JP2007207021A - Three-dimensional shape data generation method and three-dimensional shape data generation device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that it is hard to generate a polygon model to be an origin of a paper pattern of an industrial product. <P>SOLUTION: A three-dimensional shape data generation device generates a 3-dimensional shape data in which a surface shape of a reference polyhedron is smoothed when the reference polyhedron formed by approximating a shape of a target 3-dimensional solid is given. A determination point generation unit 12 generates a determination point near by the surface of the reference polyhedron. An occupancy ratio calculation unit 14 generates nearby points at random in a nearby sphere with the determination point as a center to calculate an occupancy ratio indicating a ratio in which the nearby point in the nearby sphere is included inside the reference polyhedron. An effectiveness determination point determining unit 20 determines that the determination point is included in the target 3-dimensional solid when the occupied ratio is not smaller than a determination threshold. A 3-dimensional data generation unit 28 generates a polygon in which the determination point determined that it is included in the target 3-dimensional solid is the tops of the polygon, and generates 3-dimensional shape data showing the target 3-dimensional solid by means of the polygon model. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a three-dimensional shape data generation method and a three-dimensional shape generation device for generating three-dimensional shape data representing the shape of a three-dimensional solid.

  Industrial products such as clothes, bags, and shoes are manufactured using pattern paper. In the field of apparel design, apparel CAD systems are used. In the apparel CAD system, a template of a pattern is prepared, and the user can create a pattern with a desired design by deforming the template, and can display the three-dimensional display to simulate the clothing state.

  Recently, unlike general ready-made clothes in the field of medical care and nursing care, clothes that are easy for the patient to put on and take off, and a dedicated hook that moves people with disabilities between the wheelchair and bed by lifting There is a need for special-purpose clothing such as clothing. It is necessary to newly design the shape of the clothes according to the patient's body shape, the degree of freedom of the body, and the use conditions.

  In the apparel CAD system, a template of a pattern is provided, and a user creates a pattern with a desired design by freely modifying the template. If the customer's body shape deviates significantly from the standard, special clothing such as nursing care is designed, or if the design is unique and there is no standard template, the prepared template It makes little sense and makes it very difficult to create the desired pattern. Also, when creating a pattern such as a bag or shoes, it is necessary to design various shapes according to the fashion, and the method of generating a pattern based on a prepared template is not very compatible.

  Under such circumstances, it is required to model a three-dimensional shape by computer graphics (CG) technology and automatically develop the shape of the three-dimensional model by CG on a pattern paper for use in industrial production of products. Yes.

In Patent Document 1, a customer who wants clothes draws a design image of clothes suitable for his body shape, and based on this, a pattern pattern of the clothes is quickly and easily created by applying CAD / CAM technology. A method for automatically creating a pattern pattern of a garment and an automatic creation system thereof are disclosed.
JP 2001-249957 A

  Polygon modeling is generally used as a three-dimensional shape modeling technique. In a polygon model, a three-dimensional shape is expressed by a polygon mesh that is a collection of polygons. Polygon models can express even complex shapes by splicing polygons, but interactive processing is difficult, and it is necessary to increase the number of polygons to faithfully represent smooth surface shapes, increasing the amount of data To do. The polygon mesh is not used in pursuit of the strictness of the shape state, but is used for simplifying the shape as a polyhedron and speeding up the display, or as a model for analysis.

  When modeling the three-dimensional shape of industrial products such as clothes and bags by CG, the shape of curves and curved surfaces becomes very important. A free-form surface is used to handle an arbitrary surface. A free-form surface defines a surface using a Bezier curve, a spline curve, and a NURBS curve, and can express an arbitrary smooth shape more strictly than a polygon model.

  However, in the method of defining a three-dimensional shape with a free-form surface, it is necessary to determine parameters such as control points while imagining the target shape, and although it is highly flexible, it is very difficult to design the intended shape. . Further, when designing a complicated shape, such as a flare skirt, the followability to the control points is deteriorated, so that the number of control points increases as the shape becomes complicated.

  There is a technique called Subdivision Surface, which is used for car design. The subdivided surface method is a technique for subdividing a roughly modeled polygon mesh into a smooth and seamless shape. Although a smooth shape close to a free-form surface can be expressed, there is a problem that the amount of data increases compared to a polygon mesh.

  In addition, there is a method of expressing a three-dimensional shape by combining simple figures and shaping it later using a spatial filter, but since the spatial filter specifies the characteristics in the frequency domain, It is difficult to understand how it is reflected, and it is not easy to design the intended shape.

  The present invention has been made in view of such problems, and an object thereof is to provide a three-dimensional shape data generation apparatus and a three-dimensional shape data generation method capable of easily designing an arbitrary shape such as an industrial product. It is in.

