectance) at the sample point Q. Of course, at this time, an operation taking into account the orientation of the polygon including the sample point Q is performed, and texture data mapped to the sample point Q (image data of the fiber sheet 60 defined on the uv coordinate system) is also taken into consideration. The operation entered in is performed. Therefore, if the surface of the virtual object 50 is a curved surface, a projection image 55 having a shadow corresponding to the curved surface is obtained, and the reflection characteristic data (texture data) of the virtual fiber sheet 60 is as illustrated. If there is information on the lattice pattern and the heart-shaped pattern, the lattice pattern and the heart-shaped pattern are also expressed on the projected image 55 (the illustration of the pattern is omitted in FIG. 3).

  However, in the conventional texture mapping method, when mapping texture data onto the surface of a three-dimensional virtual object, the two-dimensional data is simply mapped geometrically. When such a fiber sheet is mapped onto a curved surface, sufficient texture expression cannot be performed. The basic concept of the present invention is that, in the rendering process, the intensity calculation of the reflected light is further performed in consideration of the curvature of the virtual object 50 at the sample point Q.

  This basic concept will be explained in more detail with reference to FIG. FIG. 4 is a perspective view showing the relationship between the fiber sheet and the curvature of the object surface. Here, first, as shown in FIG. 4 (a), in a state where an object 51 made of a cylinder having a radius r1 is arranged with its central axis H oriented in the horizontal direction, a lattice pattern and a heart-shaped pattern are displayed. Let us consider a case where the fiber sheet 61 having information is pasted along the side surface of the cylinder. Further, the fiber sheet 61 is made of towel cloth, and the lattice pattern as a base is composed of warp and weft stitches, and the heart-shaped pattern dyes individual piles planted on the base. It is expressed by

  Here, a reference direction line W is defined in the longitudinal direction of the fiber sheet 61 as illustrated. The reference direction line W indicates the direction of the warp yarn as the base of the fiber sheet 61. If the fiber sheet 61 is wound around the cylindrical object 51 in the illustrated direction, the reference direction line W is directed to the circumferential direction of the cylinder. Here, for the sake of convenience, the angle formed between the projection line H ′ obtained on the side surface of the cylinder by projecting the central axis H of the cylinder in the radial direction and the reference direction line W of the attached fiber sheet 61 is referred to as a curvature angle ξ. In the case of FIG. 4A, the curvature angle ξ = 90 °.

  FIG. 4B shows the fiber sheet 61 attached to the cylindrical object 52 so that the curvature angle ξ = 90 °, and the radius of the object 52 is r2 (r2 <r1). The cylinder is slightly thinner than the object 51. Here, the curvature σ of each cylindrical side is defined as the reciprocal of its radius. Then, in the example of FIG. 4 (a), the fiber sheet 61 is attached to a curved surface with a curvature σ = 1 / r1, and in the example of FIG. 4 (b), a curved surface with a curvature σ = 1 / r2. It will be attached to. On the other hand, FIG. 4 (c) is the same as FIG. 4 (a) in that a cylindrical object 51 having a radius r1 is used, but with the center axis H of the cylinder oriented in the vertical direction, Since the sheet 61 is pasted, the projection line H ′ and the reference direction line W face the same direction, so the curvature angle defined as the angle formed by both is ξ = 0 °.

  4A to 4C are examples in which the same fiber sheet 61 is attached, but in the case of FIG. 4A, the curvature σ = 1 / r1, the curvature angle 90 °, FIG. In the case of (b), the curvature σ = 1 / r2, the curvature angle 90 °, and in the case of FIG. 4C, the curvature σ = 1 / r1, the curvature angle 0 °.

  In order to simulate these three cases on a computer, let us consider performing a rendering process by a conventional method. In this case, of course, each cylindrical side surface is treated as a curved surface on the XYZ three-dimensional coordinate system, and information on the curved surface is reflected in the calculation for obtaining the irradiation angle of illumination light from the light source, the direction of reflected light, and the like. It will be. In addition, since the texture data of the fiber sheet 61 is mapped, calculation is performed in consideration of the information on the lattice pattern and the heart-shaped pattern of the fiber sheet. However, as long as the fiber sheet 61 is the same, the calculation using the same texture data is performed in any of the cases of FIGS. 4 (a) to 4 (c). Such a conventional method is based on the premise that as long as the same fiber sheet 61 is pasted, the texture information does not change regardless of the surface to be pasted.

  However, in reality, when the fiber sheet 61 is pasted on the curved surface, the surface structure changes more or less, and the texture information changes. In the case of the example described here, the fiber sheet 61 is a towel fabric, and is composed of a lower layer that is a base and an upper layer that is made up of a number of piles planted on the base. As described above, the lattice pattern of the lower layer is a pattern that appears as stitches of warp and weft constituting the base, and the heart-shaped pattern of the upper layer is a pattern expressed by dyeing the pile. When such a towel cloth is physically curved, the flocking state on the ground of each pile changes, so the visibility ratio between the upper layer and the lower layer depends on the curvature of the three-dimensional object to be pasted. Change. Further, even when pasted on an object having the same curvature, the visible ratio of the upper layer and the lower layer changes according to the pasting direction.

  For example, such a fiber sheet 61 is attached to a cylinder having a curvature σ = 1 / r1 as shown in FIG. 4 (a), and the curvature σ = 1 / r2 as shown in FIG. 4 (b). Compared with the case where it is pasted on the cylinder, as shown in Fig. 4 (b), when it is pasted on a curved surface with a larger curvature (side surface of a cylinder with a smaller radius), the visible ratio of the base (lower layer) Will grow. Further, even when pasted on a cylinder having the same curvature σ = 1 / r1, as shown in FIG. 4 (a), when pasted to a curvature angle ξ = 90 °, FIG. 4 (c) As shown in FIG. 4, the visible ratio of the base (lower layer) differs from the case where the curvature angle ξ = 0 ° is applied. Of course, the curvature angle ξ can be any angle such as 30 °, 45 °, and 60 °, and the visible ratio of the base (lower layer) also changes according to these angles.

  In the present application, the term “curvature” is used in a narrow sense as a term indicating a parameter indicating the degree of curvature like the above-described curvature σ, but in a broad sense, the curvature angle ξ described above. Is used as a term that refers to a parameter that also takes into account. In particular, “curvature with orientation factor” means “curvature” in a broad sense, and in the above example, it means a combination of a specific σ and a specific ξ. It is.

  Eventually, the texture information of the fiber sheet 61 changes according to the curvature of the surface to be pasted (curvature in a narrow sense) and the curvature angle. Of course, such a change in the surface structure of the fiber usually does not bring about dramatic changes such as changing the heart-shaped pattern to a star pattern, but the concentration of the lattice pattern in the lower layer and the heart-shaped pattern in the upper layer. Although it is a thing which brings about the change of a balance, it is certainly a factor which influences the delicate natural texture of a CG image. In reality, as already enumerated, it appears as a particularly prominent factor when creating a CG image of an object to which a fiber sheet such as denim, iridescent weave, towel or velvet pile is attached.

  Therefore, in order to create a CG image that faithfully reproduces the natural texture, it is only necessary to handle in consideration of texture information that changes in accordance with the curvature of the surface to be pasted (curvature in a narrow sense) and the curvature angle. Of course, theoretically, as the texture information of the fiber sheet, not only simple two-dimensional image data but also data that strictly defines the three-dimensional structure of each fiber is prepared. When the handling process is performed, a CG image faithfully reproducing the texture of the actual fiber can be obtained. However, such a process requires a very complicated calculation and is not preferable in practice.

  Therefore, in the present invention, the reflection characteristics of the fiber sheet are handled separately for a plurality of layers, and when calculating the reflected light intensity from each part of the virtual object to which the fiber sheet is attached, the curvature of each part (even in a broad sense) The reflection characteristics for each layer are synthesized at a predetermined ratio determined according to the curvature in a narrow sense, and a two-dimensional image in which the texture of the fiber is sufficiently expressed is generated. The specific method will be described later.

<<< §2. Basic concept of the present invention >>
The most important feature of the present invention resides in pseudo handling of a fiber sheet in which the reflection characteristics change depending on the curvature, such as a pile ground. Originally, an actual fiber sheet such as a pile fabric is a three-dimensional structure. For example, the figure shown in the upper part of FIG. 5 is a side view showing the structure of an example of the fiber sheet 61 made of pile fabric. In the case of the illustrated example, the fiber sheet 61 is constituted by an upper layer L1 and a lower layer L2. The lower layer L2 is a fabric serving as a base, and the upper layer L1 is composed of a number of piles planted on the base. Therefore, when the rendering process is performed, if the fiber sheet 61 itself is handled as a three-dimensional structure, a highly accurate two-dimensional projection image can be obtained. However, if the object on which the fiber sheet 61 is pasted is a three-dimensional structure, and if the fiber sheet 61 is also handled as a three-dimensional structure, the computational burden of rendering processing becomes extremely large.

  Therefore, in the present invention, when the rendering process is performed, the fiber sheet 61 is handled as a two-dimensional sheet only so that the calculation load can be reduced as much as possible. However, when mapping a fiber sheet that changes its reflection characteristics according to the curvature, such as a pile, to a three-dimensional object, some ingenuity is required to reflect the reflection characteristics according to the curvature during rendering. Become. In the present invention, as a contrivance, the fiber sheet 61 is handled as a plurality of layers, and data indicating reflection characteristics is prepared for each layer, and for each layer at a predetermined ratio determined according to the curvature. The reflection characteristics are synthesized.

  For example, in the example shown in FIG. 5, since the fiber sheet 61 is composed of the upper layer L1 and the lower layer L2, the images of the two layers may be handled separately. The lower part of FIG. 5 shows an example in which the layer data LD1 of the upper layer L1 and the layer data LD2 of the lower layer L2 are separately prepared. These layer data LD1 and LD2 are both image data defined on the uv two-dimensional coordinate system, and are data indicating reflection characteristics for each layer. Here, for convenience of explanation, the case where the layer data LD1 is data indicating an image having a heart-shaped pattern and the layer data LD2 is data indicating an image having a lattice-shaped pattern is illustrated. Actually, these layer data are prepared as color image data.

  Such layer data D1 and D2 can be obtained, for example, by taking a picture of each layer. If a color photograph of each layer is taken with white illumination light applied to each layer, the pixel values of the three primary colors RGB constituting the color photograph are reflected characteristics of light of the wavelengths of RGB colors at the individual pixel positions. It will be the data indicating.

  Specifically, the layer data LD1 can be obtained by photographing the upper layer L1 from above. As shown in the upper part of FIG. 5, when the fiber sheet 61 is placed on a plane and is observed from above, only the upper layer L1 is observed and the lower layer L2 is not exposed at all. An image obtained by photographing the fiber sheet 61 from above in the state can be used as it is as the layer data LD1. If a part of the lower layer L2 can be seen through in this state, the lower layer L2 is removed by some method and only the upper layer L1 is taken from above as shown in the middle left of FIG. An image may be used as the layer data LD1.

  On the other hand, for the layer data LD2, as shown in the middle right of FIG. 5, an image obtained by removing the upper layer L1 by some method and photographing only the lower layer L2 from above may be used as the layer data LD2. When it is difficult to remove the upper layer L1 from the ready-made fiber sheet 61, the lower layer L2 of the stage before the process of flocking the pile to be the upper layer L1 is ordered from the manufacturing factory of the fiber sheet 61, This can be taken from above.

  Here, let us consider the relationship between the visible ratio and the curvature for each layer with reference to FIG. FIGS. 6A to 6D are side views showing a state in which the fiber sheet 61 shown in the upper part of FIG. 5 is bent with various curvatures. As shown in FIG. 6 (a), if the curvature σ when the fiber sheet 61 is stuck to the side surface of the cylinder is defined as the reciprocal 1 / r of the radius r of the cylinder as in the example shown in FIG. When the fiber sheet 61 is stuck on a plane, the curvature σ1 = 0, and as shown in FIGS. 6B and 6C, the curvature σ2 , Σ3 is the reciprocal of the radius of each cylinder. Also, as shown in FIGS. 6 (b) and 6 (c), the curvature when sticking to the outer surface of the cylinder so as to be convex upward is expressed by a positive numerical value, as shown in FIG. 6 (d). If the curvature of the cylinder attached to the inner surface of the cylinder so as to protrude downward is expressed by a negative value, the curvatures σ2 and σ3 are defined as positive values, whereas the curvature σ4 is negative. Will be defined as the value of.

  The important point here is that even when the same fiber sheet 61 is observed from above, the visible ratio of each layer varies depending on the value of curvature. For example, as shown in FIG. 6A, when the curvature is σ1 (= 0), it is assumed that the visible ratio of the upper layer L1 is 100% and the visible ratio of the lower layer L2 is 0%. This is because when the fiber sheet 61 is attached on a plane as shown in FIG. 6 (a), the lower layer L2 is hidden behind the upper layer L1 and cannot be seen at all. Means.

  However, as shown in FIG. 6 (b), when the curvature becomes σ2, the fiber sheet 61 is stuck to the upwardly curved surface, so that the interval between the individual piles is widened, and a gap is generated between the piles. . For this reason, when the fiber sheet 61 is observed from above, a part of the lower layer L2 is exposed from the gap between the piles. If the exposure ratio is 20%, the visible ratio of the upper layer L1 is 80% and the visible ratio of the lower layer L2 is 20% as shown in the figure. When the degree of curvature is further increased and the curvature is σ3 as shown in FIG. 6 (c), the gap between the individual piles is further widened. In the illustrated example, the visible ratio of the upper layer L1 is 70%. The visible ratio of the lower layer L2 is 30%.

  On the other hand, as shown in FIG. 6 (d), when the curvature becomes σ4 having a negative value, the fiber sheet 61 is stuck to the downwardly curved curved surface. No longer occurs. Therefore, similarly to the state of FIG. 6A, the visible ratio of the upper layer L1 is 100%, and the visible ratio of the lower layer L2 is 0%. In other words, when viewed from above, the lower layer L2 is hidden behind the upper layer L1 and cannot be seen at all.

  Such a visible ratio can be obtained by preparing the structure of the fiber sheet 61 as data and performing computer simulation. That is, the shape data of the fiber sheet structure is input to the computer, and based on this shape data, the state of bending the fiber sheet with various curvatures is simulated, and the visible ratio for each layer with respect to various curvatures is calculated. The process of creating the visible ratio information shown may be performed. FIG. 7 is a side view showing an example of such a simulation. The actual fiber sheet 61 is a three-dimensional structure, but in the embodiment shown here, by performing a geometrical analysis of the structure viewed from the side, the visible ratio is obtained by simulation on a two-dimensional plane. Arithmetic.

  The individual piles constituting the upper layer L1 are actually composed of a large number of yarns, but in this embodiment, as shown in FIG. 7 (a), only the contour line when viewed from the side is shown. The data is prepared and analyzed, and the analysis is performed by replacing it with a polygonal contour line (in the figure, a shape like a club). On the other hand, the lower layer L2 is handled as a simple line segment (indicated by a thick line in the figure), and each pile (a club-shaped polygon) is planted so as to be always perpendicular to the thick line. Simulation is performed on the premise.

