JP2009110073A - Design support device, design support method, and design support program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce the generation of the distortion of a shape in the deforming operation of a three-dimensional model configured of a curved surface patch in which a plurality of normal vectors are defined. <P>SOLUTION: This design support device includes: a means for extracting the normal vectors of each face element on an evaluation reference line configured by connecting the boundary lines of the face elements arrayed in a prescribed direction on a curved surface including a plurality of non-adjacent face elements; a means for calculating the first normal vector distribution curve indicating the distribution of the top ends of the normal vectors on the evaluation reference line; a means for calculating the second normal vector distribution curve by removing one or more normal vectors as the object of correction from the normal vectors included in the first normal vector distribution curve; a means for correcting the normal vectors as the object of correction by moving the normal vectors as the object of correction to the second normal vector distribution curve; and a means for correcting the face elements by the corrected normal vectors. <P>COPYRIGHT: (C)2009,JPO&INPIT

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, in the above conventional technique, no consideration is given to correction for distortion on the curved surface. An object of the present invention is to reduce distortion of a shape such as wrinkles or sagging of a patch or polygon in a deformation operation of a three-dimensional model including a surface element such as a patch or polygon including a curved surface in which a plurality of normal vectors are defined. It is to correct and reduce. In particular, an object of the present invention is to provide a technique for improving the quality of the entire curved surface including not only adjacent patches but also non-adjacent patches.

The present invention employs the following means in order to solve the above problems. That is, the present invention is exemplified by the configuration of a design support apparatus that forms a curved surface of a three-dimensional model by a combination of surface elements having a boundary line including a plurality of vertices and a surface surrounded by the boundary line. The design support apparatus is configured to obtain a normal vector of each surface element at a boundary position between two adjacent surface elements and a normal vector at the boundary position between two adjacent surface elements do not coincide with each other. Means for replacing with a common correction normal vector. With such a configuration, the present design support apparatus smoothly connects at least the boundary positions of two adjacent surface elements.

  In addition, the design support apparatus calculates a normal vector of each surface element on an evaluation reference line configured by connecting boundary lines of surface elements arranged in a predetermined direction on a curved surface including a plurality of non-adjacent surface elements. Means for extracting; means for obtaining a first normal vector distribution curve indicating a distribution of a tip of a normal vector on the evaluation reference line; and at least one of normal vectors included in the first normal vector distribution curve Means for obtaining a second normal vector distribution curve by removing the normal vector to be corrected, and moving the tip of the normal vector to be corrected in a direction orthogonal to the second normal vector distribution curve And means for correcting the normal vector to be corrected, and means for correcting the surface element by the corrected normal vector. With this configuration, the design support apparatus smoothes the distribution of normal vectors even between non-adjacent surface elements.

  According to the present invention, the quality of the entire curved surface including adjacent patches or non-adjacent patches can be improved.

  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.

  When the three-dimensional model covered with such a curved polygon is deformed, the present design support apparatus corrects a plurality of normal vectors in each curved polygon.

  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 present design support apparatus provides a function of correcting the normal vector in such individual curved polygons. That is, the design support apparatus receives an execution request from the user and executes a curved polygon distortion removal process.

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 computer program is composed of a plurality of modules, and each module is executed by the CPU, thereby forming each means of the present invention.

The external storage device is, for example, a hard disk drive device. Also, the external storage device is a removable storage medium drive device such as a CD-ROM (Compact Disc Read Only Memory).
) And a drive device such as 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 expressed as follows: 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 assumes that the normal angle in the curved polygon matches or does not match, the normal angle change rate, and the normal matches between multiple curved polygons near the sample point. The occurrence of distortion can also be detected from the mismatch, the rate of change of the angle between the normals, and the rate of change of curvature at the sample point or the ridge line near 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). Here, the reference value may be appropriately set or selected by the user according to the application target and design target of the three-dimensional model by the design support apparatus. The same applies to other reference values and limit values below.

  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 curved polygons is often greater than or equal to the reference value (E2) greater than the reference value 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.

