JP3641856B2 - Method for generating fillet surface - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for generating a fillet surface to be embedded in a computer-aided design (CAD) device for rounding between a corner in a previously created shape or two separate shapes, and more particularly to a fillet surface. The present invention relates to a fillet curved surface generation method capable of improving the generation calculation processing speed.
[0002]
[Prior art]
In general, as shown in FIG. 2, a CAD device is based on a central processing unit (CPU) 1 that performs operations and processing of data, a memory 2 that stores programs and data, and programs and data based on human key operations. A keyboard 3 for inputting, a printer 4 for printing out programs and data, an image display device (CRT) 5 for displaying graphics and the like on the screen, and a mark displayed on the screen of the CRT 5 based on a human operation. A device 6 such as a mouse or a stylus pen for moving and inputting data based on the movement, a storage device 7 for storing a recording medium such as a floppy disk or a hard disk, and a bus line 8 for connecting them together are provided. When the user of the CAD device operates the keyboard 3 or mouse 6 to instruct the user, Create a figure or the like by performing a calculation and processing in accordance with a predetermined program based on the content, and displays the figure and the like on the screen of the CRT 5.
[0003]
As a conventionally known method for generating a fillet curved surface to be embedded in a corner portion in a previously created shape with such a CAD apparatus, there are a spherical contact method and a cross-section connection method. "Study on the theory and practical application of curved surface solid model by cell complex model" Tatehiko Suzuki, November 1990 Spherical contact method as described in the Faculty of Engineering, Faculty of Engineering, pages 303-306 (hereinafter referred to as Reference 1) Is “the envelope surface obtained by rolling a sphere between two face groups”, and the cross-section connection method is “moving a node with a specified radius in contact between two face groups. Is a method of calculating a fillet surface by obtaining a sweep surface obtained at the time.
Note that the spherical contact method includes an offset surface intersection method, a convergence method, a plane constraint convergence method, and the like. Details of these methods can be found in JP-A-2-210581, “Corner fillet generation by moving a sphere” Masatoshi, Toshiyuki Kano JSPE-56-12, pages 81-86, “Development of CAD model creation function for molds” SUZUKI TECHNICAL REVIEW VOL. 17 (1991) 130-131. For details of the cross-section connection method, see the above-mentioned document 1 and “Fillet surface creation method for connecting a plurality of curved surfaces”, K. Hashimoto UNIVACTECHNOLOGY REWIEW No. 11, August 1986, pages 3-4.
[0004]
When generating a fillet curved surface by the cross-section connection method, the two original curved surfaces are formed on a plane orthogonal to a common ridgeline (interpenetrating line) of two original curved surfaces forming a corner portion or two separate shapes embedding the fillet curved surface. Cut a section line to obtain a plurality of fillet composition lines by repeating the process of obtaining an arc having a predetermined radius in contact with the section lines of the two original curved surfaces and making it a fillet composition line for each predetermined pitch. After determining the end curve pairs that connect the two end points of the fillet component line, respectively, determine the basic fillet shape from the adjacent fillet component lines and the end curve pairs between them, and based on the obtained multiple basic fillet shapes To generate a fillet surface. When a point where the distance between the two original curved surfaces exceeds the tolerance exists on the end curve pair, a new fillet configuration line and a new end are inserted between the fillet configuration lines sandwiching the end curve pair. By adding a partial curve pair, the point where the distance between the two original curved surfaces on the end curve exceeds the tolerance is eliminated.
In the case of the spherical contact method, the envelope when the sphere is brought into contact with the two original curved surfaces can be interpreted as corresponding to the fillet component line. An end curve pair is obtained from a plurality of fillet composition lines obtained by rolling each pitch, and can be read as a process of adding a new fillet composition line and a new end curve pair when the tolerance is exceeded.
[0005]
[Problems to be solved by the invention]
In the spherical contact method, when the two original curved surfaces F1 and F2 to be embedded with the fillet curved surface have minute irregularities as shown in FIG. 6, a desired point (black circle) that gives the center of the sphere as a result of convergence calculation. Multiple points (indicated by white circles) may be calculated for each of the points (indicated by the mark), and the distance between the fillet surface and the two original surfaces is converged within the tolerance range depending on which point is selected Sometimes failed.