  In order to solve the above problems, a method for generating three-dimensional shape data according to an aspect of the present invention is a method for generating three-dimensional shape data obtained by smoothing the surface shape of a reference polyhedron approximating a target three-dimensional solid shape. A discriminant point generating step for generating discriminant points near the surface of the reference polyhedron, and by generating a random point in a nearby sphere of a predetermined radius centered on the discriminant point, An occupancy ratio calculating step for calculating an occupancy ratio indicating the ratio of the neighboring points included in the reference polyhedron, and when the occupancy ratio is greater than or equal to a predetermined determination threshold, the determination point is the target three-dimensional A determination step for determining that the determination point is not included in the target three-dimensional solid when it is determined that the determination point is included in a solid and the occupation ratio is smaller than the determination threshold; By a polygon whose vertices are determined to be the determination point and included in the three-dimensional, and a shape data generation step of generating a three-dimensional shape data representing the 3-dimensional to the target.

  By repeating the determination point generation step, the occupancy rate calculation step, and the determination step for the reference polyhedron after being deformed by the determination point determined to be included in the target three-dimensional solid, The surface shape of the reference polyhedron may be smoothed in stages.

  Another aspect of the present invention is a three-dimensional shape data generation apparatus. This device generates 3D shape data obtained by smoothing the surface shape of a reference polyhedron approximating the shape of a target three-dimensional solid, and generates a determination point near the surface of the reference polyhedron. A generation unit generates a nearby point by a random number in a nearby sphere with a predetermined radius centered on the determination point, and an occupancy ratio indicating a ratio that the nearby point in the nearby sphere is included in the reference polyhedron When the occupation rate calculation unit to calculate and the occupation rate is greater than or equal to a predetermined determination threshold, the determination point is determined to be included in the target three-dimensional solid, and the occupation rate is smaller than the determination threshold In addition, an effective discrimination point determination unit that determines that the determination point is not included in the target three-dimensional solid, and the determination point that is determined to be included in the target three-dimensional solid by the determination is a vertex. Depending on the polygon , And a 3-dimensional data generation unit for generating a three-dimensional shape data representing the 3-dimensional to the target.

  It should be noted that any combination of the above-described constituent elements and the expression of the present invention converted between a method, an apparatus, a system, a computer program, a data structure, a recording medium, etc. are also effective as an aspect of the present invention.

  According to the present invention, an industrial product having an arbitrary shape can be easily designed.

  FIG. 1 is a configuration diagram of the three-dimensional shape data generation apparatus 100. This figure depicts a block diagram focusing on functions, and these functional blocks can be realized in various forms by hardware only, software only, or a combination thereof.

  The solid model generation unit 10 generates the shape of a target three-dimensional solid (hereinafter referred to as “target solid”) by solid modeling. In solid modeling, the shape of a target solid is approximated by repeating processing such as deleting a part of a simple solid or combining a plurality of solids.

  As an example of solid modeling, the shape of a target solid is modeled by a technique called functional modeling. In functional modeling, an object is expressed by a function f (x, y, z) of coordinates (x, y, z) in a three-dimensional space. If f (x, y, z)> 0, the inside of the object, f (x , Y, z) = 0, it is defined as the surface of the object, and if f (x, y, z) <0, it is defined as the outside of the object.

  A rectangular parallelepiped is expressed by a function, and the rectangular parallelepiped is cut by a plane to create an arbitrary polyhedron. Here, the cutting plane is also expressed as a function. In order to recognize the inside, the surface, and the outside of the object in cutting, the object is stored in a tree structure.

  For example, assuming that a function representing a rectangular parallelepiped is P and a function used for cutting is Q, the inside of the polyhedron obtained by cutting is represented as P> 0∧Q> 0. Similarly, the surface of the polyhedron is expressed as P = 0∧Q = 0, and the outside is expressed as P <0∧Q <0.

By repeating such a cutting operation, the generated polyhedron is expressed as f ₁ ≧ 0∧f ₂ ≧ 0∧f ₃ ≧ 0∧f ₄ ≧ 0∧. Here, f ₁ , f ₂ , f ₃ , f _4, etc. are functions. Since the generated polyhedron is expressed as a function, calculation errors do not accumulate in the modeling process.

  By repeating the cutting operation, the user can approximate a desired three-dimensional shape with a polyhedron. A polyhedron obtained by cutting is referred to as a “reference polyhedron”.

  The solid model generation unit 10 stores the reference polyhedron expressed as a function in the reference polyhedron storage unit 40. Although the reference polyhedron approximates the target solid, it is an angular shape because it is a polyhedron and has no smoothness. Therefore, as described below, a process for smoothing the surface shape of the reference polyhedron is performed.

  The discrimination point generation unit 12 acquires a function representation of the reference polyhedron from the reference polyhedron storage unit 40, and randomly generates discrimination points near the surface of the reference polyhedron.

  The discriminant point generation unit 12 uses the function f (x, y, z) that gives the surface of the reference polyhedron, in the vicinity of f (x, y, z) = 0, that is, f (x, y, z) = ±. A point (x, y, z) satisfying ε is randomly generated using a numerical analysis method, thereby generating a discrimination point near the surface of the polyhedron. Here, ε is a sufficiently small value.

