JP2007048084A - Two-dimensional image generation method and generation device based on three-dimensional virtual object with surface attached with fiber sheet - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To generate a two-dimensional image sufficiently expressed with a texture of fiber attached on a surface by rendering. <P>SOLUTION: A real fiber sheet is previously attached on a real object having various curvatures, reflection light obtained from the surface is measured, and a curvature-dependent reflection characteristic considering influence exercised on reflection light intensity by the curvature is found. A light source G is defined, the rendering in a mapping state of a virtual fiber sheet 60 on a virtual object 50 is performed, and a projection image 55 when performing observation from a viewpoint E is obtained on a projection plane M. At that time, when calculating the intensity of the reflection light V heading for the viewpoint E from a sample point Q, a curvature of the object surface in the sample point Q is found, and calculation considering the curvature-dependent reflection characteristic corresponding to the curvature is performed. When performing measurement finding the curvature-dependent reflection characteristic, a factor of a direction can be considered by changing the attachment direction of the fiber sheet. <P>COPYRIGHT: (C)2007,JPO&INPIT

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 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, CG images are often 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 by using the CAD data used in the design, so it is relatively easy to place a CG image in the product catalog. 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

  Many articles such as furniture such as chairs and sofas, interiors of automobiles, bags and shoes have a sheet (hereinafter referred to as a fiber sheet) made of a fibrous material such as cloth attached thereto. 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 with a fiber sheet attached to the surface,
Pasting an actual fiber sheet on an actual object having a predetermined curvature, illuminating under a predetermined condition, and observing reflected light obtained from the fiber sheet surface from a predetermined direction for each of a plurality of curvatures The curvature-dependent reflection characteristic measurement stage for obtaining the curvature-dependent reflection characteristic including the influence of the curvature on the reflected light intensity,
A 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 a computer sticks a fiber sheet to the surface of a virtual object, the intensity of reflected light from the sample point to the viewpoint position is calculated in consideration of the curvature-dependent reflection characteristics corresponding to the curvature at the sample point position. A computation stage;
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;
Is to do.

(2) A second aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the first aspect described above.
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
In the data input stage, input information on the direction of the fiber sheet attached to the virtual object.
In the curvature calculation stage, find the curvature with a factor of direction,
In the reflected light intensity calculation stage, the reflected light intensity is obtained in consideration of the curvature-dependent reflection characteristics corresponding to the curvature having the orientation factor.

(3) A third aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the second aspect described above.
At the curvature-dependent reflection characteristic measurement stage, an actual fiber sheet is attached to the side of a cylinder of an actual object in a predetermined direction, the curvature σ is defined using the inverse of the radius of the cylinder, and the center axis of the cylinder is projected in the radial direction. The angle ξ formed by the projection line obtained on the cylindrical side surface and the reference direction line of the fiber sheet is defined as the curvature angle for the curvature σ, and corresponds to each combination of the individual curvature σ and the individual curvature angle ξ. Find the curvature-dependent reflection characteristics,
In the 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 reflected light intensity calculation stage, the reflected light intensity is obtained in consideration of the curvature-dependent reflection characteristics corresponding to the combination of the curvature σ and the curvature angle ξ.

(4) A fourth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the third aspect described above.
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, assuming that the intensity of the incident illumination light at the sample point is Ii, the reflected light intensity I is used by using the reflection coefficient k given as a function of the coordinate values u and v and the curvature parameters σ and ξ. ,
I = k · Ii
It is obtained by the following formula.

(5) A fifth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the third aspect described above.
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle between the normal n standing at the sample point position on the virtual object surface and the incident illumination light is α, and the diffuse reflection coefficient is kd. Sometimes the reflected light intensity I is
I = kd ・ Ii ・ cos α
The diffuse reflection coefficient kd is determined in consideration of the curvature parameters σ and ξ.

(6) A sixth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the fifth aspect described above.
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, the diffuse reflection coefficient kd is determined in consideration of the coordinate values u and v and the curvature parameters σ and ξ.

(7) A seventh aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the third aspect described above.
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle between the normal n standing at the sample point position on the virtual object surface and the incident illumination light is α, and the reflection depends on this angle α. When the coefficient is k (α), the parameter indicating the sharpness of specular reflection is β, and the angle formed by the emission direction of the specular reflection light at the sample point and the viewpoint direction is γ, the reflected light intensity I is
I = k (α) · Ii · cos ^β γ
The coefficients k (α) and β are determined in consideration of the curvature parameters σ and ξ.

(8) According to an eighth aspect of the present invention, in the two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the seventh aspect described above,
Instead of k (α), the reflection coefficient depending on the angle α is changed to a coefficient ks that does not depend on the angle α, and the reflected light intensity I is
I = ks · Ii · cos ^β γ
The coefficients ks and β are determined in consideration of the curvature parameters σ and ξ.

(9) A ninth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the third aspect described above.
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle formed by the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and orthogonal to the normal line n The angle between the projected image of the incident illumination light on the plane and the reference line passing through the sample point on the orthogonal plane is φL, the angle between the normal n and the reflected light is θV, and the reflected light is projected on the orthogonal plane When the angle formed by the image and the reference line is φV, the reflected light intensity I is expressed using θL, φL, θV, φV and the reflection coefficient kb given as a function of the curvature parameters σ, ξ,
I = kb · Ii
It is obtained by the following formula.

(10) A tenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the third aspect described above.
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle formed by the normal line n set at the sample point position on the virtual object surface and the incident illumination light is θL, and orthogonal to the normal line n The angle between the projected image of the incident illumination light on the plane and the reference line passing through the sample point on the orthogonal plane is φL, the angle between the normal n and the reflected light is θV, and the reflected light is projected on the orthogonal plane When the angle between the image and the reference line is φV, the reflected light intensity I is used as a reflection coefficient kb given as a function of θL, φL, θV, φV, coordinate values u, v, and curvature parameters σ, ξ. And
I = kb · Ii
It is obtained by the following formula.

(11) An eleventh aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the ninth or tenth aspect described above.
At the curvature-dependent reflection characteristic measurement stage, by changing the illumination conditions and the observation direction, the direction of the incident illumination light defined by the angles θL and φL and the direction of the reflected light defined by the angles θV and φV are changed in a plurality of ways. The curvature-dependent reflection characteristics are obtained for each combination of angles θL, φL, θV, and φV,
In the reflected light intensity calculation stage, calculation using curvature-dependent reflection characteristics corresponding to the combinations of the angles θL and φL indicating the direction of the incident illumination light and the angles θV and φV indicating the direction of the reflected light at the sample point to be calculated. Is to do.

(12) A twelfth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the first to eleventh aspects described above.
In the projection condition setting stage, set illumination conditions with multiple light sources,
In the reflected light intensity calculation stage, the intensity of reflected light from one sample point toward the viewpoint position is obtained as the sum of the reflected light intensities generated based on the incident illumination light from each of a plurality of light sources. is there.

(13) A thirteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the first to twelfth aspects described above.
In the data input stage, the solid shape of the virtual object is input as a collection of polygons,
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) A fourteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the thirteenth aspect described above.
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
At the data input stage, input information on the reference direction line together,
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 reflected light intensity calculation stage, the reflected light intensity is obtained in consideration of the curvature-dependent reflection characteristics corresponding to the curvature having the factor of the direction indicated by the curvature angle ξQ.

