Surface fitting processing method, fitting processing device and fitting processing program, and computer-readable storage medium storing the fitting processing program

Abstract

The surface fitting processing method comprises the following steps: setting the nearest point (H) corresponding to each measurement point (Q) on the surface model (S); performing the least square method in such a way that the sum of the squares of the distances between the nearest point (H) and the measurement point (Q) is minimized, thereby determining each control point (R ijk ) movement (ΔR ijk ); and based on the movement amount (ΔR ijk ) performs FFD, thereby fitting the surface model (S) to the measured points (Q).

Description

Technical Field

[0001] The technology disclosed herein relates to a surface fitting processing method, a fitting processing device and a fitting processing program, and a computer-readable storage medium storing the fitting processing program. Background Art

[0002] As a method for fitting a curved surface, so-called free-form deformation (FFD) is widely known. FFD is a method of deforming a deformable body (volume) covering the curved surface to deform the curved surface via the deformable body.

[0003] For example, Patent Document 1 discloses a method of FFD based on a Gaussian function (GFFD).

[0004] Prior art literature

[0005] Patent Literature

[0006] Patent Document 1: Japanese Patent Application Publication No. 2004-78309 Summary of the invention

[0007] Problem that the invention aims to solve

[0008] In a general FFD, a plurality of grid points (so-called control points) are set in the above-mentioned deformable body, and these control points are moved respectively, thereby realizing deformation of the deformable body.

[0009] Here, when a curved surface is finely deformed, such as an outer panel of an automobile, the number of control points increases compared to a case where a simpler deformation is sufficient. So far, when the number of control points becomes large, it has not been possible to systematically determine the movement amount of each control point based on a clear theoretical basis.

[0010] The technology disclosed herein has been accomplished in view of this point, and its purpose is to systematically determine the movement amount of each control point in FFD based on a clear theoretical basis.

[0011] Solutions for solving problems

[0012] The technology disclosed herein relates to a fitting processing method for fitting a curved surface model set in a three-dimensional space to a curved surface of a plurality of target points set in the three-dimensional space by executing free shape deformation by a computer.

[0013] The surface fitting processing method comprises: a control point setting step, setting multiple control points in the free shape deformation in a manner of surrounding at least a portion of the surface model; a deformation object point setting step, setting multiple deformation object points corresponding to the multiple target points on the surface model; a movement amount determination step, performing the least squares method in a manner that minimizes the cumulative value obtained by accumulating the squares of the distances between the deformation object point and the target point corresponding to the deformation object point, thereby determining the movement amount of each of the multiple control points; and an FFD execution step, performing the free shape deformation based on the movement amount, thereby fitting the surface model to the multiple target points.

[0014] According to this method, the movement amount of each control point in free shape deformation (FFD) can be determined by the least square method using the sum of squares of the distances between the deformation target point and multiple target points. In this way, the theoretical basis can be clarified and the movement amount of each control point can be systematically determined.

[0015] Furthermore, the plurality of target points may be constituted by a plurality of measurement points obtained by measuring the surface shape of the mold.

[0016] According to this method, even when a measurement point that may contain noise or the like is set as a target point, the movement amount of each control point can be appropriately calculated.

[0017] Furthermore, the deformation target point may be set as a point on the curved surface model that is closest to the target point.

[0018] This method is advantageous in that the deformation target point can be appropriately set and the movement amount of each control point can be systematically determined.

[0019] In addition, the surface model may be composed of a plurality of surfaces, and the surface fitting processing method may execute the control point setting process, the deformation object point setting process, the movement amount determination process and the FFD execution process in such a way that the plurality of surfaces are deformed simultaneously.

[0020] According to this method, it is possible to fit curved surface models having various shapes.

[0021] In addition, it can also be set as: the surface model is a combination of a surface that divides the definition domain of the surface model and a trimming surface that trims the surface, and the surface fitting processing method performs the control point setting process, the deformation object point setting process, the movement amount determination process and the FFD execution process on the boundary line between the surface and the trimming surface.

[0022] According to this method, FFD is performed on the boundary line of the trimmed surface. Here, by using the deformation result of the surface, the surface model can be fitted while maintaining the continuity of the boundary line between the surface and the trimmed surface, the continuity of the tangent plane between the surface and the trimmed surface, and the continuity of the curvature between the surface and the trimmed surface.

[0023] In addition, the curved surface fitting processing method divides the movement amount determined in the movement amount determination step, and executes the FFD execution step based on each of the divided movement amounts, thereby repeatedly executing the free shape deformation a plurality of times.

[0024] According to this method, by executing FFD in multiple stages, it is possible to suppress the expansion of the curved surface and realize deformation with higher accuracy.

[0025] Furthermore, the curved surface fitting processing method may include the steps of: extrapolating a curved surface to the curved surface model; and setting the deformation target point on the extrapolated curved surface.

[0026] According to this method, undulations near the boundary of the curved surface can be suppressed, and smoother fitting can be achieved.

[0027] Furthermore, the curved surface fitting processing method may include a step of adding the target point so as to correspond to the extrapolated curved surface.

[0028] Furthermore, the control point setting step may be configured to set a deformable body covering the curved surface model, and to arrange the plurality of control points within the deformable body.

[0029] Another technology disclosed herein relates to a surface fitting processing device, which is composed of a computer having a computing unit, and the surface model set in a three-dimensional space is fitted to a plurality of target points set in the three-dimensional space by executing free shape deformation by the computer. The computing unit includes: a control point setting unit, which sets a plurality of control points in the free shape deformation in a manner of surrounding at least a portion of the surface model; a deformation object point setting unit, which sets a plurality of deformation object points corresponding to the plurality of target points on the surface model; a movement amount determination unit, which determines the movement amount of each of the plurality of control points by executing the least square method in a manner of minimizing the cumulative value obtained by accumulating the squares of the distances between the deformation object point and the target point corresponding to the deformation object point; and an FFD execution unit, which executes the free shape deformation based on the movement amount, thereby fitting the surface model to the plurality of target points.