On the other hand, in the cross-section connection method, a fillet curved surface can be stably obtained with respect to the shape as shown in FIG. 6, but the two original curved surfaces F1 and F2 to be embedded in the fillet curved surface are connected portions as shown in FIG. If there is an error (step), it is necessary to create a fillet composing line near the step on both curved surfaces, so convergence calculation is performed to obtain a cross section in the direction of arrow A (the direction along the intermittence line on both curved surfaces). As a result, the points on the original curved surface to which the fillet constituent lines should be connected are not determined, and there are cases where the convergence within the tolerance is failed.
[0006]
If convergence failure occurs due to the spherical contact method or cross-section connection method as described above, it is necessary to try to converge by various methods, but in that case, the calculation accuracy is sacrificed or the convergence calculation cannot be performed. I had fallen into. In addition, since the convergence calculation is expensive, there is a problem in that the cost is increased by repeating the convergence calculation.
[0007]
The present invention provides a fillet curved surface generation method that can calculate a fillet curved surface in a short calculation time without failing convergence calculation even when the two original curved surfaces have shapes as shown in FIGS. The purpose is to do.
[0008]
[Means for Solving the Problems]
For this purpose, the fillet curved surface generation method of the present invention includes a central processing unit that performs operations and processing of data, a memory that stores programs and data, and a keyboard that inputs programs and data based on key operations. An image display device that displays a graphic or the like on a screen, an input device that moves a mark displayed on the screen of the image display device and inputs data based on the movement, and a storage device that accommodates a recording medium A CAD device that creates figures and the like by performing calculations and processing according to a predetermined program based on the instruction contents of the keyboard and the input device, and displays the figures and the like on the screen of the image display device. , upon generating a fillet curved surface embedded between the corners or two separate shapes in shape created earlier, first, forming the corner After obtaining a plurality of fillet constituent lines in contact with both of the two original curved surfaces along the corner, and obtaining end curve pairs that smoothly connect the end points of the adjacent fillet constituent lines, the adjacent fillet constituent lines are obtained. Then, a basic fillet shape is obtained based on the end curve pair between them, and then the point where the distance from the corresponding original curved surface on any one end curve of the end curve pair exceeds a tolerance is If present, a point on which the distance from the corresponding original curved surface on the one end curve is a maximum and a corresponding point on the other end curve are projected onto the original curved surface to project the two The corresponding points on the original curved surface are obtained, the interpolation fillet constituent lines that touch the two original curved surfaces are obtained at the corresponding points on both sides, and the obtained interpolated fillet constituent lines and the end points of the adjacent fillet constituent lines are smoothed. New to connect After obtaining the partial curve pair, the process of obtaining the interpolation fillet shape based on the obtained interpolation fillet constituent line and the new end curve pair is performed until there is no point whose distance from the original curved surface exceeds the tolerance. The desired fillet curved surface is generated by repeating and then combining the basic fillet shape and the interpolation fillet shape.
[0009]
In the above, the CAD device obtains an intersection range in which the sectors formed by the fillet constituent lines in the basic fillet shape and the center point thereof intersect each other, and end curve pairs in the intersection occurrence range The points at the specified positions are projected onto the original curved surface to obtain corresponding points on the two original curved surfaces, respectively, and interpolation fillet constituent lines that contact the two original curved surfaces at the corresponding points on both sides are obtained and obtained. After finding a new end curve pair that smoothly connects the end points of the interpolation fillet component line and the fillet component line outside the intersection range adjacent to it, the resulting interpolated fillet component line and new end curve pair are obtained. Obtaining the interpolation fillet shape for cross removal based on this speeds up the calculation speed of the interpolation fillet shape for cross removal and generates the interpolation fillet shape for cross removal. Preferred in increasing the stability of the process.