Various algorithms for detecting points on the surface of a curved surface defined by functions are introduced in the following references, and can be used in this embodiment. As described above, when f (x, y, z) = ± ε is considered as a new curved surface with respect to the curved surface f (x, y, z) = 0, an algorithm for detecting a point on the surface of the curved surface is obtained. Can be used to generate points near the surface.
References: Jules Bloomenthal, "Polygonization of Implicit Surfaces", XEROX PARC, CSL-87-2, May 1987.

  The occupancy rate calculation unit 14 sets a nearby sphere with a predetermined radius centered on the discrimination point generated by the discrimination point generation unit 12, and generates a point inside the neighborhood sphere (hereinafter referred to as "neighbor point"). .

  The occupancy rate calculation unit 14 expresses the inside of the nearby sphere with polar coordinates (r, θ, ρ), and generates r, θ, and ρ using random numbers, thereby randomly generating nearby points inside the nearby sphere. As will be described later, when a reference polyhedron is cut by a plane perpendicular to the z-axis direction, that is, an xy plane, and a discrimination point is provided in the cut plane, a neighborhood circle centered on the discrimination point is set, and the inside of the neighborhood circle Is expressed in polar coordinates (r, θ), and random numbers are used to generate r and θ, thereby generating neighboring points randomly within the neighboring circle.

  Here, the radius of the neighboring sphere is adjusted according to the curvature of the surface of the reference polyhedron. The surface curvature calculation unit 16 calculates the curvature of the surface of the reference polyhedron and gives it to the sphere radius adjustment unit 18. The sphere radius adjustment unit 18 adjusts the radius of the neighboring sphere to be smaller as the curvature is larger. The occupation rate calculation unit 14 sets a nearby sphere with the radius adjusted by the sphere radius adjustment unit 18.

  In order to define the curvature at the vertices of the polyhedron, the Gaussian curvature at the vertices V of the polyhedron is approximated by the following approximate value K (reference: Hayano, Matsuoka, Ueda, “Simplification of polygon mesh by feature extraction and edge operation”) Ricoh Technical Report No. 24, November 1988). The shape of the vertex V having a large absolute value of the approximate Gaussian curvature K is pointed (or recessed).

K = a / S
a = 2π− (the sum of the angles of the corners of the surface gathering at V)
S = (the total area of the surfaces gathered at V) / 3

  Next, the occupancy ratio calculation unit 14 calculates the ratio of the vicinity sphere included in the reference polyhedron, that is, the ratio of the logical product of the reference polyhedron and the vicinity sphere to the entire vicinity sphere (hereinafter referred to as “occupancy ratio”). Ask.

  The occupancy ratio calculation unit 14 determines whether or not the neighborhood points randomly generated inside the neighborhood sphere are inside the reference polyhedron, obtains the number i of neighborhood points inside the reference polyhedron, and calculates the total number N of neighborhood points generated. By obtaining the value p = i / N divided by occupancy, the occupation ratio is approximately obtained. The occupation rate calculation unit 14 gives the approximate occupation rate p to the effective discrimination point determination unit 20.

  The effective discrimination point determination unit 20 determines that the discrimination point whose occupancy p is equal to or greater than the predetermined determination threshold t is on or inside the surface of the target solid, and the discrimination point whose occupancy p is smaller than the predetermined determination threshold t Is determined to be outside the target solid. When the discrimination point is on or inside the target solid, the discrimination point is “valid”, and when the discrimination point is outside the target solid, the discrimination point is “invalid”.

  By generating a discrimination point near the surface of the reference polyhedron and determining whether the discrimination point is inside the target solid (that is, whether it is valid), the reference polyhedron can be deformed so as to approach the target solid. it can. A portion determined to be outside the target solid (that is, a portion occupied by an invalid discrimination point) is cut out from the surface of the reference polyhedron, and a portion determined to be inside the target solid (that is, a portion occupied by a valid discrimination point) For), inflate the surface of the reference polyhedron. When this operation is performed near the vertex of the reference polyhedron, the corners of the reference polyhedron can be rounded and smoothed. Thereby, the surface shape of the reference polyhedron can be made smooth and close to the target solid.

  Here, the determination threshold t is normally 0.5, but when the reference polyhedron is more than necessary due to smoothing, the determination threshold t is decreased and the reference polyhedron is excessively swollen due to smoothing. Increases the determination threshold t. For this purpose, the solid model generation unit 10 generates in advance an “inclusive polyhedron” included in the reference polyhedron and an “external polyhedron” including the reference polyhedron, and stores them in the internal / external polyhedron storage unit 42. To do.

  The inside / outside determination unit 24 has a provisional effective determination point that is determined to be inside the target solid by the effective determination point determination unit 20 (referred to as a “provisional effective determination point”), and the temporary effective determination point is inside the inclusion polyhedron or outside the outer polyhedron. It is determined whether or not. The internal / external determination unit 24 notifies the determination threshold adjustment unit 26 when the provisional effective determination point is inside the internal polyhedron or outside the external polyhedron.