[0030] According to this configuration, the theoretical basis can be clarified and the movement amount of each control point can be systematically determined.

[0031] Another technology disclosed herein relates to a surface fitting processing program, which causes a computer to perform free shape deformation to fit a surface model set in a three-dimensional space to a plurality of target points set in the three-dimensional space. The surface fitting processing program causes the computer to perform the following process: setting a plurality of control points in the free shape deformation in a manner that surrounds at least a portion of the surface model; setting a plurality of deformation object points on the surface model that correspond to the plurality of target points, respectively; performing the least square method in a manner that minimizes the cumulative value obtained by accumulating the squares of the distances between the deformation object points and the target points corresponding to the deformation object points, thereby determining the movement amount of each of the plurality of control points; and performing the free shape deformation based on the movement amount, thereby fitting the surface model to the plurality of target points.

[0032] According to this program, the theoretical basis can be clarified and the movement amount of each control point can be systematically determined.

[0033] Another technology disclosed herein also relates to a computer-readable storage medium, characterized in that the fitting processing program is stored in the computer-readable storage medium.

[0034] According to this storage medium, the theoretical basis can be clarified and the movement amount of each control point can be systematically determined.

[0035] Effects of the Invention

[0036] As described above, according to the surface fitting processing method, the fitting processing device, the fitting processing program, and the computer-readable storage medium storing the fitting processing program, the movement amount of each control point can be systematically determined based on a clear theoretical basis. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 FIG. 1 is a diagram illustrating a hardware configuration of a curved surface fitting processing device.

[0038] Figure 2 It is a diagram illustrating the software configuration of a curved surface fitting processing device.

[0039] Figure 3 This is a diagram for explaining the basic concept of FFD.

[0040] Figure 4 This is a flowchart illustrating the basic procedure of the surface fitting processing method.

[0041] Figure 5 This is a diagram for explaining the process of covering a curved surface model with a deformable body.

[0042] Figure 6 is a flowchart illustrating the closest point search process.

[0043] Figure 7 It is a diagram for explaining the process of searching for the closest point.

[0044] Figure 8 is a flowchart illustrating the process of multi-stage deformation in FFD.

[0045] Fig. 9 It is a diagram for explaining the process of multi-stage deformation in FFD.

[0046] Fig.10 This is a diagram illustrating a surface model composed of trimmed surfaces.

[0047] Fig.11 A diagram illustrating a curved surface model composed of a plurality of curved surfaces.

[0048] Fig.12 This is a diagram for explaining the structure of an extrapolated surface to a surface model.

[0049] Fig.13 This is a diagram illustrating a curved surface model obtained by modeling the shape of a draw bead.

[0050] Fig.14 It is a diagram illustrating an AA cross section of a curved surface model.

[0051] Fig.15 It is a diagram showing the deformation result of the surface model.

[0052] Fig.16 This is a diagram showing the result of applying multi-stage deformation to a surface model.

[0053] Fig.17 This is a diagram illustrating the configuration of a CPU as a computing unit. DETAILED DESCRIPTION

[0054] Hereinafter, embodiments of the present disclosure will be described based on the drawings. The following description is for illustrative purposes only.

[0055] <Device Structure>

[0056] Figure 1 is a diagram illustrating a hardware configuration of a surface fitting processing device (specifically, a computer 1 constituting the processing device) according to the present disclosure. Figure 2 This is a diagram illustrating the software structure.

[0057] Figure 1The illustrated computer 1 includes a central processing unit (CPU) 3 that controls the entire computer 1, a read only memory (ROM) 5 that stores a boot program, etc., a random access memory (RAM) 7 that functions as a main memory, a hard disk drive (HDD) 9 that serves as a secondary storage device, a display 11 that displays fitting results, etc., a video RAM (VRAM) 13 that functions as a memory for storing image data displayed on the display 11, and a keyboard 15 and a mouse 17 that serve as input devices. In addition, the computer 1 can communicate with external devices via an interface 21.

[0058] like Figure 2 As illustrated, the program memory of the HDD 9 stores an operating system (OS) 19 , a curved surface fitting processing program 29 , an application program 39 , and the like.

[0059] The curved surface fitting processing program 29 is a program for executing the curved surface fitting processing method described later, and is configured to cause the CPU 3 to execute each step ( Figure 4 The process corresponding to step S1 to step S5) is as follows. Figure 1 As illustrated, the curved surface fitting processing program 29 is stored in advance in the computer-readable storage medium 19 .

[0060] On the other hand, the data memory of the HDD 9 stores model data 49 indicating the curved surface model S to be deformed and measurement data 59 indicating a plurality of target points to be deformed of the curved surface model S.

[0061] In addition, a 3D curved surface obtained by modeling a mold can be used as the curved surface model S. In this case, a plurality of measurement points Q obtained by measuring the surface shape of the mold can be used as the plurality of target points. In this embodiment, after describing the structure generally associated with the curved surface model S, the structure associated with a specific curved surface model such as the curved surface model S composed of a plurality of curved surfaces S1 and S2 is described.

[0062] In addition, the fitted curved surface model generated by executing the fitting processing program 29 and various calculation results generated by executing the application program 39 are also stored in the data memory of the HDD 9 .

[0063] In the above structure, the fitting processing program 29 and the application program 39 are started according to the command input from the keyboard 15 and the mouse 17. At this time, the fitting processing program 29 and the application program 39 are loaded from the HDD 9 to the RAM 7 and executed by the CPU 3. By executing the fitting processing program 29 and the application program 39 by the CPU 3, the computer 1 functions as a surface fitting processing device. Here, the CPU 3 corresponds to the computing unit mentioned in the present disclosure. The CPU 3 as the computing unit is as follows: Fig.17 As illustrated, the control point setting unit 31 , the deformation target point setting unit 32 , the movement amount determination unit 33 , and the FFD execution unit 34 are provided.