<Distortion correction function>
(1) Correction of Distortion Between Adjacent Patches FIG. 14 illustrates the concept of correcting distortion between adjacent patches as a first problem of distortion correction. FIG. 14 shows an example of a cross-sectional view of a curved surface in which distortion is generated above the arrow indicated by “correction”. This curved surface is composed of two adjacent curved surface patches PAT1 and PAT2. The first curved surface patch PAT1 has normal vectors V1 and V2 near the patch boundary. The second curved patch PAT2 has normal vectors V3 and V4 in the vicinity of the patch boundary. In the vicinity of the boundary line between the two curved patches PAT1 and PAT2, the normal vectors V2 and V3 are different in angle by more than a predetermined limit value. For this reason, in the vicinity of the boundary line between the two curved patches PAT1 and PAT2, a discontinuous change, that is, a steep depression occurs in the cross section of the curved surface.

  An example of a cross-sectional view of a curved surface in which the above-described distortion is corrected is shown below the arrow indicated by “correction” in FIG. However, the curved surface before correction is also displayed as a dotted line for reference. That is, after the correction, both of the two normal vectors are changed to one normal vector VC. Then, the two curved patches PAT1 and PAT2 are deformed to be PAT1C and PATC2 so that the normal vector becomes VC near the boundary between the two curved patches PAT1 and PAT2. The two curved patches PAT1C and PAT2C are connected smoothly because the normal vectors VC coincide with each other in the vicinity of the boundary line.

In this way, when a difference greater than or equal to a predetermined limit value is detected in the normal vector in the vicinity of the curved patch boundary line, a corrected target normal vector VC (corresponding to a corrected normal vector) to be shared is obtained, Further, the normal vector is set so that the normal vector of the boundary line between the two curved patches becomes the target normal vector. Then, the two curved patches may be deformed according to the target normal vector VC. For such two normal vectors V2 and V3, the target normal vector may simply be set to the direction of the vector VC passing through the center of the two normal vectors, for example.
(Equation 9)
(Vector VC) = ((Vector V2) + (Vector V3)) / 2
Here, (V) indicates that V is a vector. Further, (V1) + (V2) is the sum of each component of the vector, for example, each of the three-dimensional coordinates (x, y, z).

FIG. 15 illustrates a procedure for obtaining a three-dimensional curved surface patch again after a normal vector is determined (after being changed) for the three-dimensional curved surface patch. A three-dimensional curved surface patch PAT including three vertices P1, P2, and P3 is drawn on the left side of the center arrow in FIG. The curved patch PAT has normal vectors N1, N2, and N3 at P1, P2, and P3, respectively. If the normal vectors N1, N2, and N3 are the same (the angles are the same), the curved surface patch PAT is merely a plane. In the case of FIG. 15, the normal vectors N1, N2, and N3 have different angles. For this reason, the curved surface patch PAT has a curved surface in which the vicinity of the vertices P1, P2, and P3 is bent. The degree of curvature of the curved surface is determined by normal vectors N1, N2, and N3. Such a curved surface patch is called a PN triangle.

  A cubic triangular Bezier curved surface of such a curved surface patch PAT can be expressed by the following equation (10).

Therefore, if the vertex coordinates P1, P2, and P3 of the curved surface patch PAT and the normal vector at each vertex are known, a cubic triangular Bezier curved surface can be obtained. Now, for example, it is assumed that the normal vectors are changed to N1C and N2C at the vertices P1 and P2 in order to make the connection with adjacent patches smooth. In this case, a cubic triangular Bezier curved surface of the modified curved surface patch can be obtained by calculating using N1C instead of N1 and N2C instead of N2. That is, if a common normal vector can be set between adjacent patches, smooth connection can be realized at least for adjacent curved patches.
(2) Correction of distortion in entire curved surface including non-adjacent patches FIGS. 16 to 19 show a second problem of distortion correction. FIG. 16 is a diagram schematically illustrating a curved surface that is smooth between adjacent curved patches, but is distorted between non-adjacent curved patches. By matching the normal vectors in the vicinity of the boundary line between the adjacent patches, the smoothness between adjacent patches can be improved and the surface quality can be maintained. However, the entire surface including non-adjacent patches may not necessarily improve the surface quality. That is, even if a smooth connection can be realized between individual adjacent patches, there are cases where wrinkles, irregularities, undulations, etc. (also referred to as “slippery”) cannot be removed in a wider range.

