JP4241778B2 - Surface element distortion detection apparatus, surface element distortion detection method, and program - Google Patents

Description

  The present invention relates to design support technology.

Morphing is known as a processing technique for smoothly changing and deforming image data. Furthermore, a system in which this morphing technology is applied to a three-dimensional CAD (Computer Aided Design) is also known. In such a system, a user operation is accepted by an operating means such as a pointing device, and the three-dimensional model is deformed. Such a three-dimensional model is generally formed by combining polygons, patches (polygons themselves or a combination of a plurality of polygons), curved surfaces called surfaces, and the like.

  In general, in a three-dimensional CAD, after a three-dimensional model is created, the three-dimensional model is decomposed into a plurality of meshes (for example, a tetra mesh) for various analyses. Then, the analysis is performed, but if the analysis result is not satisfactory, it may be necessary to change the three-dimensional model. In this case, if the original three-dimensional model is changed by three-dimensional CAD, decomposition into a mesh is necessary again, and man-hours increase. Therefore, a three-dimensional shape is deformed by morphing in a state of being decomposed into a mesh.

  However, in the CAD system to which the conventional morphing technology is applied, the surface of the shape data, that is, the polygon or patch constituting the three-dimensional shape is wrinkled, sagging, or distorted as a result of the deformation processing of the three-dimensional shape data. In some cases, distortion of the shape occurred. Such distortion of the shape deteriorates the appearance and quality of the three-dimensional shape. In particular, when performing analysis by CAE (Computer Aided Engineering) using the deformed three-dimensional shape, it is necessary to correct and maintain the surface, which may increase man-hours.

As a technique related to such a three-dimensional shape deformation operation, for example, the following Patent Document 1 is known.
JP-A-11-195054 JP 2005-275596 A JP 2000-172742 A

  However, since the above-described conventional technique assumes a planar patch or polygon, the deformation limit of the polygon constituting the three-dimensional shape or the polygon included in the patch is exceeded with the deformation of the three-dimensional shape. When it is deformed, the distortion may not be recognized. For example, in the case of a curved surface in which a plurality of normal vectors are originally defined in a patch (or polygon), for example, the conventional technique may not be able to grasp the distortion of the patch itself or the polygon itself. Further, it may not be possible to detect that a deformation operation exceeding the expansion limit has been performed.

  An object of the present invention is to detect the expansion or contraction limit of a patch or a polygon in a deformation operation of a patch or polygon defined by a plurality of normal vectors and to form a shape such as a wrinkle or sagging of the patch or polygon. It is to provide a technique for reducing the occurrence of distortion.

The present invention employs the following means in order to solve the above problems. That is, the present invention provides a surface element for detecting a distortion of the surface element created by such a design support device that forms the surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model. A distortion detection apparatus, a unit for obtaining respective normal vectors at different positions on a surface element, a unit for calculating a value indicating a relative relationship between the adjacent normal vectors, and a relative of the adjacent normal vectors A surface element distortion detection device comprising: a surface element distortion generation determination unit that determines that distortion has occurred in the surface element when a value indicating a relationship exceeds a predetermined value set in advance. is there.

  According to the present invention, respective normal vectors are obtained at different positions on the surface element, a value indicating a relative relationship between the adjacent normal vectors is calculated, and a value indicating the relative relationship between the adjacent normal vectors is calculated. When it exceeds a predetermined value set in advance, it is determined that distortion has occurred in the surface element. Therefore, it can be quantitatively determined whether or not distortion exceeding the limit has occurred in the surface element.

  In that case, it may further comprise means for displaying the surface element in which the distortion has occurred. Thereby, generation | occurrence | production of distortion can be alert | reported to a user and a user's attention can be called.

  When the surface element formed by a plurality of the surface elements is determined to have no distortion by the surface element distortion occurrence determination means, the surface element adjacent to the surface element and the normal vector of the surface element A means for calculating a value indicating a relative relationship with the normal vector of the surface element, and a value indicating the relative relationship between the normal vector of the surface element and the normal vector of the surface element adjacent to the surface element is set to a predetermined value. And a means for determining that the surface data is distorted when the value is exceeded.

  With such a configuration, for example, even when it is determined that no distortion has occurred in the surface element, the occurrence of distortion can be quantitatively determined from the relationship with the adjacent surface element.

  The relative relationship is preferably an angle between adjacent normal vectors. This is because the deformation on the surface element can be detected by determining the angle between the normal vectors.

  Further, the present invention provides a surface element for detecting distortion of the surface element created by such a design support device that forms a surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model. A distortion detection device, wherein surface data formed by collecting a plurality of the surface elements is extracted by a ridge line extraction unit that extracts a ridge line that is a boundary line between the surface elements, and the ridge line extraction unit. Curvature calculation means for calculating the curvature of the ridge line, at least one of the case where the curvature calculated by the curvature calculation means exceeds a predetermined value set in advance, and the case where the change in curvature exceeds a predetermined limit In this case, ridge line distortion determination means for determining that distortion has occurred in the ridge line may be provided.

  That is, in the present invention, a ridge line that is a boundary line between the surface elements is extracted, the curvature of the extracted ridge line is calculated, and when the curvature exceeds a predetermined value set in advance, and the curvature When at least one of the cases where the change exceeds a predetermined limit, it is determined that distortion has occurred in the ridgeline. For this reason, it can be quantitatively determined whether or not distortion has occurred at the boundary between the surface elements. Here, the change in curvature means, for example, a change in the direction of curvature on one ridge line, a change in the magnitude of curvature, and the like. Further, the change in curvature also means, for example, the change in the number of inflection points on the ridgeline and the number (for example, three or more). Further, the ridge line distortion determination means may record the curvature for each ridge line one by one, and the difference in curvature between the previous determination time point and the current time point may be used as the change in curvature.

Further, the present invention provides a surface element for detecting distortion of the surface element created by such a design support device that forms a surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model. A distortion detection device, a means for extracting vertices from surface data formed by collecting a plurality of the surface elements, and a neighboring ridge line extracting a ridge line that is a boundary line between the surface elements in the vicinity of the vertices And a projection unit that forms a plane from the normal vector of the surface data at the vertex and a tangent vector of the ridge line in the vicinity of the vertex, and projects the ridge line on the formed plane; Projected curvature calculating means for calculating the curvature of the ridge line on the plane projected by the above, and when the curvature calculated by the projected curvature calculating means exceeds a predetermined value set in advance, and before In the case of at least one of the case where the change in curvature exceeds a predetermined limit, the ridgeline distortion determination means determines that distortion has occurred in the ridge, it may be those comprising a.