[0064] <Surface fitting processing method>

[0065] Figure 3 This is a diagram used to explain the basic concept of FFD. Figure 4 is a flowchart illustrating the basic process of the surface fitting processing method. Figure 5 : is a diagram for explaining the process of covering the curved surface model S with the deformable body V. Figure 6 is a flowchart illustrating the search process of the nearest point H. Figure 7 3 is a diagram for explaining the search process of the nearest point H.

[0066] Figure 4 In the fitting process shown, the computer 1 executes free-form deformation (FFD) to fit a curved surface model S set in a three-dimensional space to a plurality of target points (measurement points Q) set in the three-dimensional space.

[0067] Here, in FFD, the surface model S to be deformed is first set. Next, a deformable body V having a plurality of control points is set, and the surface model S is covered with the deformable body V. Then, each control point is moved, thereby deforming the deformable body V defining the control point, and further deforming the coordinate system itself. As the coordinate system is deformed, the surface model S covered by the deformable body V is also deformed (see Figure 3 ).

[0068] In addition, the deformation of the surface model S based on FFD is not performed using the global coordinate system, but using the parameter space. In particular, in the present embodiment, the deformation of the surface model S is performed using a free-form surface of two parameters. In the following description, as an example of such a free-form surface, an example using a B-Spline surface is described.

[0069] Specifically, the B-Spline surface can be defined by the following equation (1).

[0070] [Number 1]

[0071]

[0072] [Number 2]

[0073]

[0074] The above formula (1) is obtained by parametrically expressing the coordinates on the surface model S. In formula (1), (u, v) are variables when the B-Spline surface is parametrically expressed, which specifies the parameter space (UV space). Moreover, "n" is the degree of the B-Spline surface in the u direction, and "m" is the degree of the B-Spline surface in the v direction. In addition, as shown in formula (2), "N" is the so-called B-Spline basis function. That is, "t" in formula (2) is the so-called node column. In addition, the superscripts n and m in formula (2) represent the degrees of the B-Spline surface in the u direction and the v direction, respectively. In addition, P ij represents the i-th control point in the u direction and the j-th control point in the v direction.

[0075] (Basic concept of fitting processing method)

[0076] The following describes Figure 4 each step.

[0077] -Step S1-

[0078] In the first step S1, the computer 1 reads the model data 49 and the measurement data 59 stored in the program memory. The model data 49 and the measurement data 59 are set in the three-dimensional space as described above, and include the surface model S to be deformed by FFD and a plurality of measurement points Q to be deformation targets of the surface model S.

[0079] The surface model S is represented as a B-Spline surface that is parametrically expressed using two parameters u and v and developed using the B-Spline basis function as described above. The shape of the surface model S can be determined using the control points P ij The coordinates of the B-Spline and the node list that determines the shape of the B-Spline basis function.

[0080] -Step S2-

[0081] In the next step S2, the control point setting unit 31 covers at least a part of the curved surface model S and the plurality of measurement points Q with the deformable body V, and sets a plurality of control points P in the deformable body V. ijk As shown in the following equation (3), the deformable body V can be developed using the B-Spline basis function similarly to the surface model S.

[0082] [Number 3]

[0083]

[0084] The B-Spline body (hereinafter, also simply referred to as "deformed body V") defined by the above equation (3) V represents not a curved surface but a three-dimensional shape, and therefore uses three variables (u, v, w).

[0085] Here, in order to ensure curvature continuity, it is necessary to use B-Spline basis functions of degree 3 or more in all of the u direction, the v direction, and the w direction. In this embodiment, an example of using a B-Spline basis function of degree 3 is described.

[0086] In addition, in the above formula (3), P ijk The shape of the deformable body V can be determined by using the control points P. ijk The coordinates of the B-Spline and the node list that determines the shape of the B-Spline basis function.

[0087] Here, regarding multiple control points P ijk , it is sufficient to set it so as to surround at least a part of the curved surface model S. In this case, the deformable body V covers at least a part of the curved surface model S. In particular, in the present embodiment, the deformable body V and the control points P are set so as to cover all of the curved surface model S and the plurality of measurement points Q. ijk At the same time, each control point P ijk Arranged at equal intervals to form a simple cubic grid (see Figure 5 ).

[0088] When the deformable body V and the control point P ijk When the setting is completed, the process proceeds from step S2 to step S3. Step S2 illustrated here is an example of the "control point setting process" in this embodiment.

[0089] -Step S3-

[0090] In the next step S3, the deformation target point setting unit 32 sets a plurality of deformation target points corresponding to the plurality of measurement points Q on the curved surface model S. In the present embodiment, each deformation target point is set as the closest point H to each measurement point Q on the curved surface model S.

[0091] For example, the closest point H to a certain measurement point Q on the curve C can be calculated as follows. That is, as shown in the following equation (4), when the line segment connecting the point P and the point on the curve C is orthogonal, the point P is closest to the point on the curve C.

[0092] [Number 4]

[0093] C′(u)·(PC(u))=0……(4)

[0094] Therefore, by performing the search using the above formula (4) in both the u direction and the v direction, the closest point H to each measurement point Q on the curved surface model S can be found. Figure 6 Flowchart shown.

[0095] First, in Figure 6 In step S31, the deformation target point setting unit 32 sets the value of the parameter (u, v) in the surface model S at the center in the parameter space (UV space).

[0096] In the next step S32 , the deformation target point setting unit 32 determines whether it is an odd-numbered search, and selects the u direction if the determination is “yes”, whereas the v direction is selected if the determination in step S32 is “no”.