  As the visible ratio, a value when the fiber sheet 61 is observed from vertically above is calculated. That is, when the fiber sheet 61 is observed from vertically above, the ratio of the upper layer L1 and the lower layer L2 entering the visual field is calculated as a visible ratio. Specifically, as shown in FIG. 7 (a), a projection line segment P arranged so as to be parallel with a predetermined distance above the lower layer L2 is defined, and each point on the projection line segment P is defined. Is extended vertically downward to determine whether it collides with individual piles (crown-shaped polygons) constituting the upper layer L1 or reaches the lower layer L2 (thick line). The rate of collision with individual polygons is the visible rate of the upper layer L1, and the rate of reaching the thick line is the visible rate of the lower layer L2.

  In the example shown in FIG. 7 (a), even when the fiber sheet 61 is observed from above, the lower layer L2 is invisible behind the upper layer L1, so the visible ratio of the upper layer L1 is 100%. As a result, the visible ratio of the lower layer L2 is 0%. Further, as shown in FIG. 7 (b), when the fiber sheet 61 is curved to be convex downward (when negative curvature is simulated), the visible ratio of the upper layer L1 is 100%, The result that the visible ratio of the layer L2 is 0% is obtained. On the other hand, as shown in FIG. 7 (c), when the fiber sheet 61 is curved to be convex upward (when a positive curvature is simulated), a part of the lower layer L2 is Since it can be seen from the gap of the upper layer L1 (the portion shown in gray in the figure), for example, a result that the visible ratio of the upper layer L1 is 70% and the visible ratio of the lower layer L2 is 30% is obtained. Become. Of course, if the bending state (curvature) changes, the visible ratio also changes.

  In the simulation of the curved state of the fiber sheet 61, a line segment indicating the layer L2 is an arc having a predetermined radius, and individual piles (crown-shaped polygons) constituting the layer L1 are arranged at the arcuate line at each flocking position. This can be done by drawing perpendicular to the minutes. If the simulation is performed with various changes in the radius of the arc, the visible ratio can be obtained for various curvatures.

  In the end, this simulation shows that when the fiber sheet structure is projected vertically upward with respect to the layer surface (the surface parallel to the plane when the sheet is placed on the plane) and the hidden surface treatment is performed, It can be said that the visible ratio is determined based on the area ratio of each layer appearing in FIG.

  FIG. 8 is a table showing an example of the visible ratio information obtained as a result of such a simulation. The curvature σ is defined as the reciprocal of the radius r of the arcuate line segment indicating the layer L2 (unit: 1 / cm, for example). In the result shown in the figure, when the curvature σ is 0 or a negative value (as shown in FIGS. 7 (a) and 7 (b)), the visible rate of the upper layer L1 is 100% and the lower layer As a result, the visible ratio of L2 is 0%. On the other hand, when the curvature σ takes a positive value (as shown in FIG. 7C), the larger the curvature σ, the lower the visible ratio of the upper layer L1, and the lower layer L2 visible. The result is that the percentage increases.

  As described above, with reference to FIG. 7, an example of simulating the visible ratio using a simple two-dimensional model (a model in which data is prepared by analyzing only the outlines of individual piles when viewed from the side). Of course, it is also possible to perform a simulation using a more complicated three-dimensional model. That is, in the two-dimensional model shown in FIG. 7, each pile is handled as a geometric polygon having no thickness. In addition, if a three-dimensional model in which such plates are arranged at a predetermined pitch is defined, a three-dimensional simulation is possible.

  In 2D model simulation, curvature must be defined as a value that does not have an orientation factor (in a narrow sense), but in 3D model simulation, curvature is a value that has a direction factor ( (Curvature in a broad sense defined by a combination of a curvature σ in a narrow sense and a curvature angle ξ). As described above, when the curvature is defined by a combination of σ and ξ, a simulation is performed for each combination of various σ and ξ, and the visible ratio of each layer is obtained for each combination. Visible ratio information as shown in FIG.

  Alternatively, instead of performing simulation, it is also possible to prepare an actual fiber sheet 61 and attach it to an actual object having a cylindrical side surface, and actually measure the visible ratio for each layer. For example, an actual fiber sheet 61 in which a large number of hairs are planted is prepared in a lower layer L2 that is a white dyed base, using a pile dyed in black as an upper layer L1, and the fiber sheet 61 is attached to a cylindrical object having various radius values. If each photograph is taken, it is possible to actually measure the visible ratio for each layer as the density value of the photographed image. Specifically, if the density value of the photographed image indicates black, the result shows that the visible ratio of the upper layer L1 is 100% and the visible ratio of the lower layer L2 is 0%. If the value indicates pure white, the result indicates that the visible ratio of the upper layer L1 is 0% and the visible ratio of the lower layer L2 is 100%. If the density value of the photographed image indicates gray, , And an intermediate visible ratio.

  In the examples shown in FIGS. 8 and 9, a table indicating the visible ratio for each layer is prepared as the visible ratio information. However, such a table may be derived by some geometric calculation. For example, the visible ratio information can be prepared as a mathematical formula for performing such a calculation. For example, if the visible ratio of each layer can be expressed by a function f (σ, ξ), this function can be used as the visible ratio information.

  By the procedure described above, as a result, as shown in the lower part of FIG. 5, the layer data LD1 of the upper layer L1 and the layer data LD2 of the lower layer L2 are separated from each other for each fiber sheet 61. (These color image data are two-dimensional data indicating the reflection characteristics of each layer.) As shown in FIG. 8 (when the curvature angle ξ is considered, FIG. Visible ratio information indicating the visible ratio for each layer is prepared. In the present invention, rendering processing is performed using these pieces of information. The basic concept is shown below.

  The basic concept of a general rendering process is as described above with reference to the perspective view of FIG. 3, and image data of the virtual fiber sheet 60 on the virtual object 50 (reflection characteristic data on the uv two-dimensional coordinate system). , The reflection characteristic of the sample point Q is obtained, and a pixel P having a pixel value corresponding to the intensity of the reflected light V from the sample point Q toward the viewpoint E is defined. In the present invention, this rendering process is performed using the layer data LD1 and LD2 for each layer and the visible ratio information indicating the visible ratio for each layer.

  FIG. 10 is a perspective view showing the basic principle of rendering processing in the present invention. In this rendering process, the illumination condition, viewpoint position, and projection plane are set in exactly the same way as the conventional general rendering process shown in FIG. The point of obtaining the reflection characteristics of a predetermined sample point Q on the virtual object 50 and obtaining the reflected light intensity from the sample point Q toward the viewpoint is exactly the same as the conventional method. A feature of the rendering process in the present invention is that the reflection characteristic of the sample point Q is determined by combining the reflection characteristics indicated by the layer data LD1 and LD2 for each layer.

  For example, in the case of the illustrated example, two types of layer data LD1 and LD2 (two-dimensional image data including a set of pixels having pixel values indicating reflection characteristics) defined on the uv two-dimensional coordinate system are assumed to be virtual. It is mapped to a predetermined position on the object 50. Here, the corresponding point corresponding to the sample point Q on the image indicated by the layer data LD1 is referred to as Q1, and the corresponding point corresponding to the sample point Q on the image indicated by the layer data LD2 is referred to as Q2. In this case, the reflection characteristic of the sample point Q is determined by combining the pixel value P (Q1) of the corresponding point Q1 and the pixel value P (Q2) of the corresponding point Q2. At this time, the combination ratio of both is determined based on the curvature of the surface of the virtual object 50 near the sample point Q.

Specifically, if the curvature of the sample point Q is σ = 1/10, the visible ratio of the upper layer L1 is determined by referring to the prepared visual ratio information as shown in FIG. It can be determined that 70% and the visible ratio of the lower layer L2 is 30%. Therefore, the reflection characteristic of the sample point Q may be determined by combining the pixel value P (Q1) of the corresponding point Q1 and the pixel value P (Q2) of the corresponding point Q2. For example, the reflection characteristic of the sample point Q is obtained by combining the pixel value P (Q1) and the pixel value P (Q2) with weights of 70% and 30%,
0.7 × P (Q1) + 0.3 × P (Q2)
It can be calculated by the following formula.

  After all, the reflection characteristic of the sample point Q is such that the pixel value at the position corresponding to the sample point Q of the two images (LD1, LD2) as shown in the lower part of FIG. It is obtained by combining with weighting according to. It can be understood that such a treatment makes sense in consideration of the fact that the visibility ratio of each layer is determined by simulation as shown in FIG. For example, in the example shown in FIG. 7C, the upper layer L1 is projected on a 70% region on the projection line segment P, and the lower layer L2 is projected on a 30% region on the projection line segment P. When the projected line segment P is considered as one pixel, the pixel value of the pixel is obtained by combining the pixel value of the upper layer L1 and the pixel value of the lower layer L2 at a ratio of 70%: 30%. .

  Note that when the curvature at the sample point Q is obtained as a curvature in a broad sense with a direction factor, the curvature is indicated by two parameters σ and ξ, so that instead of the visible ratio information table shown in FIG. The visible ratio of each layer may be determined using the visible ratio information table shown in FIG.

  The pixel value combining method according to the basic principle of the present invention has been described above with reference to FIG. 10. The physical meaning of such a combining method is a two-dimensional image obtained by rendering processing (FIG. 3). In this case, the resolution of the projection image obtained on the projection plane M is somewhat smaller than the resolution of the individual piles on the fiber sheet. That is, if the width of one pixel of the projection image obtained on the projection plane M in FIG. 3 is about the same width as the projection line segment P shown in FIG. 7, the pixel values of the two different layers are set to 70%: The above-described combining method of combining at a ratio of 30% is meaningful. For example, if the width of one pixel is about 1/10 of the projected line segment P shown in FIG. The physical meaning of the method of obtaining the pixel value of the pixel by combining pixel values of two different layers is lost. Therefore, the present invention is inappropriate as a rendering technique for obtaining a high-definition two-dimensional image that allows the shape of each pile to be confirmed with the naked eye.

<<< §3. Basic procedure of two-dimensional image generation method according to the present invention >>
Next, the basic procedure of the two-dimensional image generation method according to the present invention will be described with reference to the flowchart of FIG. The purpose of this procedure is to generate two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of the object and observed from a predetermined viewpoint based on the three-dimensional data of the object. . Here, for the sake of convenience, a case where a photograph of a sofa is created using CG will be described as an example. The procedure shown in FIG. 11 is a procedure executed by the computer.

  What is necessary for executing this procedure is three-dimensional data of the sofa body and information on the fiber sheet to be attached to the sofa body. Here, it is assumed that the sofa is configured by pasting a fiber sheet made of pile fabric on the surface of the sofa main body configured by combining wood, cushion materials, etc., and images to be published in the product catalog of the sofa are created with CG Think about the case. In this case, if the sofa body is designed using CAD, the three-dimensional data of the sofa body can be diverted from the CAD data. On the other hand, if the actual sample of the pile ground having a certain area can be prepared, the information regarding the pile ground which is a fiber sheet can be extracted from the actual sample (of course, this pile ground can be obtained using CAD). If it is designed, it can be used from CAD data.)

  First, in step S1 shown in FIG. 11, layer data is input. For example, if the fiber sheet 61 made of pile material to be pasted has a two-layer structure as shown in the upper part of FIG. 5, the layer data for the two layers is shown in the lower part of FIG. LD1 and LD2 are prepared and input to the computer. These layer data LD1 and LD2 are image data indicating reflection characteristics for each layer as described in §2.

  In addition, although the example of the fiber sheet 61 which has two layers was shown in FIG. 5, in this invention, it is not necessary to handle a fiber sheet as two layers, and it is also possible to handle it as three or more layers. is there. Therefore, it can be said that the procedure of step S1 is a process of inputting m layers of data indicating reflection characteristics for each of a plurality of m layers constituting a virtual fiber sheet to be pasted to a computer.

  In subsequent step S2, a process of inputting visible ratio information indicating the visible ratio of each layer in a state where the fiber sheet to be pasted is bent with various curvatures to the computer is performed. For example, as described in §2, the visible ratio information shown in FIG. 8 (information considering only the curvature σ) or the visible percentage information shown in FIG. 9 (information considering both the curvature σ and the curvature angle ξ) is simulated. It is sufficient to perform the process of creating and inputting this.

  In the next step S3, processing for inputting three-dimensional data indicating the three-dimensional shape of the virtual object to the computer is performed. In the embodiment described here, the three-dimensional data of the sofa body is input on the XYZ three-dimensional coordinate system as data indicating the three-dimensional shape of the virtual object. As described above, the three-dimensional data of the sofa body can be created relatively easily by using the CAD data used in the design.

  Usually, such three-dimensional data is constituted by data indicating a collection of polygons or data indicating a collection of parametric curved surfaces (curved surfaces represented by function expressions and parameter values). Further, in the data input stage of step S3, information related to the direction in which the fiber sheet is attached to the virtual object is also input. That is, when the pile ground is pasted on the sofa body, information on which direction of each surface of the sofa body is pasted with the reference direction line W of the pile ground is input.

  Next, in step S4, a projection condition for rendering is set. The projection condition referred to here is a condition for obtaining the projection image 55 of the virtual object 50 on the projection plane M, as shown in FIG. Here, as illumination conditions, the shape, size, wavelength characteristics, and position of the light source are set on the XYZ three-dimensional coordinate system. Similarly, the position of the viewpoint E and the position of the projection plane M are also set on the XYZ three-dimensional coordinate system. As shown in FIG. 3, an xy two-dimensional coordinate system for obtaining the projection image 55 is defined on the projection plane M.

  The rendering process is now complete. The subsequent processes of steps S5 to S9 are procedures for performing an actual rendering process, and the process of defining pixel values is repeatedly executed for each pixel defined on the xy two-dimensional coordinate system on the projection plane M. It will be. First, in step S5, one sample point Q is defined on the surface of the virtual object 50. Specifically, a pixel array is defined in advance on the projection plane M with a desired resolution, and a line connecting the viewpoint E and a representative point (for example, the center position) of one pixel P is placed on the virtual object 50. The sample point Q may be defined at the intersection position with the virtual object surface.

  Subsequently, in step S6, a calculation for obtaining the curvature σ of the surface of the virtual object 50 is performed for the position of the sample point Q. Even if the virtual object 50 is input as three-dimensional data consisting of a collection of polygons or as three-dimensional data consisting of a collection of parametric curved surfaces, an arbitrary sample point Q Since the shape of the object surface in the vicinity is defined, the curvature σ at that position can be obtained by calculation.

  Here, a simple example of a method for obtaining the curvature σ of the surface of the virtual object 50 at the position of the sample point Q will be described. For example, as shown in the perspective view of FIG. 12, consider obtaining the curvature at the position of one point Q on the virtual object 50. In this case, first, the virtual object 50 is cut along a predetermined plane including the sample point Q. In the figure, this cut surface is shown hatched. For the cut surface, for example, a predetermined reference plane may be determined in advance and defined as a plane that passes through the sample point Q and is parallel to the reference plane. For example, when the object data of the virtual object 50 is input in step S3, the reference plane may be designated by the operator as “specific surface of the object” or may be referred to as “YZ plane in the XYZ three-dimensional coordinate system”. It may be determined uniquely as follows.