  According to the present invention, the ridgeline is projected on a plane, the curvature of the ridgeline on the projected plane is calculated, and when the curvature exceeds a predetermined value, and the change in curvature is a predetermined Since it is determined that distortion has occurred in the ridge line in at least one of cases where the limit is exceeded, distortion of the ridge line can be quantitatively determined.

  The present invention may be a program for causing a computer to execute any one of the processes described above. Further, the present invention may be a computer-readable recording medium in which such a program is recorded, for example, a CD-ROM, a DVD, a flash memory card, or the like. Further, the present invention may be realized as a method in which a computer executes such processing.

  According to the present invention, in a deformation operation of a three-dimensional model composed of patches or polygons in which a plurality of normal vectors are defined, the expansion limit of the patch or polygon is detected, and the shape of the patch or polygon such as wrinkles or sagging is detected. Generation of distortion can be reduced.

  A design support apparatus according to the best mode for carrying out the present invention (hereinafter referred to as an embodiment) will be described below with reference to the drawings. The configuration of the following embodiment is an exemplification, and the present invention is not limited to the configuration of the embodiment.

<Outline of the invention>
The design support apparatus accepts a user operation by an operating means such as a pointing device for a three-dimensional model constituted by polygons or patches combining polygons, and deforms (morphs) the three-dimensional model. Polygons constituting the three-dimensional model are called curved polygons, and have normal vectors in a plurality of directions within the polygon surface.

  FIG. 1 shows an example in which a three-dimensional model composed of curved polygons is modified. Distortion occurs in a circle indicated by a reference C1 in FIG. FIG. 2 shows an example in which the curved polygon of FIG. 1 is divided into meshes. In this example, the curved polygon is configured by combining a plurality of triangular meshes. Such a curved surface is known as a Bezier curved surface, for example.

  A Bezier curve is a polynomial curve defined according to a plurality of points (a series of points) called control points, and a Bezier curved surface is a curved surface defined based on a plurality of points arranged two-dimensionally. In this embodiment, a unit constituting a curved surface is called a patch, and the patch is composed of one or a plurality of curved polygons. That is, a plurality of curved polygons (for example, a cubic triangular Bezier curved surface) may be collected to form a patch.

At the time of deformation of a solid model covered with such a curved polygon, this design support device
Monitor multiple normal vectors in each curved polygon. Then, the value of the angle between the adjacent normal vectors and the rate of change of the angle between the adjacent normal vectors caused by the three-dimensional model deformation (the ratio of the changed angle to the original angle) are obtained. When the angle between adjacent normal vectors exceeds a predetermined value, and when the rate of change in angle between adjacent normal vectors exceeds a predetermined value, it is determined that the surface of the curved polygon is distorted. To do.

  FIG. 3 shows an example of a three-dimensional model using triangular patches. In FIG. 3, a polyhedron composed of triangular planes is shown. In FIG. 3, triangular patches are displayed in a plane for simple display. However, in general, a patch or a curved polygon is a curved surface defined by a polynomial on the basis of control points, and thus actually has a plurality of normal lines in each triangle in FIG. In FIG. 3, the normal line on the curved polygon is indicated by an arrow.

  The design support apparatus monitors the normal vector in such individual curved polygons and detects the occurrence of distortion of the curved polygons.

  Furthermore, this design support apparatus confirms that each polygon itself has no distortion as a result of monitoring the normal vector, and then in the curved polygon to be noticed and the curved polygon adjacent to the curved polygon, Each representative normal vector is selected, and the occurrence of distortion is similarly detected between two adjacent curved polygons.

  That is, when the angle between normal vectors belonging to two adjacent curved polygons exceeds a predetermined value, and when the rate of change in angle between adjacent normal vectors exceeds a predetermined value, It is determined that the surface is distorted.

  Furthermore, a sample point of interest is set on the curved polygon, a ridge line passing through the sample point or the vicinity of the sample point is extracted, and the curvature of the ridge line is obtained. Then, when the curvature exceeds a predetermined value, it is determined that distortion has occurred on the surface of the curved polygon. Here, the ridge line is a boundary line between the curved polygon and the curved polygon.

  In this way, when the distortion of the curved polygon is detected during the deformation of the three-dimensional shape, the design support apparatus displays a warning indicating that the distortion of the curved polygon has been detected. By this warning, the user recognizes that the distortion has occurred and stops the deformation of the three-dimensional model. Then, the user obtains a deformed three-dimensional model with no distortion of the curved polygon by changing the procedure of the deforming operation.

  Alternatively, the user may continue the deformation work after recognizing that the distortion has occurred, and correct the portion where the distortion of the curved polygon has occurred after completing the work.

  The above functions are realized by a computer program executed on the computer as one function of the CAD system realized on the computer. Here, the computer includes a CPU (Central Processing Unit), a memory, an input / output interface, an external storage device connected to the input / output interface, a display device, an input device, a communication device, and the like.

  The external storage device is, for example, a hard disk drive device. The external storage device includes a drive device for a removable storage medium, for example, a drive device such as a CD-ROM (Compact Disc Read Only Memory) or a DVD (Digital Versatile Disk). Further, a flash memory card input / output device may be used as an external storage device.

  The display device is, for example, a CRT (Cathode Ray Tube), a liquid crystal display, or the like. The input device is a keyboard, a pointing device, or the like. Examples of the pointing device include a mouse, a joystick, a touch panel, an electrostatic flat pointing device, a stick-shaped pointing device, and the like. The communication device is, for example, a LAN board.

<Data structure of the curved surface of the solid model>
4 to 10 show an example of the data structure when the design support apparatus defines the curved surface of the three-dimensional model. FIG. 4 shows a cubic Bezier curve. In general, a curve defined by a polynomial based on n + 1 control points is referred to as an nth-order Bezier curve. The n-th order Bezier curve is given by the following general formula (1). Here, Qn is a position vector of the control point, t is a parameter, and P is a position vector on the nth-order Bezier curve.

For example, the cubic Bezier curve P is given by P = (1-t) ³ Q0 + 3t (1-t) ² Q1 + 3t ² (1-t) Q2 + t ³ Q3.