[0010]
According to the method of the present invention, there is a point where the distance from the corresponding original curved surface exceeds the tolerance on either one of the end curve pairs that smoothly connect the end points of the adjacent fillet constituent lines. If present, a point on which the distance from the corresponding original curved surface on the one end curve is a maximum and a corresponding point on the other end curve are projected onto the original curved surface to project the two The corresponding points on the original curved surface are obtained, the interpolation fillet constituent lines that touch the two original curved surfaces are obtained at the corresponding points on both sides, and the obtained interpolated fillet constituent lines and the end points of the adjacent fillet constituent lines are smoothed. After obtaining a new end curve pair connected to, an interpolation fillet shape is obtained based on the obtained interpolation fillet constituent line and the new end curve pair. This process of obtaining the interpolation fillet shape is repeated until there is no point where the distance from the original curved surface exceeds the tolerance, and the desired fillet curved surface is synthesized by combining the obtained interpolation fillet shape and the basic fillet shape. Generated.
[0011]
Therefore, according to the method of the present invention, when the two original curved surfaces to be filled with the fillet curved surface have minute irregularities as shown in FIG. 6, or the two original curved surfaces to be filled with the fillet curved surface are as shown in FIG. Even if there is an error (step) in the connecting portion, the corresponding points on the two original curved surfaces that define the interpolation fillet constituent lines are always obtained by a simple graphic process called projection, so the above-mentioned conventionally known Convergence calculation failures such as the spherical contact method and cross-section connection method do not occur, and it is possible to always converge. In addition, since complicated convergence calculation like the above-described conventionally known spherical contact method and cross-section connection method is not required, the calculation time is shortened and the cost is reduced.
[0012]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is a flowchart showing a processing procedure of a fillet curved surface generation method according to the first embodiment of the present invention. Specifically, the method of the present embodiment is executed by a program given in advance to a normal CAD device as shown in FIG.
[0013]
In the fillet curved surface generation method of the present embodiment, first, in step 11 of FIG. 1, two corners for embedding the fillet curved surface in the previously created shape or two original curved surfaces forming two separate shapes are designated. In step 12, the section for embedding the fillet curved surface is designated. In the next step 13, conditions (for example, radius and pitch) that define the shape of the fillet constituent lines are instructed, and a plurality of fillet constituent lines in contact with both of the two original curved surfaces forming the corner are calculated. The fillet composing line can be instructed by, for example, an instruction of an equal pitch or an instruction of a different distance for each part according to the shapes of the two original curved surfaces.
[0014]
In the next step 14, end curve pairs that smoothly connect the end points of the adjacent fillet constituent lines among the plurality of fillet constituent lines obtained in step 13 above are obtained, and the adjacent fillet constituent lines and the adjacent fillet constituent lines are determined. The basic fillet shape is obtained based on the end curve pair. The processing for obtaining the basic fillet shape is repeated until the determination in the next step 15 becomes YES, and when the basic fillet shape of all the sections indicated in step 12 is obtained, the processing proceeds to the next step 16. In the present embodiment, the basic fillet shape is calculated based on the cross-section connection method, but the same processing is performed when the basic fillet shape is calculated based on the spherical contact method.
[0015]
In step 16, the distance between each end curve of the end curve pair and the corresponding original curved surface is calculated. Here, the corresponding original curved surface indicates an original curved surface closer to each end curve of the two original curved surfaces. In the next step 17, it is determined whether or not there is a point whose distance from the corresponding original curved surface on any one of the end curve pairs exceeds a tolerance. In this determination, if there is at least one point whose distance from the original curved surface corresponding to at least one of the end curves constituting the end curve pair exceeds the tolerance, processing for creating an interpolation fillet constituent line The process proceeds to step 18, and if it does not exist, step 18 is skipped and the process immediately proceeds to step 19.
[0016]
In step 18, a point at a specified position on the end curve pair is projected onto the original curved surface from the normal direction to obtain corresponding points on the two original curved surfaces, and the two original curved surfaces are obtained at corresponding points on both sides. Interpolated fillet composing line that touches, and the obtained interpolating fillet composing line and new end curve pairs that smoothly connect the end points of the adjacent fillet composing line, respectively, and then the interpolated fillet composing line obtained. And the interpolation fillet shape is calculated based on the new end curve pair. At this time, a new end curve pair is generated between the fillet component line adjacent to the left side and the interpolation fillet component line, and between the interpolation fillet component line and the fillet component line adjacent to the right side. Are generated. In addition, as the point of the specified position, the point where the distance is the maximum among the points where the distance from the corresponding original curved surface on one end curve of the end curve pair exceeds the tolerance, A point on the other end curve corresponding to the point (a point having the same positional relationship as the positional relationship on the end curve of the maximum point) is designated. Therefore, if there are points where the distance from the original curved surface corresponding to both end curves exceeds the tolerance, an interpolation fillet component line, a new end curve, and an interpolation fillet shape are individually set for each end curve. Will be calculated.