  Next, the contour line 56 of the virtual object 50 appearing on the cut surface is extracted, the curvature of the contour line 56 near the sample point Q is obtained, and this is set as the curvature of the sample point Q. FIG. 13 is a plan view showing one method for defining the curvature of the contour 56 near the sample point Q. FIG. In this method, first, two points QL and QR that are equidistant from the sample point Q along the contour line 56 are defined on both sides of the sample point Q on the contour line 56. That is, the distance between the two points Q / QL along the contour 56 is equal to the distance between the two points Q / QR. Next, on this cut surface, the tangent line TL of the contour line 56 at the point QL and the tangent line TR of the contour line 56 at the point QR are obtained, and the lines are orthogonal to the tangent lines TL and TR (indicated by a one-dot chain line in the figure). To obtain the intersection QQ of the two. Finally, the distance r between the sample point Q and the intersection QQ is obtained, and the reciprocal 1 / r is set as the curvature σ for the sample point Q.

  By using such a method, a predetermined curvature σ can be determined for an arbitrary sample point Q on the virtual object 50. However, this method can only find a curvature in a narrow sense that does not have an orientation factor. A method for obtaining a curvature in a broad sense having an orientation factor (curvature angle ξ) for an arbitrary sample point will be described in detail in §5.

  When the curvature is obtained for the sample point Q in this way, the reflected light intensity calculation from the sample point Q is subsequently performed in step S7. That is, since the shading model as shown in FIG. 3 can be defined by the projection condition set in step S4, the calculation for obtaining the intensity of the reflected light V from the sample point Q toward the viewpoint E is performed in this model. The basic principle is as described with reference to FIG. That is, when the conventional general rendering method is applied to the model shown in FIG. 3, the factors that affect the intensity of the reflected light V from the sample point Q toward the viewpoint E are the intensity of the illumination light L and the sample point Q. In the present invention, the reflection characteristic mapped to the position of the sample point Q is a factor such as the inclination of the object surface in the vicinity of the object and the reflection characteristic mapped to the position of the sample point Q when the fiber sheet 60 is attached. Since each layer is prepared, according to the curvature of the position of the sample point Q obtained in step S6, the visible percentage information input in step S2 is referred to, and the visible percentage corresponding to the curvature is obtained. The reflection characteristics of the sample point Q are determined by synthesizing the reflection characteristics according to the visible ratio.

  FIG. 14 is a flowchart showing a more detailed procedure of the reflected light intensity calculation in step S7 shown in FIG. This reflected light intensity calculation is an operation for obtaining the intensity of reflected light from each sample point toward the viewpoint when a fiber sheet is attached to the surface of the virtual object. The reflected light intensity is calculated from one sample point. In doing so, as shown in the figure, three steps S71, S72, and S73 are executed.

  First, in the first step S71, the visible ratio for each layer corresponding to the curvature at the position of the sample point Q is obtained with reference to the visible ratio information. For example, in the case of the example shown in FIG. 10, since the curvature at the position of the sample point Q is obtained as σ = 1/10 by step S6 in the flowchart of FIG. 11, in step S71, for example, the visible in FIG. By referring to the ratio information (already input in step S2), the visible ratio for the sample point Q is obtained as L1: 70% and L2: 30%.

  In addition, in the visible ratio information input stage in step S2, when the visible ratio information for each of a plurality of discretely defined curvatures such as the visible ratio table shown in FIG. 8 is input, the curvature calculation in step S6. The curvature that exactly matches the curvature for the sample point Q obtained in the stage may not be listed on the visible ratio table. In such a case, the visible proportion corresponding to the curvature for the sample point Q may be obtained by interpolating the visible proportion defined for the discrete curvature.

  For example, when the curvature for the sample point Q is σ = 1/20, the visible ratio corresponding to σ = 1/30 and the visible ratio corresponding to σ = 1/10 in the table of FIG. What is necessary is just to obtain | require a ratio as an interpolation value. Various interpolation methods can be used. For example, if linear interpolation is performed by taking the reciprocal of the curvature σ, the reciprocal 20 of the curvature for the sample point Q is the reciprocal 30 of σ = 1/30. Therefore, the visible ratio obtained by interpolation is L1: 75% and L2: 25%.

Subsequently, in the second step S72, a process of obtaining the reflection characteristics at the position of the sample point Q by combining the reflection characteristics of m layer data according to the visible ratio obtained in the first step S71. Done. In the example shown in FIG. 10, m = 2, and reflection characteristics for each layer are prepared as two types of layer data LD1 and LD2. Moreover, these layer data have already been input in step S1 in the flowchart of FIG. Therefore, in step S72, as shown in FIG. 10, the reflection characteristic (pixel value P (Q1)) of the corresponding point Q1 of the layer data LD1 and the reflection characteristic of the position of the corresponding point Q2 of the layer data LD2 ( The pixel value P (Q2)) is synthesized at a ratio of 70:30, so that an operation for obtaining the reflection characteristic at the position of the sample point Q is performed. Specifically, the reflection characteristic at the position of the sample point Q is
0.7 × P (Q1) + 0.3 × P (Q2)
Is obtained by the following calculation.

  In the final third step S73, the intensity of the reflected light from the sample point Q toward the viewpoint E is obtained based on the reflection characteristic obtained in the second step S72. This is a calculation process similar to the conventional general rendering method, and the reflected light intensity is calculated in consideration of factors such as the intensity of the illumination light L and the inclination of the object surface near the sample point Q. become.

  Thus, when the calculation for obtaining the intensity of the reflected light V from one sample point Q toward the viewpoint E is completed in step S7 of FIG. 11, one pixel is defined in the subsequent step S8. That is, a pixel P having a pixel value corresponding to the intensity of the reflected light V is defined at the intersection of the reflected light V from the sample point Q and the projection plane M. When a color image is handled, as described above, the layer data LD1 and LD2 are data indicating the reflection characteristics for the three primary colors RGB, so the intensity calculation of the reflected light V in step S7 is also performed for each color component. be able to. Accordingly, in step S8, a pixel having a predetermined pixel value can be defined for each of the three primary colors RGB.

  Thus, the pixel value of one pixel P on the projection plane M can be defined through the procedures of steps S5 to S8. Therefore, the process of returning from step S9 to step S5 again is repeatedly executed until all necessary pixels are defined. Finally, in step S10, a process of generating two-dimensional projection data indicating the projection image 55 of the virtual object 50 is performed using a set of a large number of pixels defined for a large number of sample points. The generated two-dimensional data is output from the computer.

  When a curvature in a broad sense having a direction factor is used as the curvature, the visible ratio indicating the visible ratio for each layer is shown for each curvature having a direction factor in the visual ratio information input stage in step S2. Enter percentage information. Specifically, as described above, the visible ratio for each layer in a state where the fiber sheet is attached to the side surface of the cylinder in a predetermined direction is defined, the curvature σ is defined using the reciprocal of the radius of the cylinder, The angle ξ formed by the projection line obtained on the cylindrical side surface by projecting the central axis in the radial direction and the reference direction line of the fiber sheet is defined as a curvature angle with respect to the curvature σ, and each curvature σ and each curvature Visibility ratio information (for example, a table as shown in FIG. 9) indicating the visibility ratio for each layer corresponding to each combination of angles ξ may be input.

  Further, in the object data input stage of step S3, information related to the direction in which the fiber sheet is attached to the virtual object (for example, information related to the direction of the reference direction line of the fiber sheet) is also input. Then, in the curvature calculation stage of step S6, the curvature having the direction factor is obtained for the sample point Q by referring to the information regarding the fiber sheet sticking direction input in step S3. Specifically, a curvature angle ξ indicating a curvature σ and a deviation between the bending direction corresponding to the curvature σ and the reference direction line may be obtained (a specific method will be described in §5).

  Then, in the first step S71 in the reflected light intensity calculation stage, the visible ratio for each layer corresponding to the curvature having the orientation factor can be obtained. Specifically, the visible ratio for each layer corresponding to the combination of the curvature σ and the curvature angle ξ can be obtained. For example, if the curvature having the orientation factor with respect to the sample point Q is obtained with numerical values of σ = 1/30 and ξ = 20 ° at the curvature calculation stage in step S6, in step S71, the table in FIG. By referring to the column of ξ = 20 ° and σ = 1/30, the visible ratio for each layer corresponding to the curvature having the orientation factor can be obtained.

  As described above, the procedure shown in FIG. 11 basically follows the conventional general rendering technique and is based on a general shading model as shown in FIG. However, in step S1, layer data indicating each reflection characteristic is input for a plurality of layers, visible ratio information is input in step S2, the curvature of the sample point is calculated in step S6, and in step S7, According to the curvature, a plurality of layer data is synthesized at a predetermined visible ratio to obtain the reflection characteristic of the sample point, and the reflected light intensity is calculated. It becomes a characteristic procedure that should be called.

  As already described, a pile fabric or the like is a fiber sheet having a property that its appearance changes depending on the curved state of the surface. Therefore, when these fabrics are pasted on the curved surface of a virtual object and rendering processing is performed, the texture of the fibers cannot be sufficiently expressed on the obtained CG image. However, when the rendering process is performed according to the procedure according to the present invention shown in FIG. 11, an image in which the texture of the fiber is expressed more faithfully than the conventional method can be obtained.

<<< §4. Application to various shading models >>>
Here, some more specific methods of the reflected light intensity calculation shown in the flowchart of FIG. 14 will be described. Conventionally, various shading models have been proposed to perform such reflected light intensity calculation. Many of these shading models define predetermined reflection characteristics at sample points on virtual objects (or sample points after mapping when mapping textures), and the illumination light L and the reflection characteristics defined at each part Is used to calculate the intensity of the reflected light. Usually, an illumination condition (illumination condition using a plurality of light sources) in which a plurality of illumination lights are incident on one sample point is set, so that a plurality of light generated based on incident illumination light from each light source is set. As the sum of the reflected light intensities, the intensity of the reflected light from the sample point toward the viewpoint is calculated.

  The basic idea of the present invention is not in the proposal of a new shading model, but when performing the reflected light intensity calculation for one sample point, each reflection characteristic defined for each of a plurality of m layers is The combination is based on the visible ratio corresponding to the curvature of the sample points, and the reflected light intensity is obtained using the combined reflection characteristics. Therefore, it is not important what kind of shading model is used in carrying out the present invention. In fact, the present invention can be applied to various shading models. Hereinafter, some specific examples in which the present invention is applied to a general shading model used conventionally will be described.

(1) Simple texture mapping model This model is a simple model that inputs a 2D image as a texture using a scanner device or digital camera and uses it as reflection characteristic data indicating the reflectance distribution. The basic embodiments described in Sections 2 and 3 are based on this simple texture mapping model.

  If the present invention is applied to this model, first, a process of capturing a two-dimensional image for each layer using a digital camera or the like, preparing each layer data, and inputting this in step S1 of FIG. Keep going. In this case, each layer data becomes, for example, pattern data T (u, v) defined on the uv two-dimensional coordinate system, such as data LD1 and LD2 shown in the lower part of FIG. The reflection characteristic data indicating

Next, in the second step S72 of the reflected light intensity calculation stage shown in FIG. 14, first, the value of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the position of the sample point Q. Take out (reflection characteristics). In the example shown in FIG. 10, the pixel value P (Q1) is extracted from the upper layer data LD1, and the pixel value P (Q2) is extracted from the lower layer data LD2. Then, the reflection coefficient k at the position of the sample point Q is obtained by synthesizing the extracted reflection characteristic value for each layer according to the weighting by the visible ratio obtained in the first step S71. In the case of the example shown in FIG.
k = 0.7 * P (Q1) + 0.3 * P (Q2)
Thus, the reflection coefficient k (reflection coefficient obtained by combining the layers) at the position of the sample point Q is obtained. This reflection coefficient k is a value that takes into account 70% of the reflection coefficient of the upper layer (pixel value P (Q1)) and 30% of the reflection coefficient of the lower layer (pixel value P (Q2)).

In the third step of the reflected light intensity calculation stage shown in FIG. 14, when the intensity of the incident illumination light at the sample point Q is Ii (this is determined by the projection condition set in step S4 of FIG. 11). , The reflected light intensity I using the reflection coefficient k,
I = k · Ii
It can be obtained by the following formula.

(2) Classic diffuse reflection model The diffuse reflection model is a model that has been used for rendering processing for a long time. The intensity of incident illumination light at the sample point Q is set to Ii, and the sample point Q position on the virtual object surface is set. When the angle between the normal n and the incident illumination light is α and the diffuse reflection coefficient is kd, the reflected light intensity I is
I = kd ・ Ii ・ cos α
This is a model obtained by the following formula. Here, in the case of a classic diffuse reflection model, the diffuse reflection coefficient kd is determined by predetermined reflection characteristic data given as a constant.

  When this classical diffuse reflection model is applied to the present invention, first, a diffuse reflection coefficient is determined for each layer. Since the diffuse reflection coefficient in this model does not have a two-dimensional distribution, one diffuse reflection coefficient may be determined for one layer. For example, as shown in the upper part of FIG. 5, in the case of a fiber sheet composed of two layers L1 and L2, the diffuse reflection coefficient kd1 for the upper layer L1 and the diffuse reflection coefficient kd2 for the lower layer L2 may be determined. Therefore, in this model, each layer data is given by simple numerical values such as layer data LD1 = kd1, layer data LD2 = kd2, and the pattern data T (u, v) is not in the form. In step S1 of FIG. 11, diffuse reflection coefficients kd1 and kd2 for each layer are input as layer data.

On the other hand, in the second step S72 of the reflected light intensity calculation stage shown in FIG. 14, the diffuse reflection coefficient for each layer is synthesized according to the weighting by the visible ratio obtained in the first step S71, thereby obtaining a sample. The diffuse reflection coefficient kd at the position of the point Q is obtained. For example, when the curvature σ at the position of the sample point Q is obtained in the first step S71, and the visible ratios of the two layers L1 and L2 corresponding to the curvature σ are L1: 70% and L2: 30%. The diffuse reflection coefficient kd at the position of the sample point Q is
kd = 0.7 × kd1 + 0.3 × kd2
It is calculated by the following.

Therefore, in the third step of the reflected light intensity calculation stage shown in FIG. 14, the intensity of the incident illumination light at the sample point Q is Ii, the normal n standing at the position of the sample point Q on the virtual object surface, and the incident illumination light When the angle formed by α is α, the reflected light intensity I is
I = kd ・ Ii ・ cos α
What is necessary is just to obtain | require by the type | formula which becomes.

  Thus, since the classic diffuse reflection model does not have the concept of texture mapping, this classic diffuse reflection model cannot be applied as it is when a fiber sheet having some texture pattern is handled. In such a case, a model obtained by further combining a texture mapping model with this classic diffuse reflection model may be used. Specifically, similarly to the simple texture mapping model described above, each layer data LD1, LD2 is prepared as picture data T (u, v) defined on the uv two-dimensional coordinate system, and the layer in step S1 is prepared. In the data input stage, a two-dimensional image having a diffuse reflection coefficient indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system is input as layer data for each individual layer.

  On the other hand, in the second step S72 of the reflected light intensity calculation stage, first, the pixel value (diffuse reflection coefficient) of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the position of the sample point Q ). Then, the diffuse reflection coefficient kd at the position of the sample point Q may be obtained by combining these pixel values according to the weighting by the visible ratio obtained in the first step S71.