  The determination threshold adjustment unit 26 decreases the determination threshold t when the temporary effective determination point is inside the inclusion polyhedron, and increases the determination threshold t when the temporary effective determination point is outside the inclusion polyhedron. The determination threshold adjustment unit 26 provides the adjusted determination threshold t to the effective determination point determination unit 20.

  The valid discrimination point determination unit 20 redoes the discrimination point validity / invalidity determination based on the determination threshold t adjusted by the determination threshold adjustment unit 26. A determination point determined to be valid under the determination threshold t adjusted by the determination threshold adjustment unit 26 is finally an effective determination point. Hereinafter, the determination point finally determined to be effective is simply referred to as “effective determination point”. The effective determination point determination unit 20 stores the effective determination point in the effective determination point storage unit 44.

  In this way, by providing the inclusion / exterior polyhedron and obtaining the effective discrimination point, the surface shape of the reference polyhedron is inflated or dented based on the effective discrimination point in the space region sandwiched between the envelope polyhedron and the inclusion polyhedron. Can be deformed and brought close to the target solid.

  Here, when there is one effective determination point near the surface of the reference polyhedron, the effective determination point inside is unnecessary for the purpose of deforming the reference polyhedron. Only the effective discrimination points are obtained and stored in the effective discrimination point storage unit 44. For this purpose, the discrimination point generation unit 12 generates discrimination points so as to gradually approach the inside from the outside with respect to the surface of the reference polyhedron, thereby generating a discrimination point sequence. Then, the valid discrimination point determination unit 20 determines the validity / invalidity of each discrimination point in the discrimination point sequence, determines the boundary between the invalid discrimination point and the effective discrimination point, and obtains the outermost effective discrimination point. Alternatively, as another method, a valid search point located on the outermost side in the vicinity of the surface of the reference polyhedron may be searched using a binary search (binary search) technique.

  The surface shape deforming unit 22 deforms the surface shape of the reference polyhedron based on the valid discrimination points, and stores the deformed reference polyhedron shape data in the reference polyhedron storage unit 40. The surface shape deforming unit 22 extracts a feature point such as a vertex or a point on the surface of the reference polyhedron, and moves the feature point to the position of the effective determination point, thereby deforming the surface shape of the reference polyhedron.

  The reference polyhedron deformed by the surface shape deforming unit 22 is displayed on the display, and the user can confirm the three-dimensional shape after deformation. If necessary, the user can set a discrimination point in the vicinity of the surface shape of the deformed reference polyhedron, obtain an occupancy ratio, deform the surface shape by the effective discrimination point, and approximate the target solid. For this purpose, the discrimination point generation unit 12, the occupation rate calculation unit 14, the surface curvature calculation unit 16, the sphere radius adjustment unit 18, the effective discrimination point determination unit 20, the inside / outside determination unit 24, the determination threshold adjustment unit 26, and the surface shape deformation unit Each of the components 22 performs the above-described processing for the reference polyhedron after deformation. Here, the deformed reference polyhedron is no longer strictly a polyhedron due to rounding of the corners by smoothing processing, but will be referred to as a polyhedron for convenience. Thereby, starting from the reference polyhedron, the user can proceed with the smoothing process step by step while checking the deformation results one by one.

  The three-dimensional data generation unit 28 acquires a set of effective determination points from the effective determination point storage unit 44, generates a polygon having the effective determination points as vertices by connecting adjacent effective determination points, and generates a polygon model. Is generated. This polygon model is a three-dimensional model that smoothly approximates the surface of the target solid. The three-dimensional data generation unit 28 stores the generated polygon model information in the polygon information storage unit 46.

  The three-dimensional data generation unit 28 generates a polygon using only the set of effective discrimination points, but generates a polygon by reading out the feature points of the reference polyhedron from the reference polyhedron storage unit 40 and using them in combination with the effective discrimination points. May be.

  The pattern paper development unit 30 acquires polygon model information from the polygon information storage unit 46, generates a target three-dimensional pattern by developing the polygon model on a two-dimensional plane, and uses the obtained pattern data as a pattern data storage unit 48. To remember. The pattern data is sent to a manufacturing factory or the like and used to create a product.

  FIG. 2 is a flowchart showing a rough flow of a procedure for generating three-dimensional shape data by the three-dimensional shape data generating apparatus 100.

  The three-dimensional shape data generation apparatus 100 cuts a rectangular parallelepiped with an image like a wood carving sculpture, and roughly shapes a target solid shape of an industrial product such as clothes, a bag, or shoes (S100). As a cutting method, in addition to the above-described function modeling, a solid is expressed by a solid model such as a function expression, and a set shape such as a sum operation or a difference operation is applied to two solids to express a solid shape including a concave surface. You may do it. Thereby, a reference polyhedron approximating the shape of the target solid is obtained.

  Next, the three-dimensional shape data generation apparatus 100 smoothes the surface shape of the reference polyhedron (S110). In addition to rounding the corners of the reference polyhedron, the smoothing process includes inflating and indenting each surface of the reference polyhedron. This smoothing process brings the reference polyhedron closer to the target solid.