[0017]
In step 19, it is determined whether or not the processing has been completed for all the sections, and the processing is returned to step 16 and thereafter until the processing is completed. In step 16, the distance between each end curve of the new end curve pair calculated in step 18 and the corresponding original curved surface is calculated, and in step 17, any one end of the end curve pair is calculated. It is determined whether there is a point on the curve whose distance from the corresponding original curved surface exceeds a tolerance. In this determination, if at least one point whose distance from the corresponding original curved surface exceeds the tolerance is present in at least one of the end curves constituting the end curve pair, an interpolation fillet constituting line is newly determined in step 18. A simple end curve and interpolated fillet shape.
[0018]
As described above, the interpolation fillet until the point where the distance from the corresponding original curved surface exceeds the tolerance does not exist in the range of the end curve pair where the distance from the corresponding original curved surface exceeds the tolerance exists. A series of processes for adding a component line, a new end curve, and an interpolation fillet shape are repeated until the process is completed for all the sections, and when the processes are completed for all the sections, the process proceeds to step 20. In step 20, the basic fillet shape and the interpolation fillet shape obtained as described above are synthesized to generate a desired fillet curved surface.
[0019]
Next, the operation of this embodiment will be described with reference to FIG.
For example, as shown in FIG. 3, when the two original curved surfaces F1 and F2 forming the corners in the previously created shape are designated in step 11 of FIG. 1, and the range in which the fillet curved surface is embedded is designated in step 12, Fillet constituent lines L1, L2, and L3 that are in contact with both the original curved surfaces F1 and F2 at the radius and pitch specified in step 13 are calculated. In step 14, the end curve pairs C11, C12 and end portions smoothly connecting between the end points of adjacent fillet constituent lines, that is, between P11-P21 and P12-P22, and between P21-P31 and P22-P32, respectively. The curve pairs C21 and C22 are calculated, and the basic fillet shapes are calculated from the fillet composition lines L1 and L2 and the end curve pairs C11 and C12, and the fillet composition lines L2 and L3 and the end curve pairs C21 and C22, respectively.
[0020]
Next, if, for example, a point Q1 on the end curve C11 is designated as a point where the distance from the corresponding original curved surface F1 exceeds the tolerance and becomes a maximum as a result of the processing in steps 16 and 17, the end of the point A point Q2 on the end curve C12 having the same positional relationship as that on the partial curve C11 is simultaneously designated. Next, at step 18, the points Q1 and Q2 are projected from the normal direction to the original curved surfaces F1 and F2, respectively, and corresponding points Q1x and Q2x on the original curved surfaces are obtained, respectively, and the original points are obtained at the corresponding points Q1x and Q2x on both sides. An interpolation fillet component line L12 that is in contact with the curved surfaces F1 and F2 is obtained, and between the obtained interpolation fillet component line L12 and the end points of the adjacent fillet component line, that is, between P11-Q1x and between P12-Q2x, and between Q1x-P21. , New end curve pairs C111, C121 and C112, C122 that smoothly connect between Q2x and P22 are calculated. Then, the interpolation fillet shape is calculated by the interpolation fillet constituting line L12 and the new end curve pair C111, C121, and the interpolation fillet constituting line L12 and the new end curve pair C112, C122, respectively.
[0021]
Since the new end curve pair is closer to the original curved surface than the original end curve, most of the points whose distance from the corresponding original curved surface exceeds the tolerance are eliminated by the processing of step 18 above. However, if there is still a point where the distance from the corresponding original curved surface exceeds the tolerance, the point at which the distance from the corresponding original curved surface exceeds the tolerance is resolved by repeating the process of step 18 above. Is done.