(3) Phong's specular reflection model
Phong's specular reflection model is a representative shading model of specular reflection, where the intensity of incident illumination light at the sample point Q is Ii, the normal n standing at the position of the sample point Q on the virtual object surface, and the incident illumination light Is the reflection coefficient depending on the angle α, k is the reflection coefficient, β is the parameter indicating the sharpness of the specular reflection, and γ is the angle between the emission direction of the specular reflection light at the sample point Q and the viewing direction. When the reflected light intensity I is
I = k (α) · Ii · cos ^β γ
This is a model obtained by the following formula.

  When applying this Phong specular reflection model to the present invention, first, the reflection coefficient k (α) and the parameter β are determined for each layer. Since the reflection coefficient k (α) and the parameter β in this model do not have a two-dimensional distribution, k (α) and β may be determined for each layer. However, since the reflection coefficient k (α) depends on the angle α, a predetermined coefficient value is determined for each of the discrete values of the angle α, or the angle α and the coefficient k It is necessary to prepare a function expression. In practice, as described above, the reflection coefficient k (α) and the parameter β are determined for each layer by computer simulation using the structure data of the fiber sheet. In step S1 of FIG. Input as layer data.

On the other hand, in the second step S72 of the reflected light intensity calculation stage shown in FIG. 14, first, the angle α formed between the normal n set at the position of the sample point Q on the virtual object surface and the incident illumination light, and the sample point An angle γ formed by the exit direction of the specular reflection light at Q and the viewpoint direction is obtained (these are obtained by the projection condition set in step S4 in FIG. 11). Then, using these angles α and γ, the reflection coefficient for each layer is referred to for each layer data,
k (α) ・ cos ^β γ
The following formula is used. The reflection coefficient k at the position of the sample point Q can be obtained by combining the reflection coefficient for each layer thus obtained in accordance with the weighting by the visible ratio obtained in the first step S71. For example, in the first step S71, the visible ratios of the two layers L1 and L2 with respect to the position of the sample point Q are L1: 70% and L2: 30%, and the two layers L1, L2 obtained by the above formula are used. If the reflection coefficients for L2 are k1 and k2, the reflection coefficient k at the position of the sample point Q is
k = 0.7 × k1 + 0.3 × k2
It is calculated by the following.

Therefore, in the third step of the reflected light intensity calculation stage shown in FIG. 14, when the intensity of the incident illumination light at the sample point Q is Ii, the reflected light intensity I is
I = k · Ii
What is necessary is just to obtain | require by the type | formula which becomes.

It should be noted that in using this Phong specular reflection model, in practice, instead of using the reflection coefficient k (α) depending on the angle α, the reflection coefficient ks independent of the angle α is used, and the reflected light intensity I is expressed as follows:
I = ks · Ii · cos βγ
There are many cases where it is calculated by the following formula. In this case, the layer data for each layer is configured by the reflection coefficient ks and the parameter β that do not depend on the angle α, and in the second step S72, the reflection coefficient for each layer is referred to the respective layer data. ,
ks ・ cos ^β γ
What is necessary is just to obtain | require by the type | formula which becomes.

  Also, this specular reflection model of Phong does not have the concept of texture mapping, so when handling a fiber sheet with some texture pattern, this model should be used in combination with a texture mapping model. . Specifically, similarly to the simple texture mapping model described above, each layer data LD1, LD2 is prepared as picture data T (u, v) defined on the uv two-dimensional coordinate system, and the layer in step S1 is prepared. In the data input stage, layer data for each layer is input as the pattern data T (u, v) defined on the uv two-dimensional coordinate system. In this case, the reflection coefficient k (α) and the parameter β (or ks instead of k (α)) are defined for each pixel of the pattern data T (u, v).

  In the second step S72 of the reflected light intensity calculation stage, first, pixels of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the position of the sample point Q are defined. The reflection coefficient k (α) (or ks) and the parameter β are extracted, and the reflection coefficient for each layer may be obtained by the above formula.

(4) BRDF model In the above-mentioned classic diffuse reflection model and specular reflection model of Phong, the reflection characteristics of the sample point Q are handled as independent of the incident angle of illumination light and the reflection angle of reflected light. Strictly speaking, in the case of a fiber sheet having a three-dimensional structure such as a pile ground, it must be handled in consideration of anisotropic reflection characteristics depending on the incident angle of illumination light and the reflection angle of reflected light. As a model for such handling, a model called BRDF (Bi-directional Reflection Distribution Function) has been proposed.

FIG. 15 is a perspective view for explaining the principle of the BRDF model. As shown in the figure, a normal line n is set at the position of the sample point Q on the virtual object surface, and an orthogonal plane S including the sample point Q and orthogonal to the normal line n is defined. An angle formed between the normal line n and the incident illumination light L is θL, a projection image L ′ of the incident illumination light L on the orthogonal plane S, and a predetermined reference line ζ passing through the sample point Q on the orthogonal plane S and Is defined as a combination of an angle θL and an angle φL. Similarly, the angle formed between the normal line n and the reflected light V is θV, the angle formed between the projected image V ′ of the reflected light V on the orthogonal plane S and the reference line ζ is φV, and the direction of the reflected light V is the angle. It is defined by a combination of θV and angle φV. Then, when the intensity of the incident illumination light L at the sample point Q is Ii, the intensity I of the reflected light V from the sample point Q is expressed using a reflection coefficient kb given as a function of θL, φL, θV, φV,
I = kb · Ii
It is obtained by the following formula. As described above, the BRDF model is characterized in that the reflection coefficient kb is given as a function of the parameters “θL, φL” indicating the direction of the incident illumination light L and the parameters “θV, φV” indicating the direction of the reflected light V. .

  When this BRDF model is applied to the present invention, the following may be performed. First, in the layer data input stage in step S1 of FIG. 11, the angle is defined on each layer as in the example shown in FIG. That is, a predetermined point on the layer is a point Q, an angle formed by the normal line n standing at the predetermined point Q on the layer surface and the illumination light L is θL, a projection image L ′ of the illumination light L on the layer surface and the layer The angle formed by the reference line ζ passing through the predetermined point Q on the surface is φL, the angle formed by the normal line n and the reflected light V is θV, the projected image V ′ of the reflected light V on the layer surface and the reference line ζ Is defined as φV. Then, the reflection coefficient kb (θL, φL, θV, φV) given as a function of “θL, φL, θV, φV” is prepared as layer data for each layer, and this is input in step S1.

  For example, as shown in the upper part of FIG. 5, in the case of a fiber sheet composed of two layers, an upper layer L1 and a lower layer L2, the reflection coefficient kb1 for the upper layer L1 has four variables “θL, φL, θV, kb1 (θL, φL, θV, φV) defined using the function “φV”, and the reflection coefficient kb2 for the lower layer L2 is kb2 using the same four variables “θL, φL, θV, φV”. It is defined in the form of a function (θL, φL, θV, φV). The layer data for each layer input in the layer data input stage of step S1 is eventually these functions kb1 (θL, φL, θV, φV), kb2 (θL, φL, θV, φV). . Although these functions can be given as mathematical expressions, it is preferable to prepare as a table having four-dimensional variables “θL, φL, θV, φV” in practice. Such a table can be obtained by computer simulation using the structural data of the fiber sheet, or can be obtained by actual measurement using each layer of the actual fiber sheet.

  On the other hand, in the visible ratio information input stage of step S2, the visible ratio information indicating the visible ratio for each layer is input for each of various combinations of “curvature, θL, φL, θV, φV”. The “curvature” here is a broadly defined curvature having a direction factor, and is defined by a narrowly defined curvature σ and a curvature angle ξ in the case of the above-described embodiment. Therefore, an example in the case where this curvature in the broad sense is treated as the curvature σ and the curvature angle ξ will be described below. It is not something that must be defined). Therefore, the visible ratio information input in step S2 is information indicating the visible ratio for each layer for each of various combinations of “σ, ξ, θL, φL, θV, φV”. In practice, this visible ratio information is preferably prepared as a table having six-dimensional variables “σ, ξ, θL, φL, θV, φV”. Such information indicating the visible ratio can also be obtained by computer simulation using the structural data of the fiber sheet, or can be obtained by actual measurement using each layer of the actual fiber sheet.

  Next, in the first step S71 of the reflected light intensity calculation stage shown in FIG. 14, first, the angles θL, φL, θV, and φV shown in FIG. 15 are respectively defined for the positions of the sample points Q on the virtual object surface. . At this time, the direction of the incident illumination light L and the direction of the reflected light V with respect to the sample point Q are determined by the projection conditions set in step S4. The six variables “σ, ξ, θL, φL, θV, φV” obtained by adding the curvatures (that is, σ and ξ) obtained in step S6 to these angles θL, φL, θV, and φV are used. Then, the visible ratio for each layer corresponding to the position of the sample point Q is obtained by referring to the visible ratio information (table having 6-dimensional variables) input in step S2.

  Here, for convenience of explanation, it is assumed that the visible ratios of the sample points Q for the two layers L1 and L2 are determined as L1: 70% and L2: 30%. A characteristic when the BRDF model is applied to the present invention is that the specific visible ratio at the position of the sample point Q is not only the curvature parameters σ and ξ but also the parameters of the direction of the incident illumination light L and the reflected light V. In other words, it is determined depending on θL, φL, θV, and φV. That is, since the visibility ratio of each layer is determined in consideration of the illumination condition set in step S4, the viewpoint position, and the like, more precise and fine handling is possible.

  In the second step S72 in the subsequent reflected light intensity calculation stage, first, the layer data input in step S1 is referred to, thereby corresponding to the combination of “θL, φL, θV, φV” at the position of the sample point Q. The reflection coefficient kb (θL, φL, θV, φV) to be obtained is obtained for each layer. Then, the reflection coefficient kb obtained at the position of the sample point Q is determined by combining the reflection coefficients kb thus obtained in accordance with the weighting by the visible ratio obtained in the first step S71.

For example, if the reflection coefficients for the two layers L1 and L2 corresponding to the combination of four variables “θL, φL, θV, and φV” at the position of the sample point Q are kb1 and kb2, respectively, In step S71, if the visible ratio of the two layers L1 and L2 with respect to the position of the sample point Q is determined as L1: 70% and L2: 30% as described above, the position of the sample point Q The reflection coefficient kb at
kb = 0.7 × kb1 + 0.3 × kb2
It is calculated by the following.

Therefore, in the third step of the reflected light intensity calculation stage shown in FIG. 14, when the intensity of the incident illumination light at the sample point Q is Ii, the reflected light intensity I is
I = kb · Ii
What is necessary is just to obtain | require by the type | formula which becomes.

(5) BTF model Since the BRDF model described above has no concept of texture mapping, when this is applied as it is to the present invention, a fiber sheet having a texture pattern cannot be handled. The BTF (Bi-directional Texture Function) described here is a model in which a texture mapping model is combined with the BRDF model described above. Therefore, in order to apply this BTF model to the present invention, the following may be performed.

  First, in the layer data input stage in step S1 of FIG. 11, the same angle definition as the BRDF model described above (angle definition shown in FIG. 15) is performed. That is, a predetermined point on the layer is a point Q, an angle formed by the normal line n standing at the predetermined point Q on the layer surface and the illumination light L is θL, a projection image L ′ of the illumination light L on the layer surface and the layer The angle formed by the reference line ζ passing through the predetermined point Q on the surface is φL, the angle formed by the normal line n and the reflected light V is θV, the projected image V ′ of the reflected light V on the layer surface and the reference line ζ Is defined as φV. Then, a uv two-dimensional coordinate system is defined on this layer surface, and given as a function of “θL, φL, θV, φV, u, v” for each point located at a predetermined coordinate value (u, v). The reflection coefficient kb (θL, φL, θV, φV, u, v) is defined and input as layer data for each layer.

  For example, as shown in the upper part of FIG. 5, in the case of a fiber sheet composed of two layers of an upper layer L1 and a lower layer L2, the reflection coefficient kb1 for the upper layer L1 has six variables “θL, φL, θV, is defined in the form of a function kb1 (θL, φL, θV, φV, u, v) using “φV, u, v”, and the reflection coefficient kb2 for the lower layer L2 is also defined by six variables “θL, φL, It is defined in the form of a function kb2 (θL, φL, θV, φV, u, v) using “θV, φV, u, v”. The layer data for each layer input at the layer data input stage of step S1 is, after all, these functions kb1 (θL, φL, θV, φV, u, v), kb2 (θL, φL, θV, φV, u, v). Although these functions can be given as mathematical expressions, it is preferable to prepare them as a table having six-dimensional variables “θL, φL, θV, φV, u, v” in practice. Such a table can be obtained by computer simulation using the structural data of the fiber sheet, or can be obtained by actual measurement using each layer of the actual fiber sheet.

  On the other hand, in the visible ratio information input stage of step S2, the visible ratio information indicating the visible ratio for each layer is input for each of various combinations of “curvature, θL, φL, θV, φV, u, v”. Since the “curvature” here is a curvature in a broad sense that also has a factor of orientation, an example in which this broad curvature is treated as a curvature σ and a curvature angle ξ will be described below. After all, the visible ratio information input in step S2 is information indicating the visible ratio for each layer for each of various combinations of “σ, ξ, θL, φL, θV, φV, u, v”. Become. In practice, this visible ratio information is preferably prepared as a table having eight-dimensional variables “σ, ξ, θL, φL, θV, φV, u, v”. Such information indicating the visible ratio can also be obtained by computer simulation using the structural data of the fiber sheet, or can be obtained by actual measurement using each layer of the actual fiber sheet.

  Next, in the first step S71 of the reflected light intensity calculation stage shown in FIG. 14, first, the angles θL, φL, θV, and φV shown in FIG. 15 are respectively defined for the positions of the sample points Q on the virtual object surface. . At this time, the direction of the incident illumination light L and the direction of the reflected light V with respect to the sample point Q are determined by the projection conditions set in step S4. Then, eight variables “σ, ξ, Each layer corresponding to the position of the sample point Q by referring to the visible ratio information (table having eight-dimensional variables) input in step S2 using “θL, φL, θV, φV, u, v”. Find the visible percentage of each.

  In the second step S72 in the subsequent reflected light intensity calculation stage, first, the combination of “θL, φL, θV, φV, u, v” of the position of the sample point Q is referred to by referring to the layer data input in step S1. The reflection coefficient kb (θL, φL, θV, φV, u, v) corresponding to is obtained for each layer. Then, the reflection coefficient kb obtained at the position of the sample point Q is determined by combining the reflection coefficients kb thus obtained in accordance with the weighting by the visible ratio obtained in the first step S71.

For example, it is assumed that the reflection coefficients for the two layers L1 and L2 corresponding to combinations of six variables “θL, φL, θV, φV, u, v” at the position of the sample point Q are kb1 and kb2, respectively. In the first step S71, if the visible ratios of the two layers L1 and L2 with respect to the position of the sample point Q are determined as L1: 70% and L2: 30% as described above, the sample The reflection coefficient kb at the position of the point Q is
kb = 0.7 × kb1 + 0.3 × kb2
It is calculated by the following.

Therefore, in the third step of the reflected light intensity calculation stage shown in FIG. 14, when the intensity of the incident illumination light at the sample point Q is Ii, the reflected light intensity I is
I = kb · Ii
What is necessary is just to obtain | require by the type | formula which becomes.