(15) A fifteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the first to twelfth aspects described above.
In the 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) A sixteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the fifteenth aspect described above.
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) A seventeenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the fifteenth or sixteenth aspect described above.
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) An eighteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the fifteenth or sixteenth aspect described above.
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) A nineteenth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the fifteenth to eighteenth aspects described above.
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
At the data input stage, input information on the reference direction line together,
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.
When calculating the reflected light intensity for the sample point Q in the reflected light intensity calculation stage, the corresponding curvature-dependent reflection characteristic is determined using the curvature σQ having a factor in the direction of the curvature angle ξQ. is there.

(20) A twentieth aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the nineteenth aspect described above.
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 a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the nineteenth aspect described above,
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) A twenty-second aspect of the present invention is a two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the first to twelfth aspects described above.
In the data input stage, the three-dimensional shape of the virtual object is input as a parametric surface represented 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) A twenty-third aspect of the present invention is a method other than the curvature-dependent reflection characteristic measurement step in the two-dimensional image generation method based on a three-dimensional virtual object having a fiber sheet attached to the surface according to the first to twenty-second aspects described above. A computer program is prepared for causing a computer to execute each stage.

(24) According to a twenty-fourth 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 A two-dimensional image generation device based on a three-dimensional virtual object with a fiber sheet attached to the surface,
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 curvature-dependent reflection characteristic storage unit that stores a curvature-dependent reflection characteristic that includes “the influence of the curvature on the reflected light intensity” 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 a fiber sheet is attached to the surface of a virtual object, the intensity of the reflected light from the sample point to the viewpoint position is expressed by three-dimensional data, illumination conditions, the viewpoint position, and a curvature-dependent reflection characteristic corresponding to the curvature at the sample point position. A reflected light intensity calculation unit to be determined in consideration;
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;
It is made up by.

(25) A twenty-fifth aspect of the present invention is a two-dimensional image generation device based on a three-dimensional virtual object in which a fiber sheet is attached to the surface according to the twenty-fourth aspect described above.
When the fiber sheet is attached to the virtual object, the data input unit has a function of inputting information on the direction of the reference direction line defined on the fiber sheet,
The curvature-dependent reflection characteristic storage unit has a function of storing curvature-dependent reflection characteristics corresponding to various combinations of the curvature and the curvature angle indicating the deviation between the bending direction corresponding to the curvature and the reference direction line. ,
The curvature calculator has a function to calculate the curvature angle along with the curvature at the sample point position.
The reflected light intensity calculation unit is provided with a function for obtaining the reflected light intensity in consideration of the curvature dependent reflection characteristics corresponding to the curvature and the curvature angle at the sample point position.

  According to the two-dimensional image generation method and generation device according to the present invention, when calculating the reflected light intensity from each part of the virtual object pasted with the fiber sheet, the calculation considering the curvature of each part is performed. 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 the present invention >>
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, the basic concept of rendering processing according to the present invention 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. In other words, the pattern information of the two-dimensional sheet is prepared as two-dimensional texture data (data indicating the two-dimensional reflection characteristic distribution), and the reflectance of each part is set with this texture data attached to the surface of the 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 The area where the material becomes is increased. 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 weave, the area ratio between the warp and weft projected onto the field of view will have a large effect 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 represented 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 illustrated example, the light and shade of the fiber of the virtual fiber sheet 60 and a heart-shaped picture are expressed as image data defined on the uv two-dimensional coordinate system. 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 the projection image 55 (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 density and heart-shaped pattern of each fiber, the density and heart-shaped pattern of this fiber will be expressed on the projected image 55 (in FIG. 3, this pattern is shown). Is omitted).

  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), an actual object 51 made of a cylinder having a radius r1 is knitted by warp and weft while the central axis H is arranged in the horizontal direction. Let us consider a case where an actual fiber sheet 61 having information on a fiber and a heart-shaped pattern is pasted along the side surface of a cylinder. At this time, 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 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, an operation is performed in consideration of information on the warp and weft of the fiber sheet and the heart-shaped picture. 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. For example, when the fiber sheet 61 is a woven fabric composed of warp and weft, as shown in FIG. 4A, when the fiber sheet 61 is pasted so as to have a curvature angle ξ = 90 °, it is exposed from between the weft and the weft. The warp area increases. As shown in FIG. 4 (b), when it is attached to a curved surface having a larger curvature (a cylindrical side surface having a smaller radius), the warp yarn exposure ratio is further increased. On the other hand, as shown in FIG. 4 (c), when the curvature angle ξ = 0 °, the area of the weft exposed between the warp and the warp increases. Of course, the curvature angle ξ can take any angle such as 30 °, 45 °, 60 °, and the area of the weft exposed between the warp and the warp or the warp exposed between the weft and the weft. The area varies depending on these angles.

  After all, the texture information of the fiber sheet 61 changes according to the curvature of the surface to be pasted and the curvature angle. Of course, such a change in the surface structure of the fiber usually does not bring about a dramatic change such as changing the heart-shaped pattern into a star shape, but often a slight change in hue. This is certainly a factor that affects the subtle natural texture of CG images. 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 according to the curvature and curvature angle of the surface to be pasted. 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, a plurality of measurements are performed in which a real fiber sheet is pasted on a real object having a predetermined curvature, illuminated under a predetermined condition, and reflected light obtained from the fiber sheet surface is observed from a predetermined direction. The curvature-dependent reflection characteristics including the influence of the curvature on the reflected light intensity are obtained by performing each of the curvatures, and the reflected light intensity calculation is performed in consideration of the curvature-dependent reflection characteristics when performing rendering processing on a computer. Like to do.

  For example, as shown in FIG. 4 (a), a real fiber sheet 61 is attached to a real cylindrical object 51 with a radius r1, and as shown in FIG. 4 (b), a real circle with a radius r2 is attached. Observing the object attached to the columnar object 52 from the same direction in the same illumination environment and comparing the obtained images, the two images are naturally different. Factors for the difference between the two images include an effect due to a difference in the three-dimensional shape of the objects 51 and 52 (a difference in spatial occupation position) and an effect based on the curvature of the attachment surface of the fiber sheet 61. Therefore, if you use a cylindrical object with various radii, you can quantitatively measure the curvature-dependent reflection characteristics including the effect of the curvature σ (the reciprocal of the radius) on the reflected light intensity. In the rendering processing on the computer, the reflected light intensity calculation may be performed in consideration of the actually measured curvature-dependent reflection characteristics. The specific method will be described later.

<<< §2. 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. Here, for the sake of convenience, description will be given by taking as an example a case where an interior photo of a vehicle to be published in a car catalog is created using CG.

  In this case, what is needed is the three-dimensional data of the interior parts and the actual fiber sheet actually used for the interior. For example, in the case where a fiber sheet made of denim is attached to the surface of a seat body made of urethane to form a seat in a vehicle, a case where an image of the seat is created by CG is considered. In this case, since the seat body made of urethane is normally designed using CAD, the three-dimensional data of the seat body can be used from CAD data. On the other hand, it is sufficient for the actual denim fabric to have a sample with a certain area.

  The procedure shown in FIG. 5 includes an actual measurement stage in step S1 and a computer processing stage in steps S2 to S9. The first measurement stage is a stage in which the inherent curvature-dependent reflection characteristics of the fiber sheet are measured using the actual denim fabric provided as the fiber sheet, and the subsequent computer processing stage is the third order of the seat body. This is a stage where rendering processing using original data is performed.

  In the present invention, the “curvature-dependent reflection characteristic” of the fiber sheet is a reflection characteristic that includes the influence of the curvature of the curved surface on the reflected light intensity when the fiber sheet is attached to the curved surface of the object. Is a reflection characteristic measured in the actual measurement stage. As described with reference to FIG. 4, the curvature-dependent reflection characteristic is not only a function of the curvature σ of the curved surface of the object, but also the bending direction (circumferential direction in the case of a cylindrical model) and the fiber corresponding to the curvature σ. It is also a function of the curvature angle ξ indicating the deviation from the reference direction W of the sheet. Here, the curvature σ and the curvature angle ξ are referred to as a curvature parameter.

