JP3087497B2 - Figure operation stabilization method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a computer aided design (CAD) having a modeler such as a solid modeler or a curved surface three-dimensional coexistence model having phase data representing a relation between surfaces.
The present invention relates to a method for stabilizing a graphic operation performed by an apparatus.

[0002]

2. Description of the Related Art Among the modelers provided in a conventional CAD apparatus, a surface modeler in which a connection relationship between curved surfaces is left to a user's rule, when a problem occurs in the connection relationship, the processing is manually performed by the user. Although it is possible, the solid modeler who handles the solid as it is, and the inventor first
In a modeler that has phase data that represents the mutual relationship between surfaces, such as a model that coexists with a solid surface, such as the model that was proposed in a paper published in the Journal of Precision Engineering in November, “Problems of Solid Modeler and Development of a Surface Solid Coexistence Modeler,” a model operation was performed. Since there is little freedom for the user due to the aim of the automation of the image processing, the stabilization of the graphic operation is extremely important in order not to reduce the efficiency of the modeling.

Incidentally, since the graphic operation performed by the CAD apparatus is performed with finite calculation accuracy, it is inevitable that a certain degree of error occurs. Therefore, if a theory for handling the error has not been established, a calculation error causes a defect in the resulting figure or a calculation failure. Here, a defect of the figure is caused by a contradiction between the phase data and the geometric data, for example, as shown in FIG. 11, where adjacent edges are separated from each other in phase data but partially intersect in geometric data. This reduces the efficiency of modeling and brings about the possibility of causing a tool path failure in subsequent cutting or the like. In addition to the inconsistency between the above data, the calculation failure may be caused by processing such as, for example, when the intersection between edges approximately obtained by the intersection calculation of the curved surface is obtained by the convergence calculation with the tolerance set more strictly. This is caused by the failure of the algorithm due to the setting of inconsistent tolerances that make it impossible, and reduces the efficiency of modeling as in the case of the above-mentioned problem of the figure.

However, in the conventional CAD apparatus having a solid modeler, the tolerance is set on an ad hoc basis, for example, by setting all the same values to the same value. It was difficult to avoid problems caused by calculation errors. Further, even in the CAD apparatus having the curved surface solid coexistence modeler proposed by the present inventor, the same problem has conventionally occurred when performing operations between adjacent graphic elements such as fillet surface embedding and division connection operation. .

For this reason, regarding the solid modeler,
Conventionally, various methods for stabilizing graphic operations have been proposed. The methods include a “required calculation accuracy securing method” for obtaining a calculation accuracy required for correctly determining a phase structure, and a finite accuracy. Given that it is given, classify the calculation results as reliable and unreliable under the accuracy, and adopt unreliable calculation results only when there is no inconsistency between topological data and geometric data. It is known that the method can be broadly divided into the "geometric topology failure correction method" and the "phase priority method" that prevents failure by giving priority to the consistency of the target phase structure without limiting the magnitude of the numerical error in advance. (September 1992, Information Processing Symposium, Vol.92, No.5, "Graphics and CAD Symposium" published by Information Processing Society of Japan, pages 95-104. Topological First Method-Geometric Al Method for Numerically Stabilizing the Algorithm ").

[0006]

However, in the case of designing a complicated three-dimensional shape such as a casting and forging die using a CAD apparatus having a modeler having the above-mentioned phase data, it is necessary to generate a figure and to combine the figures. Since the figure calculations such as embedding of fillet surfaces and pasting of curved surfaces are complicated and diversified, if the above-mentioned necessary calculation accuracy securing method is used to stabilize the figure calculations, the required precision becomes extremely high. A problem arises in terms of calculation time and required memory. On the other hand, when trying to stabilize the graphic operation by the above-described geometric topology failure correction method, processing for evaluating numerical errors becomes too complicated,
This also causes problems in terms of calculation time and required memory.

In addition, the above-mentioned phase-priority method does not perform a redundant judgment of numerically determining an item that can be derived as a logical result from an already determined item independently of the logical data. It is said that it is possible to prevent the occurrence of inconsistency between the algorithms and to prevent runaway and failure of the algorithm.However, when the above-mentioned phase-first method is complicated and a wide variety of graphic operations are performed, the various graphic operations are consistently performed. Applying to stabilization is practically difficult.