  Finally, the three-dimensional shape data generation apparatus 100 expresses the smoothed three-dimensional shape of the reference polyhedron with a polygon model or the like and develops it on the pattern (S120). The paper pattern data makes it possible to produce industrial products.

  FIG. 3 is a flowchart showing a detailed procedure of the smoothing process S110 shown in FIG.

  The discrimination point generator 12 generates a discrimination point k near the surface of the reference polyhedron (S10). The occupation rate calculation unit 14 initializes a variable i for counting the number of neighboring points determined to be inside the reference polyhedron and a variable N for counting the total number of generated neighboring points to 0 ( S12).

  The occupancy rate calculation unit 14 randomly generates neighboring points inside the neighboring sphere with the radius r centered on the discrimination point k (S14). The occupancy rate calculation unit 14 determines whether or not the generated neighboring point is inside the reference polyhedron (S16). If the neighboring point is inside the reference polyhedron (Y in S16), the counter i is incremented by one. (S18) If the neighboring point is not inside the reference polyhedron, the counter i is not incremented.

  The occupation rate calculation unit 14 increments the total number N of neighboring points by 1 (S20), and obtains the occupation rate p by i / N (S22). The occupation rate calculation unit 14 determines whether or not the obtained value of the occupation rate p has converged (S24). For this purpose, the occupancy rate calculation unit 14 saves a history of the values of the occupancy rate p obtained while randomly generating neighboring points inside the nearby sphere, and occupies the rate p based on the time change of the occupancy rate p. Determine whether has converged. When the fluctuation range of the occupation rate becomes smaller than a predetermined level, it is determined that the occupation rate p has converged.

  If it is determined that the occupancy rate p has not yet converged (N in S24), the process returns to step S14, and further neighboring points are generated inside the nearby sphere, and the occupancy rate p is updated (S14 to S22).

  When it is determined that the occupancy rate p has converged (Y in S24), the effective determination point determination unit 20 checks whether the occupancy rate p is greater than or equal to the determination threshold value t (S26).

  When the occupation rate p is equal to or greater than the determination threshold t (Y in S26), the effective determination point determination unit 20 determines that the determination point k is included in the target solid (S28), and uses the determination point k as an effective determination point. This is stored in the effective discrimination point storage unit 44.

  When the occupation ratio p is smaller than the determination threshold t (N in S26), the effective determination point determination unit 20 determines that the determination point k is not included in the target solid (S30), and the determination point k is stored as an effective determination point. Not stored in part 44.

  When the user instructs the end of the smoothing process (Y in S32), this procedure ends. If the smoothing process is not yet completed (N in S32), the process returns to step S10, and a new discrimination point is set near the reference polyhedron surface or the already smoothed polyhedron surface, and the same process is repeated.

  FIG. 4 is a diagram for explaining discrimination points and neighboring spheres provided near the surface of the reference polyhedron.

  Assume that the discrimination point 220a is provided outside the surface 200 of the reference polyhedron (the lower side is inside the reference polyhedron and the upper side is outside the reference polyhedron). The determination threshold t is assumed to be 0.5. Considering the neighboring sphere 210a having a radius r centered on the discrimination point 220a, the volume of the neighboring sphere 210a (the portion 230a indicated by hatching) included inside the reference polyhedron is smaller than half of the total volume. Therefore, since the occupation rate p is smaller than 0.5 and smaller than the determination threshold t, it is determined that the determination point 220a is not included in the target solid, that is, the determination point 220a is invalid. Hereinafter, the discrimination points determined to be invalid are indicated by white circles.

  When the discriminant point 220b is provided on the surface 200 of the reference polyhedron, exactly half of the neighboring sphere 210b centered on the discriminant point 220b (the portion 230b shown by hatching) is included inside the reference polyhedron. Therefore, since the occupation ratio p is 0.5 and is equal to the determination threshold t, it is determined that the determination point 220b is included in the target solid, that is, the determination point 220b is valid. Hereinafter, the discrimination points determined to be valid are illustrated by black circles.

  When the determination point 220c is provided on the inner side of the surface 200 of the reference polyhedron, more than half of the neighboring sphere 210c centered on the determination point 220c (the portion 230c indicated by hatching) is included in the reference polyhedron. Therefore, since the occupation rate p is greater than 0.5 and greater than the determination threshold t, it is determined that the determination point 220c is included in the target solid, that is, the determination point 220b is valid.

  In the example of FIG. 4, since the discrimination point is generated in the vicinity of the flat surface of the reference polyhedron, if the judgment threshold t is 0.5, the surface shape does not swell or dent. However, if a discrimination point is generated in a non-planar portion of the reference polyhedron, for example, in the vicinity of a corner or a dent, the surface shape is inflated or dent.

  FIGS. 5A to 5C are diagrams for explaining discrimination points and neighboring spheres provided in the vicinity of the corners of the reference polyhedron. In this example, a discrimination point is generated near the corner (vertex) of the reference polyhedron. In this example, it is assumed that the determination threshold t is 0.5.