[0097] In the next step S33, the deformation target point setting unit 32 changes the unselected direction on the surface model S while fixing the direction selected in step S32. Then, the parameter closest to each measurement point Q is found. The processing related to step S33 is performed using the above formula (4). In addition, when performing numerical calculations on the above formula (4), the dichotomy method, Newton's method, etc. can be used.

[0098] In the next step S34 , the deformation target point setting unit 32 substitutes the parameters found in step S33 into the coordinates of the closest point H, thereby updating the coordinates of the closest point H.

[0099] In the next step S35, the deformation target point setting unit 32 determines whether the coordinates of the closest point H updated in step S34 satisfy the specified conditions. If "yes", the process ends. On the other hand, if "no", it returns to step S32 after increasing the search count by 1.

[0100] In addition, the predetermined conditions in step S35 include whether the amount of change in the parameters (u, v) during the search and / or the distance between the nearest point H and the measurement point Q is less than a predetermined threshold. In addition or instead of this, a threshold may be set for the number of searches for the nearest point H, and whether the number of searches exceeds the threshold may be determined.

[0101] For example Figure 7As shown in FIG. 1 , in the first search, the v direction is changed while the u direction is fixed, and the value of the parameter v that is closest to the measurement point Q is searched. The value of v thus searched is used to update the coordinates of the nearest point H, and it is determined whether the updated coordinates meet the prescribed conditions. Here, if the updated coordinates do not meet the prescribed conditions, the u direction is changed while the v direction is fixed, and the value of the parameter u that is closest to the measurement point Q is searched. The coordinates of the nearest point H are updated with the value of u thus searched, and it is determined again whether the updated coordinates meet the prescribed conditions.

[0102] Such a process is repeatedly performed, and the values ​​of the parameters (u, v) at a time point when the predetermined conditions are satisfied are set as the coordinates of the final closest point H.

[0103] in addition, Figure 6 The processing shown is executed for all the measurement points Q covered by the deformable body V. For example, when the number of measurement points Q is N, the coordinates of the closest point H are searched for each of the N measurement points Q.

[0104] Below, the coordinates of the pth closest point H among the N closest points H are marked as (u p , v p In the following description, the coordinates of the measurement point Q corresponding to the closest point H are sometimes specifically indicated as Q (u p , v p ).

[0105] In addition, when the measurement point Q is far away from the nearest point H corresponding thereto, it is not suitable for fitting by the least square method described later, and therefore needs to be removed. Therefore, the surface fitting processing method involved in this embodiment includes a step of removing the measurement point Q from the object of fitting when the distance between the measurement point Q and the nearest point H exceeds a predetermined threshold.

[0106] When all measurement points Q are executed Figure 6 When the processing shown is completed, Figure 6 The process from Figure 4 The process proceeds from step S3 to step S4. Step S3 illustrated here is an example of the "deformation target point setting process" in this embodiment.

[0107] -Step S4-

[0108] Below, it should be noted that in order to prevent the control point P of the surface model S ij Confusion, the control point P of the deformed body V ijk Marked "R ijk ”.

[0109] In step S4 following step S3, the movement amount determination unit 33 performs the least square method so as to minimize the cumulative value obtained by accumulating the squares of the distances between the deformation target point (the closest point H) included in the deformable body V and the measurement point Q corresponding to the closest point H. By executing the least square method, the CPU 3 determines the plurality of control points R in the FFD. ijk The respective movement amount ΔR ijk .

[0110] When using FFD, the control points R of the deformable body V are ijk The deformable body V is used to deform the curved surface model S. On the other hand, the shape of the curved surface model S is determined by the control points P ij To characterize.

[0111] Therefore, in order to deform the surface model S using FFD, the control points R of the deformable body V are required. ijk and the control point P of the surface model S ij Here, in order to prevent the control point R of the deformable body V from ijk The control point P of the surface model S is mixed with the corner mark ij When it is denoted as P(I, J), the control point P(I, J) itself can be expressed as the control point R of the deformable body V in the same way as in equation (3). ijk To expand.

[0112] [Number 5]

[0113]

[0114] s, t, and w can be determined from I and J, respectively. ijk Arranged in a grid pattern, the correspondence between the two parameters (I, J) in the curved surface model S and the three parameters (s, t, w) in the deformable body V can be easily calculated.

[0115] Then, after replacing n and m in the equation (1) with L and M, respectively, the equation (5) is substituted into the equation (1), whereby the curved surface model S can be expressed as in the following equation (6).

[0116] [Number 6]

[0117]

[0118] This can be used to define the objective function (Cost Function) as shown in the following equation (7).

[0119] [Number 7]

[0120]

[0121] Here, the first term in the brackets of equation (7) represents the control point R of the deformable body V. ijk Moved by a specified amount ΔR ijk On the other hand, the second term in the brackets of equation (7) represents the coordinates of the measurement point Q corresponding to the closest point H.

[0122] That is, the objective function F represents the control point R ijk Moved by a specified amount ΔR ijk The sum of the squares of the distances between the closest point H and the measured point Q at the time (the cumulative value obtained by accumulating the squares of the distances). Therefore, the objective function F can be regarded as the objective function in the least squares method. If we search for the movement amount ΔR that minimizes the objective function F, ijk And the control point R ijk Move the searched movement amount ΔR ijk , then the sum of the squares of the distances between the nearest point H and the measurement point Q can be minimized.

[0123] Specifically, the movement amount determination unit 33 uses the movement amount ΔR ijk Partially differentiate the objective function F and set it to 0, thereby finding the movement amount ΔR that minimizes the objective function F. ijk .

[0124] Here, for simplicity, it is set as:

[0125] [Number 8]

[0126] R′ ijk =R ijk +ΔR ijk ……(8)

[0127] When using R ijk 'When the objective function F is partially differentiated, it becomes:

[0128] [Number 9]

[0129]

[0130] When the left side of equation (9) is set to 0, the following equation (10) is obtained.