  In the embodiment shown here, the curvature σ is defined as the reciprocal of the radius of the cylinder. This is a definition for convenience on the premise that the fiber sheet is attached to the side surface of the cylinder, but of course, the curved surface to which the fiber sheet is actually attached may not necessarily be the side surface of the cylinder. On the other hand, the curvature angle ξ should be a variable indicating the relationship between the reference direction of the fiber sheet and the bending direction according to the curvature (90 ° −ξ = deviation angle). As described above, it is defined as an angle formed by 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 fiber sheet. In the case of the curvature angle ξ = 90 °, as shown in FIGS. 4 (a) and 4 (b), it is shown that the fiber sheet reference line W is oriented so as to face the circumferential direction of the cylinder. This corresponds to the case where the deviation angle between the bending direction and the reference direction is 0 °. On the other hand, when the curvature angle ξ = 0 °, as shown in FIG. 4 (c), the fiber sheet is attached so that the reference direction line W faces a direction parallel to the center line H of the cylinder. This corresponds to the case where the deviation angle between the bending direction and the reference direction is 90 °.

  In step S <b> 1 shown in FIG. 5, a process for measuring curvature-dependent reflection characteristics specific to the denim fabric is performed using the prepared real denim fabric (fiber sheet). FIG. 6 is a diagram showing a specific example of such a measurement method. In this example, first, as shown in FIG. 6 (a), a denim fiber sheet 61 is attached to the side surface of an object 71 made of a quadrangular prism, and illumination light L from a light source G arranged at a predetermined position is irradiated. The intensity of the reflected light V reflected from the measurement region F1 toward the viewpoint E is measured. In the same measurement, as shown in FIG. 6 (b), when the fiber sheet 61 is attached to the side surface of the object 72 made of a cylinder having a radius r1, as shown in FIG. 6C, the fiber sheet 61 is made of a cylinder having a radius r2. It repeats also about the case where the fiber sheet 61 is stuck on the side surface of the object 73. FIG. In the case of FIG. 6B, the reflected light V from the measurement region F2 is the measurement target, and in the case of FIG. 6C, the reflected light V from the measurement region F3 is the measurement target.

  In any case, the positions of the light source G and the viewpoint E are exactly the same. In addition, the measurement areas F1 to F3 have a minute size in the vertical direction in the figure, and are all areas having the same slit-like area in a direction perpendicular to the paper surface. The normal vectors of the respective areas are all It is assumed that they are in the same direction (left direction on the page). When three kinds of measurements are performed under such conditions, the light source G, the viewpoint E, and the measurement areas F1 to F3 are almost the same, and the pasted fiber sheet 61 is also the same. If so, it can be considered that it is caused by the difference in curvature between the measurement regions F1 to F3. As described above, if the value corresponding to the reciprocal of the radius of the cylinder is defined as the curvature σ, the surface of the object 71 made of a quadrangular column shown in FIG. And the curvature σ = 0. On the other hand, the curvature of the surface of the object 72 made of a cylinder with a radius r1 shown in FIG. 6B is σ = 1 / r1, and the surface of the object 73 made of a cylinder with a radius r2 shown in FIG. The curvature is σ = 1 / r2 (in consideration of the thickness d of the fiber sheet 61, 1 / (r1 + d) and 1 / (r2 + d), respectively).

  Here, for example, when the intensity of the reflected light V actually measured in the measurement system shown in FIG. 6A is set to the reference value “1”, the reflected light V actually measured in the measurement system shown in FIG. If the intensity of the reflected light V actually measured in the measurement system shown in FIG. 6C is “0.8”, the same denim fabric is used. Although the measurement was performed under exactly the same conditions except for the curvature parameter, different reflection characteristics were obtained. The reflection characteristic thus obtained can be said to be a curvature-dependent reflection characteristic.

  FIG. 6 shows an example of measurement when pasted on two types of cylinders with radii r1 and r2, but actually, actual measurements were performed when pasted on multiple types of cylinders with slightly different radius values. Although it is discrete, the curvature-dependent reflection characteristics may be obtained for a wider range of curvature. As described above, the curvature-dependent reflection characteristic depends not only on the curvature σ but also on the curvature angle ξ. Therefore, in practice, we measured the curvature-dependent reflection characteristics as a function of the curvature σ and the curvature angle ξ by measuring the direction of the denim fabric (fiber sheet) a little at a time on a cylinder with the same radius. To keep. For that purpose, a reference direction line W (for example, the direction of the warp yarn) is defined in advance on the denim fabric, and pasted in a plurality of directions so that the reference direction line W faces various directions. What is necessary is just to actually measure the curvature-dependent reflection characteristic. Then, curvature-dependent reflection characteristics can be obtained for each curvature having a direction factor.

  FIG. 7 shows a total of 80 curvature-dependent reflections as a combination of 8 curvatures σ including a plane (σ = 0) and 10 curvature angles ξ determined every 10 ° from 0 ° to 90 °. It is a figure which shows an example (The specific numerical value in a table is abbreviate | omitting illustration) which measured the characteristic. As a unit of the curvature σ, for example, “1 / cm” can be used. In this case, the curvature of the side surface of the cylinder having a radius of 100 cm is σ = 1/100. In the case where the curvature-dependent reflection characteristics are different for each wavelength component of light, for example, separate curvature-dependent reflection characteristics are measured for each wavelength component of the three primary colors RGB, and the curvature-dependent reflection for the color component R is measured. The characteristic, the curvature-dependent reflection characteristic related to the color component G, and the curvature-dependent reflection characteristic related to the color component B may be obtained as separate tables.

  Of course, the curvature-dependent reflection characteristic obtained in this way is a value unique to the denim fabric, and can be used only for the rendering process for a virtual object to which the denim fabric is attached. The curvature-dependent reflection characteristic does not necessarily have to be obtained in the form of a table as shown in FIG. For example, if a measurement result that can be approximated by some function is obtained, the curvature-dependent reflection characteristic can be defined by a function including the variable σ and the variable ξ as arguments. In the table shown in FIG. 7, the single reflection characteristic value is obtained in each column is a plain fabric having no pattern on the fiber sheet to be measured, and the same at any position. This is a case where a simple model is assumed in which a reflection characteristic value is obtained and the reflection characteristic value does not depend on the direction of incident illumination light or the direction of reflected light. In the case of a more complicated model, the reflection characteristic value is not uniquely determined only by the curvature parameters σ and ξ, but the two-dimensional coordinate values u and v defined on the fiber sheet, and the parameter indicating the direction of the incident illumination light It is determined in consideration of parameters such as θL and φL and parameters θV and φV indicating the direction of reflected light. This will be described in detail in §3.

  As described above, in the process of step S1 in FIG. 5, the actual fiber sheet is pasted on an actual object having a predetermined curvature, illuminated under a predetermined condition, and reflected light obtained from the fiber sheet surface from a predetermined direction. It can be said that the measurement to be observed is performed for each of a plurality of curvatures, thereby obtaining a curvature-dependent reflection characteristic including the influence of the curvature on the reflected light intensity.

  In subsequent step S2, a process of inputting the three-dimensional data indicating the three-dimensional shape of the virtual object to the computer is performed. Specifically, the three-dimensional data of the virtual object is input on the XYZ three-dimensional coordinate system. In the embodiment described here, the three-dimensional data of the seat body of the vehicle is input as data indicating the three-dimensional shape of the virtual object. As described above, the three-dimensional data of the seat 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 S2, information related to the direction in which the fiber sheet is attached to the virtual object is also input. That is, when the denim fabric is pasted on the seat body, information on which direction of each surface of the seat body is pasted with the reference direction line W of the denim fabric is input.