  FIG. 5 shows an example of a cubic Bezier curved surface using a quadrangular patch. In general, a Bezier curved surface constituted by (n + 1) × (n + 1) arrayed control points is called an nth-order Bezier curved surface. The nth-order Bezier curved surface by the quadrangular patch is given by the following general formula (2). Here, Qij is a position vector of the control point, u and v are parameters, and P is a position vector on the nth-order Bezier surface.

  A cubic Bézier curved surface with a quadrangular patch has 16 control points (4 internal control points). The surface of the three-dimensional model can be formed by connecting such square Bezier curved surfaces.

  FIG. 6 shows the arrangement of the internal control points with the tertiary square patch. FIG. 7 shows the arrangement of the internal control points with the quaternary square patch. In the case of a square patch, the internal control points increase to 4, 9, 16... As the order increases to 3rd order, 4th order, 5th order,.

  FIG. 8 shows an example of a cubic Bezier curved surface using triangular patches. An n-order Bezier curved surface by a triangular patch is given by the following general formula (3). Here, Qijk is a position vector of the control point, and u, v, and w are parameters.

  A cubic Bézier curved surface with a triangular patch has 10 control points (one internal control point). The surface of the three-dimensional model can be formed by connecting such triangular Bezier curved surfaces.

  FIG. 9 shows the arrangement of the internal control points with the tertiary triangular patch. FIG. 10 shows the arrangement of the internal control points with the quaternary triangular patch. In the case of a triangular patch, the internal control points increase to 1, 3, 6, 9... As the order increases to 3rd order, 4th order, 5th order, 6th order,.

  The design support apparatus uses an n-order Bezier curved surface (for example, the triangular cubic Bezier curved surface shown in FIG. 6) as a curved polygon (also referred to as a patch), and configures a three-dimensional model by combining such curved polygons. Note that a patch may be configured by combining a plurality of curved polygons, and a three-dimensional model may be configured by such a patch.

<Distortion detection function>
This design support device is able to match / disagree normal angle in curved polygon, change rate of normal angle, match / mismatch normal between multiple curved polygons near sample point, The occurrence of distortion is detected from the rate of change of the angle of and the rate of change of curvature at the sample point or the ridgeline in the vicinity of the sample point. In the present embodiment, a boundary line between two or more curved polygons is called a ridge line.
(1) Normal match check in curved polygons For a single curved polygon, all of the normal vectors inside it match, or the difference in angle between the normal vectors is predetermined. Is often within the reference value (E1).

  Therefore, the present design support device calculates normal vectors at a plurality of positions in each curved polygon, and determines whether or not the angle between the normal vectors is within a predetermined reference value (E1). If the position vector on the curved polygon is S (u, v), the normal vector at that position is given by the following equation (4).

That is, the position vector on the curved polygon (surface shape) may be partially differentiated in the line element u direction and the line element v direction, respectively, to obtain the outer product. Furthermore, the angle between the normal vectors may be obtained from the inner product of the normal vectors and the inverse trigonometric function. Thereby, the occurrence of distortion in the curved polygon is detected.
(2) Normal line matching check between curved polygons Even when the occurrence of distortion in the curved polygon is not detected, distortion may occur due to the positional relationship between the curved polygons. Normally, for adjacent curved polygons that cover the surface of a three-dimensional model, the normal vectors of the curved polygons match at locations other than the portion where the slope changes discontinuously on the ridgeline (the portion where the surface is bent). In many cases, the difference in angle between normal vectors is within a predetermined reference value (E1). On the other hand, in a portion where the slope changes discontinuously on the original ridgeline, the difference in angle between the normal vectors of the respective curved polygons is often greater than the reference value (E2) greater than the reference tsu E1. Therefore, an empirical rule related to a general three-dimensional shape is incorporated into the processing on the computer.

  FIG. 11 shows the relationship between the designated sample point Pa and the normal vectors N1-N5 of the plurality of curved polygons 11-15 existing around it. In this case, the normal vector of the sample point Ps is given by the following formula 5.

Equation 5 shows the weight addition of a plurality of normal vectors. The weight may be determined by the area of each patch, for example. Also, the weight may be 1. The generation of distortion is detected depending on whether or not the angle between these normal vectors N1-N5 and the normal vector NA of the sample point PA is in the range of the reference value E1 to the reference value E2. .
(3) Normal line coincidence check on ridge lines On the ridge line located at the boundary between two curved polygons, a plurality of curved polygon normals are obtained, and whether or not the angle between the normal lines is within a predetermined reference value (E1). Determine. The processing procedure is the same as (1) except that the position for obtaining the normal is on the ridge line.
(4) Curvature analysis of ridgeline The curvature of a ridgeline is calculated | required on the ridgeline which is a boundary line of a curved surface patch. And the curvature of a ridgeline is monitored at the time of deformation | transformation operation, and the point where a curvature is larger than a reference value is detected. Alternatively, a point having a large change in curvature (for example, a point where the inner product in the curvature direction <0, that is, a change greater than an angle of 90 degrees) is detected. That is, as a change in curvature, a change in the direction of curvature on one ridge line may be detected. Moreover, you may detect the change of the magnitude | size on one ridgeline. That is, it is possible to detect a point on the ridge line where the direction of curvature changes significantly or the value of curvature changes extremely greatly. Furthermore, a change in the number of inflection points on the ridge line or the like may be detected, and a ridge line having a predetermined number of inflection points or more may be used as a ridge line in which distortion is detected. Furthermore, the ridge line distortion determination means may record the curvature for each ridge line one by one, and the difference in curvature between the previous determination time and the current time may be used as the change in curvature.

  The curvature can be obtained as the second derivative of the position vector P of the point on the curve. The first derivative P ′ = dP / ds with respect to the length s of the position vector P of the point on the curve is given by the following equation (6). Here, a pea dot (a vector P added with a black circle) represents a time derivative of the vector P. Pedot represents a vector in the tangential direction of the curve, and Equation 6 is a unit vector in the tangential direction.

  When the equation 6 is further differentiated by the length s of the curve, the curvature is obtained. The curvature R = P ″ is expressed by the following formula 7. Here, the P2 dot (the one in which two black circles are added to the top of the vector P) represents the second-order time differentiation (acceleration) of the vector P.

  The curvature R can also be expressed in the following formula 8.

  When the position vector of the point on the curve is P, the relationship between the curvature R = P ″, the speed pea dot, and the acceleration pe two dot can be conceptually shown in FIG. , A tangential vector of the curve, and the curvature P ″ is a direction orthogonal to the tangent.