[0131] [Number 10]

[0132]

[0133] When formula (10) is recorded in a matrix form, the following formula (11) is obtained.

[0134] [Number 11]

[0135] AR′ ijk =b……(11)

[0136] In the formula (11), the matrix A is a square matrix of (i×j×k) order. Each element of the matrix A is represented by the following formulas (12) to (14).

[0137] [Number 12]

[0138]

[0139] [Number 13]

[0140] r(ri, rj, rk)=(ri×m×n)+(rj×n)+rk……(13)

[0141] [Number 14]

[0142] c(ci,cj,ck)=(ci×m×n)+(cj×n)+ck……(14)

[0143] By transforming formula (11) about R ijk 'Solve and find the R that minimizes the objective function F ijk ', and then the movement amount ΔR can be calculated ijk As a solution to equation (11), for example, the LU decomposition method can be used. The movement amount determination unit 33 calculates the movement amount ΔR by numerical calculation using the LU decomposition method or the like. ijk .

[0144] When the movement amount ΔR ijk At the end of the calculation, from Figure 3 The process proceeds from step S4 to step S5. Step S4 illustrated here is an example of the "movement amount determination process" in this embodiment.

[0145] -Step S5-

[0146] In step S5 following step S4, the FFD execution unit 34 calculates the movement amount ΔR based on the movement amount ΔR calculated in step S4. ijk FFD is performed, thereby fitting a surface model S to a plurality of measurement points Q.

[0147] Specifically, the FFD execution unit 34 sets the control point R ijk Move and update to the new control point R ijk +ΔR ijk . Thus, the deformable body V is deformed based on equation (3). Then, the control point P(I, J) of the surface model S is updated based on equation (5), and at the same time, the surface model S is deformed based on equation (1). Figure 4 The process shown ends.

[0148] In addition, step S5 illustrated here is an example of the “FFD execution step” in this embodiment.

[0149] Thus, according to the present embodiment, each control point R in the FFD can be determined by using the least square method of the sum of squares of the distances between the nearest point H as the deformation target point and each measurement point Q corresponding thereto. ijk Movement ΔR ijk In this way, the theoretical basis can be clarified, and the movement amount ΔR of each control point can be systematically determined. ijk .

[0150] Furthermore, by using a plurality of measurement points Q representing the surface shape of the mold as a plurality of target points, even when the measurement points Q that may contain noise or the like are used as target points, each control point R can be appropriately calculated. ijk Movement ΔR ijk .

[0151] -Structure associated with multi-stage deformation-

[0152] Figure 8 is a flowchart illustrating the process of multi-stage deformation in FFD. Fig. 9 It is a diagram for explaining the process of multi-stage deformation in FFD.

[0153] In addition, when the surface model S is far away from each measurement point Q, it is possible that Figure 4 The process is not enough. That is, when using FFD based on the least squares method, whether the surface model S and each measurement point Q are close enough depends on the search accuracy of the closest point H as the deformation target point. When the surface model S and each measurement point Q are relatively far away from each other, the parameters obtained as the closest point H may not be optimal. Therefore, by repeating the deformation based on FFD multiple times and searching for the closest point H each time, it is possible to perform deformation with higher accuracy.

[0154] Specifically, the computer 1 as the surface fitting processing device converts the shift amount ΔR determined in the above-mentioned step S4 (shift amount determination step) into ijk The segmentation is performed, and based on the movement amount ΔR after the segmentation ijk By executing the aforementioned step S5 (FFD execution process), FFD is repeatedly executed a plurality of times.

[0155] Figure 8 is a flow chart illustrating the process of such a multi-stage deformation. Figure 8 In FIG. 1 , “N” represents the number of repetitions of FFD. The number of repetitions N is preset and stored in the RAM 7, HDD 9, etc.

[0156] First, although in Figure 8 is omitted, but computer 1 is as Figure 4The model data 49 is read and the deformable body V is set as in steps S1 to S2 of FIG. 1. At this time, the computer 1 also reads the number of repetitions N of the FFD.

[0157] Then, if Figure 8 As shown in step S101, the CPU 3 sets a variable i to zero. The variable i represents the number of repetitions at this point in time.

[0158] In the next step S102, the deformation target point setting unit 32 searches for the closest point H corresponding to each measurement point Q on the curved surface model S. i Here, the nearest point H i The subscript i in the code indicates the number of repetitions i. Specifically, in step S102, the same Figure 4 The same process as step S3, that is, using Figure 6 Here, in the case of i=0, that is, the closest point H0 found in the first search is Figure 4 The nearest point H obtained in step S3 is consistent.

[0159] In the next step S103, the movement amount determination unit 33 determines the movement amount based on the nearest point H found in step S102. i , use the least squares method to calculate the movement amount ΔR of the control point i . Movement ΔR i The subscript i and the nearest point H i Specifically, in step S103, the same as Figure 4 The same processing is performed as in step S4.

[0160] In the next step S104, the movement amount determination unit 33 calculates the movement amount ΔR obtained in step S103. i Divide and calculate the new movement amount ΔR i Specifically, the movement amount ΔR is obtained by the following formula (15): i '.

[0161] [Number 15]

[0162]

[0163] In the next step S105, the FFD execution unit 34 performs the operation based on the new movement amount ΔR obtained in step S104. i ', so that the control point R of the deformable body V moves, and then the control point P (I, J) of the surface model S moves.

[0164] In the next step S106, the CPU 3 determines whether the number of repetitions i has reached N-1, that is, whether steps S102 to S105 have been repeated N times. If the determination is "yes", the deformation by FFD is terminated.