FIG. 17 is a diagram illustrating wrinkles, irregularities, undulations, and the like on such a surface. FIG. 17A is a diagram in which a specific boundary line is set on a curved surface made up of a plurality of curved patches, and the distribution of normal vectors on the boundary line is drawn. The starting point of the normal vector is each point on the boundary line. Further, the tip (end point) of the normal vector is located in the direction of the respective three-dimensional space from each start point. The boundary line is a line that connects the edges of the curved surface patch to partition the curved surface into two. A normal vector distribution curve is constructed as a curve indicating the distribution of the tip (end point) of the normal vector of the curved surface located on this boundary line. As shown in FIG. 16, the normal vector distribution curve normal is generally three-dimensional in the case of, for example, a curve in which the tips of the normal vectors are connected, a curve having the tips of the normal vectors as control points, and the like. It becomes a curve in space. If the tips of the normal vectors are not aligned, the normal vector distribution curve changes rapidly. That is, even if the normal vectors are on the same curved surface, a large undulation occurs in the distribution of normal vectors between non-adjacent patches. This indicates that even when the adjacent patches are smooth, the magnitude of the curvature and the bending direction may differ greatly between the non-adjacent patches. It also means that the rate of change of the curve is extremely large. The upper limit value of the magnitude of the curvature and the rate of change of the curve may be provided with a function that can be appropriately set by the user according to the design target to which the present design support apparatus is applied.

  FIG. 17 (2) shows FIG. 17 (1) converted into a surface model, and the direction of the normal vector is color-coded (pattern-divided). FIG. 17 (3) is a diagram showing the distribution of normal vectors at sample points by selecting sample points one by one for each curved surface patch included in the curved surface. In this example, the sample points are set on the boundary lines of a plurality of curved patches. Furthermore, the direction of the normal vector at the sample point is matched between the plurality of curved surface patches. By this method, a smooth connection between the curved patches can be realized around each sample point. However, as described above, there may remain a problem of improving the surface quality in a wider range including non-adjacent curved patches.

  FIG. 18 shows an example in which wrinkles, irregularities, undulations, etc. of a surface are generated by morphing, that is, a deformation operation on a curved surface model. In FIG. 18, the left side of the center arrow (indicating morphing operation) is the example of the curved surface before the morphing is performed. In this case, the distribution 100 of normal vectors on a specific boundary line is substantially uniform.

  On the other hand, a surface distorted as a result of deformation is shown on the right side of the arrow indicating the morphing operation. In this case, the normal vector distribution 101 generates a large swell as in FIG.

  FIG. 19 is a diagram illustrating distortion and connectivity between regions by color-coded display. That is, FIG. 19 (1) shows the surface distorted as a result of deformation by color (pattern classification), and FIG. 19 (2) is divided by a boundary line on a specific boundary line. It is a figure which shows the connectivity between area | regions according to a color classification (dividing by line type). Here, the connectivity on the boundary line is indicated by four lines: a thick solid line, a thick dotted line, a thin solid line, and a thin dotted line. A thick solid line indicates a tangential discontinuity. When the tangent is discontinuous, no breakage occurs at the boundary line, but there is no continuity of the tangent. On the other hand, a thin dotted line is a boundary where tangent continuity is maintained.

  20 and 21 show the problem of distortion correction on a curved surface as described above and the concept of the solution. As described above, when normal vectors are displayed on curved patch boundary lines in a specific direction in a range including non-adjacent curved patches, the vertices of the respective normal vectors may be distributed randomly. This becomes conspicuous by performing morphing as shown in FIG.