[0022]
According to the present embodiment, even if the two original curved surfaces have the shapes as shown in FIGS. 6 and 7, as described above, the simple graphic processing of projecting the points on the end curves onto the original curved surface is performed. Since the corresponding points on the two original curved surfaces that define the interpolation fillet constituent lines are always obtained, the convergence calculation failure as in the conventional known spherical contact method and cross-section connection method described above does not occur, and the convergence can always be achieved. In addition, since complicated convergence calculation like the above-described conventionally known spherical contact method and cross-section connection method is not required, the calculation time is shortened and the cost is reduced.
[0023]
FIG. 4 is a flowchart showing a processing procedure of a main part of the fillet curved surface generation method according to the second embodiment of the present invention. The flowchart of FIG. 4 is activated only when the intersection of the fillet constituent lines occurs as a result of the processing of steps 11 to 15 of FIG. 1, and performs the removal processing of the intersection. It is inserted between YES in step 15 and step 16 for use.
[0024]
That is, in the flowchart of FIG. 4, first, in step 31, the basic fillet shape obtained in step 14 of FIG. 1 is read, and in the next step 32, it is formed by the fillet constituent lines in the basic fillet shape and its center point. The intersection range in which the fan shapes intersect each other is calculated. In addition, as a calculation method of the said intersection range, the method described in Unexamined-Japanese-Patent No. 6-259515 which the applicant of this application applied previously, for example shall be used.
[0025]
In the next step 33, the end curve pair in the intersection range is read, and in the next step 34, the point at the designated position on the end curve pair in the intersection range is projected onto the original curved surface from the normal direction. . As the point of the designated position, for example, the midpoint of each end curve is designated (the end curve can be connected even on the intersecting side). In the next step 35, an intermediate curve for obtaining a passing point or a plane determining point used for determining the fillet curved surface is calculated.
[0026]
In the next step 36, corresponding points on the two original curved surfaces of the point at the designated position are obtained. In the next step 37, interpolated fillet composing lines that contact the two original curved surfaces at the corresponding points on both sides are obtained, and the interpolated fillet composing line and the adjacent end points of the fillet composing line outside the intersecting range are smoothed respectively. After obtaining a new end curve pair connected to, an interpolated fillet shape for intersection removal is calculated based on the obtained interpolation fillet constituent line and the new end curve pair. In the next step 38, the fillet constituent lines and end curves in the intersection range are replaced with the interpolation fillet constituent lines and new end curves obtained in step 37.
[0027]
Next, the operation of this embodiment will be described with reference to FIG.
For example, as shown in FIG. 5, among the plurality of fillet constituent lines having a predetermined radius and a predetermined pitch along the corner formed by the two original curved surfaces F1 and F2, the fillet constituent lines L1 and L2 are on the original curved surface F2 side. In the case of intersection, the intersection range is calculated in step 32 of FIG. 4, the end curve pair C11, C12 in the intersection range is read in step 33, and the point Q1, on the end curve pair C11, C12 is read in step 34. Q2 is projected onto the original curved surfaces F1 and F2, respectively, and corresponding points Q1x and Q2x on the original curved surfaces F1 and F2 are obtained at step 36, respectively. In step 37, an interpolation fillet composition line L12 that is in contact with the original curved surfaces F1 and F2 at the corresponding points Qn1x and Qn2x on both sides is obtained, and between the end points of the obtained interpolation fillet composition line L12 and the adjacent fillet composition line outside the intersection range. That is, new end curve pairs C111, C121 and C112, C122 that smoothly connect between P01 and Q1x, between P02 and Q2x, between Q1x and P31, and between Q2x and P32 are calculated. Then, an interpolation fillet shape is calculated from the interpolation fillet constituting line L12 and the new end curve pair C111, C121, and the interpolation fillet constituting line L12 and the new end curve pair C112, C122, respectively.
[0028]
According to the present embodiment, as described above, the corresponding points on the two original curved surfaces that define the interpolation fillet constituent lines are always obtained by a simple graphic process of projecting the points on the end curves onto the original curved surface. The intersection of the constituent lines can be easily eliminated. At this time, since complicated calculation is not required, the calculation speed of the interpolation fillet shape for removing the intersection is increased, and the stability of the generation process of the interpolation fillet shape for removing the intersection is increased.