[0165] On the other hand, if the determination in step S106 is "No", in step S107, the number of repetitions i is incremented by 1, and the process returns to step S102. When the process returns to step S102, the new movement amount ΔR is used. i 'Search for the nearest point H on the deformed surface model S i+1 By recursively repeating this process, the nearest point H i , H i+1 , H i+2 Gradually approach the measuring point Q (refer to Fig. 9 ).

[0166] In addition, it can be seen from the above formula (15) that when the number of repetitions i is relatively small, the new movement amount ΔR i 'It becomes the original movement amount ΔR i On the other hand, as the number of repetitions i increases, the new movement amount ΔR i 'Become close to the original movement amount ΔR i In particular, when the number of repetitions i reaches N-1, the new movement amount ΔR i ' and the original movement ΔR i Consistent.

[0167] In this way, by deforming the curved surface model S in multiple stages, it is possible to suppress the expansion of the curved surface and realize deformation with higher accuracy.

[0168] <Structure associated with a specific surface model>

[0169] -Structures associated with clipping surfaces-

[0170] Fig.10 3 is a diagram illustrating a curved surface model S composed of trimmed curved surfaces St.

[0171] As described above, as the curved surface model S, a 3D curved surface obtained by modeling the mold can be used, and as the plurality of target points, a plurality of measurement points Q representing the surface shape of the mold can be used. Here, in the case of a mold having a complex and fine shape such as a mold for an outer panel part of an automobile, it may not be modeled as Figure 3 Instead of being a single surface as shown in FIG. 1 , it is modeled as a surface composed of so-called trimming surfaces.

[0172] That is, Fig.10As illustrated, fitting may be performed on a curved surface model S′ that is a combination of a curved surface Sd that partitions the domain of the curved surface model S′ and a trimmed curved surface St that trims the curved surface Sd.

[0173] However, when only the control point P(I, J) of the curved surface model S is set as the moving object to determine the control point R of the deformable body V ijk Movement ΔR ijk In this case, the control points of the trimming surface St cannot be moved.

[0174] Therefore, the computer 1 according to the present embodiment is configured to perform FFD-based fitting on not only the curved surface Sd constituting the curved surface model S′ but also the boundary line C between the curved surface Sd and the trimmed curved surface St.

[0175] Specifically, the surface Sd is fitted in the same manner as the surface model S described above. On the other hand, the boundary line C between the surface Sd and the trimmed surface St is defined as a closed loop in the UV space (see Fig.10 ) based on which the closed loop can be subjected to FFD using the least squares method.

[0176] More specifically, first, based on the trimming surface St in the UV space, the sampled points are arranged at appropriate intervals on the surface Sd so as to follow the boundary line C between the trimming surface St and the surface Sd. By executing the aforementioned steps S2 (control point setting process), S3 (deformation target point setting process), S4 (movement amount determination process), and S5 (FFD execution process) on the sampled points arranged in this way, the boundary line C can be deformed using FFD. Then, by reflecting the deformation result of the boundary line C on the deformation result of the surface Sd, the trimming surface St can also be indirectly fitted.

[0177] In this way, by using the execution results of FFD for the boundary line C defined as a closed loop and the deformation results for the surface Sd, the surface model S can be fitted while maintaining the continuity of the boundary line C between the surface Sd and the trimmed surface St, the continuity of the tangent plane between the surface Sd and the trimmed surface St, and the continuity of the curvature between the surface Sd and the trimmed surface St.

[0178] -Structure associated with the trimming surface of multiple surfaces-

[0179] Fig.11 This is a diagram illustrating a curved surface model composed of a plurality of curved surfaces S1 and S2.

[0180] Generally speaking, when a model such as a mold is composed of multiple curved surfaces, it is desirable to deform the surfaces while maintaining the connection relationship between the curved surfaces. Fig.11As illustrated, the curved surface fitting processing method according to the present embodiment can deform a plurality of curved surfaces simultaneously.

[0181] That is, the surface model S is composed of a plurality of surfaces S1, S2, ... set in three-dimensional space, and the computer 1 as a surface fitting processing device can execute the aforementioned steps S2 (control point setting process), step S3 (deformation object point setting process), step S4 (movement amount determination process) and step S5 (FFD execution process) in a manner that deforms these plurality of surfaces S1, S2, ... simultaneously.

[0182] Here, basically the same processing as when there is one curved surface is performed, but when there are multiple curved surfaces, it is necessary to perform processing to select a curved surface to be deformed for each measurement point Q. Specifically, before and after step S3, the computer 1 calculates the distance between each measurement point Q and all the curved surfaces S1, S2, ..., and selects the curved surface with the shortest calculated distance. In this way, the process of associating the shortest curved surface and further associating the closest point H is performed for each measurement point Q.

[0183] When the least square method is performed based on equation (11) or the like, the sum of the squares of the distances from the corresponding curved surface is accumulated for each measurement point Q. By appropriately selecting the corresponding curved surface for each measurement point Q, a curved surface model S composed of a plurality of curved surfaces can be fitted.

[0184] For example, in Fig.11 In the example shown, the distance between the measurement point Q and the curved surface S1 and the distance between the measurement point Q and the curved surface S2 are calculated in sequence, and the curved surface S1 with the shorter distance is selected.

[0185] In this way, even a surface model S composed of multiple surfaces can be fitted using FFD.

[0186] -Structure associated with extrapolation of free-form surfaces-

[0187] Fig.12 It is used to illustrate the extrapolation of the surface model S to the surface S e Diagram of the structure.

[0188] In general, the curved surface obtained by fitting may be close enough to each measurement point Q, but may fluctuate unnaturally in places (especially near the boundary of the curved surface) away from each measurement point Q. For example, such a situation may occur when the curved surface model S has a complex shape or a large number of measurement points Q are arranged. This is not suitable for a mold having a complex and fine shape such as a mold for an outer panel part of a vehicle.