  In FIG. 5A, a discrimination point 220a is provided near the corner of the reference polyhedron and outside the surface 200 of the reference polyhedron. Considering the neighboring sphere 210a centered on this discrimination point 220a, the volume of the neighboring sphere 210a (the portion 230a indicated by hatching) included in the reference polyhedron is smaller than half of the total volume. Therefore, since the occupation rate p is smaller than 0.5, it is determined that the discrimination point 220a is outside the target solid, that is, invalid.

  In FIG. 5B, a discrimination point 220b is provided near the corner of the reference polyhedron and inside the surface 200 of the reference polyhedron. Considering the neighborhood sphere 210b centered on this discrimination point 220b, the volume of the neighborhood sphere 210b (the portion 230b shown by hatching) included in the reference polyhedron is still smaller than half of the total volume. Therefore, the occupation rate p is smaller than 0.5, and it is determined that the discrimination point 220b is outside the target solid, that is, invalid.

  In FIG. 5C, a discrimination point 220c is provided on the inner side of the surface 200 of the reference polyhedron as compared with FIG. 5B. In this case, more than half of the neighboring sphere 210c centered on the discrimination point 220c (the portion 230c shown by diagonal lines) is included in the reference polyhedron. Therefore, the occupation ratio p is greater than 0.5, and it is determined that the discrimination point 220b is inside the target solid, that is, is valid.

  In the example of FIGS. 5A to 5C, since the effective determination point determined to be included in the target solid is present inside the reference polyhedron, the angle of the reference polyhedron is recessed to the position of the effective determination point, The corners will be rounded off.

  FIG. 6 is a diagram for explaining effective discrimination points at the corners of the reference polyhedron. Here again, it is assumed that the determination threshold t is 0.5. In the vicinity of the corner of the reference polyhedron, the effective discrimination point exists inside the corner. In the flat surface of the reference polyhedron, the effective discrimination point exists on that surface. Therefore, although the flat surface of the reference polyhedron is not cut, an effective discrimination point is provided near the corner as shown by the dotted line in FIG.

  FIGS. 7A and 7B are diagrams for explaining the change in the position of the effective discrimination point when the radius of the neighboring sphere is changed near the corner of the reference polyhedron. FIG. 7A shows a case where the radius of the nearby sphere is reduced, and the position of the effective discrimination point approaches the corner. FIG. 7B shows a case where the radius of the nearby sphere is increased, and the position of the effective discrimination point moves away from the corner. In this way, the corner scraping can be changed by changing the radius of the neighboring sphere.

  FIGS. 8A and 8B are diagrams for explaining the change in the position of the effective discrimination point when the occupancy determination threshold is changed near the corner of the reference polyhedron. FIG. 8A shows a case where the determination threshold t of the occupation ratio p is smaller than 0.5, and the volume of the neighboring sphere included in the reference polyhedron may be smaller than half. Therefore, the effective determination point is a dotted line. As shown, it moves to a position away from the surface 200 of the reference polyhedron.

  FIG. 8B shows a case where the determination threshold t of the occupation ratio p is larger than 0.5, and the volume of the neighboring sphere included in the reference polyhedron needs to be larger than half. As indicated by the dotted line, the position moves to a position inside the surface 200 of the reference polyhedron.

  Note that, if the determination threshold value t is changed in the middle, a step is created, so that the determination threshold value t is set constant in principle. When changing the threshold value, it is preferable to provide a threshold value transition region and continuously change the determination threshold value t in the threshold value transition region.

  FIG. 9 is a diagram for explaining how the radius of the neighboring sphere is changed in accordance with the complexity of the shape of the surface 200 of the reference polyhedron. For complex and fine surface shapes such as sharp and sharp corners, the radius of the neighboring sphere is set small as indicated by reference numerals 210a and 210b. This is because the corner cannot be sharpened if a nearby sphere having a large radius with respect to the sharp corner is set. For a complicated and finely shaped surface shape, the radius of the neighboring sphere needs to be made sufficiently small in accordance with the fineness of the shape. This is because when the radius of the nearby sphere is small, the corners are cut off less and the original polyhedral shape can be well preserved.

  On the other hand, for a surface shape that is not very finely shaped, the radius of the nearby sphere is set large, as indicated by reference numeral 210c. For a rough shape, the surface can be greatly sharpened by increasing the radius of the neighboring sphere accordingly.

  From the standpoint of preserving the original shape as much as possible, it is possible to start with a smaller radius of the nearby sphere, and to repeatedly smooth the reference polyhedron while gradually increasing the radius while observing the roundness of the corners. preferable. Here, the roundness of the corner can be evaluated by the curvature.

  FIGS. 10A to 10C are diagrams for explaining a polygon obtained by connecting a plane for generating a discrimination point and an effective discrimination point.

  FIGS. 10A and 10B show the reference polyhedron cut along a plane perpendicular to the z-axis, that is, the xy plane. The solid line indicates the surface of the reference polyhedron. A discrimination point is generated near the surface of the reference polyhedron to obtain an effective discrimination point. A state in which a corner is cut off by an effective discrimination point is indicated by a dotted line.