<<< §5. Specific Example Using Polygon >>>
In the present invention, “curvature” is a very important parameter. In particular, when dealing with a curvature having a direction factor, parameters such as a curvature σ and a curvature angle ξ are set for the sample point Q on the virtual object. It is very important to seek. Here, the curvature σ and the curvature angle ξ can be easily defined by using a cylindrical model as shown in FIG. For example, in the case of the example shown in FIG. 4A, the reciprocal of the radius r1 of the cylindrical object 51 is defined as the curvature σ, and the projection obtained on the side surface of the cylinder by projecting the center axis H of the cylinder in the radial direction. An angle ξ formed by the line H ′ and the reference direction line W of the fiber sheet 61 is defined as a curvature angle with respect to the curvature σ.

  Therefore, when preparing the visible ratio information (for example, the information shown in FIG. 9) to be input in step S2 of FIG. 11, whether it is a simulation method or a measurement method, it is applied to the cylindrical side surface of the object. It is possible to determine the visible ratio for each layer in a state where the fiber sheet is stuck in a predetermined direction, and it is possible to define the visible ratio corresponding to each combination of a specific curvature σ and a specific curvature angle ξ. . In other words, it is sufficient to consider only the cylindrical model in order to create the visible ratio information as shown in FIG.

  However, in step S6 of FIG. 11, since it is necessary to obtain the curvature σ and the curvature angle ξ for the sample point Q on the virtual object having an arbitrary shape, in practice, the definition of the curvature σ and the curvature angle ξ is The cylinder model cannot be used as it is. However, since various methods are known for defining the curvature of an arbitrary curved surface, in step S6, the curvature σ and the curvature angle ξ are defined in some form using any of these known methods. If you can, there is no problem.

  Here, an example of a specific method for defining the curvature σ and the curvature angle ξ in step S6 when the three-dimensional data indicating the three-dimensional shape of the virtual object is input as an aggregate of minute polygons (polygons). Will be described. In particular, a specific example using a triangle as a polygon will be described here. That is, in the example shown below, the surface shape of the virtual object is expressed as a collection of minute triangles, and the curved surface of the virtual object is actually a collection of many minute triangles (planar figures). It will consist of the body.

  Consider the case where one sample point Q on the virtual object is a point on one triangle Tq as shown in FIG. Here, for convenience of explanation, the triangle Tq including the sample point Q is referred to as a target triangle. Further, as shown in the figure, the three sides of the target triangle Tq are referred to as side A, side B, and side C, and the adjacent triangle with side A as the boundary is adjacent with the adjacent triangle Ta and side B as the boundary. A triangle is called an adjacent triangle Tb, and a triangle adjacent to the side C as a boundary is called an adjacent triangle Tc. Further, the three vertices of the target triangle Tq are set as vertices D1, D2, and D3, respectively, and the other vertices of the adjacent triangles Ta, Tb, and Tc are set as vertices D4, D5, and D6, respectively.

  In FIG. 16, all the triangles are drawn on the same plane. Actually, the vertices D1, D2, and D3 are points on the paper surface, but the vertices D4, D5, and D6 are points outside the paper surface. (A point located above or below the page). In other words, the target triangle Tq is a triangle on the paper surface, but the adjacent triangles Ta, Tb, and Tc are all triangles that are not on the paper surface. In the end, FIG. 16 shows a figure composed of four triangles Tq, Ta, Tb, and Tc. (Of course, actually, there are many other triangles outside the triangles Ta, Tb, and Tc. This figure is continuously bent at a predetermined angle with the sides A, B, and C as creases.

  The values to be obtained in step S6 are the curvature σ and the curvature angle ξ with respect to the sample point Q. Here, first, the one with the curvature σ with respect to the target triangle Tq is defined. However, the target triangle Tq itself is a simple planar figure and does not form a curved surface. In the case of the embodiment shown here, the curved surface of the virtual object is merely represented in a pseudo manner by a collection of minute triangles. Therefore, if the curvature σ for the target triangle Tq is defined, it must be defined as a value corresponding to the formation angle between the three adjacent triangles Ta, Tb, and Tc.

  Therefore, the angle formed by the target triangle Tq and the adjacent triangle Ta is defined as the forming angle ωa using the side A as the boundary line, and the angle formed by the target triangle Tq and the adjacent triangle Tb is defined as the forming angle ωb using the side B as the boundary line. The angle formed by the target triangle Tq and the adjacent triangle Tc is defined as the forming angle ωc with the side C as the boundary line. Then, the curvature of the target triangle Tq in relation to the adjacent triangle Ta is defined as “curvature σa related to the side A”, and the curvature in relation to the adjacent triangle Tb of the target triangle Tq is defined as “curvature σb related to the side B”. The curvature in the relationship between the target triangle Tq and the adjacent triangle Tc is defined as “curvature σc with respect to side C”. In this case, the curvature σa related to the side A is a value determined based on the formation angle ωa, the curvature σb related to the side B is determined based on the formation angle ωb, and the curvature σc related to the side C is determined based on the formation angle ωc. Then, it becomes a meaningful value as the curvature in the relationship with each adjacent triangle.

  Specifically, the curvature may be set to be smaller as each forming angle becomes closer to 180 °. For example, if the vertex D4 is a point on the drawing sheet, the target triangle Tq and the adjacent triangle Ta are triangles on the same sheet, and the formation angle ωa of both is 180 °. In this case, the surface connected from the target triangle Tq to the adjacent triangle Ta is a complete plane, and the curvature σa related to the side A may be set to the minimum value 0.

  Thus, it is reasonable to set the curvature for each side according to the formation angle of the two triangles sandwiching the side so that the smaller the formation angle is, the smaller the curvature is. It can be intuitively understood that this is a typical method of setting curvature. However, the inventor of the present application has found that it is more preferable to define the curvature not only based on the formation angle of both triangles but including the factor of the size of both triangles.

  The small triangles representing the virtual object are all very small figures compared to the size of the entire virtual object. However, when individual triangles are compared with each other, the sizes thereof are various. Some triangles have a large area and others have a small area. Then, for a triangle with a large area, the plane is continuous over a wide area, so it makes more sense to define a smaller curvature than a small triangle. Conversely, for a triangle with a small area, it is more reasonable to define a larger curvature than for a large triangle because the area where the planes are continuous is narrow.

  Therefore, the curvature for each side is determined depending on the size (area) of the target triangle itself and the size (area) of the adjacent triangle, and the smaller the size, the smaller the curvature is defined. It can be seen that such settings should be made. Specifically, the curvature σa of the side A is such that the smaller the formation angle ωa is closer to 180 °, and the smaller the size of the target triangle Tq and the adjacent triangle Ta, the smaller the curvature σa. The curvature σb is defined so that the curvature with respect to the side B becomes smaller as the forming angle ωb becomes closer to 180 ° and becomes smaller as the size of the target triangle Tq and the adjacent triangle Tb becomes larger. The curvature σc may be defined so that the curvature of the side C becomes smaller as the formation angle ωc approaches 180 ° and becomes smaller as the size of the target triangle Tq and the adjacent triangle Tc becomes larger. .

  The basic concept for defining the curvature for each side has been described above. Based on such a basic concept, for example, the following method can be used to actually define the curvature for each side. it can. Here, an example of a specific method for obtaining the curvature σa related to the side A in FIG. 16 will be described. As described above, the curvature σa related to the side A is a curvature in the relationship with the adjacent triangle Ta of the target triangle Tq. According to the basic concept described above, the smaller the formation angle ωa is, the smaller the angle is. And a value that becomes smaller as the size of the target triangle Tq and the adjacent triangle Ta increases.

  Therefore, first, as shown in FIG. 16, a perpendicular is drawn from the diagonal D3 with respect to the side A of the target triangle Tq to the side A, and the length hqa of this perpendicular is obtained. Similarly, a perpendicular to the side A is drawn from the diagonal D4 with respect to the side A of the adjacent triangle Ta, and the length ha of the perpendicular is obtained. The lengths hqa and ha of the perpendiculars obtained in this way are amounts related to the sizes of the target triangle Tq and the adjacent triangle Ta to some extent, and as each triangle becomes larger, the lengths of these perpendiculars tend to become longer.

  Next, a drawing as shown in FIG. 17 is performed using the perpendicular lengths hqa and ha thus obtained and the forming angle ωa between the target triangle Tq and the adjacent triangle Ta. That is, one end of the “line segment having the length hqa” and the “line segment having the length ha” are connected at the connection point Ja on the plane, and both the line segments at the connection point Ja are connected. It arrange | positions so that the angle | corner which becomes may become the formation angle (omega) a. Subsequently, in FIG. 17, an intersection Oa between the vertical bisector of “line segment having length hqa” and the vertical bisector of “line segment having length ha” is obtained and obtained. The distance Ra between the intersection point Oa and the connection point Ja is obtained as shown in the figure. The reciprocal of the distance Ra is defined as the curvature σa related to the side A.

  In FIG. 17, the distance Ra corresponds to a radius when a “line segment having a length hqa” and a “line segment having a length ha” are approximated by a smooth arc. Here, if the formation angle ωa is 180 °, the two perpendicular bisectors indicated by broken lines in the figure are parallel to each other, so that the position of the intersection Oa is infinity and the distance Ra = infinity. . As a result, the curvature σa = 0. The smaller the formation angle ωa, the closer the intersection Oa is to the connection point Ja, and the smaller the distance Ra, the larger the curvature σa. Eventually, the curvature σa becomes a value that matches the above-mentioned basic concept that the smaller the formation angle ωa becomes, the smaller the angle ωa becomes.

  On the other hand, it can be easily understood from FIG. 17 that when the length hqa or the length ha becomes longer, the intersection Oa is further away from the connection point Ja, the distance Ra becomes larger, and the curvature σa becomes smaller. As described above, the length hqa and the length ha are amounts related to the sizes of the target triangle Tq and the adjacent triangle Ta to some extent, so that the curvature σa eventually has the sizes of the target triangle Tq and the adjacent triangle Ta. The value agrees with the above basic concept that the larger the value is, the smaller the value is.

  From the above, the length hqa of the perpendicular line from the diagonal D3 to the side A of the triangle Tq of interest Tq and the length ha of the perpendicular line from the diagonal D4 to the side A of the adjacent triangle Ta to the side A On the plane, “a line segment having a length hqa” and “a line segment having a length ha” are connected to each other at one end at a connection point Ja, and both at the connection point Ja. The angle formed by the line segments is the formation angle ωa, and the vertical bisector of the “line segment having the length hqa” and the vertical bisector of the “line segment having the length ha” If the reciprocal of the distance Ra between the intersection point Oa and the connection point Ja is defined as the curvature σa related to the side A, the curvature σa can be defined so as to match the basic concept described above.

  Similarly, in order to define the curvature σb with respect to the side B, although illustration is omitted, the following drawing may be performed. That is, the length hqb of the perpendicular line from the diagonal D2 with respect to the side B of the triangle Tq of interest to the side B and the length hb of the perpendicular line from the diagonal D5 to the side B of the adjacent triangle Tb with respect to the side B are obtained. , “A line segment having a length hqb” and “a line segment having a length hb” are connected to each other at one end at a connection point Jb and both line segments at the connection point Jb. The angle formed is the formation angle ωb, and the intersection Ob of the vertical bisector of the “line segment with the length hqb” and the vertical bisector of the “line segment with the length hb” And the reciprocal of the distance Rb from the connection point Jb may be defined as the curvature σb related to the side B.

  Similarly, in order to define the curvature σc with respect to the side C, the following drawing may be performed. First, the length hqc of the perpendicular line from the diagonal D1 with respect to the side C of the triangle Tq of interest to the side C and the length hc of the perpendicular line from the diagonal D6 to the side C of the adjacent triangle Tc with respect to the side C are obtained. On the plane, “a line segment having a length hqc” and “a line segment having a length hc” are connected at one end at a connection point Jc, and both line segments at the connection point Jc. The intersection angle Oc between the vertical bisector of the “line segment having the length hqc” and the vertical bisector of the “line segment having the length hc” is arranged so that the formed angle is the formation angle ωc. The reciprocal of the distance Rc between and the connection point Jc may be defined as the curvature σc with respect to the side C.

  With the procedure described above, three kinds of curvatures, that is, the curvature σa with respect to the side A, the curvature σb with respect to the side B, and the curvature σc with respect to the side C, can be defined for the target triangle Tq. However, the curvature that needs to be obtained in step S6 in FIG. 11 is the curvature σQ with respect to the sample point Q located in the target triangle Tq. Therefore, the curvature σQ for the sample point Q is obtained by combining the three curvatures σa, σb, and σc. The basic concept for this synthesis is the idea that the curvatures σa, σb, and σc are prorated according to the distance between the sample point Q and the sides A, B, and C. That is, the shorter the distance between the sample point Q and the side A, the greater the influence of the curvature σa, and the shorter the distance between the sample point Q and the side B, the greater the influence of the curvature σb. It is reasonable to combine the curvatures σa, σb, and σc to obtain the curvature σQ for the sample point Q so that the shorter the distance to the side C is, the larger the influence of the curvature σc is. Can determine the curvature σQ.

A first method for obtaining the curvature σQ based on such a basic concept will be described with reference to FIG. Each triangle shown in FIG. 18 is exactly the same as each triangle shown in FIG. 16, and the sample point Q is located in the target triangle Tq. Therefore, first, the distance La between the diagonal D3 with respect to the side A of the target triangle Tq and the sample point Q is obtained, and the distance between the diagonal D2 with respect to the side B of the target triangle Tq and the sample point Q is obtained as Lb. Lc is obtained as the distance between the diagonal D1 and the sample point Q with respect to the side C of And the curvature σQ for the sample point Q is
σQ = (La · σa + Lb · σb + Lc · σc) / (La + Lb + Lc)
It is defined by the following operation. If the curvature σQ is defined by such a method, it can be defined by a method that matches the basic concept described above.

On the other hand, FIG. 19 is a diagram showing a second method for obtaining the curvature σQ based on the basic concept described above. Also in this figure, each triangle is exactly the same as each triangle shown in FIG. 16, and the sample point Q is located in the target triangle Tq. In this second method, a perpendicular line is first drawn from the sample point Q to the side A, and the foot is set to a. Similarly, a perpendicular is dropped from the sample point Q to the side B, the leg is b, a perpendicular is dropped from the sample point Q to the side C, and the leg is c. Then, the target triangle Tq is divided into three regions Ua, Ub, Uc by these three perpendicular lines (indicated by broken lines in the figure). Here, the region Ua is a region including a diagonal D3 with respect to the side A, the region Ub is a region including a diagonal D2 with respect to the side B, and the region Uc is a region including a diagonal D1 with respect to the side C. . Here, the area of each region Ua, Ub, Uc is indicated by the same symbol Ua, Ub, Uc, respectively, and the curvature σQ for the sample point Q is
σQ = (Ua · σa + Ub · σb + Uc · σc) / (Ua + Ub + Uc)
It is defined by the following operation. If the curvature σQ is defined by such a method, it can be defined by a method that matches the basic concept described above.

  The specific method for defining the curvature σQ at an arbitrary sample point Q when the three-dimensional data indicating the three-dimensional shape of the virtual object is input as a collection of minute triangles has been described above. According to this method, the curvature σQ at the position of an arbitrary sample point Q on a virtual object having an arbitrary curved surface can be determined without being limited to a cylindrical curved surface.