[0008]

SUMMARY OF THE INVENTION An object of the present invention is to provide a stabilizing method which advantageously solves the above-mentioned problems of the conventional method. In stabilizing the figure operation performed by the device,
In each step of the figure calculation, a figure operator combining a topological operator and a geometric operator is used, and a topological figure model having a predetermined geometric error for each of vertices and edges is set. In the topological operator by the topological operator of the graphic operator so as not to cause a topological inconsistency. The operation is performed so that the figure after the calculation is kept within the geometrical error range of the phase figure model.

[0009] In the graphic operation according to the present invention, the error of the intersecting line between the geometrical surfaces, the error of the projection line of the geometric curve onto the geometrical surface, and the error of assuming that the two geometrical surfaces are the same are calculated as follows. By managing the error to the error range τ _cs or less for the convergence calculation, the geometric error of the topological model is calculated between the vertex of the composite surface and the end point of the geometric curve of the edge of the face constituting the composite surface. The distance is equal to or less than a predetermined tolerance λ, and the distance between vertices is equal to or greater than the tolerance λ, and the normal of the geometric curve of the edge defining the faces of the composite surface to the geometric surface of the face on both sides of the edge If the error in the directional distance is larger than twice the error range τ _cs for the convergence calculation or equal to or less than the error range τ _ef when the bonding of the curved surfaces is performed, the convergence is performed when the bonding of the curved surfaces is not performed. Computational Error range tau is the error range tau _ef than or equal to greater than _cs for geometric curve of any two edges, except when connected to each other through the one vertex of the error range tau _ef two The distance may be set to be greater than or equal to the minimum distance τ _ee or more.

Further, the intersection calculation between the compound curved surfaces in the graphic operation according to the present invention is performed by first selecting two faces and projecting a geometric curve of an edge of one of the faces onto the other face. Examining the relationship between the one face and the other face, based on the examined relationship, if the geometric curve of the edge of the one face intersects the geometric surface of the other face,
The intersection between the geometric curve or vertex of the edge of the one face and the geometric surface of the other face is set as the vertex, and the intersection between the geometric surfaces of the faces is calculated to find the geometric curve of the edge serving as the intersection line. When the distance between the geometric curve of the edge of one face and the geometric surface of the other face is less than the error range τ _ef , the geometric curve of the edge is defined as the intersection of the two faces, If the distance between the geometric curves of the respective edges is less than or equal to the minimum distance τ _ee and the other face is connected to the other face via the edge of the face, the one face The distance between the geometric curve of the edge and the geometric surface of the other face, and the geometric curve of the edge of the one face and the geometric curve of the edge connected to the other face In the case of less than both said error range tau _ef distance between geometric curved surface of the other face, the edge of the one face a line of intersection of the two faces,
When at least one of the two distances is equal to or _larger than the error range τ _ef , an intersection line is obtained by calculating an intersection between the two remaining faces in consideration of a subsequent graphic operation, and two of the two faces are calculated. Since the vertex error spheres each having a radius centered on a vertex and having the tolerance λ have a common point, when the intersection of the two faces passes through the vertex error spheres, the two A geometric curve passing through a vertex may be set as an intersection.

Further, the modeler of the CAD apparatus according to the present invention expresses the entire shell including the two intersecting faces as a non-manifold forming a hierarchy in accordance with the procedure of graphic operation. The distance between the geometric curves of each edge is equal to or less than the minimum distance τ _ee , and the other face is connected to the other face via the edge of the face, and the edge of the one face is At least one of the distance between the geometric curve and the geometric surface of the other face, and the distance between the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face is the same Since the error range was equal to or greater than τ _ef , the intersection was determined by calculating the intersection between the two remaining faces in consideration of the subsequent figure calculation. For the same intersection line edges and vertices, use the geometric data of the newly calculated edges and vertices for the intersection lines and vertices of the remaining two faces of the live shell displayed as a figure. For the intersection lines and vertices of the dead shell that are not displayed as figures, the geometric data of the edges and vertices of the original face are stored, and when the shape is restored, the original data stored in the dead shell is stored. Geometric data of face edges and vertices may be used.

Further, in the present invention, the determination regarding at least one of the error range τ _cs , the tolerance λ, the error range τ _ef, and the minimum distance τ _ee for the convergence calculation is performed for each fixed edge length. Alternatively, the processing may be performed at every n division points obtained by dividing the vertices of the edge by an arbitrary integer n.