  In FIG. 10A, the determination point is generated on the xy plane with z = 1 fixed. In FIG. 10B, the determination point is generated on the xy plane with z = 2 fixed. For this reason, only the x-coordinate value and the y-coordinate value of the discrimination point need only be randomly generated, and the discrimination point generation process can be simplified.

  FIG. 10C shows a set of effective discrimination points obtained by the xy plane cut by z = 1 (reference numeral 250a), a set of effective discrimination points obtained by the xy plane cut by z = 2 (reference numeral 250b), z. A set of effective discrimination points (reference numeral 250c) obtained on the xy plane cut by = 3 is shown. It is shown that a rectangular polygon is generated by connecting effective discrimination points between these cut planes.

  In this way, the effective discrimination points are obtained on the xy plane while discretely changing the z coordinate value, and the polygons are generated by connecting the effective discrimination points on the xy planes in the z-axis direction, so that the three-dimensional shape of the target solid is obtained. Shape data can be represented by a polygon model. When generating a polygon model, the feature points of the original reference polyhedron may be used as the vertices of the polygons as appropriate, in addition to generating polygons having the effective discrimination points as vertices.

  As a method for selecting discriminant points, it is generally considered that a random number is uniformly generated inside a rectangular parallelepiped (a cuboid slightly larger than that if bulging is considered) before cutting out the polyhedron, This makes the calculation amount enormous. Therefore, when pattern paper development is assumed, as shown in FIGS. 10A to 10C, the reference polyhedron is cut into circles at equal intervals in a certain direction such as the height direction and the depth direction. It is advantageous in terms of calculation amount to generate a discrimination point in the cut plane. In addition, when a three-dimensional shape is represented by a rectangular polygon having apexes positioned at a predetermined interval in a certain direction such as a height direction, there is an advantage that the polygon model can be easily developed on a pattern.

  As described above, according to the three-dimensional shape data generation apparatus 100 of the present embodiment, a target three-dimensional shape can be given as a polyhedron, and can be rounded as much as possible along the shape. Since the final shape data is determined as a set of valid discrimination points, a polygon mesh is created by connecting adjacent valid discrimination points, and the final form is displayed in three-dimensional form, or expanded into pattern data can do.

  In the three-dimensional shape data generation apparatus 100, the user repeatedly adjusts parameters such as the radius of the nearby sphere and the determination threshold for the occupancy while repeating the smoothing process while confirming the roundness of the corner on the display. A three-dimensional shape can be created. While the user can realize the intended curved surface shape while checking the shape deformation result, a highly interactive system can be provided.

  In the present embodiment, a reference polyhedron that approximates a target three-dimensional shape is given by function expression, and smoothing processing is performed based on the reference polyhedron, so that the accumulation of calculation errors is small. Therefore, the method for generating three-dimensional shape data according to the present embodiment is particularly effective in a field where accuracy is required, such as patterning for industrial products.

  The present invention has been described based on the embodiments. The embodiments are exemplifications, and it will be understood by those skilled in the art that various modifications can be made to combinations of the respective constituent elements and processing processes, and such modifications are within the scope of the present invention. .

  In the embodiment, the polygon model that approximates the target solid is generated by performing the smoothing process by starting from the reference polyhedron obtained by cutting the rectangular parallelepiped with a plane, but the polygon generated by CG is used as the reference polyhedron for performing the smoothing process. A model may be used.

It is a block diagram of a three-dimensional shape data generation apparatus. It is a flowchart which shows the rough flow of the production | generation procedure of the three-dimensional shape data by a three-dimensional shape data generation apparatus. It is a flowchart which shows the detailed procedure of the smoothing process shown in FIG. It is a figure explaining the discrimination | determination point provided in the surface vicinity of a reference polyhedron, and a nearby sphere. It is a figure explaining the discrimination | determination point provided in the vicinity of the corner | angular of a reference polyhedron, and a nearby sphere. It is a figure explaining the effective discrimination point in the corner of a reference polyhedron. It is a figure explaining the change of the position of the effective discrimination | determination point when the radius of a nearby sphere is changed near the corner of the reference polyhedron. It is a figure explaining the change of the position of the effective discrimination | determination point at the time of changing the determination threshold value of an occupation rate in the corner vicinity of a reference polyhedron. It is a figure explaining a mode that the radius of a neighborhood sphere is changed according to the complexity of the surface shape of a standard polyhedron. It is a figure explaining the polygon obtained by connecting the plane which produces | generates a discrimination | determination point, and an effective discrimination | determination point.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Solid model production | generation part, 12 Discriminant point production | generation part, 14 Occupancy rate calculation part, 16 Surface curvature calculation part, 18 Sphere radius adjustment part, 20 Effective discrimination | determination point determination part, 22 Surface shape deformation part, 24 Inside / outside determination part, 26 Determination Threshold adjustment unit, 28 three-dimensional data generation unit, 30 pattern paper development unit, 40 reference polyhedron storage unit, 42 inclusion / exterior inclusion polyhedron storage unit, 44 effective discrimination point storage unit, 46 polygon information storage unit, 48 pattern paper data storage unit, 100 3D shape data generator.