  Next, a method for obtaining the curvature angle ξQ at the position of an arbitrary sample point Q on a virtual object having an arbitrary curved surface will be described. In the first place, the curvature angle ξ is an element indicating a deviation between the bending direction corresponding to the curvature σQ and the reference direction line on the fiber sheet when a predetermined curvature σQ is defined at the position of the sample point Q. For example, in the case of the cylindrical curved surface shown in FIG. 4, the curvature angle ξ is defined as the angle formed by the reference direction line W and the projection line H ′ of the central axis H of the cylinder. The direction in which the curvature angle ξ = 90 ° is the bending direction corresponding to the curvature σ (that is, the circumferential direction).

  In both the example shown in FIG. 4A and the example shown in FIG. 4C, the value of the curvature is the same as σ = 1 / r1. However, the curvature angle ξ is 90 ° in the former case and 0 ° in the latter case, and they are greatly different. This is because, when focusing on the direction of the reference direction line W of the fiber sheet 61, in the former case, the reference direction line W is stuck so as to face the bending direction (circumferential direction) corresponding to the curvature of 1 / r1. On the other hand, in the latter, the reference direction line W has a direction (ie, a direction parallel to the central axis H) forming 90 ° with respect to the bending direction (circumferential direction) corresponding to the curvature of 1 / r1. It shows that it is stuck to face. In the former case where the curvature angle ξ = 90 °, the direction of the reference direction line W matches the bending direction (circumferential direction) corresponding to the curvature σ = 1 / r1. Thus, the curvature angle ξ is a parameter corresponding to an angle indicating the amount of deviation of the reference direction line W with respect to the bending direction according to the curvature, and ranges from 90 ° to 0 °, where ξ = 90 °. This means that there is no deviation amount. When ξ = 0 °, this means that the deviation amount is maximum.

  The visible ratio information input in step S2 of FIG. 11 (for example, a table referred to by two variables σ and ξ as shown in FIG. 9) is used as a curvature σ and a curvature angle ξ assuming such a cylindrical curved surface. In the step S6, it is necessary to define the curvature angle ξ by a method close to the definition based on this cylindrical curved surface. Therefore, in the following, an example of a specific method for defining the curvature angle ξQ at the position of an arbitrary sample point Q when the three-dimensional data indicating the three-dimensional shape of the virtual object is input as a collection of minute triangles. State.

  First, as shown in FIG. 20, a target triangle Tq including a sample point Q and three adjacent triangles Ta, Tb, and Tc adjacent thereto are considered. Each of these triangles is exactly the same as each triangle shown in FIG. Further, in step S3, as described above, since the information regarding the fiber sheet sticking direction with respect to the virtual object is also input, in step S6, the direction of the reference direction line W of the fiber sheet is defined as shown in FIG. can do. Here, the reference direction line W is defined as a straight line on the same plane as the target triangle Tq. In step S3, when the reference direction line W is input as a straight line on the XYZ three-dimensional coordinate system, the projection obtained by projecting the reference direction line W onto the plane including the target triangle Tq in the normal direction of the plane. What is necessary is just to define an image as the reference direction line W shown in figure. When texture mapping or BTF is applied, the two-dimensional coordinate system (u, v) already given to the polygon is used as a reference, and for example, the v-axis direction in the polygon is used as the reference direction line W. do it.

  Subsequently, as shown in FIG. 20, angles formed by the reference direction line W and each of the sides A, B, and C of the target triangle Tq (when not intersecting, angles formed by extension lines of the sides). ) Ξa, ξb, ξc are determined as the curvature angles for the sides A, B, C, respectively. Then, the curvature angle ξQ for the sample point Q may be obtained by synthesizing the curvature angles ξa, ξb, and ξc for these sides. The basic concept in performing this synthesis is the idea that the curvature angles ξa, ξb, and ξc are apportioned according to the distance between the sample point Q and the sides A, B, and C. That is, the shorter the distance between the sample point Q and the side A, the greater the influence of the curvature angle ξa, and the shorter the distance between the sample point Q and the side B, the greater the influence of the curvature angle ξb. The curvature angle ξQ for the sample point Q may be determined by combining the curvature angles ξa, ξb, and ξc so that the influence of the curvature angle ξc increases as the distance between Q and side C decreases.

A first method for obtaining the curvature angle ξQ based on such a basic concept will be described with reference to FIG. Each triangle shown in FIG. 21 is exactly the same as each triangle shown in FIG. 20, and the sample point Q is located in the target triangle Tq. Therefore, first, the distance La between the diagonal D3 with respect to the side A of the target triangle Tq and the sample point Q is obtained, and the distance between the diagonal D2 with respect to the side B of the target triangle Tq and the sample point Q is obtained as Lb. Lc is obtained as the distance between the diagonal D1 and the sample point Q with respect to the side C of And the curvature angle ξQ about the sample point Q is
ξQ = (La · ξa + Lb · ξb + Lc · ξc) / (La + Lb + Lc)
It is defined by the following operation. If the curvature angle ξQ is defined by such a method, it can be defined by a method that matches the basic concept described above. The principle of this method is in common with the principle of the method for defining the curvature σQ described with reference to FIG.

On the other hand, as a second method for obtaining the curvature angle ξQ, a method using the principle of the method for defining the curvature σQ described with reference to FIG. 19 is also possible. That is, as shown in FIG. 19, a perpendicular line is drawn from the sample point Q to each side A, B, C, and the target triangle Tq is divided into three regions Ua, Ub, Uc by these three perpendicular lines. The areas of these three regions Ua, Ub, Uc are indicated by the same symbols Ua, Ub, Uc, respectively, and the curvature angle ξQ for the sample point Q is
ξQ = (Ua · ξa + Ub · ξb + Uc · ξc) / (Ua + Ub + Uc)
It is defined by the following operation. If the curvature angle ξQ is defined by such a method, it can be defined by a method that matches the basic concept described above.

  As described above, when the three-dimensional data indicating the three-dimensional shape of the virtual object is input as a collection of minute triangles, the curvature σQ and the curvature at an arbitrary sample point Q can be obtained by applying the specific method described above. It is possible to define an angle ξQ. However, when a three-dimensional shape is expressed using polygons, triangles are not always used, and three-dimensional data including a set of arbitrary polygons such as quadrangles and hexagons is often used. In this way, even if the virtual object is given as three-dimensional data consisting of a set of arbitrary polygons, the polygon can always be divided into a plurality of triangles. The example is widely applicable when a three-dimensional shape is expressed using polygons.

  However, the basic principle for the case where 3D data consisting of a set of triangles is used is that the polygon is divided into a plurality of triangles even when 3D data consisting of a set of arbitrary polygons is used. It is also possible to apply a polygon as it is. That is, when this basic principle is extended to a general J-gon, the curvature σQ and the curvature angle ξQ for the sample point Q may be obtained by the following method.

  First, a J-polygon (a polygon having J sides) including the sample point Q for which the curvature is to be obtained is extracted as a target polygon. Then, for the target polygon, formation angles ω1 to ωJ between the target polygon and a plurality of J adjacent polygons adjacent to the target polygon are obtained. Subsequently, as the curvature of the jth side forming the boundary with the jth (j = 1 to J) adjacent polygon, the curvature becomes smaller as the jth formation angle ωj is closer to 180 °. And the curvature σj is defined such that the larger the size of the target polygon and the jth adjacent polygon, the smaller the curvature σj for the first side to the Jth side, respectively. Define Finally, the shorter the distance between the sample point Q and the j-th side, the greater the influence of the j-th curvature σj. The curvature σQ for the point Q may be obtained.

  On the other hand, with respect to the curvature angle ξ, angles ξ1 to ξJ formed by the reference direction line W and each of the first side to the Jth side of the target polygon are obtained as the curvature angles for each side, respectively. By combining the J curvature angles ξ1 to ξJ so that the influence of the jth curvature angle ξj increases as the distance between the point Q and the jth side becomes shorter, What is necessary is just to obtain | require the curvature angle (xi) Q.

  As described above, in the object data input stage shown in step S3 of FIG. 11, when the three-dimensional shape of the virtual object is input as three-dimensional data indicating a set of polygons, the curvature σQ and the curvature angle ξQ for an arbitrary sample point Q. In the implementation of the present invention, it is not always necessary to input the three-dimensional shape of the virtual object as three-dimensional data indicating a set of polygons. For example, when the three-dimensional shape of the virtual object is input as a mathematical expression and a parametric curved surface expressed by the parameter values used in the mathematical expression, the curvature σQ and the curvature angle ξQ for a specific sample point Q are expressed by this mathematical expression. It may be obtained by calculation using values of parameters and parameters.

<<< §6. Two-dimensional image generation apparatus according to the present invention >>
Steps S1 to S10 shown in the flowchart of FIG. 11 are processes performed inside the computer, and each procedure is actually executed based on a computer program. The two-dimensional image generation apparatus according to the present invention is an apparatus configured by a computer having a function of executing each procedure of FIG. 11, and is an apparatus including the components shown in the block diagram of FIG. The configuration and operation of this apparatus will be described below.

  This two-dimensional image generation device is a function for generating two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of an object based on the three-dimensional data of the object and observed from a predetermined viewpoint. As shown in FIG. 22, the data input unit 110, the three-dimensional data storage unit 120, the layer data storage unit 130, the visible ratio information storage unit 140, the reflected light intensity calculation unit 150, the curvature calculation, as shown in FIG. A unit 160, a projection condition setting unit 170, a pixel definition unit 180, and a projection data storage unit 190. Actually, each of these components is realized by incorporating a dedicated program into the computer.

  The data input unit 110 is a component for inputting various data given from the outside, and the various data input in steps S1 to S4 in FIG. 11 are taken into the computer from the data input unit 110. become. Specifically, the data input unit 110 is configured by devices such as a computer keyboard, a mouse, a scanner device, a digital camera, and a magnetic or optical data reading device.

  The three-dimensional data storage unit 120 is a component for storing “three-dimensional data indicating a three-dimensional shape of a virtual object” input from the data input unit 110. In practice, the three-dimensional data storage unit 120 is a magnetic recording device or memory for a computer. It is realized by a device. The object data input in step S3 in FIG. 11 is stored in the three-dimensional data storage unit 120.

  The layer data storage unit 130 stores “m layer data indicating reflection characteristics for each of a plurality of m layers constituting a virtual fiber sheet to be pasted” input from the data input unit 110. It is a component and is actually realized by a magnetic recording device or a memory device for a computer. The layer data input in step S1 of FIG. 11 is stored in this layer data storage unit 130.

  The visible ratio information storage unit 140 receives “visible ratio information indicating the visible ratio for each layer in a state where the fiber sheet is bent at various curvatures” input from the data input unit 110 (for example, as shown in FIGS. 8 and 9). Information), and is actually realized by a magnetic recording device or a memory device for a computer. The visible ratio information input in step S2 of FIG. 11 is stored in the visible ratio information storage unit 140.

  The projection condition setting unit 170 is a component that sets the illumination condition, the position of the viewpoint E, and the projection plane M based on the data input from the data input unit 110. In practice, the projection condition setting unit 170 is a computer magnetic recording device or memory. It is realized by a device.

  The curvature calculation unit 160 uses the curvature σQ and the curvature of the virtual object surface for the position of the predetermined sample point Q defined on the surface of the virtual object based on the three-dimensional data stored in the three-dimensional data storage unit 120. This is a component having a function for obtaining the angle ξQ. A specific method for obtaining the curvature σQ and the curvature angle ξQ for the sample point Q on the arbitrary curved surface is as illustrated in §5.

  The reflected light intensity calculation unit 150 is a component that performs rendering processing. When the fiber sheet is attached to the surface of the virtual object, the reflected light intensity V from the individual sample points Q toward the viewpoint E is expressed as three-dimensional data. 3D data stored in the storage unit 120, layer data stored in the layer data storage unit 130, visible rate information stored in the visible rate information storage unit 140, set in the projection condition setting unit 170 It has a function of calculating based on the projected projection conditions (illumination conditions, viewpoint position, projection plane). The specific calculation is as shown in the three steps S71 to S73 shown in the flowchart of FIG.

  In other words, the reflected light intensity calculation unit 150 refers to the visible rate information stored in the visible rate information storage unit 140 and calculates the visible rate for each layer corresponding to the curvature at one sample point position. By combining the first functional unit to be obtained and the reflection characteristics of the m kinds of layer data stored in the layer data storage unit 130 according to the visible ratio obtained by the first functional unit, the sample point A second functional unit for obtaining the reflection characteristic at the position, and a third functional unit for obtaining the intensity of the reflected light from the sample point based on the reflection characteristic obtained by the second functional unit. Will be. In addition, when the 1st functional part calculates | requires a visible ratio, or the 2nd functional part calculates | requires a reflection characteristic, as needed, the three-dimensional data stored in the three-dimensional data storage part 120, and projection conditions Calculations using the projection conditions set in the setting unit 170 are performed.

  The pixel definition unit 180 is a component that defines a pixel P having a pixel value corresponding to the intensity of the reflected light V at the intersection between the reflected light V from the sample point Q and the projection plane M, and stores projection data. The unit 190 is a component that stores a set of a large number of pixels P defined for a large number of sample points Q as two-dimensional projection data indicating a projection image of a virtual object.

  The operation for obtaining a desired two-dimensional projection image using the two-dimensional image generation apparatus shown in FIG. 22 is as follows. First, the operator prepares three-dimensional data of a virtual object, fiber sheet layer data, and visible ratio information, and inputs these data from the data input unit 110. As the three-dimensional data of the virtual object, for example, data obtained by diverting CAD data may be used as it is. The fiber sheet layer data and visible ratio information can be prepared by actual measurement or computer simulation using an actual fiber sheet. Further, by operating the data input unit 110, the illumination condition, the viewpoint position, and the projection plane are set for the projection condition setting unit 170.

  Thus, the substantial operation performed by the operator is completed. Thereafter, if an instruction to start the rendering process is given to this apparatus, the curvature calculator 160 calculates the curvature σQ and the curvature angle ξQ for each sample point Q necessary for the rendering process, and the reflection The light intensity calculation unit 150 calculates the intensity of the reflected light V from each sample point Q toward the viewpoint E, and the pixel definition unit 180 defines a pixel P having a pixel value corresponding to the intensity of each reflected light V. Thus, the target two-dimensional image is stored in the projection data storage unit 190 as a set of these pixels P. The operator may output the two-dimensional image thus obtained in the projection data storage unit 190 onto a desired medium as necessary.

  In this apparatus, in order to handle a curvature having an orientation factor, the orientation of the reference direction line defined on the fiber sheet when the fiber sheet is pasted to the virtual object in the data input unit 110. The function to input the information on the visual ratio is stored, and the visible ratio information storage unit 140 has the function of inputting the visible ratio information indicating the visible ratio of each layer for each curvature having the orientation factor. Keep it. In addition, the curvature calculation unit 160 has a function of obtaining a curvature having a direction factor, and the reflected light intensity calculation unit 150 uses a visible ratio for each layer corresponding to the curvature having a direction factor. A function for obtaining the reflected light intensity may be provided.

<<< §7. Some variations >>>
As mentioned above, although this invention was demonstrated based on embodiment shown in figure, this invention is not limited to these embodiment, In addition to this, it can implement in a various aspect.