The acceleration pe-to-dot is obtained for the speed pea dot, and the rectangle 22 is drawn with the speed pea dot as one side and the opposite side passing through the tip of the acceleration pe-dot. In this case, an intersection 26 of a straight line 24 that passes through the tip 21 of the speed peadot and is orthogonal to the diagonal line 23 of the rectangle 22 and a straight line 25 that is perpendicular to the speed peadot drawn from the contact point 20 with the curve of the speed peadot. Ask. In this case, the length from the contact 20 to the intersection 26 is the curvature P ″.
(5) Curvature Analysis of Curved Polygon FIG. 13 is a diagram showing the concept of curvature analysis of a curved polygon. The curved polygon, that is, the patch is configured by one or more Bezier curved surfaces, for example. Unlike edge lines, curved surface polygons cannot perform curvature analysis using general formulas (see Equations 7 and 8). Therefore, in the design support apparatus of the present embodiment, the curvature analysis of the curved polygon is executed by the following procedure.
(A) A region of the three-dimensional model to be analyzed is specified. For example, it is only necessary to select a target analysis region by a user operation.
(B) Extract vertices of curved polygons included in the analysis region, for example, external control points (control points on ridge lines) of Bezier curved surfaces.
(C) At each vertex, a normal vector N (referred to as normal Nk when distinguished for each vertex) is obtained.
(D) A ridgeline L connected to each vertex (referred to as ridgeline Li when distinguished for each ridgeline) is obtained. Moreover, you may select all the ridgelines of predetermined distance from the vertex. Then, a tangent line T of the ridge line L in the vicinity of the vertex (referred to as tangent line Ti when distinguished for each ridge line) is obtained.
(E) The ridge line L is projected onto the plane formed by the normal line N of the vertex and the tangent line T of the ridge line L. Thus, the ridge line L in the three-dimensional space becomes a projection line on the plane. The curvature on the projection line is calculated by Equation 7 or Equation 8. Furthermore, the maximum value R of the curvature on the projection line (referred to as the maximum value Ri of the curvature when distinguished for each ridgeline) is obtained.
(F) Of such maximum values of curvature, (c) to (e) are repeated for all vertices connected to each vertex for all vertices in the analysis region. As a result, the maximum curvature in the analysis region is obtained and used as the curvature of the curved polygon. The occurrence of distortion is determined by whether or not the curved polygon exceeds a predetermined reference value E3. It should be noted that the curvature Ri obtained by repeating (c) to (e) may be displayed as a histogram to display the occurrence of distortion.

<Processing flow>
FIG. 14 shows a processing flow of the deformation operation processing of the three-dimensional model by this design support apparatus. These processes are realized as a computer program executed on the CPU of the design support apparatus.

  In this process, first, the user operates an input device such as a pointing device, and deforms the three-dimensional model on the screen of the display device. The design support device detects a user input through the input device and sequentially transforms the three-dimensional model. That is, morphing is executed (S1).

  In the process of morphing, the design support apparatus executes a distortion occurrence detection process (S2). The CPU of the design support apparatus that executes this process corresponds to the surface element distortion detection apparatus of the present invention. When the distortion is detected, the design support device displays a warning on the display device (S3). In that case, the color of a portion (such as a patch) determined to be distorted may be displayed on the three-dimensional model. Further, in this case, attention may be drawn by outputting a sound from a speaker. The CPU of the design support apparatus that executes this processing corresponds to means for displaying the surface element in which the distortion has occurred in the present invention.

  When the warning is displayed, the user stops the deformation operation and starts the work again (S4). With such a guide of the design support apparatus, the user can create data without distortion such as wrinkles and sagging on the surface (S7).

  However, even when a warning is displayed, the user may continue the work as it is. In this case, the user needs to perform an operation of correcting the stereo model on the screen through the input device in order to reduce the distortion of the stereo model (S6). However, even in that case, the user generally recognizes which position of the stereo model is distorted by the warning in S3, so that the efficiency of the correction work is improved as compared with the conventional case. Through such correction work, the user can create data without distortion such as wrinkles and sagging on the surface (S7).

  FIG. 15 shows details of the distortion occurrence detection process (S2 in FIG. 14). The distortion generation detection process is repeatedly executed along with the deformation of the stereo model when the user executes the deformation operation of the stereo model. Thereby, the distortion of the curved polygon is detected at a predetermined interval.

  In the distortion occurrence detection process, the design support apparatus first executes a normal vector check process in the curved polygon (S21). Next, the design support apparatus executes a normal vector check process between curved polygons (S22). Next, the design support apparatus executes a normal vector check process on the ridge line (S23). Next, the design support apparatus executes a curvature analysis process on the ridgeline (S24). Furthermore, the design support apparatus executes curvature polygon curvature analysis processing (S25).

  The above processes need not be executed in the order of S21 to S25, and the execution order may be changed. Further, it is not necessary to execute all the processes of S21 to S25. Each process may be executed independently at different time intervals.

In addition, in the correction vector check processing in the curved polygon in S21, when there is no distortion (when the normal vectors substantially match in each curved polygon).
The normal vector check process between curved polygons in S22 may be executed. By doing so, after confirming that the normal vectors in the curved polygons match (after confirming that there is a single normal vector in the curved polygons), the normals between the curved polygons Compare vectors.

  FIG. 16 shows details of the normal vector check process (S21 in FIG. 15) in the curved polygon. In this process, the design support apparatus selects a curved polygon that is a distortion detection target (S211). As a method of selecting curved polygons, for example, all curved polygons may be selected. For example, a predetermined number of curved polygons may be selected at random. In addition, for example, a curved polygon included in a region on the stereo model designated by the user with the input device may be selected. In the present embodiment, the curved polygon is defined by identification information for identifying each curved polygon, the number of control points constituting the curved polygon (degree of the curved surface), and the coordinates of the control points.

  Next, the design support apparatus sets sample points in the curved polygon (S212). The sample points may be determined, for example, according to u and v values (for example, user set values or system default parameters) set in advance on the curved polygon S (u, v). . The design support apparatus may designate the control point itself as the sample point.

  Next, the design support apparatus calculates each normal vector at each sample point (S213). The normal vector is calculated according to Equation 4. A CPU (not shown) of the design support apparatus that executes this processing corresponds to means for obtaining a normal vector of the present invention.