  Next, in step S3, 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. 3, and is composed of three elements: an illumination condition, a viewpoint position, and a projection plane. 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 steps S4 to S8 are procedures for performing an actual rendering process, and each pixel value defined on the xy two-dimensional coordinate system on the projection plane M is repeatedly executed. It will be. First, in step S4, 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 S5, 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. However, in the case of the embodiment described here, in the actual measurement stage of step S1, since the measurement was performed by attaching a fiber sheet to a cylindrical real object, the curvature σ could be defined as the reciprocal of the radius of the cylinder. Since the virtual object 50 to be subjected to curvature calculation in step S5 is a seat body of a vehicle having an arbitrary curved surface shape, the definition of curvature in a cylinder cannot be used as it is. Therefore, in order to execute this step S5, it is necessary to previously define a curvature definition method at an arbitrary point on an arbitrary curved surface. The specific method will be described in detail in §4.

  In step S5, the curvature σ is obtained together with the direction factor. Here, the orientation factor indicates a bending direction according to the curvature σ with respect to the reference direction line W of the fiber sheet when the fiber sheet is pasted in a predetermined direction, and the radius of the cylinder is used. When the curvature σ is defined, it is an amount defined as the curvature angle ξ as described above. For example, for an arbitrary point on the cylindrical side surface of the cylindrical object 51 shown in FIG. 4 (a), values of curvature σ = 1 / r1 and curvature angle ξ = 90 ° are defined, but FIG. As for an arbitrary point on the cylindrical side surface of the cylindrical object 51 shown in FIG. 2, the values of curvature σ = 1 / r1 and curvature angle ξ = 0 ° are defined. ξ is different. This is because the attaching direction of the fiber sheet 61 is different. As described above, in step S2, information related to the direction in which the fiber sheet is attached to the virtual object (information indicating the direction of the reference direction line W of the denim fabric) is input. If this information is used, an arbitrary sample point Q is used. It is possible to calculate the curvature angle ξ together with the curvature σ at the position. However, since the definition of the curvature in the cylinder cannot be used as it is for the virtual object 50, the definition of the curvature angle in the cylinder cannot be used as it is. It is also necessary to determine in advance a method for defining the curvature angle at an arbitrary point. The specific method will be described later in §4.

  Thus, when the curvature σ and the curvature angle ξ are obtained as the curvature parameters for the defined sample point Q, the reflected light intensity calculation from the sample point Q is subsequently performed in step S6. That is, since the shading model as shown in FIG. 3 can be defined by the projection condition set in step S3, 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. Some specific shading models will be described in §3. The feature of the present invention is that this reflected light intensity calculation is performed using the curvature-dependent reflection characteristics measured in step S1. .

  When the conventional general rendering technique is applied to the model shown in FIG. 3, 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 vicinity of the sample point Q. In the present invention, this reflection characteristic depends on the curvature σ at the position of the sample point Q and the reflection characteristic mapped to the position of the sample point Q when the fiber sheet 60 is attached. The characteristic depends on the curvature angle ξ.

  For example, if the curvature-dependent reflection characteristics as shown in FIG. 7 are obtained as a table in the actual measurement stage in step S1, the curvature parameters σ, ξ for the position of the sample point Q are calculated in the reflected light intensity calculation in step S6. A calculation using a specific curvature-dependent reflection characteristic obtained by subtracting this table using is performed. Specifically, for example, if specific values such as curvature σ = 1/50 and curvature angle ξ = 30 ° are obtained for a specific sample point Q in step S5, the curvature σ in the table of FIG. = 1/50, curvature angle ξ = 30 ° The curvature-dependent reflection characteristic described in the column is obtained, and the reflected light intensity calculation is performed using this curvature-dependent reflection characteristic.

  In the table shown in FIG. 7, since the values of the curvature σ and the curvature angle ξ are given as discrete values, the curvature σ and the curvature angle ξ calculated in step S5 are intermediate values of these discrete values. In this case, it is preferable to perform an interpolation operation for the curvature-dependent reflection characteristic as necessary.

  Thus, when the calculation for obtaining the intensity of the reflected light V from one sample point Q toward the viewpoint E is completed, one pixel is defined in step S7. 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 curvature-dependent reflection characteristic table as shown in FIG. 7 is prepared for each of the three primary colors RGB, so that the intensity calculation of the reflected light V in step S6 is also performed for each color component. It can be carried out. Therefore, in step S7, 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 by going through steps S4 to S7. Therefore, the process of returning from step S8 to step S4 again is repeatedly executed until all necessary pixels are defined. Finally, in step S9, 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.

  As described above, the procedure shown in FIG. 5 basically follows the conventional general rendering technique and is based on the general shading model shown in FIG. However, the measurement procedure of the curvature dependent reflection characteristic shown in step S1 of FIG. 5 is a procedure unique to the present invention, and the curvature calculation procedure of the sample point shown in step S5 is also a procedure unique to the present invention. In the reflected light intensity calculation in step S6, the characteristic procedure that should be called the essence of the present invention is that the calculation in consideration of the curvature parameters σ and ξ is performed using the results of steps S1 and S5.

  As already mentioned, fabrics such as denim, iridescent weave, towels, and velvet are fiber sheets that have the property that their 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 rendering processing is performed according to the procedure of the present invention shown in FIG. 5, an image in which the texture of the fiber is expressed more faithfully than in the conventional method can be obtained.

<<< §3. Application to various shading models >>>
Here, some specific methods of the reflected light intensity calculation performed in step S6 of the flowchart of FIG. 5 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 to propose a new shading model, but when performing the reflected light intensity calculation for one sample point, the calculation considering the curvature of the object surface at the sample point is performed. In the point. 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 in which a two-dimensional image as a texture is input using a scanner device or a digital camera and used as reflection characteristic data indicating a reflectance distribution. If the present invention is applied to this model, in step S1 of FIG. 5, the denim fabric provided as a real object may be attached to a curved surface of various curvatures, and the planar image may be captured using a digital camera or the like. The captured image of denim becomes pattern data T (u, v) defined on the uv two-dimensional coordinate system, and is used as reflection characteristic data indicating the reflectance distribution of the fiber sheet. However, the pattern data T (u, v) is data that also depends on the curvature parameters σ and ξ, and the reflection characteristics at the positions indicated by the coordinate values u and v are functions of u, v, σ, and ξ. As given. In the reflected light intensity calculation stage of step S6, when the intensity of the incident illumination light at the sample point Q is Ii, the reflected light intensity I is calculated using the reflection coefficient k.
I = k · Ii
It can be calculated by the following formula. Here, in the case of the conventional general texture mapping model, the reflection coefficient k is only obtained as a function of the coordinate values u and v, but in the present invention, the reflection coefficient k is determined by the coordinate values u and v. And a function of the curvature parameters σ and ξ.

(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. In the present invention, the diffuse reflection coefficient kd is the step of FIG. Based on the actual measurement result performed in S1, the curvature parameters σ and ξ are determined as values.

  Since the classic diffuse reflection model does not have the concept of texture mapping, when this is applied as it is to the present invention, a texture pattern composed of warp yarns or weft yarns of fiber sheets is not expressed. Of course, if it is not necessary to reproduce the pattern of the fiber sheet, it may be used. However, in practice, it is preferable to use a model obtained by further combining this classic diffuse reflection model with a texture mapping model. In this case, the diffuse reflection coefficient kd may be determined as a function of the coordinate values u and v and the curvature parameters σ and ξ based on the actual measurement result, as in the simple texture mapping model described above.