  For example, in the embodiments described so far, the description has been made based on the example of the fiber sheet 61 having two layers as shown in the upper part of FIG. 5, but in the present invention, two fiber sheets are not necessarily provided. It is not necessary to handle it as a layer, and it is possible to handle it as three or more layers. Specifically, in the case of a fiber sheet having a structure in which two types of piles, a long pile and a short pile, are planted on the ground, it is composed of an upper layer composed of a long pile, a middle layer composed of a short pile, and a ground It can be handled as three layers of the lower layer.

  In this case, in step S1 of FIG. 11, layer data for each of the three layers is input, and in step S2, the visible ratios for the three layers (for example, L1: 70%, L2: 20%, L3: 10%). In step S7, the calculation of the reflected light intensity is performed by combining the three reflection characteristics. Of course, it is possible to handle it as four or more layers. As a general rule, if the virtual fiber sheet to be attached can be handled as multiple m sheets (m is an integer of 2 or more), The invention can be applied.

  In the embodiment described so far, as shown in the upper part of FIG. 5, the present invention is applied to a so-called pile ground in which the upper layer L1 is constituted by a number of piles planted in the lower layer L2 as a base. However, the application of the present invention is not limited to such a pile land. For example, for a fiber sheet formed by knitting warp and weft, as described above, if a first layer mainly composed of warp and a second layer mainly composed of weft are defined, The present invention can be applied similarly to the embodiment. In short, the present invention can be applied to any fiber sheet that has the property that a plurality of layers can be defined in some form and the visible ratio of each layer changes based on the curvature.

It is a perspective view which shows the state which affixes a fiber sheet on the virtual object comprised from a plane. It is a perspective view which shows the state which sticks a fiber sheet on the virtual object which has a curved surface. It is a perspective view which shows the principle of a general rendering process. It is a perspective view which shows the relationship between a fiber sheet and the curvature of an object surface. It is a figure which shows the basic concept which handles a fiber sheet as a structure with a some layer. It is a side view which shows the change of the visible ratio for every layer at the time of bending a fiber sheet with various curvature. It is an enlarged view which shows the change of the visible ratio for every layer at the time of bending a fiber sheet with various curvature. It is a table which shows the relationship between curvature (sigma) and the visible ratio for each layer. It is a table which shows the relationship between curvature (sigma) and curvature angle (xi), and the visible ratio for each layer. It is a figure which shows the rendering process by the basic principle of this invention. It is a flowchart which shows the procedure of the two-dimensional image generation method which concerns on this invention. 4 is a perspective view showing a cut surface at a position of a sample point Q on a virtual object 50. FIG. It is a top view which shows an example of the method of calculating | requiring the curvature of the sample point Q shown in FIG. It is a flowchart which shows the detailed procedure of step S7 of the flowchart shown in FIG. It is a perspective view for demonstrating the principle of the BRDF model which determines a reflectance in consideration of the direction of illumination light and reflected light. It is a top view which shows the principle which defines the curvature about the one side of a triangle about the virtual object expressed by the collection of many triangles. In the example shown in FIG. 16, it is a top view which shows the principle which defines the curvature about the edge | side A. FIG. In the example shown in FIG. 16, it is a top view which shows the principle which defines the curvature about the sample point Q in a triangle. In the example shown in FIG. 16, it is a top view which shows another principle which defines the curvature about the sample point Q in a triangle. In the example shown in FIG. 16, it is a top view which shows the principle which defines the curvature angle about each edge | side A, B, and C. FIG. In the example shown in FIG. 16, it is a top view which shows the principle which defines the curvature angle about the sample point Q in a triangle. It is a block diagram which shows the structure of the two-dimensional image generation apparatus which concerns on this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 ... Virtual object 11 ... Upper surface 12 of virtual object ... Front surface 13 of virtual object ... Side surface 20 of virtual object ... Virtual object 21 which stuck fiber sheet ... Upper surface 22 of virtual object which stuck fiber sheet ... Virtual which stuck fiber sheet Front surface 23 of object: Side surface 30 of virtual object pasted with fiber sheet ... Virtual object 31 ... Upper surface 32 of virtual object ... Side surface 40 of virtual object ... Virtual object 41 pasted with fiber sheet ... Upper surface 42 of virtual object pasted with fiber sheet A side surface 50 of a virtual object to which a fiber sheet is attached ... Virtual objects 51, 52 ... A cylindrical object 55 ... A projected image 56 of a virtual object ... A contour line 60 on a cut surface ... A virtual fiber sheet 61 ... A fiber sheet 110 ... Data input Unit 120 ... three-dimensional data storage unit 130 ... layer data storage unit 140 ... visible ratio information storage unit 150 ... reflected light intensity calculation unit 160 ... curvature performance Unit 170 ... projection condition setting unit 180 ... pixel definition unit 190 ... projection data storage unit A, B, C ... triangle sides a, b, c ... perpendicular legs D1 to D6 ... triangle vertex E ... viewpoint G ... light source H ... Center axis of cylinder H '... Projection lines ha, hqa ... Length of perpendicular line Ja ... Connection point L ... Illumination light L' ... Projection image L1 of illumination light ... Upper layer L2 of fiber sheet ... Fiber Lower layer La of sheet: Distance Lb between point Q and point D3: Distance Lc between point Q and point D2: Distance LD1, LD2 between point Q and point D1: Layer data M: Projection plane n: Normal line Oa ... Intersection P of vertical bisectors ... Pixel / projection line segments P (Q1), P (Q2) ... Pixel value Q ... Sample points Q1, Q2 ... Corresponding points QL, QR ... Two points equidistant from the sample point Q QQ ... intersection Ra ... distance between point Oa and point r ... distance r1, r2 between points Q and QQ Cylinder radius S ... Orthogonal planes S1 to S10 orthogonal to the normal line Steps S71 to S73 of the flowchart ... Ta, Tb, Tc of the flowchart ... Adjacent triangle Tq ... Triangle of interest TL, TR ... Tangent Ua, Ub, Uc ... divided regions and their areas u, v ... coordinate axes V of the two-dimensional coordinate system representing the picture ... reflected light V '... projected image W of the reflected light ... reference direction lines X, Y, Z ... of the three-dimensional coordinate system Each coordinate axis x, y: Each coordinate axis ζ of the two-dimensional coordinate system on the projection plane M: Reference line θL: Incident angle θV of the illumination light L ... Ejection angle ξ: Curvature angle ξa ... Curvature angle ξb with respect to the side A ... curvature angle ξc with respect to side B ξQ ... curvature angle with respect to side C ξQ ... curvature angle σ with respect to sample point Q ... curvature σa ... curvature with respect to side A σb ... curvature with respect to side B σc ... curvature σQ with respect to side C ... curvature φL of sample point Q ... Azimuth angle φV of illumination light L ... Reflected light V Azimuth angle ωa ... Formation angle of plane or line segment

Claims (28)