  Next, the design support apparatus calculates an angle between the normal vectors (S214). The angle between normal vectors is based on inner product calculation and inverse trigonometric function. The CPU of the design support apparatus that executes this processing corresponds to means for calculating a value indicating the relative relationship of the normal vectors of the present invention.

  Then, the design support apparatus determines whether or not those angles are larger than the reference value E1 (S215). The reference value E1 is, for example, a user-specified value or a system default parameter. The reference value E1 may be set from an empirical value that is acceptable as distortion. The CPU of the design support apparatus that executes this processing corresponds to the surface element distortion occurrence determination means of the present invention.

  If the angle between any of the normal vectors is larger than the reference value E1, the curved polygon is displayed with distortion, and an error code is set together with the identification information of the curved polygon or the coordinates of the control point (S216). ). For example, the display color of the curved polygon may be changed as the display indicating that the curved polygon is distorted. The error code is read, for example, in the warning display in S3 of FIG. 14 and displayed on the display device. Note that the display color of the curved polygon may be changed at S3 in FIG.

  Next, the design support apparatus determines whether or not all the curved polygons to be checked have been checked. When not all the curved polygons to be checked are checked, the design support apparatus returns the control to S211. On the other hand, when all the curved polygons to be checked are checked, the design support apparatus ends the process.

FIG. 17 shows details of the normal vector check process between curved polygons (S22 in FIG. 15). In this process, the design support apparatus selects a sample point to be monitored on the three-dimensional model (S221). As a method of selecting the sample points, for example, a predetermined point (for example, one control point on the ridge line) may be selected one by one from all the curved polygons and may be monitored. Further, for example, a predetermined number of curved polygons may be selected at random, and each of the predetermined points included therein may be selected and monitored. Further, for example, a predetermined point may be selected from curved polygons included in a region on the stereo model designated by the user with the input device. In addition, in the process of S21 in FIG. 15, an object in which no distortion is detected in the curved polygon may be extracted and used as the target of this process.

  Next, the design support apparatus searches for a curved polygon around the sample point (S222). As the curved polygon, the curved polygon to which the sample point selected in S221 belongs may be extracted.

  Next, the design support apparatus calculates a normal vector for each curved polygon (S223). The normal vector may be calculated, for example, at any of the internal control points in each curved polygon, or at the center of gravity of the curved polygon. The normal vector is calculated according to Equation 4.

  Next, the design support apparatus calculates an angle between the normal vectors (S224). The angle between the normal vectors is determined according to the inner product calculation and the inverse trigonometric function.

  Then, the design support apparatus determines whether or not those angles are within the range of the reference values E1 to E2 (S215). The reference values E1 and E2 are, for example, user-specified values or system default parameters. The reference value E1 may be set from an empirical value that is acceptable as distortion. The reference value E2 is originally a value for excluding two polygons having a boundary between such folds as a boundary when there is a fold between curved polygons (a sufficiently large angle, For example, a value of 20 degrees or more may be set. The CPU of the design support apparatus that executes this processing corresponds to means for determining that distortion has occurred in the surface data of the present invention.

  If the angle between any of the normal vectors is within the range of the reference values E1 to E2, the curved polygon is displayed with distortion, and an error code is displayed together with the identification information of the curved polygon or the coordinates of the control point. The setting is made (S216). In this way, the design support apparatus can detect distortion from the difference in the angle of the normal vector exceeding the allowable value, and can exclude a portion that originally existed as a fold and reduce erroneous error display.

  Next, the design support apparatus determines whether all sample points to be checked have been checked. If not all the curved polygons to be checked are checked, the design support apparatus returns the control to S221. On the other hand, when all the curved polygons to be checked are checked, the design support apparatus ends the process.

  In the ridge line vector check process (S23 in FIG. 15), the sample points may be limited to the ridge line in the normal vector check process in the curved polygon (FIG. 16). Therefore, the check procedure is the same as that in FIG.

  FIG. 18 shows details of the curvature analysis process on the ridgeline (S24 in FIG. 15). In this process, the design support apparatus selects a sample point (S241). This process is the same as S221 in FIG.

Next, the design support apparatus selects a ridge line around the sample point (S242). In this process, for example, a curved polygon around the sample point may be searched and a ridge line belonging to the curved polygon may be selected. The number of ridge lines to be selected may be determined, for example, by setting a predetermined number of upper limits for sample points. Further, all the ridgelines at a predetermined distance from the sample point may be selected. The CPU of the design support apparatus that executes this processing corresponds to the ridge line extraction means of the present invention.

  Next, the design support apparatus obtains the maximum curvature value R on the ridge line (S243). For example, the maximum value may be obtained by obtaining the curvature at predetermined intervals on the ridgeline and selecting the maximum value. Or you may narrow down to the direction where a curvature increases in the bisection method from the both ends of a ridgeline. Then, when the increase rate of the curvature falls within a predetermined limit, it may be determined as the maximum value of the curvature. The curvature may be obtained according to Equation 7 or Equation 8. The CPU of the design support apparatus that executes this processing corresponds to the ridge line distortion determination means of the present invention.

  Next, the design support apparatus determines whether or not the maximum curvature value R exceeds a predetermined reference value E3 (S245). The CPU of the design support apparatus that executes this process corresponds to the curvature calculation means of the present invention. When the maximum curvature value R exceeds the predetermined reference value E3, the design support apparatus displays the curved polygon including the ridge line as being distorted, and displays an error code together with the identification information of the curved polygon or the coordinates of the control point. Setting is made (S246).

  In the above process, it is determined whether or not the magnitude of the curvature exceeds a predetermined reference value E3. Alternatively, it may be determined whether or not the change in the curvature exceeds a predetermined limit.

  Furthermore, a part that is broken from this place may be excluded from the check target. That is, in the processing of S242 and S243, it may be excluded that the curvature has already exceeded the predetermined limit value E4 at the start of the deformation operation. Further, if it is determined in S245 that the maximum curvature value R has already exceeded a predetermined limit value E4 at the start of the deformation operation, the maximum curvature value R may be ignored.

  Further, when a bending operation is performed during the deformation operation of the three-dimensional model, a portion folded by the bending operation may be excluded from the check target. That is, the curvature is monitored together with the deformation operation, and it is only necessary to exclude those in which the curvature exceeds the predetermined limit value E4 in the processes of S242 and S243. In addition, in the deformation operation, the curvature is monitored, and if the maximum value R of the curvature exceeds a predetermined limit value E4 in the determination in S245, the maximum value R of the curvature may be ignored.