[0189] Therefore, the surface fitting processing method involved in this embodiment is as follows Fig.12As shown in the example, the surface S e The surface model S is extrapolated, and the nearest point H as the deformation target point is also set on the extrapolated surface (hereinafter referred to as the "extrapolated surface", with the reference symbol "S e In addition, it is also possible to connect the external plug-in surface S e The corresponding method is to virtually add measurement points Q as needed. e Such a process is added, for example, Figure 4 Before and after step S1 in .

[0190] Here, the external surface S e The shape of the external surface S is not limited. e For example, it may be set as a tangent plane extending from the end of the curved surface model S. In addition, regarding the additional measurement point Q e , and there is no need to pay special attention to its accuracy.

[0191] With this configuration, it is possible to suppress fluctuations near the boundary of the curved surface, and achieve smoother fitting.

[0192] <Specific example of the surface fitting processing method>

[0193] Generally speaking, in the production of molds for outer panel parts, there are many factors that involve manual work by craftsmen, and it is desired to improve efficiency. In particular, when the mold deteriorates and the same mold is manufactured again, if the same manual work as the initial manufacturing is performed, the efficiency is poor. Therefore, the so-called No. 1 mold is three-dimensionally measured, and the measurement results are fed back to the CAD system, so that the manual work of the craftsmen from the No. 2 mold onwards can be made more efficient.

[0194] Here, when feeding back to the CAD system, it is necessary to reflect the influence of the manual work of the craftsman on the three-dimensional CAD data used when manufacturing a new mold, for example. Therefore, the method of using the FFD method using the least squares method, that is, the surface fitting processing method involved in this embodiment, is applied on the basis of setting the measurement result of the physical mold as the measurement value Q and the three-dimensional CAD data before the feedback as the surface model S. In this way, the movement amount of the control point in the FFD can be systematically determined, and the three-dimensional CAD data can be fitted to the measurement value Q.

[0195] In this way, the surface fitting processing method involved in this embodiment can be used for so-called reverse engineering. In particular, the mold for the outer panel of the automobile has a complex and delicate shape, so the surface model obtained based on the mold may be composed of multiple cut surfaces or multiple surfaces. As mentioned above, the surface fitting processing method involved in this embodiment can clarify the theoretical basis even for such a surface model, and can perform fitting in a systematic manner.

[0196] In particular, the method for determining the movement amount of the control point has no theoretical basis at all, or it is not possible to determine whether the theoretical basis is appropriate. However, according to this embodiment, the theoretical basis can be clarified, and even if the number of control points increases, the movement amount can be automatically determined without causing a burden on the user.

[0197] Below, use Figure 13 to Figure 16 Here, a specific example of the surface fitting processing method is described. Fig.13 : is a figure which illustrates the curved surface model Sb which models the shape of a drawbead. Fig.14 is a diagram illustrating the AA section of the curved surface model Sb. Fig.15 is a diagram showing the deformation result of the surface model Sb. Fig.16 It is a diagram showing the result of applying multi-stage deformation to the curved surface model Sb.

[0198] Fig.13 The illustrated curved surface model Sb is a model of the shape of the draw bead in the die used to manufacture the outer panel component, and is composed of three-dimensional CAD data at the time of new manufacturing. Fig.13 The target points in the figure are composed of, for example, measurement points representing the surface shape of the actual mold processed by a craftsman through manual work.

[0199] At least Fig.14 In the illustrated cross section, the curved surface model Sb is divided into the first curved surface Sb1, the second curved surface Sb2, the third curved surface Sb3, the fourth curved surface Sb4, and the fifth curved surface Sb5 in order from the left side of the paper. In addition, the first external interpolation surface Sx1 is extrapolated from the first curved surface Sb1 toward the left side of the paper, and the second external interpolation surface Sx2 is extrapolated from the fifth curved surface Sb5 toward the right side of the paper. In addition, with the extrapolation of the first external interpolation surface Sx1 and the second external interpolation surface Sx2, a new measurement point Qe is added.

[0200] like Fig.15 As shown, the curved surfaces with relatively small curvatures such as the first curved surface Sb1 and the fifth curved surface Sb5 are deformed without excess or deficiency compared to the curved surfaces with relatively large curvatures such as the second curved surface Sb2 and the fourth curved surface Sb4.

[0201] in addition, Fig.16 In the case of a one-stage deformation (in Figure 8 The case where N is set to 1) and the case where the deformation is performed in 10 stages (in Figure 810) (where N is set to 10). As can be seen from the figure, when the surface model Sb is deformed in 10 stages, the distance between the closest point H on the deformed surface model Sb and the measurement point Q corresponding to the closest point H is substantially smaller than when the surface model Sb is deformed in 1 stage. This means that deformation in multiple stages achieves higher-precision fitting.

[0202] <Other Implementation Methods>

[0203] In the above embodiment, a configuration in which a B-Spline surface is used as a free-form surface is described, but the present disclosure is not limited to this configuration. For example, a Bezier surface, a NURBS surface, etc. may be used instead of the B-Spline surface exemplified in equation (1).

[0204] In addition, in the above-described embodiment, a structure in which the measurement point Q obtained by measuring the surface shape of the mold is used as the target point is illustrated, but the present disclosure is not limited to this structure. For example, numerical data used when a new mold is manufactured may also be set as the target point. That is, the technology disclosed herein can be used for purposes other than reverse engineering of molds.

[0205] Furthermore, in the above-mentioned specific examples, as a mold, a mold for an outer panel component of an automobile is exemplified, but the application object of the present disclosure is not limited thereto. The present disclosure can be applied to a mold for an inner panel component, a mold for a frame component, and all other molds. In addition, the method involved in the present disclosure is useful not only when a new mold is manufactured, but also when a mold is repaired, such as when a mold is corrected due to changes over the years.