[0013]

According to the method of the present invention, a figure having a topological structure is usually generated or updated using a topological operator. While using the "graphic operator" that combines children and
Set an "error figure model" which is a topological figure model having a predetermined geometric error for each of the vertices and edges, and operate the phase data in the figure operation by the phase operator of the "figure operator". By doing so, the inconsistency of the phase data does not occur, and the integrity of the phase data is guaranteed. In addition, the geometrical operator of the “graphical operators” causes the figure after the operation to be performed using the above “error figure”. Since the graphic operation is performed so as to be kept within the error range of the `` model '', it is possible to clarify the handling of the error of the geometric data without requiring a major change in the conventional modeling technique, and to reduce the calculation time and the required memory. This makes it possible to stabilize the graphic operation with a small number of development man-hours without causing any problem in terms of the operation. Moreover, according to the method of the present invention, the graphic operator is caused to perform a graphic operation such that the figure after the calculation is kept within the error range of the common error graphic model. Can be stabilized.

In the graphic operation, an error of an intersection line between geometric surfaces, an error of a projection line of a geometric curve onto the geometric surface, and an error of assuming that the two geometric surfaces are the same,
By managing the error to the error range τ _cs or less for the convergence calculation, the geometric error of the topological model is calculated between the vertex of the composite surface and the end point of the geometric curve of the edge of the face constituting the composite surface. The distance is equal to or less than a predetermined tolerance λ,
The distance between the vertices is equal to or larger than the tolerance λ, and the error in the normal direction distance of the geometric curve of the edge that partitions between the faces of the composite curved surface with respect to the geometric curved surfaces of the faces on both sides of the edge causes the bonding of the curved surfaces. the convergence equal error range greater than or twice the error range tau _cs for calculating tau _ef less, if not performed bonding of the curved surface is larger than the error range tau _cs for the convergence calculation when performing Or less than or equal to the error range τ _ef , and the minimum distance greater than or equal to twice the error range τ _ef , unless the geometric curves of any two edges are connected to each other via one vertex. if, apart over _ee tau, in various graphical operation, when performing the operation between closely spaced graphic elements, falling into unhandled due to collapse of the algorithm by setting inconsistent tolerance It is possible to prevent.

Further, in the graphic operation, the intersection calculation between the compound curved surfaces is performed by first selecting two faces and projecting a geometric curve of an edge of one of the faces onto the other face. Investigate the relationship between one face and the other face, and if the geometric curve of the edge of the one face intersects the geometric surface of the other face based on the examined relationship, The intersection of the geometric curve or vertex of the edge and the geometric surface of the other face is set as the vertex, and the intersection between the geometric surfaces of those faces is calculated to find the geometric curve of the intersection line. of cases less than the geometric curve distance is the error range of the geometric curved surface of the other face tau _ef, the two face geometric curve of the edge And the line of intersection, the distance between the geometric curve of each edge of said two face is equal to or less than the _ee minimum distance tau, to the other face, the other face via the edges of the face are connected in case of,
The distance between the geometric curve of the edge of the one face and the geometric surface of the other face, and the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face; If both distances are less than the error range τ _ef , the edge of the one face is the intersection of the two faces, and if at least one of the two distances is greater than or equal to the error range τ _ef , In consideration of the subsequent graphic calculation, an intersection line is obtained by calculating the intersection between the two remaining faces, and the vertex error spheres whose radius centered on the two vertices of the two faces is the tolerance λ are shared by the spheres. By having points, if the intersection of the two faces passes through the vertex error sphere, the geometric curve passing through the two vertices is taken as the intersection. If in fact it performed sequentially, even if the relationship between the compound curves spans various, it is possible to obtain a reasonable curve smoothly and reliably as a line of intersection between their compound curves in the error mark model.

Further, the modeler of the CAD apparatus expresses the entire shell including the two intersecting faces as a non-manifold in a hierarchy along the procedure of the graphic operation. The distance between the geometric curves of the edges is equal to or less than the minimum distance τ _ee , the other face is connected to the other face via the edge of the face, and the geometric curve of the edge of the one face is And the distance between the other face and the geometric surface,
Since at least one of the distance between the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face was _{equal to} or _larger than the error range τ _ef , consideration was given to subsequent graphic calculations. Then, when the intersection line is calculated by the intersection calculation between the two remaining faces,
For topologically identical intersection lines and vertices, use the newly calculated geometric data of the edges and vertices for the intersection lines and vertices of the remaining two faces of the live shell displayed as a figure. On the other hand, the geometric data of the edges and vertices of the original face are stored for the intersection lines and vertices of the dead shell which are not displayed as figures, and when restoring the shape, the original data stored in the dead shell are stored. If the geometric data of the edges and vertices of the face is used, the original figure can be reliably restored when the shape is restored in the error figure model for correcting the shape or the like.