  Next, the design support apparatus determines whether or not all the ridgelines to be monitored have been checked around the sample point (S247). When not all the ridgelines to be monitored are checked, the design support apparatus returns the control to S242. When all the ridgelines to be monitored are checked around the sample point, the design support apparatus determines whether or not all the sample points to be checked have been checked (S248).

  If all sample points to be checked have not been checked, the design support apparatus returns the control to S241. On the other hand, when all the sample points to be checked are checked, the design support apparatus ends the process.

  FIG. 19 shows details of the curvature polygon (patch) curvature analysis processing (S25 in FIG. 15). In this process, the design support apparatus receives designation of an analysis region to be analyzed on the three-dimensional model by a user operation through the input device (may be set in advance before the deformation operation) (S250). ).

  Next, the design support apparatus selects a vertex in the analysis area (S251). Then, the design support apparatus calculates the normal Ni of the vertex and the tangent line Ti of the ridge line Li (or the ridge line near the vertex) connected to the vertex (S252). The CPU of the design support apparatus that executes this process corresponds to the neighborhood ridge line extraction means.

  Next, the design support apparatus projects the ridgeline Li onto a plane formed by the normal line Nk and the tangent line Ti, and obtains the maximum curvature Ri on the projection line on the plane (S253). The maximum curvature Ri on the projection line may be obtained by a procedure similar to S243 in FIG. That is, the curvature Ri may be obtained sequentially according to Equation 7 or Equation 8 at predetermined intervals on the projection line. Further, a direction in which the curvature Ri is maximized may be searched by a bisection method from both ends on the projection line. The CPU of the design support apparatus that executes this process corresponds to the projection curvature calculation means.

  Next, the design support apparatus determines whether or not all the ridge lines around the vertex have been checked (S254). If all the ridge lines around the vertex have not been checked, the design support apparatus returns the control to S252 and repeats the process for the next ridge line.

  When all the ridge lines around the vertices have been checked, the design support apparatus determines whether all the vertices in the analysis area to be checked have been checked (S255). If all the vertices in the analysis area have not been checked, the design support apparatus returns the control to S251 and repeats the process for the next vertex.

  When the check of all the vertices to be checked is completed, the design support apparatus obtains the maximum value Rmax of the maximum curvature Ri for each obtained ridgeline (S256). Then, the design support device determines whether or not the maximum value Rmax of the maximum curvature Ri for each ridge line exceeds a predetermined reference value E3 (S257). The CPU of the design support apparatus that executes this processing corresponds to the ridge line distortion determination means of the present invention. When the maximum value Rmax exceeds the reference value E3, the design support apparatus sets the curved polygon as a display with distortion, and sets an error code together with the identification information of the curved polygon (S258).

  In the above process, it is determined whether or not the magnitude of the curvature exceeds a predetermined reference value E3. Alternatively, it may be determined whether or not the change in the curvature exceeds a predetermined limit.

  Furthermore, a part that is broken from this place may be excluded from the check target. That is, in the process of S253, a case where the maximum curvature Ri has already exceeded the predetermined limit value E4 at the start of the deformation operation may be excluded. In addition, when the maximum curvature Ri already exceeds a predetermined limit value E4 at the start of the deformation operation in the determination of S257, the maximum curvature Ri may be ignored.

  Further, when a bending operation is performed during the deformation operation of the three-dimensional model, a portion folded by the bending operation may be excluded from the check target. In other words, the curvature is monitored in both the deformation operations, and it is only necessary to exclude those in which the maximum curvature Ri exceeds the predetermined limit value E4 in the process of S253. In addition, in the deformation operation, the curvature is monitored, and if the maximum curvature Ri exceeds a predetermined limit value E4 in the determination in S257, the maximum curvature Ri may be ignored.

  As described above, the design support apparatus according to the present embodiment monitors the occurrence of distortion in the curved polygon constituting the stereo model when the stereo model is deformed. The distortion is determined based on whether or not the angle (or the amount of change in angle) of normal vectors at a plurality of points on the curved polygon exceeds a predetermined reference value. When the occurrence of distortion of the curved polygon is detected, a warning is displayed.

Further, even when no distortion in the curved polygon is detected, the present design support apparatus obtains the angle of the normal vector between the curved polygons, and the angle (or the amount of change in the angle) is in the range of the reference values E1 to E2. The occurrence of distortion is detected by determining whether or not it exists. In this case, when the angle between the normal vectors (or the amount of change in the angle) exceeds the reference value E1, it can be determined that the distortion has exceeded the allowable amount. When the angle between the normal vectors (or the amount of change in angle) exceeds the reference value E2, the two curved polygons are inherently in a broken state and are excluded from distortion detection targets. be able to. In this way, the present design support apparatus can report the occurrence of distortion to be detected while suppressing unnecessary warning display.

  Furthermore, this design support apparatus analyzes an angle between a plurality of normal vectors on a ridge line that is a boundary line between curved polygons, and whether or not the angle (or change rate of the angle) exceeds a predetermined reference value E1. The occurrence of distortion is detected.

  Further, the design support apparatus monitors the curvature of the ridge line that is a boundary line between the curved polygons, and detects the occurrence of the distortion of the curved polygon depending on whether or not the curvature exceeds a predetermined reference value E1. Alternatively, the occurrence of distortion of the curved polygon is detected based on whether or not the change in curvature exceeds a predetermined limit.

  Further, the design support apparatus projects the ridge line on the plane formed by the normal vector of the vertex on the curved surface area and the tangent line of the ridge line in the vicinity of the vertex, obtains the curvature of the ridge line, and the curvature is predetermined. The occurrence of distortion of the curved polygon is detected based on whether or not the reference value E1 is exceeded. Alternatively, the occurrence of distortion of the curved polygon is detected based on whether or not the change in curvature exceeds a predetermined limit. In this way, for example, when a specific area is designated, the distortion of the entire curved surface covering the area can be monitored.

  As described above, the present design support apparatus can monitor the occurrence of distortion on the three-dimensional model according to a plurality of determination criteria, and can warn that the distortion occurs. As a result, the user may stop the deformation operation and restart the deformation operation with an operation procedure that does not cause such distortion. Further, the user can continue the deformation operation as it is, and after the deformation operation is completed, the user can remove the distortion by performing the deformation operation again in the vicinity where the occurrence of the distortion is detected.