  Therefore, it is possible to improve the surface quality by matching the normal vectors as much as possible on a continuous curved patch boundary line in a specific direction. Therefore, here, the target curve is set, and the normal vector is aligned at least on the curve by moving the tip of the normal vector on the curved patch boundary line in a specific direction onto the curve. I will do it.

  FIGS. 20 (2) and 21 (2) show the concept of examples of correction of curved patches by such normal vector alignment. That is, the normal vector is corrected by correcting the distortion of the curve formed by the tip of the normal vector on the curved patch boundary line (corresponding to the evaluation reference line) directed in a specific direction, thereby improving the surface quality.

FIG. 22 shows a processing example in which such normal vector correction is executed in two directions. The two directions mean that a direction intersecting one boundary line on the curved surface is included. By performing normal vector correction in two directions, the correction target is expanded two-dimensionally. As a result, the surface quality is further improved. Surface quality is further improved by providing a plurality of curved patch boundary lines to be corrected. For example, a normal vector may be corrected by setting a plurality of vertical and horizontal boundary lines as shown in FIG.

  FIG. 23 shows an outline of a procedure for correcting a normal vector on a curved patch boundary line directed in a specific direction. Now, a curved surface constituted by curved patches is assumed as a curved surface to be corrected. Further, on this curved surface, it is assumed that the normal vector has already been corrected between adjacent patches. That is, it is assumed that the normal vectors match between adjacent patches.

  On this curved surface, a boundary line 112 is set over the entire curved surface including non-adjacent patches and connecting the boundary lines of a plurality of curved surface patches. Then, the vertex coordinates of the normal vector 114 on the boundary line 112 are acquired. As the starting point of the normal vector, for example, one or several sample points may be set for each curved surface patch on the boundary line. The sample points may include both ends of the curved patch edge. A curve connecting the vertices of all normal vectors is defined as a normal distribution curve 115. Then, the vertex 116 (and its normal vector) of the sudden change portion is extracted from the vertex coordinates of the normal vector on the normal distribution curve. Such a sudden change portion may be obtained based on whether or not the curvature or change rate of the normal distribution curve 115 exceeds a predetermined limit value. The curvature or rate of change may be calculated near the tip (end point) of each normal vector.

  Then, a curve (hereinafter referred to as a correction curve 117) passing through the vertex row excluding the extracted vertex 116 of the sudden change portion is generated. The correction curve 117 may be obtained as a spline curve in the form of a coordinate value polynomial, for example. Alternatively, it may be obtained as a Bezier curve.

  Next, a normal plane is obtained in the correction curve 117. The normal plane is a plane orthogonal to the correction curve 117. And the intersection of the calculated | required normal plane and a correction curve is calculated | required. That is, such a normal plane is moved by the correction curve 117. Then, when the normal plane passes through the start point of the normal vector of the sudden change portion, a straight line from the start point of the normal vector to the intersection of the normal plane and the correction curve 117 is used as a corrected normal line, and the normal vector is Correct it. As described above, the start point (end point) of the normal vector can be moved in a direction orthogonal to the correction curve while the start point of the correction normal vector remains unchanged.

  According to the above procedure, the correction is performed in the same manner so that the normal vector is directed to the intersection with the normal plane on the correction curve at all sudden change points on the normal distribution curve. Then, a cubic Bezier curved surface is generated according to Equation 10 for all curved surface patches whose normal vectors are corrected. As a result, a curved surface is reconstructed from which normal vectors of portions that change sharply between non-adjacent curved patches are excluded.

<Processing flow>
24 and 25 illustrate a non-adjacent normal correction processing flow of the present design support apparatus. This process is realized by a program executed on a computer constituting the CAD. In this process, the design support apparatus receives an input of a normal vector sequence Ni (i = 1, K) (S1). Here, accepting an input means, for example, that a subroutine of a program executed on a computer is handed over data with an argument. In addition, for example, it means that a program executed on a computer reads data from a file on a hard disk designated by a file name.

Next, this design support apparatus generates a normal distribution curve (S2). This normal distribution curve corresponds to the first normal distribution curve. The normal distribution curve may be described by, for example, an n-order Bezier curve shown in Equation 1. That is, the point P (t) on the curve may be described using the tip (end point) of the normal vector of n + 1 涸 as the control point Qi (i is 1 to n + 1) shown in FIG.