[0206] In addition, in the above-described embodiment, a configuration is exemplified in which the closest point H on the curved surface model S is used as a deformation target point, but the present disclosure is not limited to this configuration. A point other than the closest point H may be used as a deformation target point.

[0207] In addition, in the above-described embodiment, a computer having one CPU 3 is illustrated as an example of the computer 1, but the present invention is not limited to such a structure. The computer 1 also includes parallel computers such as supercomputers and PC clusters. When the computer 1 is set as a parallel computer, a plurality of computers are used to execute the surface fitting processing program 29.

[0208] Industrial Applicability

[0209] As described above, the present disclosure is useful for the manufacture and maintenance of various molds represented by molds for outer panel components, and has industrial applicability.

[0210] Description of Reference Numerals

[0211] 1 Computer (surface fitting processing device)

[0212] 3 CPU (computing unit)

[0213] 31 Control point setting unit

[0214] 32 Deformation target point setting section

[0215] 33 Movement amount determination unit

[0216] 34 FFD Executive Department

[0217] 19 Storage Media

[0218] H Nearest point (deformation target point)

[0219] R ijk Control Points

[0220] ΔR ijk Movement

[0221] Q Measurement point (target point)

[0222] Q e Additional measurement points

[0223] S-surface model

[0224] S1, S2 multiple surfaces

[0225] Sd surface (surface that divides the domain)

[0226] St trimming surface

[0227] S e External surface (surface to be externalized)

[0228] V Deformation

Claims

1. A surface fitting processing method, wherein a surface model set in a three-dimensional space is fitted to a plurality of target points set in the three-dimensional space by executing free shape deformation by a computer, wherein: have: A control point setting step of setting a plurality of control points in the free shape deformation so as to surround at least a portion of the curved surface model; A deformation object point setting step of setting a plurality of deformation object points corresponding to the plurality of target points respectively on the surface model; A movement amount determination step is to determine the movement amount of each of the plurality of control points by performing a least square method in such a way that a cumulative value obtained by accumulating the squares of the distances between the deformation target point and a target point corresponding to the deformation target point is minimized; as well as an FFD execution step of executing the free shape deformation based on the movement amount, thereby fitting the curved surface model to the plurality of target points, The surface model is formed by combining a surface that divides the definition domain of the surface model and a cutting surface that cuts the surface. The control point setting step, the deformation target point setting step, the movement amount determination step, and the FFD execution step are performed on a boundary line between the curved surface and the trimming curved surface.

2. The surface fitting processing method according to claim 1, characterized in that: The plurality of target points are composed of a plurality of measurement points obtained by measuring the surface shape of the mold.

3. The surface fitting processing method according to claim 1 or 2, characterized in that: The deformation object point is set as the closest point on the curved surface model to the target point.

4. The surface fitting processing method according to claim 1 or 2, characterized in that: The surface model is formed by combining multiple surfaces. The control point setting step, the deformation target point setting step, the movement amount determination step, and the FFD execution step are performed so that the plurality of curved surfaces are deformed simultaneously.

5. The surface fitting processing method according to claim 1 or 2, characterized in that: The free shape deformation is repeatedly performed a plurality of times by dividing the movement amount determined in the movement amount determination step and executing the FFD execution step based on the divided movement amounts.

6. The surface fitting processing method according to claim 1 or 2, characterized in that: The following processes are available: extrapolating a surface to the surface model; and The deformation object point is set on the extrapolated curved surface.

7. The surface fitting processing method according to claim 6, characterized in that: A step of adding the target point so as to correspond to the extrapolated curved surface is provided.

8. The surface fitting processing method according to claim 1 or 2, characterized in that: The control point setting step sets a deformable body covering the curved surface model, and arranges the plurality of control points in the deformable body.

9. A surface fitting processing device, the surface fitting processing device comprising a computer having a computing unit, wherein the surface model set in a three-dimensional space is fitted to a plurality of target points set in the three-dimensional space by executing free shape deformation by the computer, wherein: The computing unit comprises: a control point setting unit that sets a plurality of control points in the free shape deformation in a manner that surrounds at least a portion of the curved surface model; A deformation object point setting unit, which sets a plurality of deformation object points corresponding to the plurality of target points respectively on the surface model; a movement amount determination unit that determines the movement amount of each of the plurality of control points by performing a least square method so as to minimize a cumulative value obtained by accumulating squares of distances between the deformation target point and a target point corresponding to the deformation target point; as well as an FFD execution unit that executes the free shape deformation based on the movement amount, thereby fitting the curved surface model to the plurality of target points, The surface model is formed by combining a surface that divides the definition domain of the surface model and a cutting surface that cuts the surface. The calculation unit executes the processing of the control point setting unit, the deformation target point setting unit, the movement amount determination unit, and the FFD execution unit on the boundary line between the curved surface and the trimming curved surface.

10. A computer-readable storage medium storing a surface fitting processing program, wherein the surface fitting processing program fits a surface model set in a three-dimensional space to a plurality of target points set in the three-dimensional space by causing a computer to perform free-form deformation, wherein the computer-readable storage medium is characterized in that: The surface fitting processing program enables the computer to perform the following steps: In a first step, a plurality of control points in the free shape deformation are set in a manner of surrounding at least a portion of the surface model; The second step is to set a plurality of deformation object points corresponding to the plurality of target points respectively on the surface model; The third step is to perform the least square method in such a way that the cumulative value obtained by accumulating the squares of the distances between the deformation object point and the target point corresponding to the deformation object point is minimized, thereby determining the movement amount of each of the plurality of control points; as well as In a fourth step, the free-form deformation is performed based on the movement amount, thereby fitting the curved surface model to the plurality of target points. The surface model is formed by combining a surface that divides the definition domain of the surface model and a cutting surface that cuts the surface. The curved surface fitting processing program causes a computer to execute the first step, the second step, the third step, and the fourth step on a boundary line between the curved surface and the trimming curved surface.

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