  Furthermore, by excluding the part that has been folded from this site, or by excluding the part that has been folded by the bending operation when the bending operation has been performed in the course of the deformation operation, unnecessary error display can be reduced. It is possible to reduce the adverse effect that the error display to be recognized is buried in a number of noisy error displays.

<Modification>
In the above embodiment, along with the deformation operation by the user, the normal vector in the curved polygon and the normal vector between different curved polygons are monitored, and the occurrence of distortion is detected from the angle of the normal vector and the angle change rate. In addition to the deformation operation by the user, the curvature of the ridgeline and the curvature of the curved polygon were monitored to detect the occurrence of distortion.

  However, instead of such processing, it may be determined whether or not distortion has occurred on the existing three-dimensional model separately from the deformation operation. The procedure of the determination process is the same as that in the above embodiment except that the determination process is performed separately from the deformation operation.

  FIG. 20 is a diagram for explaining the concept of distortion detection processing using normal vectors at the time of data creation. The design support device calculates a normal vector at a plurality of sample points for a curved polygon existing in a portion to be inspected, for example, a circle, and determines whether the mutual angle is within a predetermined reference value. What is necessary is just to judge. Moreover, what is necessary is just to determine whether the curvature of a ridgeline is less than a predetermined reference value.

FIG. 21 shows the procedure of distortion detection processing using a normal vector when creating such data. In this process, the design support apparatus executes product data drawing in response to a user operation (S
80). Then, the product data drawing is completed (S81).

  Then, the design support apparatus extracts all the defective surfaces (surfaces where distortion has occurred) described in FIGS. 15 to 18 (S82).

  Based on the extraction result, the user corrects the surface and performs an operation for maintaining the three-dimensional model. The design support apparatus receives the user operation and executes surface correction / maintenance (S83).

  Instead of detecting the distortion in the entire stereo model in this way, the distortion may be detected for each predetermined work unit or for each part of the stereo model (S91). The user performs an operation of correcting the surface and maintaining the three-dimensional model for each work unit and each part. The design support apparatus receives the user operation and executes surface correction / maintenance for each unit of work or for each part (S92). Such work is repeated to complete the creation of product data (S93).

  By such processing, product data free from distortion such as wrinkles and distortion can be created.

  In the above-described embodiment, the process of detecting distortion at the time of deforming a three-dimensional model or detecting distortion at the time of forming a three-dimensional model has been described using a design support apparatus that forms a three-dimensional model by curved polygons as an example. However, the three-dimensional model is not limited to those composed of curved polygons. For example, instead of combining curved polygons, a combination of a curved line such as a spline curve, a circle, an ellipse, or a curved surface obtained by rotating a polynomial function with a predetermined rotation axis, or a curved surface that is a trajectory obtained by moving the curve in a predetermined direction is used. Even when a dimensional model is configured, the present invention can be implemented. For example, sample points may be set at predetermined intervals on each curved surface, and the angle of the normal vector, change in angle, etc. may be monitored between adjacent sample points. Also, a plane is formed from the normal vector and the tangent vector of the curved surface near the sample point, and a projected ridge line is formed by projecting the curved surface onto such a plane, and the curvature is monitored in the same procedure as in FIG. That's fine.

It is a figure which shows the example which deform | transformed the solid model comprised by the curved surface polygon. It is a figure which shows the example which divided | segmented the curved-surface polygon into the mesh. It is a figure which shows the example of the solid model by a triangular patch. It is a figure which shows a cubic Bezier curve. It is a figure which shows the example of the cubic Bezier curved surface by a quadrangular patch. It is a figure which shows arrangement | positioning of the internal control point with a tertiary square patch. It is a figure which shows arrangement | positioning of the internal control point with a quartic square patch. It is a figure which shows the example of the cubic Bezier curved surface by a triangular patch. It is a figure which shows arrangement | positioning of the internal control point with a tertiary triangular patch. It is a figure which shows arrangement | positioning of the internal control point with a quartic triangular patch. It is a figure which shows the relationship between a sample point and the some curved surface polygon which exists around it. It is a figure which shows the position vector of the point on a curve, and the relationship between the 1st derivative and the 2nd derivative. It is a figure which shows the concept of the curvature analysis of a curved-surface polygon. It is a figure which shows the processing flow of a deformation | transformation operation process of a stereo model. It is a figure which shows the detail of distortion generation | occurrence | production detection processing. It is a figure which shows the detail of the normal vector check process in a curved surface polygon. It is a figure which shows the detail of the normal vector check process between curved surface polygons. It is a figure which shows the detail of the curvature analysis process on a ridgeline. It is a figure which shows the detail of the curvature analysis process of a curved surface polygon (patch). It is a figure explaining the concept of the distortion detection process by the normal vector at the time of data creation. It is a figure which shows the procedure of the distortion detection process by the normal vector at the time of data creation.

Claims (17)