  However, in the practice of the present invention, the description format for describing the normal distribution curve is not limited. For example, a spline curve (X, Y, Z) as shown in Equation 11 may be used. Here, Xi, Yi, Zi are the coordinates of the tip (end point) of the normal vector, Bi (t) is a coefficient, and t is a curve section (t1 = <t = <t2). The parameter to be set.

A B-spline curve may be used as the normal distribution curve.

  Next, the design support apparatus calculates the curvature Ri of the normal distribution curve at the tip Pi of each normal vector (S3). The curvature Ri can be obtained by, for example, Equation 7 or Equation 8. Then, the design support apparatus determines whether or not the calculated curvature Ri is larger than a predetermined limit epsR (S3). When the curvature Ri is larger than the predetermined limit epsR, the design support apparatus excludes the point Pi (S4). The excluded points are points that are thinned out when creating a correction curve.

  Next, this design support apparatus determines whether or not the analysis of the curvature has been completed for all the normal lines Ni (S6). When the analysis of curvature has not been completed for all the normal lines Ni, the design support apparatus returns the control to S3. On the other hand, when the analysis of the curvature is finished for all the normal lines Ni, the present design support apparatus uses the points excluding the excluded points from the end points Pi (i = 1, K) of the normal vectors. Is generated (S7). This normal distribution curve corresponds to the second normal distribution curve. The procedure for generating the correction curve is the same as the normal distribution curve of S2.

  Next, the following correction process is executed at each exclusion point. That is, now, let Bj (Xbj, Ybj, Zbj) be the starting point of the normal vector Nj whose end point is the excluded point Pj. A plane including the start point Bj and orthogonal to the correction curve is generated. More specifically, a plane passing through the start point Bj is obtained from the planes orthogonal to the tangent line of each point of the correction curve (S8). This plane is called the normal plane of the correction curve. For example, if the unit vector in the tangential direction at the point Q (Qx, Qy, Qz) of the correction curve is V1 (a, b, c), the normal plane is a · (X−Qx) + b · (Y−Qy). ) + C · (Z−Qz) = 0 (see FIG. 23). Among such plane equations, the one passing through the start point Bj is obtained. More specifically, a plane equation is obtained while moving the correction curve point Q (Qx, Qy, Qz) at a predetermined pitch, and the start point Bj satisfies the plane equation within a predetermined error epsH. It is determined whether or not. An intersection point Q (Qxj, Qyj, Qzj) between such a normal plane and the correction curve is set as a point Qj (S9).

  Then, the end point Pj of the normal vector is moved in the direction of the straight line BjQj. More specifically, the starting point is Bj, and the unit vector in the direction of the straight line BjQj is the corrected normal vector Nj (S10). The CPU of the design support apparatus that executes this processing corresponds to means for correcting the normal vector.

  Such corrected normal vectors are obtained for all exclusion points. As a result, the points on the original normal distribution curve are removed with respect to the points where the curvature is larger than the predetermined value epsR. Then, the normal vector is moved in a direction orthogonal to the smooth correction curve.

  FIG. 26 illustrates a curved surface correction process flow of the present design support apparatus. In this process, the design support apparatus inputs a curved surface patch Pi (i = 1, N) included in the curved surface to be corrected. Each curved surface patch Pi can be described by, for example, Equation 3, Equation 4, and the like. For example, when a cubic Bezier curved surface is used, the curved surface patch Pi is defined by giving ten control points shown in FIG.

  Next, as shown in FIG. 20, a patch boundary point sequence PPi (i = 1, L) that crosses (or vertically cuts) the curved surface in a predetermined direction is set (S22). Here, the predetermined direction may be determined by receiving a user operation on the three-dimensional model displayed on the display device of the CAD system, for example. For example, the user may point on the three-dimensional model with a pointing device such as a mouse pointer. Here, the patch boundary point sequence is selected one by one with a point on the boundary line between each patch and an adjacent patch as a representative point. More specifically, one end point on one edge of each patch may be selected.