(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 sample point Q position on the virtual object surface, and the incident illumination light Is a reflection coefficient depending on the angle α, k is a parameter indicating the sharpness of the specular reflection, β is an angle formed by the emission direction of the specular reflection light at the sample point Q and the viewpoint direction is γ. When the reflected light intensity I is
I = k (α) · Ii · cos ^β γ
This is a model obtained by the following formula. Here, in the case of the conventional specular reflection model of Phong, the reflection coefficient k (α) and the parameter β are determined based on predetermined reflection characteristic data given as constants. In the present invention, the reflection coefficient k (α) And β are determined as functions of the curvature parameters σ and ξ based on the actual measurement result.

However, practically, 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
I = ks · Ii · cos ^β γ
There are many cases in which this is calculated using In this case, the coefficients ks and β may be determined as functions of the curvature parameters σ and ξ.

  This Phong specular reflection model also has no concept of texture mapping, so if this is applied as it is to the present invention, a texture pattern composed of warp or weft of the fiber sheet is not expressed. The reflection coefficient k (α) (or coefficient ks) and β may be determined as a function of the coordinate values u and v and the curvature parameters σ and ξ using a combination of the above simple texture mapping models.

(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. When it is necessary to express anisotropic reflection, such as silk fabric or brushed metal, the reflection characteristics should be treated as an amount that depends on the incident angle of the illumination light and the reflection angle of the reflected light. Is preferred. As a model for such handling, a model called BRDF (Bi-directional Reflection Distribution Function) has been proposed.

FIG. 8 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 reflection coefficient kb may be given as a function of θL, φL, θV, φV and curvature parameters σ, ξ. That is, this BRDF model uses the function BRDF to calculate the intensity I of the reflected light V from the sample point Q.
I = BRDF ・ Ii
In the case of the conventional BRDF model, the function BRDF is defined as a function having four variables θL, φL, θV, and φV.
I = BRDF (θL, φL, θV, φV) · Ii
In the case of the model according to the present invention, the function BRDF is defined as a function having six variables θL, φL, θV, φV, σ, and ξ.
I = BRDF (θL, φL, θV, φV, σ, ξ) · Ii
The reflected light intensity I can be obtained by an expression of the form

(5) BTF model Since the BRDF model described above does not have the concept of texture mapping, when this is applied as it is to the present invention, a texture pattern composed of warp yarns, weft yarns, etc. of the fiber sheet is not expressed. 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 use this BTF model, the coordinate values u and v on the uv two-dimensional coordinate system are added as parameters, and the reflection characteristics are set to θL, φL, θV, It may be defined as a value determined by eight parameters φV, u, v, σ, and ξ.

On the other hand, in the reflected light intensity calculation stage, similarly to the BRDF model described above, 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 set as the reflection coefficient kb. make use of,
I = kb · Ii
It will be obtained by the following formula. However, in the case of this BTF model, the reflection coefficient kb is given as a function of θL, φL, θV, φV, u, v, σ, ξ.

In other words, in the conventional BTF model, the intensity I of the reflected light V from the sample point Q is calculated using a function called BTF.
I = BTF ・ Ii
In the case of the conventional BTF model, the function BTF is defined as a function having six variables θL, φL, θV, φV, u, v.
I = BTF (θL, φL, θV, φV, u, v) · Ii
In the case of the model according to the present invention, the function BTF is a function having eight variables θL, φL, θV, φV, u, v, σ, and ξ. Defined as
I = BTF (θL, φL, θV, φV, u, v, σ, ξ) · Ii
The reflected light intensity I can be obtained by an expression of the form

(6) Measurement of curvature-dependent reflection characteristics When the above-described BRDF model is applied to the present invention, it is defined by angles θL and φL by changing the illumination condition and the observation direction in the curvature-dependent reflection characteristic measurement stage in step S1. The direction of the incident illumination light L and the direction of the reflected light V defined by the angles θV and φV are measured in various ways, and further, the measurement is performed by changing the curvature σ and the curvature angle ξ in various ways. The reflection characteristics may be obtained for each combination of σ, ξ, θL, φL, θV, and φV. That is, a predetermined curvature-dependent reflection characteristic value may be obtained for each combination of six factors “σ, ξ, θL, φL, θV, φV” including the curvature σ and the curvature angle ξ. Specifically, the table shown in FIG. 7 is a two-dimensional table for two variables σ and ξ, while it is a six-dimensional table for six variables “σ, ξ, θL, φL, θV, φV”. Will be created. In the case of the BTF model, an eight-dimensional table is created for eight variables “σ, ξ, θL, φL, θV, φV, u, v” to which coordinate values u and v are added.

  Then, in the reflected light intensity calculation stage of step S6, in the case of the BRDF model, the curvature σ and the curvature angle ξ obtained in step S5 for the sample point Q to be calculated and the angle indicating the direction of the incident illumination light L Curvature-dependent reflection characteristics corresponding to combinations of θL and φL and angles θV and φV indicating the direction of reflected light V can be obtained by a process of drawing a six-dimensional table. In the case of the BTF model, an eight-dimensional table with the coordinate values u and v added may be further drawn.

  In step S1, in order to perform an operation of actually measuring the curvature-dependent reflection characteristics by changing the angles θL, φL, θV, and φV, the irradiation direction of the illumination light L is set to the angle θL, A light source device that can be changed with two degrees of freedom of φL and an imaging device that can change the observation direction of the reflected light V with two degrees of freedom of angles θV and φV may be prepared. Since the light source device and the photographing device having such functions are already known devices, detailed description thereof is omitted here.

(7) Handling for each primary color As described above, when a color image is created, the reflected light L generated from one sample point Q is separately handled for each primary color component. Each model described above is a simple model that does not take into account each color component. However, if these models are applied to color image creation, individual equations should be prepared for each of the three primary colors RGB, for example. That's fine.

<<< §4. Specific Example Using Polygon >>>
As described above, in the present invention, it is very important to obtain the curvature σ and the curvature angle ξ for the sample point Q on the virtual object. 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, in the actual measurement stage of step S1 of FIG. 5, as shown in FIG. 6, if the actual fiber sheet 61 is stuck in a predetermined direction on the cylindrical side surfaces of the actual objects 72 and 73 having a cylindrical shape, the curvature σ And the curvature angle ξ can be easily defined, and the curvature-dependent reflection characteristics corresponding to the respective combinations of the individual curvature σ and the individual curvature angles ξ can be measured.

  However, in step S5 in FIG. 5, 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 as follows. 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 S5, the curvature σ and the curvature angle ξ are defined in some form by 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 S5 when the three-dimensional data indicating the three-dimensional shape of the virtual object is input as a collection 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. 9, all triangles are drawn on the same plane, but in reality, 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. 9 shows a figure composed of four triangles Tq, Ta, Tb, Tc (in fact, many other triangles are actually outside the triangle Ta, Tb, 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 S5 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 forming 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. 9 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 curvature σa decreases as the formation angle ωa approaches 180 °. 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. 9, a perpendicular is drawn from the diagonal D3 to the side A of the triangle Tq of interest 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 thus obtained 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, using the perpendicular lengths hqa and ha thus obtained and the forming angle ωa between the target triangle Tq and the adjacent triangle Ta, the drawing as shown in FIG. 10 is performed. 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. 10, an intersection Oa between the vertical bisector of “line segment with length hqa” and the vertical bisector of “line segment with 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. 10, 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. 10 that when the length hqa and the length ha become 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. And the reciprocal of the distance Rc between the connection point Jc and the curvature C with respect to the side C may be defined.