A method of generating two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of the object based on the three-dimensional data of the object and observed from a predetermined viewpoint,
A layer data input stage in which the computer inputs m layer data indicating reflection characteristics for each of a plurality of m layers constituting a virtual fiber sheet to be pasted;
A visible ratio information input step in which a computer inputs visible ratio information indicating a visible ratio for each layer in a state where the fiber sheet is bent with various curvatures;
An object data input stage in which a computer inputs three-dimensional data indicating a three-dimensional shape of a virtual object;
A projection condition setting stage in which a computer sets illumination conditions, a viewpoint position, and a projection plane;
A curvature calculating step of calculating a curvature of the surface of the virtual object for a position of a predetermined sample point defined on the surface of the virtual object;
When the computer sticks the fiber sheet to the surface of the virtual object, the reflected light intensity calculation step of calculating the intensity of the reflected light from each sample point toward the viewpoint position;
A computer defining step in which a computer defines a pixel having a pixel value corresponding to the intensity of the reflected light at an intersection position between the reflected light from a sample point and the projection plane;
A projection data generation step in which a computer generates two-dimensional projection data indicating a projection image of the virtual object by a set of a plurality of pixels defined for a number of sample points;
Have
In calculating the reflected light intensity from one sample point in the reflected light intensity calculation step,
A first step of obtaining a visible ratio for each layer corresponding to the curvature at the sample point position with reference to the visible ratio information;
A second step of obtaining the reflection characteristic at the sample point position by combining the reflection characteristics of the m layer data according to the visible ratio obtained in the first step;
A third step for determining the intensity of the reflected light from the sample point based on the reflection characteristic obtained in the second step;
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface. The two-dimensional image generation method according to claim 1,
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, find the curvature with a factor of direction,
In the first step of the reflected light intensity calculation stage, two-dimensional based on a three-dimensional virtual object in which a fiber sheet is attached to the surface, wherein a visible ratio for each layer corresponding to a curvature having a direction factor is obtained. Image generation method. The two-dimensional image generation method according to claim 2,
In the visible ratio information input stage, the visible ratio for each layer in a state where the fiber sheet is stuck to the cylinder side in a predetermined direction is defined, the curvature σ is defined using the reciprocal of the radius of the cylinder, and the central axis of the cylinder is defined. The angle ξ formed by the projection line obtained by projecting in the radial direction on the side surface of the cylinder and the reference direction line of the fiber sheet is defined as a curvature angle with respect to the curvature σ, and each curvature σ and each curvature angle ξ Enter visibility ratio information that indicates the visibility ratio for each layer corresponding to each combination,
In the object data input stage, information on the direction of the reference direction line of the fiber sheet attached on the virtual object is input,
In the curvature calculation stage, by referring to information on the direction of the reference direction line with respect to the position of a predetermined sample point, the curvature angle indicating the curvature σ and the deviation between the bending direction corresponding to the curvature σ and the reference direction line ξ is obtained,
In the first step of the reflected light intensity calculation stage, a visible ratio for each layer corresponding to the combination of the curvature σ and the curvature angle ξ is obtained, and this is based on a three-dimensional virtual object with a fiber sheet attached to the surface. Two-dimensional image generation method. In the two-dimensional image generation method in any one of Claims 1-3,
In the layer data input stage, a two-dimensional image having reflection characteristics indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system is input as layer data for each individual layer,
In the second step of the reflected light intensity calculation stage, the value of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the sample point position is determined by the visible ratio obtained in the first step. By combining in accordance with the weighting, the reflection coefficient k at the sample point position is obtained,
In the third step of the reflected light intensity calculation stage, when the intensity of incident illumination light at the sample point is Ii, the reflected light intensity I is calculated using the reflection coefficient k.
I = k · Ii
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. In the two-dimensional image generation method in any one of Claims 1-3,
At the layer data input stage, the diffuse reflection coefficient for each layer is input as layer data.
In the second step of the reflected light intensity calculation stage, the diffuse reflection coefficient kd at the sample point position is synthesized by combining the diffuse reflection coefficient for each individual layer according to the weighting by the visible ratio obtained in the first step. Seeking
In the third step of the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, and the angle formed between the normal n set at the sample point position on the virtual object surface and the incident illumination light is α. When the reflected light intensity I is
I = kd ・ Ii ・ cos α
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. The two-dimensional image generation method according to claim 5,
In the layer data input stage, a two-dimensional image having a diffuse reflection coefficient indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system is input as layer data for each individual layer,
In the second step of the reflected light intensity calculation stage, the value of the pattern data T (u, v) for each layer corresponding to the coordinate values u, v of the sample point position is determined by the visible ratio obtained in the first step. A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, wherein a diffuse reflection coefficient kd at the sample point position is obtained by combining in accordance with weighting. In the two-dimensional image generation method in any one of Claims 1-3,
In the layer data input stage, the reflection coefficient k (α) depending on the angle α formed by the normal n standing on the layer surface and the illumination light, and the parameter β indicating the sharpness of specular reflection are input as layer data. ,
In the second step of the reflected light intensity calculation stage, the angle formed between the normal n set at the sample point position on the virtual object surface and the incident illumination light is α, and the emission direction and the viewpoint direction of the specular reflection light at the sample point When the angle formed by γ is γ, the reflection coefficient for each layer is referred to the layer data,
k (α) ・ cos ^β γ
The reflection coefficient k at each sample point position is obtained by combining the obtained reflection coefficient for each layer according to the weighting by the visible ratio obtained in the first step,
In the third step of the reflected light intensity calculation stage, when the intensity of incident illumination light at the sample point is Ii, the reflected light intensity I is calculated using the reflection coefficient k.
I = k · Ii
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. The two-dimensional image generation method according to claim 7,
Instead of k (α), the reflection coefficient depending on the angle α is a coefficient ks that does not depend on the angle α.
ks ・ cos ^β γ
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. In the two-dimensional image generation method in any one of Claims 1-3,
In the layer data input stage, the angle formed between the normal line n set at a predetermined point on the layer surface and the illumination light is θL, and the projection image of the illumination light on the layer surface passes through the predetermined point on the layer surface. When the angle formed with the reference line is φL, the angle formed between the normal line n and the reflected light is θV, and the angle formed between the projected image of the reflected light on the layer surface and the reference line is φV, The reflection coefficient kb (θL, φL, θV, φV) given as a function of “θL, φL, θV, φV” is input as layer data for each layer,
In the visible ratio information input stage, for each of various combinations of “curvature, θL, φL, θV, φV”, the visible ratio information indicating the visible ratio for each layer is input.
In the reflected light intensity calculation stage, the angle formed between the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and the incident illumination light is projected onto the orthogonal plane orthogonal to the normal line n. An angle formed by an image and a reference line passing through the sample point on the orthogonal plane is φL, an angle formed by the normal line n and the reflected light is θV, and a projected image of the reflected light on the orthogonal plane and the reference The angle formed with the line is defined as φV,
In the first step of the reflected light intensity calculation step, the visible ratio for each layer corresponding to the combination of “curvature, θL, φL, θV, φV” at the sample point position is obtained by referring to the visible ratio information. ,
In the second step of the reflected light intensity calculation stage, the reflection coefficient kb (θL, φL, θV, φV) corresponding to the combination of “θL, φL, θV, φV” at the sample point position is referred to by referring to the layer data. For each layer, and by combining the obtained reflection coefficients kb according to the weighting by the visible ratio obtained in the first step, the reflection coefficient kb at the sample point position is obtained,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflection coefficient kb at the sample point position obtained in the second step is used to calculate the sample. The reflected light intensity I from the point is
I = kb · Ii
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. In the two-dimensional image generation method in any one of Claims 1-3,
In the layer data input stage, the angle formed between the normal line n set at a predetermined point on the layer surface and the illumination light is θL, and the projection image of the illumination light on the layer surface passes through the predetermined point on the layer surface. The angle between the reference line and the reference line is φL, the angle between the normal line n and the reflected light is θV, the angle between the projected image of the reflected light on the layer surface and the reference line is φV, and on the layer surface When the coordinate value of the predetermined point in the defined uv two-dimensional coordinate system is (u, v), the reflection coefficient kb (θL, θ, given as a function of “θL, φL, θV, φV, u, v”) φL, θV, φV, u, v) are input as layer data for each layer,
In the visible ratio information input stage, for each of various combinations of “curvature, θL, φL, θV, φV, u, v”, the visible ratio information indicating the visible ratio for each layer is input.
In the reflected light intensity calculation stage, the angle formed between the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and the incident illumination light is projected onto the orthogonal plane orthogonal to the normal line n. An angle formed by an image and a reference line passing through the sample point on the orthogonal plane is φL, an angle formed by the normal line n and the reflected light is θV, and a projected image of the reflected light on the orthogonal plane and the reference Define the angle formed by the line as φV and the coordinate value of the sample point as (u, v),
In the first step of the reflected light intensity calculation stage, each layer corresponding to the combination of “curvature, θL, φL, θV, φV, u, v” of the sample point position is referred to by referring to the visible ratio information. Find the visible percentage,
In the second step of the reflected light intensity calculation stage, the reflection coefficient kb (θL, φL, corresponding to the combination of “θL, φL, θV, φV, u, v” at the sample point position is referred to by referring to the layer data. θV, φV, u, v) is obtained for each layer, and the obtained reflection coefficients kb are synthesized in accordance with the weighting by the visible ratio obtained in the first step, thereby obtaining the reflection coefficient at the sample point position. Find kb,
In the third step of the reflected light intensity calculation stage, when the intensity of the incident illumination light at the sample point is Ii, the reflection coefficient kb at the sample point position obtained in the second step is used to calculate the sample. The reflected light intensity I from the point is
I = kb · Ii
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, which is obtained by the following formula. In the two-dimensional image generation method in any one of Claims 1-10,
In the curvature calculation stage, as a curvature for a specific sample point Q, a curvature in the vicinity of the sample point Q of the contour line of the virtual object appearing on a cut surface obtained by cutting the virtual object along a predetermined plane including the sample point Q is obtained. A two-dimensional image generation method based on a three-dimensional virtual object having a fiber sheet attached to a surface. The two-dimensional image generation method according to claim 11,
Two points QL and QR that are equidistant from the sample point Q along the contour line are defined on both sides of the sample point Q on the contour line of the virtual object that appears on the cut surface, and the point QL is defined on the cut surface. An intersection point QQ between a line orthogonal to the tangent line TL of the contour line and a line orthogonal to the tangent line TR of the contour line at the point QR is obtained, and the reciprocal of the distance r between the sample point Q and the intersection point QQ is determined as the sample number. A method of generating a two-dimensional image based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, characterized by a curvature σ for a point Q. In the two-dimensional image generation method in any one of Claims 1-10,
In the object data input stage, the solid shape of the virtual object is input as a polygonal aggregate,
When obtaining the curvature for a specific sample point Q in the curvature calculation stage, for the target polygon having J sides including the specific sample point, the target polygon and a plurality of J adjacent to the target polygon are adjacent to the target polygon. The formation angles ω1 to ωJ with respect to the inside of the virtual object between the polygon and the jth side as the curvature of the jth side forming the boundary with the jth adjacent polygon are obtained. The j-th angle has an absolute value that decreases as the formation angle ωj approaches 180 ° and decreases as the size of the target polygon and the j-th adjacent polygon increases. Defining a curvature σj having a sign corresponding to the magnitude relationship between the formation angle ωj and 180 °, defining curvatures σ1 to σJ for the first side to the Jth side, respectively, Jth side The curvature σQ for the sample point Q is obtained by synthesizing J curvatures σ1 to σJ so that the influence of the j-th curvature σj becomes larger as the distance of is shorter. A two-dimensional image generation method based on a three-dimensional virtual object with a fiber sheet attached to the surface. The two-dimensional image generation method according to claim 13,
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the reference direction line indicating the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, angles ξ1 to ξJ formed by the reference direction line and each of the first side to the Jth side of the polygon of interest are respectively obtained as curvature angles for each side, and sample points Q and By combining the J curvature angles ξ1 to ξJ so that the influence of the jth curvature angle ξj becomes larger as the distance to the jth side becomes shorter, the curvature of the sample point Q is increased. Find the angle ξQ,
In the first step of the reflected light intensity calculation stage, a visible ratio for each layer corresponding to the curvature having a factor of the direction indicated by the curvature angle ξQ is obtained, and a tertiary with a fiber sheet attached to the surface A two-dimensional image generation method based on an original virtual object. In the two-dimensional image generation method in any one of Claims 1-10,
In the object data input stage, the three-dimensional shape of the virtual object is input as a collection of triangles,
When calculating the curvature for a specific sample point Q in the curvature calculation stage, the target triangle Tq including the specific sample point is adjacent to the target triangle Tq and sides A, B, and C as boundaries. The formation angles ωa, ωb, and ωc for the inside of the virtual object between the adjacent triangles Ta, Tb, and Tc are respectively obtained, and the curvature for the side A is smaller as the formation angle ωa is closer to 180 °. And a curvature σa having an absolute value that decreases as the size of the target triangle Tq and the adjacent triangle Ta increases and has a sign corresponding to the magnitude relationship between the formation angle ωa and 180 °. And the curvature with respect to the side B is smaller as the formation angle ωb is closer to 180 °, and the curvature of the target triangle Tq and the adjacent triangle Tb is larger. The curvature σb having an absolute value that decreases as the height increases and has a sign corresponding to the magnitude relationship between the formation angle ωb and 180 ° is defined, and the formation angle ωc is 180 as the curvature related to the side C. According to the magnitude relationship between the formation angle ωc and 180 °, it has an absolute value that becomes smaller as it gets closer to ° and becomes smaller as the size of the triangle of interest Tq and the adjacent triangle Tc becomes larger. The curvature σc having the same sign is defined. The shorter the distance between the sample point Q and the side A, the greater the influence of the curvature σa, and the shorter the distance between the sample point Q and the side B, the curvature σb. By combining the curvatures σa, σb, and σc so that the influence of the curvature σc increases as the distance between the sample point Q and the side C decreases. Two-dimensional image generating method which is based on a three-dimensional virtual object pasted the fiber sheet to the surface, characterized in that to determine the curvature σQ about Le point Q. The two-dimensional image generation method according to claim 15,
When defining the curvature with respect to the side A, the length hqa of the perpendicular line from the diagonal to the side A of the triangle Tq of interest to the side A and the length of the perpendicular line from the diagonal to the side A of the adjacent triangle Ta to the side A And a line segment having a length hqa and a line segment having a length ha are connected to each other at a connection point Ja, and the connection The angle formed by the two line segments at the point Ja is the formation angle ωa, and the vertical bisector of the “line segment having the length hqa” and the “line segment having the length ha” The reciprocal of the distance Ra between the intersection Oa with the perpendicular bisector and the connection point Ja is defined as the absolute value of the curvature σa with respect to the side A,
When defining the curvature with respect to the side B, the length hqb of the perpendicular line from the diagonal of the triangle Tq to the side B to the side B and the length of the perpendicular line from the diagonal to the side B of the adjacent triangle Tb to the side B The length hb is obtained, and one end of each of the “line segment having the length hqb” and the “line segment having the length hb” is connected at the connection point Jb on the plane, and the connection The angle formed by the two line segments at the point Jb is the formation angle ωb, and the vertical bisector of the “line segment having the length hqb” and the “line segment having the length hb” The reciprocal of the distance Rb between the intersection Ob with the perpendicular bisector and the connection point Jb is defined as the absolute value of the curvature σb with respect to the side B;
When defining the curvature with respect to the side C, the length hqc of the perpendicular line from the diagonal to the side C of the triangle Tq of interest to the side C and the length of the perpendicular line from the diagonal to the side C of the adjacent triangle Tc to the side C The length hc is obtained, and one end of each of the “line segment having the length hqc” and the “line segment having the length hc” is connected at the connection point Jc on the plane, and the connection The angle formed by the two line segments at the point Jc is the formation angle ωc, and the vertical bisector of the “line segment having the length hqc” and the “line segment having the length hc” The reciprocal of the distance Rc between the intersection point Oc with the perpendicular bisector and the connection point Jc is defined as the absolute value of the curvature σc with respect to the side C. 2D image generation method based. The two-dimensional image generation method according to claim 15 or 16,
When obtaining the curvature σQ for the sample point Q, the distance between the diagonal of the target triangle Tq with respect to the side A and the sample point Q is La, the distance between the diagonal of the target triangle Tq with respect to the side B and the sample point Q is Lb, When the distance between the diagonal to the side C of the triangle of interest Tq and the sample point Q is Lc,
σQ = (La · σa + Lb · σb + Lc · σc) / (La + Lb + Lc)
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, characterized by performing the following calculation. The two-dimensional image generation method according to claim 15 or 16,
In determining the curvature σQ for the sample point Q, a perpendicular line from the sample point Q to the side A, a perpendicular line from the sample point Q to the side B, and a perpendicular line from the sample point Q to the side C, The target triangle Tq is divided into three regions, the area of the region including the diagonal to the side A is Ua, the area of the region including the diagonal to the side B is Ub, and the area of the region including the diagonal to the side C is Uc. When
σQ = (Ua · σa + Ub · σb + Uc · σc) / (Ua + Ub + Uc)
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, characterized by performing the following calculation. In the two-dimensional image generation method in any one of Claims 15-18,
At the visible rate information input stage, for each curvature with a factor of orientation, enter the visible rate information indicating the visible rate for each layer,
In the object data input stage, information on the reference direction line indicating the direction of the fiber sheet attached to the virtual object is also input,
In the curvature calculation stage, angles ξa, ξb, and ξc formed by the reference direction line and the sides A, B, and C of the target triangle are respectively obtained as curvature angles for the respective sides, and the sample point Q and the side A are obtained. The shorter the distance between the sample point Q, the greater the influence of the curvature angle ξa, and the shorter the distance between the sample point Q and the side B, the greater the influence of the curvature angle ξb, the greater the distance between the sample point Q and the side C. By combining the curvature angles ξa, ξb, and ξc so that the shorter the shorter the influence of the curvature angle ξc, the curvature angle ξQ for the sample point Q is obtained.
In the first step of the reflected light intensity calculation stage, a visible ratio for each layer corresponding to the curvature having a factor of the direction indicated by the curvature angle ξQ is obtained, and a tertiary with a fiber sheet attached to the surface A two-dimensional image generation method based on an original virtual object. The two-dimensional image generation method according to claim 19,
When obtaining the curvature angle ξQ for the sample point Q, the distance between the diagonal of the target triangle Tq with respect to the side A and the sample point Q is La, and the distance between the diagonal of the target triangle Tq with respect to the side B and the sample point Q is Lb. When the distance between the diagonal to the side C of the triangle Tq of interest and the sample point Q is Lc,
ξQ = (La · ξa + Lb · ξb + Lc · ξc) / (La + Lb + Lc)
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, characterized by performing the following calculation. The two-dimensional image generation method according to claim 19,
When determining the curvature angle ξQ for the sample point Q, a perpendicular line from the sample point Q to the side A, a perpendicular line from the sample point Q to the side B, and a perpendicular line from the sample point Q to the side C The target triangle Tq is divided into three regions, the area of the region including the diagonal to the side A is Ua, the area of the region including the diagonal to the side B is Ub, and the area of the region including the diagonal to the side C is Uc And when
σQ = (Ua · ξa + Ub · ξb + Uc · ξc) / (Ua + Ub + Uc)
A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, characterized by performing the following calculation. In the two-dimensional image generation method in any one of Claims 1-10,
In the object data input stage, the three-dimensional shape of the virtual object is input as a parametric curved surface expressed by a mathematical formula and the parameter value used in the mathematical formula,
A method for generating a two-dimensional image based on a three-dimensional virtual object in which a fiber sheet is attached to a surface, wherein a curvature for a specific sample point Q is obtained by a calculation using the mathematical formula and parameter values in a curvature calculation stage. . In the two-dimensional image generation method according to any one of claims 1 to 22,
The computer inputs the shape data of the fiber sheet structure, and based on this shape data, simulates the state where the fiber sheet is bent with various curvatures, and shows the visible ratio of each layer for various curvatures. The method further comprises a visible ratio information creating stage for creating ratio information, and the created visible ratio information is input at the visible ratio information input stage, and is based on a three-dimensional virtual object with a fiber sheet attached to the surface. Dimensional image generation method. The two-dimensional image generation method according to claim 23,
When the fiber sheet structure is projected vertically upward with respect to the layer surface and the hidden surface treatment is performed, the visible ratio is determined based on the area ratio of each layer appearing on the projection surface. A two-dimensional image generation method based on a three-dimensional virtual object with a fiber sheet attached thereto. In the two-dimensional image generation method in any one of Claims 1-24,
In the visual ratio information input stage, enter the visual ratio information for each of a plurality of discretely defined curvatures.
In the first step of the reflected light intensity calculation stage, the visible ratio corresponding to the curvature for the specific sample point obtained in the curvature calculation stage is set as the visible ratio defined for the discrete curvature by the visible ratio information. A two-dimensional image generation method based on a three-dimensional virtual object obtained by pasting a fiber sheet on a surface, which is obtained by interpolation.   The program for making a computer perform each step in the two-dimensional image generation method in any one of Claims 1-25. An apparatus for generating two-dimensional data indicating a projection image obtained when a fiber sheet is attached to the surface of the object based on the three-dimensional data of the object and observed from a predetermined viewpoint,
A data input unit for inputting various data given from the outside;
A three-dimensional data storage unit that stores three-dimensional data that is input from the data input unit and indicates a three-dimensional shape of a virtual object;
A layer data storage unit that stores m layer data indicating reflection characteristics for each of a plurality of m layers constituting a virtual fiber sheet to be pasted, which is input from the data input unit;
Visible rate information storage unit that stores the visible rate information indicating the visible rate for each layer in a state where the fiber sheet is bent with various curvatures, which is input from the data input unit;
A projection condition setting unit configured to set an illumination condition, a viewpoint position, and a projection plane based on data input from the data input unit;
Based on the three-dimensional data, for a position of a predetermined sample point defined on the surface of the virtual object, a curvature calculation unit that calculates the curvature of the virtual object surface;
When the fiber sheet is attached to the surface of the virtual object, a reflected light intensity calculation unit that calculates the intensity of reflected light from each sample point toward the viewpoint position;
A pixel definition unit that defines a pixel having a pixel value corresponding to the intensity of the reflected light at the intersection position between the reflected light from the sample point and the projection plane;
A projection data storage unit that stores a set of a large number of pixels defined for a large number of sample points as two-dimensional projection data indicating a projection image of the virtual object;
With
The reflected light intensity calculation unit is
A first functional unit that obtains a visible ratio for each layer corresponding to the curvature at one sample point position with reference to the visible ratio information;
A second function unit for determining the reflection characteristic at the sample point position by combining the reflection characteristics of the m layer data according to the visible ratio determined by the first function unit;
A third functional unit for determining the intensity of the reflected light from the sample point based on the reflection characteristics obtained by the second functional unit;
A two-dimensional image generation device based on a three-dimensional virtual object in which a fiber sheet is attached to the surface. The two-dimensional image generation device according to claim 27,
The data input unit has a function of inputting information regarding the orientation of the reference direction line defined on the fiber sheet when the fiber sheet is attached to the virtual object,
The visible ratio information storage unit has a function of inputting visible ratio information indicating the visible ratio of each layer for each curvature having a direction factor,
The curvature calculator has a function to calculate the curvature with the orientation factor,
The reflected light intensity calculation unit has a function to obtain the reflected light intensity by using the visible ratio of each layer corresponding to the curvature having the orientation factor, and a three-dimensional virtual with a fiber sheet attached to the surface A two-dimensional image generation device based on an object.