  Next, the design support apparatus executes correction processing for matching the normal vector R1Ni (I = 1, L) between adjacent patches in the patch boundary point sequence PPi (I = 1, L) (S23). . That is, when the normal vectors do not match between adjacent patches, a common correction normal vector VC is obtained. This processing may be obtained according to Equation 9 as described in FIG. Further, the normal vector in the patch boundary point sequence PPi is replaced with the corrected normal vector VC obtained. The CPU of the design support apparatus that executes this processing corresponds to means for replacing the correction normal vector. As a result, the normal vector R1Ni is directed in the same direction between adjacent patches.

  Next, non-adjacent correction processing is executed on the normal vector R1Ni (I = 1, L) (S24). This procedure is the same as the description in FIGS. The CPU of the design support apparatus that executes the process of S24 corresponds to means for correcting the surface element of the present invention.

  Next, a patch boundary point sequence PQi (i = 1, M) that intersects the patch boundary point sequence PPi (I = 1, L) is set (S25). The procedure is the same as in S22 except that the patch boundary point sequence PQi (i = 1, M) is in the direction intersecting the patch boundary point sequence PPi (I = 1, L). However, the patch boundary line including the patch boundary point sequence PQi (i = 1, M) is set so as to intersect the patch boundary point sequence PPi (I = 1, L) (see FIG. 22).

  Next, correction processing for matching the normal vector R2Ni (I = 1, M) between adjacent patches is executed in the patch boundary point sequence PQi (I = 1, M) (S25). This process is the same as S23.

  Next, non-adjacent correction processing is executed on the normal vector R2Ni (I = 1, M) obtained in S25 (S26). This procedure is the same as S24. By the processing of S24 and S26, the normal vector is corrected in two directions as shown in FIG.

  Next, the present design support device replaces the normal vector of the representative point of each curved surface patch with the corrected normal vector sequences R1Ni (i = 1, L) and R2Ni (i = 1, M). Then, the generation of the curved surface patch is executed again for the entire normal vector including the replaced normal vector (S27). This procedure is as shown in FIG. 15, and a curved surface patch is generated according to the equation (10).

  As a result of the above processing, the normal vectors are unified at the boundary between adjacent patches for a curved surface consisting of curved patches, and the tips of non-adjacent normal vector groups are moved onto a smooth correction curve. . As a result, the distortion of the curved patch defined by the normal vector group is corrected in a wide range including non-adjacent curved patches.

<Example>
FIGS. 27 to 31 show the results of curved surface correction processing by the present design support apparatus. FIG. 27 is an example of a curved surface in which distortion occurs. In FIG. 27, there are distortions called wrinkles, sagging, and distortion in the plane. For this reason, the normal vectors N1 and N2 of the curved patches do not match at the boundary between adjacent patches. In addition, the direction of the normal vector also does not match between non-adjacent patches.

  FIG. 28 illustrates the change in the normal distribution curve in this case. FIG. 28 (1) is an example of a corrected normal distribution curve. FIG. 28 (3) is a view of the normal distribution curve in the direction of arrow A indicating the view direction of FIG. 28 (1). On the other hand, FIG. 28 (2) shows a state before correction of FIG. 28 (3).

  As shown in FIG. 28 (2), the non-uniform normal lines can be aligned as shown in FIG. 28 (3). This is because the normal distribution curve is smoothed by thinning out the constituent points in the portion of the normal distribution curve where the curvature is large from the sequence of non-uniform normal lines, and each normal is placed on the smooth normal distribution curve. It was because it was able to move to.

  FIG. 29 shows the normal line by enlarging the curved surface of FIG. It can be seen that the normal vectors match between adjacent patches, and the alignment of normals is uniform between non-adjacent patches, and the distortion of the curved surface is removed.