  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 S5 in FIG. 5 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. 11 is exactly the same as each triangle shown in FIG. 9, 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. 12 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. 9, 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.

  Also in step S1 of FIG. 5, the definition of the curvature σ and the curvature angle ξ on the assumption of such a cylindrical curved surface is performed. Therefore, also in step S5, the curvature is determined by a method close to the definition assuming the cylindrical curved surface. It is necessary to define the angle ξ. 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. 13, 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. In step S2, as described above, information on the direction in which the fiber sheet is attached to the virtual object is also input. Therefore, in step S5, the direction of the reference direction line W of the fiber sheet is defined as illustrated. 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 S2, 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. 13, 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 combining 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. 14 is exactly the same as each triangle shown in FIG. 13, 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. 12 is also possible. That is, as shown in FIG. 12, a perpendicular 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 perpendiculars. 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, when the three-dimensional shape of the virtual object is input as three-dimensional data indicating a set of polygons in the data input stage shown in step S2 of FIG. 5, the curvature σQ and the curvature angle ξQ for an arbitrary sample point Q are obtained. Although a specific method to be obtained has been described, it is not always necessary to input the three-dimensional shape of a virtual object as three-dimensional data indicating a set of polygons in implementing the present invention. 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.

<<< §5. Two-dimensional image generation apparatus according to the present invention >>
In the flowchart shown in FIG. 5, step S <b> 1 is a procedure performed by actual measurement in which an actual fiber sheet is pasted on an actual object, but steps S <b> 2 to S <b> 9 are processes performed inside the computer. 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 shown in steps S2 to S9 in FIG. It is a device consisting of components. 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. 15, a data input unit 110, a three-dimensional data storage unit 120, a curvature-dependent reflection characteristic storage unit 130, a curvature calculation unit 140, a reflected light intensity calculation unit 150, a projection condition, as shown in FIG. The setting unit 160, the pixel definition unit 170, and the projection data storage unit 180 are configured. 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 step S2 of FIG. 5 are taken into the computer from the data input unit 110. . 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 the three-dimensional data indicating the three-dimensional shape of the 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 device for computers. Etc. In the case of the above-described embodiment, the three-dimensional data storage unit 120 stores three-dimensional data created by using CAD data.

  The curvature-dependent reflection characteristic storage unit 130 is a component that stores the curvature-dependent reflection characteristic including “the influence of the curvature on the reflected light intensity” input from the data input unit 110 and actually includes the fiber sheet. It is realized by a magnetic recording device or a memory device for a computer. The curvature-dependent reflection characteristic is data specific to each fiber sheet, which is actually measured in step S1 of FIG. 5, and is stored in the curvature-dependent reflection characteristic storage unit 130 as data in a table format as shown in FIG. 7, for example. Will be. The projection condition setting unit 160 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 160 is a magnetic recording device for a computer. Or a memory device.

  The curvature calculation unit 140 uses the curvature σQ and the curvature of the virtual object surface for the position of a 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 §4.

  The reflected light intensity calculation unit 150 is a component that performs a rendering process. When the fiber sheet is attached to the surface of the virtual object, the reflected light V intensity from the sample point Q toward the viewpoint E is expressed as a three-dimensional data storage unit. The three-dimensional data stored in 120, the curvature-dependent reflection corresponding to the curvature σQ and the curvature angle ξQ for the sample point Q calculated by the curvature calculation unit 140, stored in the curvature-dependent reflection characteristic storage unit 130. Characteristics ”and a function of calculating based on the projection condition (illumination condition, viewpoint position, projection plane) set in the projection condition setting unit 160. The specific calculation contents are as illustrated in §3.

  The pixel definition unit 170 is a component that defines a pixel P having a pixel value corresponding to the intensity of the reflected light V at the intersection of the reflected light V from the sample point Q and the projection plane M, and stores projection data. The unit 180 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. 15 is as follows. First, the operator prepares three-dimensional data of a virtual object and an actual fiber sheet. As the three-dimensional data of the virtual object, for example, data obtained by diverting CAD data may be used as it is. Then, the actual measurement work described in step S1 in FIG. 5 is performed, and curvature-dependent reflection characteristics such as the table shown in FIG. 7 are obtained for the prepared actual fiber sheet. Subsequently, by operating the data input unit 110, the three-dimensional data of the virtual object is stored in the three-dimensional data storage unit 120, and the curvature-dependent reflection characteristic obtained by actual measurement is stored in the curvature-dependent reflection characteristic storage unit 130. And store. 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 160.

  Thus, the substantial operation performed by the operator is completed. Thereafter, when an instruction to start the rendering process is given to the apparatus, the curvature calculator 140 calculates the curvature σQ and the curvature angle ξQ for each sample point Q necessary for the rendering process, and the reflection is performed. 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 170 defines a pixel P having a pixel value corresponding to the intensity of each reflected light V. As a set of these pixels P, the target two-dimensional image is stored in the projection data storage unit 180. The operator may output the two-dimensional image thus obtained in the projection data storage unit 180 onto a desired medium as necessary.

  As mentioned above, although this invention was demonstrated based on embodiment shown in figure, this invention is not limited to these embodiment, In addition, it can implement in a various aspect. For example, in the above-described embodiment, the curvature parameter is defined by adding a factor of the direction of the curvature angle ξ to the curvature σ, but the concept of the curvature angle ξ is not necessarily required depending on the usage form. Specifically, when using a denim fabric knitted with warp and weft as a fiber sheet or an iridescent weave, since the fabric itself has directionality, for example, a reference direction line W is defined in the direction of warp. be able to. However, in the case of using a fabric obtained by flocking a pile such as a towel as a fiber sheet, it is meaningless to define the direction of application to an object because the fabric is isotropic. In such a case, only the curvature σ is defined as the curvature parameter, and the operation without using the concept of the curvature angle ξ may be performed.

<<< §6. Curvature definition using sign >>>
In the embodiments described so far, only the example in which the curvature of the masquerade object is convex is shown, but actually, the surface of the masquerade object is not necessarily composed only of the convex curvature. In some cases, a disguised object having a concave curvature is used. Of course, the present invention can be applied not only to a disguised object having a convex curve, but also to a disguised object having a concave curve.

  By the way, whether a curved surface is convex or concave is a matter determined depending on the position where the viewpoint is placed, and even if it is the same curved surface, it becomes a convex curved surface or a concave curved surface depending on the viewpoint position. It becomes. Therefore, if the concept of a sign is introduced in the definition of curvature, it becomes possible to handle convex curved surfaces and concave curved surfaces in a unified manner. Here, a specific method of handling both convex curved surfaces and concave curved surfaces by defining the curvature using such a code will be described.

  For example, FIG. 16 (a) is the same diagram as FIG. 6 (b), and an actual fiber sheet 61 is pasted on an actual object 72 having a cylindrical side surface with a curvature σ = 1 / r 1. The work of irradiating the measurement area F2 with the illumination light L and measuring the intensity of the reflected light V toward the viewpoint E is shown. In this measurement operation, the curvature-dependent reflection characteristic with respect to the curvature σ = 1 / r1 of the fiber sheet 61 (here, the thickness is neglected for convenience of description) can be obtained. On the other hand, FIG. 16B also applies an actual fiber sheet 61 to an actual object 74 having a cylindrical side surface with a curvature σ = 1 / r1, and irradiates the measurement region F4 with the illumination light L from the light source G. FIG. 5 is a diagram illustrating an operation of measuring the intensity of the reflected light V toward the viewpoint E. In this measurement operation, the curvature-dependent reflection characteristic with respect to the curvature σ = 1 / r1 can be obtained for the fiber sheet 61 (here, the thickness is ignored for convenience of explanation).