A surface element distortion detecting device for detecting distortion of the surface element created by such a design support device, which forms a surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model. ,
Means for obtaining respective normal vectors on a plurality of surface elements around sample points on the solid model;
Means for weighted average of normal vectors of the respective surface elements by a weighting factor designated for the respective surface elements;
Means for calculating a value indicating a relative relationship between the normal vector of each of the surface elements and the normal vector obtained by the weighted average ;
Surface element distortion occurrence determination means for determining that distortion has occurred in the surface element when a value indicating the relative relationship exceeds a predetermined value set in advance;
A surface element distortion detection device comprising:   2. The surface element distortion detection apparatus according to claim 1, further comprising means for displaying the surface element in which the distortion has occurred. For the face data to which the surface element is formed by a plurality sets, means for calculating a value indicating a relative relationship between the normal vector of the adjacent surface elements to each other,
Characterized in that it comprises when the value indicating the relative relationship between the normal vector of the adjacent surface elements to each other exceeds a predetermined value set in advance, and a determining means and distortion occurs in the surface data The surface element distortion detection device according to claim 1 or 2.   The surface element distortion detection apparatus according to claim 3, further comprising means for displaying two adjacent surface elements determined to have the distortion. Distortion detection unit of the surface element according to any one of claims 1 to 4, wherein the relative relationship, which is a angle between the legal line vector. A surface element distortion detecting device for detecting distortion of the surface element created by such a design support device, which forms a surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model. ,
Means for extracting vertices from surface data formed by collecting a plurality of the surface elements;
A neighboring ridge line extracting means for extracting a plurality of ridge lines that are boundary lines between the surface elements in the vicinity of the vertex;
A projection unit that forms a plane from a normal vector of the surface data at the vertex and a tangent vector of the ridge line in the vicinity of the vertex, and projects the ridge line on the formed plane;
Projected curvature calculating means for calculating the curvature of the ridgeline on the plane projected by the projecting means;
By applying the projection unit and the projection curvature calculation unit to the plurality of extracted ridge lines, the curvature of each ridge line is calculated, and the maximum curvature acquisition is performed from the calculated curvature of each ridge line. Means,
Surface elements, characterized in that the maximum curvature maximum curvature acquired by the acquiring means if exceeding a predetermined value set in advance, and a ridge line distortion determination means determines that distortion has occurred in the ridge Distortion detection device. When a plurality of vertices are extracted from the surface data, the maximum curvature acquisition unit further applies the projection unit and the projection curvature calculation unit to the ridgelines of the plurality of extracted vertices. The surface element distortion detection device according to claim 6, wherein the curvature of each ridge line extracted from the vicinity of the vertex is calculated, and the maximum curvature is obtained from the calculated curvature of each ridge line near the vertex.   8. The surface element distortion detection apparatus according to claim 6, further comprising means for displaying a surface element related to a ridge line in which distortion has occurred.   The distortion detection apparatus for a surface element according to claim 1, wherein the surface element is either a polygon or a surface. A surface element distortion detection method in which a computer detects a distortion of the surface element created by such a design support device, which forms a surface of the solid model by combining surface elements that cover at least a part of the three-dimensional model. And the computer
Obtaining normal vectors on a plurality of surface elements around sample points on the stereo model in response to an instruction input for detecting the distortion of the surface elements from the input means;
A weighted average of normal vectors of the respective surface elements by a weighting factor specified for the respective surface elements;
Calculating a value indicating a relative relationship between the normal vector of each of the surface elements and the normal vector obtained by the weighted average ;
And a surface element distortion determination step for determining that distortion has occurred in the surface element when a value indicating the relative relationship exceeds a predetermined value set in advance. Method. For the surface data surface element is formed by a plurality sets, calculating a value indicating the relative relationship between the normal vector of the adjacent surface elements to each other,
If the value indicating the relative relationship between the normal vector of the adjacent surface elements to each other exceeds a predetermined value set in advance, and determining the distortion occurs on the surface data, it further executes The surface element distortion detection method according to claim 10. A surface element distortion detection method in which a computer detects a distortion of the surface element created by such a design support device, which forms a surface of the solid model by combining surface elements that cover at least a part of the three-dimensional model. And the computer
Extracting vertices from surface data formed by collecting a plurality of surface elements;
A neighboring ridge line extracting step of extracting a plurality of ridge lines that are boundary lines between the surface elements in the vicinity of the vertex;
Forming a plane from a normal vector of the surface data at the vertex and a tangent vector near the vertex of the ridge, and projecting the ridge on the formed plane;
A projected curvature calculating step of calculating a curvature of a ridge line on the plane projected by the projecting step;
By applying the projection unit and the projection curvature calculation unit to the plurality of extracted ridge lines, the curvature of each ridge line is calculated, and the maximum curvature acquisition is performed from the calculated curvature of each ridge line. Process,
Surface elements, characterized in if it exceeds a predetermined value the maximum curvature obtained at the maximum curvature acquisition process has been set in advance, and the ridge line distortion determination step determines that distortion has occurred in the ridge, to perform Distortion detection method. In the maximum curvature obtaining step, when a plurality of vertices are extracted from the surface data, the computer further applies the projection step and the projected curvature calculation step to the ridge lines of the plurality of extracted vertices. The distortion detection method for a surface element according to claim 12, wherein the curvature of each ridge line extracted from each vertex vicinity is calculated, and the maximum curvature is obtained from the calculated curvature of each ridge line near each vertex. . A computer-executable program for detecting distortion of the surface element created by such a design support device, which forms the surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model, On the computer,
Obtaining normal vectors on a plurality of surface elements around sample points on the stereo model in response to an instruction input for detecting the distortion of the surface elements from the input means;
A weighted average of normal vectors of the respective surface elements by a weighting factor specified for the respective surface elements;
Calculating a value indicating a relative relationship between the normal vector of each of the surface elements and the normal vector obtained by the weighted average ;
And a step of determining that distortion has occurred in the surface element when a value indicating the relative relationship exceeds a predetermined value set in advance. Possible program. For the surface data surface element is formed by a plurality sets, calculating a value indicating the relative relationship between the normal vector of the adjacent surface elements to each other,
If the value indicating the relative relationship between the normal vector of the adjacent surface elements to each other exceeds a predetermined value set in advance, and determining the distortion occurs on the surface data, it further executes 15. A computer-executable program for detecting distortion of a surface element according to claim 14. A computer-executable program for detecting distortion of the surface element created by such a design support device, which forms the surface of the three-dimensional model by a combination of surface elements covering at least a part of the three-dimensional model, On the computer,
Extracting vertices from surface data formed by collecting a plurality of surface elements;
A neighboring ridge line extracting step of extracting a plurality of ridge lines that are boundary lines between the surface elements in the vicinity of the vertex;
Forming a plane from a normal vector of the surface data at the vertex and a tangent vector near the vertex of the ridge, and projecting the ridge on the formed plane;
A projected curvature calculating step of calculating a curvature of a ridge line on the plane projected by the projecting step;
By applying the projection unit and the projection curvature calculation unit to the plurality of extracted ridge lines, the curvature of each ridge line is calculated, and the maximum curvature acquisition is performed from the calculated curvature of each ridge line. Process,
Wherein the maximum curvature acquisition process prescribed value field <br/> case beyond that obtained maximum curvature preset at a ridgeline distortion determination step determines that distortion has occurred in the ridge, that is the execution A computer-executable program characterized. In the maximum curvature acquisition step, when a plurality of vertices are extracted from the surface data, the projection step and the projection curvature calculation step are further applied to the ridge lines of the plurality of extracted vertices. The computer-executable program according to claim 16, wherein the curvature of each ridge line extracted from each vertex vicinity is calculated, and the maximum curvature is obtained from the calculated curvature of each ridge line near each vertex.

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