  FIG. 30 shows an example in which the correction of the present design support apparatus is applied to a curved surface during morphing. FIG. 30 (1) shows a curved surface before morphing. A belt-like portion 100 indicated by diagonal lines is a normal distribution on the rectangular boundary line 101. That is, the upper end of the strip-like portion 100 corresponds to a normal distribution curve.

  When the curved surface is manipulated by morphing, the normal distribution 102 is greatly distorted as shown in FIG. Therefore, the curved patch is non-uniform. In this case, the normal distribution greatly fluctuates not only between adjacent curved patches but also between non-adjacent curved patches.

  FIG. 30 (3) shows the normal distribution 103 when the normal correction (normal alignment in FIG. 30) of the present embodiment is executed. It can be seen that the normal distribution 103 becomes substantially uniform by the normal correction. FIG. 31 (1) is a diagram showing curved surface distortion as a pattern. FIG. 31 (2) shows the connectivity between adjacent patches. According to the design support apparatus of the present embodiment, curved surface distortion can be reduced and the connectivity between adjacent patches can be maintained. Here, the connectivity of adjacent patches is, for example, that the connectivity is maintained when tangential connection is maintained between adjacent patches.

<Modification>
In the above embodiment, as shown in FIGS. 22 and 26, the normal vector of the curved surface is corrected along the boundary line in two directions on the curved surface. However, the process of this design support apparatus is not limited to such a process. For example, the normal vector of the curved surface may be corrected along the boundary line in one direction as shown in FIG. Moreover, you may correct | amend the normal vector of a curved surface along several boundary lines in each direction. For this procedure, for example, the processing of S21 to S24 shown in FIG. 26 may be repeated.

  In the above embodiment, Expression 11 is used as the description format of the curved surface patch including the corrected normal vector. That is, according to Equation 11, the control points of the cubic triangular Bezier surface were calculated from the vertex vectors and normal vectors included in the PN triangle, and the points on the cubic triangular Bezier surface were obtained. However, the implementation of the present invention is not limited to such a procedure, and a fourth-order or higher-order Bezier curved surface may be used. Further, a square Bezier curved surface may be used instead of the triangular Bezier curved surface. Further, a description format of a curved surface other than a Bezier curved surface, for example, a B-spline curved surface may be used.

In the above embodiment, as the exclusion point, the curvature of the normal distribution curve near the tip of each normal vector is obtained, and when the curvature is equal to or greater than a predetermined limit value, the normal corresponding to the tip of the normal vector is obtained. Points on the distribution curve were excluded. However, the implementation of the present invention is not limited to such processing. For example, the curvature may be calculated in a predetermined section (section including one or a plurality of normal vectors) on the boundary line 112. And when a curvature is more than a predetermined limit value, it is good also considering the whole normal distribution curve contained in the section as an exclusion point. And you may correct | amend the normal vector contained in such an area collectively.
The normal vector with the distribution is selected.

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 illustrates the concept of distortion correction of a solid model. It is a figure which illustrates the procedure which calculates | requires a three-dimensional curved surface patch after a normal vector is determined. It is a figure which illustrates typically the curved surface which distortion has generate | occur | produced between non-adjacent curved patches. It is a figure which illustrates the wrinkle of a surface, unevenness | corrugation, a wave | undulation, etc. An example is shown in which wrinkles, irregularities, undulations, etc. of the surface occur due to the deformation operation on the curved surface model. It is a figure which illustrates distortion and the connectivity between area | regions by a color-coded display. It is a figure which shows the subject of the distortion correction in a curved surface, and the concept of the solution. It is a figure which shows the subject of the distortion correction in a curved surface, and the concept of the solution. It is an example of a process which performs correction | amendment of a normal vector in two directions. It is a figure which shows the outline | summary of the procedure when correct | amending the normal vector on the curved surface patch boundary line which goes to a specific direction. It is a figure which illustrates the non-adjacent normal correction processing flow of a design support apparatus. It is a figure which illustrates the non-adjacent normal correction processing flow of a design support apparatus. It is a figure which illustrates the curved surface correction process flow of a design support apparatus. It is an example of the curved surface which distortion generate | occur | produced. It is a figure which illustrates the change of a normal distribution curve. It is the figure which expanded the curved surface and illustrated the normal line. This is an example in which the correction of the design support device is applied to the curved surface during morphing. It is a figure which illustrates distortion and the connectivity between area | regions by a color-coded display.