  Both the object 72 shown in FIG. 16 (a) and the object 74 shown in FIG. 16 (b) are objects having geometric cylindrical side surfaces on the surface. In the former, the outer surface of the cylinder is the outer surface of the object. Therefore, the fiber sheet 61 is curved in a convex shape when viewed from the viewpoint E, whereas the latter has a concave shape when viewed from the viewpoint E because the inner surface of the cylinder is the outer surface of the object. Is curved. However, when viewed from the inside of each of the objects 72 and 74 instead of viewing from the viewpoint E (outside of each of the objects 72 and 74), the above-described unevenness relationship is reversed. Here, if the curvature σ is defined as the reciprocal of the radius of each cylinder, the curvature is σ = 1 / r1 in any case (considering the thickness of the fiber sheet 61, the former curvature is σ = 1 / (r1 + d). And the latter curvature is σ = 1 / (r1-d)).

  Therefore, here, even if the curvature is the same, a positive sign is given when it is convexly curved when viewed from the viewpoint E, and a negative sign when it is concavely curved when viewed from the viewpoint E. It will be shown with the symbol. That is, even when a cylindrical side surface having a radius r1 is given, a positive curvature value σ = 1 / r1 is given to the outer surface of the cylindrical side surface as shown in FIG. As shown in FIG. 16 (b), the negative curvature value σ = −1 / r1 is given to the inner surface of, so that even if the absolute value is the same, the two can be distinguished by the sign. (Of course, the sign may be defined in reverse). In addition, the “cylindrical side surface” referred to in the present application is used as a word meaning both the outer surface and the inner surface of the curved surface constituting the side of the geometric cylinder.

  Practically, in the actual measurement stage of the curvature-dependent reflection characteristic in step S1 in FIG. 5, measurement using an object having a positive curvature as shown in FIG. 16 (a) and as shown in FIG. 16 (b). It is only necessary to perform both measurement using an object having a negative curvature. In this case, the curvature-dependent reflection characteristic table obtained by the measurement is obtained by adding a region where σ takes a negative value to the table shown in FIG. 7 (that is, on the left side of the table of FIG. = -1,-1/3,-1/5, ..., -1/100 are added).

  On the other hand, the curvature calculation in step S5 in FIG. 5 and the curvature calculation unit 140 in FIG. 15 may obtain the curvature of the disguise object at a predetermined sample point position as a signed value. That is, a positive curvature may be defined when the lens is convexly convex as viewed from the viewpoint, and a negative curvature may be defined when the lens is curved concavely.

  For example, a formation angle ω between two adjacent polygons is defined as an angle measured with respect to the inside of the virtual object. In the case of the example shown in FIG. 10, if the part shown on the lower side of the figure is inside the object and the part shown on the upper side of the figure is outside the object, the target triangle Tq and the adjacent triangle Ta The forming angle between the two is the angle ωa shown in the figure. And, if the formation angle ωa is smaller than 180 ° as in the example shown in the figure, it is curved in a convex shape when viewed from the viewpoint (outside of the disguise object), so that a positive curvature is given and reversed On the other hand, if the formation angle ωa is larger than 180 °, it is curved in a concave shape when viewed from the viewpoint (outside of the disguise object), so a negative curvature may be given.

  Thus, if the sign is determined according to the magnitude relationship between the formation angle and 180 °, the curvature calculation in step S5 in FIG. 5 or the curvature calculation unit 140 in FIG. Since the curvature of the disguise object at the position can be obtained as a signed value, it is possible to handle both the convex curved surface and the concave curved surface. Of course, for the absolute value of the curvature, the calculation method in the specific embodiment described in §4 may be used as it is.

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 flowchart which shows the procedure of the two-dimensional image generation method which concerns on this invention. It is a figure which shows the specific measuring method of curvature-dependent reflection characteristic measurement step S1 in the flowchart of FIG. It is a figure which shows an example of the table of the curvature dependence reflection characteristic obtained by implementing the curvature dependence reflection characteristic measurement step S1 in the flowchart of 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. FIG. 10 is a plan view showing the principle of defining the curvature for side A in the example shown in FIG. 9. In the example shown in FIG. 9, 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. 9, it is a top view which shows another principle which defines the curvature about the sample point Q in a triangle. FIG. 10 is a plan view showing the principle of defining the curvature angle for each side A, B, C in the example shown in FIG. 9. In the example shown in FIG. 9, 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. In this invention, it is a figure which shows the handling which defined the negative curvature.

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 ... A virtual object 51, 52 ... A cylindrical real object 55 ... A projected image 60 of a virtual object ... A virtual fiber sheet 61 ... A real fiber sheet 71 ... An object 72 made of a square pillar ... object 73 made of a cylinder of radius r1 ... object 74 made of a cylinder of radius r2 ... object 110 having a hollow of a cylinder of radius r1 ... data input unit 20 ... 3D data storage unit 130 ... Curvature-dependent reflection characteristic storage unit 140 ... Curvature calculation unit 150 ... Reflected light intensity calculation unit 160 ... Projection condition setting unit 170 ... Pixel definition unit 180 ... Projection data storage unit A, B, C ... Triangular sides a, b, c ... perpendicular legs D1-D6 ... triangle vertices E ... viewpoints F1-F4 ... measurement area G ... light source H ... cylindrical center axis H '... projection line ha of cylindrical center axis hqa ... perpendicular length Ja ... connection point L ... illumination light L '... projection image La of illumination light ... distance Lb between point Q and point D3 ... distance Lc between point Q and point D2 ... point Q and point D1 Distance M ... projection plane n ... normal line Oa ... intersection point P of vertical bisector ... pixel Q ... sample point Ra ... distances R1 and r2 between point Oa and point Ja ... cylinder radius S ... perpendicular to normal line Orthogonal planes S1 to S9 ... each step Ta, Tb, Tc of the flowchart ... adjacent triangle Tq ... triangle of interest Ua, Ub, Uc: Individual divided regions and their areas u, v ... Coordinate axes V of a two-dimensional coordinate system showing a picture ... Reflected light V '... Projected image W of reflected light ... Reference direction lines X, Y, Z ... Each coordinate axis x, y of the three-dimensional coordinate system, 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, emission angle ξ of the reflected light V, curvature angle ξa, side Curvature angle with respect to A ξb Curvature angle with respect to side B ξc ... Curvature angle with respect to side C ξQ ... Curvature angle σ at the sample point Q ... Curvature σa ... Curvature σb with respect to side A Curvature φL of point Q: azimuth angle φV of illumination light L: azimuth angle ωa of reflected light V: formation angle of plane or line segment

Claims (25)