Claims (11)

A method of generating three-dimensional shape data obtained by smoothing a surface shape of a reference polyhedron approximating a target three-dimensional solid shape,
A discrimination point generating step for generating a discrimination point near the surface of the reference polyhedron;
An occupancy ratio that generates a nearby point by a random number in a nearby sphere with a predetermined radius centered on the discrimination point, and calculates an occupancy ratio that indicates a ratio of the nearby point in the nearby sphere included in the reference polyhedron A calculation step;
When the occupancy is equal to or higher than a predetermined determination threshold, the determination point is determined to be included in the target three-dimensional solid, and when the occupancy is smaller than the determination threshold, the determination point is the target A determination step of determining that the three-dimensional solid is not included in
A shape data generation step for generating three-dimensional shape data representing the target three-dimensional solid by a polygon having the determination point determined to be included in the target three-dimensional solid by the determination; A method for generating three-dimensional shape data, comprising:   By repeating the determination point generation step, the occupancy rate calculation step, and the determination step for the reference polyhedron after being deformed by the determination point determined to be included in the target three-dimensional solid, The method of generating three-dimensional shape data according to claim 1, wherein the surface shape of the reference polyhedron is smoothed in stages.   The occupancy rate calculating step evaluates the degree of convergence of the occupancy rate as the number of generated neighboring points increases, and terminates the generation of the random number when the degree of convergence of the occupancy rate reaches a predetermined level. The three-dimensional shape data generation method according to claim 1 or 2, characterized in that   4. The three-dimensional image according to claim 1, further comprising a step of reducing a radius of the neighboring sphere set in the vicinity of the surface as the complexity of the surface of the reference polyhedron increases. Shape data generation method.   Providing an inclusion polyhedron included inside the reference polyhedron, and reducing the determination threshold when the determination point determined to be included in the target three-dimensional solid by the determination is inside the inclusion polyhedron The method for generating three-dimensional shape data according to claim 1, further comprising:   Providing an envelope polyhedron including the reference polyhedron on the inside, and increasing the determination threshold when the determination point determined to be included in the target three-dimensional solid by the determination is outside the envelope polyhedron; The three-dimensional shape data generation method according to any one of claims 1 to 5, further comprising:   In the process of repeating the discrimination point generation step, the occupancy rate calculation step, and the determination step, the degree of roundness of the corners of the reference polyhedron is evaluated by curvature, and the radius of the neighboring sphere is increased to increase the degree of roundness of the corners. The method for generating three-dimensional shape data according to any one of claims 1 to 6, wherein the three-dimensional shape data generation method according to any one of claims 1 to 6 is performed.   Each surface of the reference polyhedron is represented by a plane equation, and the discrimination point generation step uses the means for detecting a point on the plane represented by the plane equation to determine the discrimination near the surface of the reference polyhedron. The method for generating three-dimensional shape data according to claim 1, wherein a point is generated.   The three-dimensional shape according to any one of claims 1 to 8, further comprising a deforming step of deforming a surface shape of the reference polyhedron according to a discrimination point determined to be included in the target three-dimensional solid. Data generation method. An apparatus for generating three-dimensional shape data obtained by smoothing a surface shape of a reference polyhedron approximating a target three-dimensional solid shape,
A discrimination point generator for generating discrimination points near the surface of the reference polyhedron;
An occupancy ratio that generates a nearby point by a random number in a nearby sphere with a predetermined radius centered on the discrimination point, and calculates an occupancy ratio that indicates a ratio of the nearby point in the nearby sphere included in the reference polyhedron A calculation unit;
When the occupancy is equal to or higher than a predetermined determination threshold, the determination point is determined to be included in the target three-dimensional solid, and when the occupancy is smaller than the determination threshold, the determination point is the target An effective discrimination point determination unit that determines that the three-dimensional solid is not included in
A three-dimensional data generation unit that generates three-dimensional shape data representing the target three-dimensional solid by a polygon having the determination point determined to be included in the target three-dimensional solid by the determination; A three-dimensional shape data generating apparatus comprising: A program for causing a computer to execute a process of generating three-dimensional shape data obtained by smoothing a surface shape of a reference polyhedron approximating a target three-dimensional solid shape,
A discrimination point generating step for generating a discrimination point near the surface of the reference polyhedron;
An occupancy ratio for generating an occupancy ratio indicating a ratio in which the neighboring point in the neighboring sphere is included in the reference polyhedron by generating a neighboring point by a random number in a neighboring sphere having a predetermined radius centered on the discrimination point A calculation step;
When the occupancy is greater than or equal to a predetermined determination threshold, the determination point is determined to be included in the target three-dimensional solid, and when the occupancy is smaller than the determination threshold, the determination point is the target A determination step of determining that the three-dimensional solid is not included in
Generating, in a computer, three-dimensional shape data representing the target three-dimensional solid from a polygon whose vertex is the discrimination point determined to be included in the target three-dimensional solid by the determination A program characterized by letting

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