Explanation of symbols

PAT1, PAT2 Curved patch V1, V2, V3, V4, N1, N2 Normal vector 112 Boundary line 114 Normal vector 115 Normal distribution curve 116 Apex of sudden change portion 117 Correction curve

Claims (6)

A design support device that supports operation of a solid model formed by a combination of surface elements having a boundary line including a plurality of vertices and a surface surrounded by the boundary line,
Means for obtaining a normal vector of each surface element at a boundary position between two adjacent surface elements;
Means for replacing with a common correction normal vector when respective normal vectors at the boundary positions of the two adjacent surface elements do not match;
Means for extracting a normal vector of each surface element on an evaluation reference line formed by connecting boundary lines of surface elements arranged in a predetermined direction on a curved surface including a plurality of non-adjacent surface elements;
Means for obtaining a first normal vector distribution curve indicating a distribution of a tip of the normal vector on the evaluation reference line;
Means for obtaining a second normal vector distribution curve by removing one or more normal vectors to be corrected from normal vectors included in the first normal vector distribution curve;
Means for correcting the normal vector of the correction target by moving the tip of the normal vector of the correction target in a direction orthogonal to the second normal vector distribution curve;
Means for correcting the surface element by the corrected normal vector.   The design support apparatus according to claim 1, wherein the normal vector to be corrected is selected from normal vectors included in a distribution of a curved portion where a curvature or change rate of the normal vector distribution curve exceeds a predetermined limit value. . A design support method for supporting the operation of a solid model formed by a combination of surface elements having a boundary line including a plurality of vertices and a surface surrounded by the boundary line, the computer comprising:
Obtaining a normal vector of each surface element at a boundary position between two adjacent surface elements;
Replacing each normal vector at the boundary position of the two adjacent surface elements with a common correction normal vector when they do not match;
Extracting a normal vector of each surface element on an evaluation reference line configured by connecting boundary lines of surface elements arranged in a predetermined direction on a curved surface including a plurality of non-adjacent surface elements;
Obtaining a first normal vector distribution curve indicating a distribution of a tip of the normal vector on the evaluation reference line;
Obtaining a second normal vector distribution curve by removing one or more normal vectors to be corrected from normal vectors included in the first normal vector distribution curve;
Correcting the normal vector to be corrected by moving the tip of the normal vector to be corrected in a direction perpendicular to the second normal vector distribution curve;
And correcting the surface element with the corrected normal vector.   The design support method according to claim 3, wherein the normal vector to be corrected is selected from normal vectors included in a distribution of a curved portion where a curvature or change rate of the normal vector distribution curve exceeds a predetermined limit value. . A design support program for supporting the operation of a solid model formed by a combination of surface elements having a boundary line including a plurality of vertices and a surface surrounded by the boundary line, the computer comprising:
Obtaining a normal vector of each surface element at a boundary position between two adjacent surface elements;
Replacing each normal vector at the boundary position of the two adjacent surface elements with a common correction normal vector when they do not match;
Extracting a normal vector of each surface element on an evaluation reference line configured by connecting boundary lines of surface elements arranged in a predetermined direction on a curved surface including a plurality of non-adjacent surface elements;
Obtaining a first normal vector distribution curve indicating a distribution of a tip of the normal vector on the evaluation reference line;
Obtaining a second normal vector distribution curve by removing one or more normal vectors to be corrected from normal vectors included in the first normal vector distribution curve;
Correcting the normal vector to be corrected by moving the tip of the normal vector to be corrected in a direction perpendicular to the second normal vector distribution curve;
And a step of correcting the surface element with the corrected normal vector.   The design support program according to claim 5, wherein the normal vector to be corrected is selected from normal vectors included in a distribution of a curved portion where a curvature or change rate of the normal vector distribution curve exceeds a predetermined limit value. .

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