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,
Pasting an actual fiber sheet on an actual object having a predetermined curvature, illuminating under a predetermined condition, and observing reflected light obtained from the surface of the fiber sheet from a predetermined direction, for each of a plurality of curvatures A curvature-dependent reflection characteristic measurement stage for obtaining a curvature-dependent reflection characteristic including an influence of the curvature on the reflected light intensity,
A 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 intensity of the reflected light from the sample point toward the viewpoint position is considered in consideration of the curvature-dependent reflection characteristic corresponding to the curvature at the sample point position. The desired reflected light intensity calculation stage;
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;
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,
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
In the data input stage, input information on the direction of the fiber sheet attached to the virtual object.
In the curvature calculation stage, find the curvature with a factor of direction,
In the reflected light intensity calculation stage, the reflected light intensity is calculated in consideration of the curvature-dependent reflection characteristic corresponding to the curvature having the orientation factor. Image generation method. The two-dimensional image generation method according to claim 2,
At the curvature-dependent reflection characteristic measurement stage, an actual fiber sheet is attached to the side of a cylinder of an actual object in a predetermined direction, the curvature σ is defined using the inverse of the radius of the cylinder, and the center axis of the cylinder is projected in the radial direction. The angle ξ formed by the projection line obtained on the cylindrical side surface and the reference direction line of the fiber sheet is defined as the curvature angle for the curvature σ, and corresponds to each combination of the individual curvature σ and the individual curvature angle ξ. Find the curvature-dependent reflection characteristics,
In the 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 reflected light intensity calculation stage, the reflected light intensity is obtained in consideration of the curvature-dependent reflection characteristics corresponding to the combination of the curvature σ and the curvature angle ξ, and is based on a three-dimensional virtual object having a fiber sheet attached to the surface. Two-dimensional image generation method. The two-dimensional image generation method according to claim 3,
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, assuming that the intensity of the incident illumination light at the sample point is Ii, the reflected light intensity I is used by using the reflection coefficient k given as a function of the coordinate values u and v and the curvature parameters σ and ξ. ,
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 3,
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle between the normal n standing at the sample point position on the virtual object surface and the incident illumination light is α, and the diffuse reflection coefficient is kd. 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, wherein the diffuse reflection coefficient kd is determined in consideration of curvature parameters σ and ξ. The two-dimensional image generation method according to claim 5,
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, the diffuse reflection coefficient kd is determined in consideration of the coordinate values u and v and the curvature parameters σ and ξ, and is two-dimensional based on a three-dimensional virtual object with a fiber sheet attached to the surface. Image generation method. The two-dimensional image generation method according to claim 3,
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle between the normal n set at the sample point position on the virtual object surface and the incident illumination light is α, and this angle α depends The reflected light intensity I is expressed as follows, where the reflection coefficient is k (α), the parameter indicating the sharpness of the specular reflection is β, and the angle between the emission direction of the specular reflection light at the sample point and the viewpoint direction is γ.
I = k (α) · Ii · 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, wherein the coefficients k (α) and β are determined in consideration of curvature parameters σ and ξ. The two-dimensional image generation method according to claim 7,
Instead of k (α), the reflection coefficient depending on the angle α is changed to a coefficient ks that does not depend on the angle α, and the reflected light intensity I is
I = ks · Ii · 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, wherein the coefficients ks and β are determined in consideration of curvature parameters σ and ξ. The two-dimensional image generation method according to claim 3,
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle formed by the normal n standing at the sample point position on the virtual object surface and the incident illumination light is θL, and the normal n The angle between the projection image of the incident illumination light on the orthogonal plane orthogonal to the reference line passing through the sample point on the orthogonal plane is φL, the angle between the normal n and the reflected light is θV, and the orthogonal When the angle between the projected image of the reflected light on the plane and the reference line is φV, the reflected light intensity I is reflected as a function of θL, φL, θV, φV and curvature parameters σ, ξ. Using the coefficient kb,
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. The two-dimensional image generation method according to claim 3,
In the curvature dependent reflection characteristic measurement stage, measurement is performed using an actual fiber sheet having a pattern indicated by the pattern data T (u, v) defined on the uv two-dimensional coordinate system, and the coordinate value u, Obtain curvature-dependent reflection characteristics according to the value of v,
In the reflected light intensity calculation stage, the intensity of the incident illumination light at the sample point is Ii, the angle formed by the normal n standing at the sample point position on the virtual object surface and the incident illumination light is θL, and the normal n The angle between the projection image of the incident illumination light on the orthogonal plane orthogonal to the reference line passing through the sample point on the orthogonal plane is φL, the angle between the normal n and the reflected light is θV, and the orthogonal When the angle between the projected image of the reflected light on the plane and the reference line is φV, the reflected light intensity I is θL, φL, θV, φV, coordinate values u, v, and curvature parameters σ, ξ. Using the reflection coefficient kb given as a function of
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. The two-dimensional image generation method according to claim 9 or 10,
At the curvature-dependent reflection characteristic measurement stage, by changing the illumination conditions and the observation direction, the direction of the incident illumination light defined by the angles θL and φL and the direction of the reflected light defined by the angles θV and φV are changed in a plurality of ways. The curvature-dependent reflection characteristics are obtained for each combination of angles θL, φL, θV, and φV,
In the reflected light intensity calculation stage, calculation using curvature-dependent reflection characteristics corresponding to the combinations of the angles θL and φL indicating the direction of the incident illumination light and the angles θV and φV indicating the direction of the reflected light at the sample point to be calculated. A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface. In the two-dimensional image generation method in any one of Claims 1-11,
In the projection condition setting stage, set illumination conditions with multiple light sources,
In the reflected light intensity calculation stage, the intensity of the reflected light from one sample point toward the viewpoint position is obtained as the sum of the reflected light intensities generated based on the incident illumination light from each of the plurality of light sources, A two-dimensional image generation method based on a three-dimensional virtual object in which a fiber sheet is attached to a surface to be processed. In the two-dimensional image generation method in any one of Claims 1-12,
In the data input stage, the solid shape of the virtual object is input as a collection of polygons,
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,
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
In the data input stage, information on the reference direction line 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 reflected light intensity calculation stage, the reflected light intensity is determined in consideration of the curvature-dependent reflection characteristic corresponding to the curvature having the orientation factor indicated by the curvature angle ξQ. A two-dimensional image generation method based on an original virtual object. In the two-dimensional image generation method in any one of Claims 1-12,
In the 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,
In the curvature-dependent reflection characteristic measurement stage, when an actual fiber sheet is pasted on an actual object, a reference direction line is defined on the actual fiber sheet, and the reference direction line has different directions on the actual object. To be oriented in multiple orientations, define the curvature with the orientation factor, find the curvature-dependent reflection characteristics for each curvature with the orientation factor,
In the data input stage, information on the reference direction line 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.
When calculating the reflected light intensity at the sample point Q in the reflected light intensity calculation stage, the curvature-dependent reflection characteristic corresponding to the curvature angle ξQ is used to determine the corresponding curvature-dependent reflection characteristic. 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 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 1-12,
In the data input stage, the three-dimensional shape of the virtual object is input as a parametric surface represented 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. .   A program for causing a computer to execute each step other than the curvature-dependent reflection characteristic measurement step in the two-dimensional image generation method according to any one of claims 1 to 22. 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 curvature-dependent reflection characteristic storage unit that stores a curvature-dependent reflection characteristic that includes the `` effect of the curvature on the reflected light intensity '' input from the data input unit, and the fiber sheet;
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, the intensity of reflected light from the sample point toward the viewpoint position is changed to the three-dimensional data, the illumination condition, the viewpoint position, and the curvature at the sample point position. A reflected light intensity calculation unit obtained in consideration of the corresponding curvature-dependent reflection characteristics;
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;
A two-dimensional image generation device based on a three-dimensional virtual object in which a fiber sheet is attached to a surface. The two-dimensional image generation device according to claim 24,
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 curvature-dependent reflection characteristic storage unit has a function of storing curvature-dependent reflection characteristics respectively corresponding to various combinations of the curvature and the curvature angle indicating the deviation between the bending direction corresponding to the curvature and the reference direction line. Have
The curvature calculation unit has a function of obtaining a curvature angle together with the curvature at the sample point position,
The reflected light intensity calculation unit has a function of obtaining the reflected light intensity in consideration of curvature-dependent reflection characteristics corresponding to the curvature and the curvature angle at the sample point position, and a three-dimensional virtual sheet with a fiber sheet attached to the surface. A two-dimensional image generation device based on an object.