[0029]
In the second embodiment, the intersection removal process when two fillet constituent lines intersect has been described. However, when three or more fillet constituent lines intersect, adjacent fillets within the intersecting range are described. By performing the above processing between constituent lines, the intersection removal processing can be performed in the same manner as described above. In the second embodiment, two intersecting fillet constituent lines are replaced with one interpolating fillet intersecting line, but the designated points are equal to or more than two points equally divided on the end curve. By making this point, two intersecting fillet constituent lines may be replaced with two or more interpolating fillet intersecting lines.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a processing procedure of a fillet curved surface generation method according to a first embodiment of the present invention.
FIG. 2 is a diagram illustrating a CAD apparatus used in the implementation of the fillet curved surface generation method according to the present invention.
FIG. 3 is a diagram for explaining the operation of the first embodiment.
FIG. 4 is a flowchart showing a processing procedure of a main part of a fillet curved surface generation method according to a second embodiment of the present invention.
FIG. 5 is a diagram for explaining the operation of the second embodiment.
FIG. 6 is a diagram for explaining a problem of the spherical contact method.
FIG. 7 is a diagram for explaining a problem of a cross-sectional connection method.
[Explanation of symbols]
1 Central processing unit (CPU)
2 Memory 3 Keyboard 5 Image display device (CRT)
6 Mouse F1, F2 Original curved surface L1, L2, L3 Fillet component line L12 Interpolated fillet component line C11, C12, C21, C22 End curve C111, C121, C112, C122 New end curve P11, P12, P21, P22 End point Q1, Q2 Specified points on the end curve Q1x, Q2x Corresponding points on the original curved surface

Claims (2)

A central processing unit for calculating and processing data, a memory for storing programs and data, a keyboard for inputting programs and data based on key operations, an image display device for displaying figures on a screen, It comprises an input device that moves a mark displayed on the screen of the image display device and inputs data based on the movement, and a storage device that accommodates a recording medium, and includes instructions on the keyboard and the input device. A CAD device that creates figures and the like by performing calculations and processes according to a predetermined program and displays the figures and the like on the screen of the image display device is either a corner in the previously created shape or two apart When generating fillet surfaces to be embedded between shapes,
First, a plurality of fillet constituent lines contacting both of the two original curved surfaces forming the corner portion were obtained along the corner portion, and end curve pairs that smoothly connected between the end points of the adjacent fillet constituent lines were obtained. Later, a basic fillet shape is determined based on the adjacent fillet constituent lines and the end curve pairs between them,
Next, when there is a point whose distance from the corresponding original curved surface on any one of the end curve pairs exceeds the tolerance , the corresponding original curved surface on the one end curve And the corresponding point on the other end curve is projected onto the original curved surface to obtain corresponding points on the two original curved surfaces, and the two corresponding points on both sides Interpolation fillet composing line in contact with the original curved surface is obtained, and after obtaining new end curve pairs that smoothly connect the end points of the obtained interpolating fillet composing line and the adjacent fillet composing line, the obtained interpolation fillet is obtained. The process of obtaining the interpolation fillet shape based on the component line and the new end curve pair is repeated until there is no point whose distance from the original curved surface exceeds the tolerance,
Then, a desired fillet curved surface is generated by synthesizing the basic fillet shape and the interpolation fillet shape. The CAD device obtains an intersection range in which the sectors formed by the fillet constituting line in the basic fillet shape and its center point intersect with each other, and designates on the end curve pair within the intersection occurrence range Each point of the position is projected onto the original curved surface to obtain corresponding points on the two original curved surfaces, and interpolation fillet composition lines that contact the two original curved surfaces at corresponding points on both sides are obtained, and the obtained interpolation fillet configuration is obtained. After finding a new end curve pair that smoothly connects each end point of the line and the fillet constituent line outside the intersection range adjacent to the line, intersect based on the obtained interpolation fillet constituent line and the new end curve pair 2. The method for generating a fillet curved surface according to claim 1, wherein an interpolation fillet shape for removal is obtained.

Images