The determination regarding at least one of the error range τ _cs , the tolerance λ, the error range τ _ef, and the minimum distance τ _ee for the convergence calculation is performed for each fixed length of the edge, or Any integer n between the vertices of
If the determination is made for each of the n division points, a valid determination result can be obtained over the entire edge, so that inconvenience can be prevented when the edge is divided after the determination, and the error can be prevented. More robustness can be given to the graphic model.

[0018]

Embodiments of the present invention will be described below in detail with reference to the drawings. FIG. 1A shows a vertex error spherical surface and an effective edge geometric curve of an error graphic model in one embodiment in which the graphic operation stabilizing method of the present invention is applied to the CAD apparatus having the above-mentioned curved solid coexistence modeler. (B) and (c) are explanatory diagrams respectively showing a normal face and a non-normal face determined by the face geometric normality determination method in the above embodiment. The vertices 2 and 2 are vertex error spheres, and 3 is a valid edge geometric curve.

In the graphic operation stabilizing method of this embodiment, a graphic operator obtained by combining a phase operator and a geometric operator is used at each stage of the graphic operation performed by the CAD apparatus having the above-mentioned curved solid coexistence modeler. By performing the operation of the phase data in the figure operation with the phase operator of the figure operator, the integrity as the topological data is assured. A figure operation is performed so as to be kept within the error range of the error figure model which is a topological figure model having a geometric error.

That is, here, the above-mentioned error graphic model is assumed as a graphic model capable of modeling and handling an error of geometric data. However, the phase data obtained in the error graphic model may be different from the phase data obtained when it is assumed that the geometric calculation is performed with infinitely high precision. Therefore, in this method, the integrity of the phase data is assured by operating the phase data with the phase operator. On the other hand, here, tolerances are set for vertices and edges in the above error graphic model, and contradiction between the phase data and the geometric data is allowed if the tolerances are within the tolerances. Then, if there is a contradiction between the two, the figure calculation is executed on the assumption that the phase data is correct.

Here, the figure operator is created by combining a geometric operator with a topological operator, and the figure operator always generates only a figure that conforms to the framework of the error figure model. Create to be guaranteed. That is, the tolerance is used not only for determining the end of the calculation but also for ensuring that the graphic is included in the framework of the error graphic model. Note that the phase operator can be realized by a single algorithm, but the graphic operator depends on the graphic targeted by the modeler of the CAD apparatus and cannot be realized in a single form. For this reason,
The graphic operators that must be processed by the modeler are classified into a plurality of types from the viewpoint of error management as described later. Although a large number of tolerances are set in the modeler of the CAD apparatus, here, the tolerance set by the error graphic model is used as a base, and all other tolerances are used as the base tolerances. Subordinate.

Incidentally, the geometric calculation performed by the modeler of the CAD apparatus essentially has an error. Therefore, the error graphic model is based on the following geometric calculation error. That is, the distance between the geometric curve connecting the given points and the given point,
The distance between the end points of the divided geometric curves, the distance between the free-form surface and the free curve expressing its outer circumference, the error of the foot of the perpendicular to the geometric curve from the given point, and the geometric surface from the given point And the error of the intersection of the geometric curve and the geometric surface can be made sufficiently small, so here the range of these errors is the minimum handling error range δ, and this error range δ The following errors are excluded. In addition, since the intersection line between the geometric surfaces and the projection line of the geometric curve onto the geometric surface have errors for convergence calculation, here, it is assumed that these errors are managed to be within a certain range. , The range of which is an error range τ _cs for convergence calculation. The error range τ _ss for assuming that the two geometric surfaces are the same is also assumed to be equal to the error range τ _cs for the convergence calculation.

On this assumption, the error graphic model is determined as a model in which the following conditions are applied to the orientable manifold cell complex model. That is, in the above error graphic model, the distance between the vertex of the composite curve and the end point of the geometric curve of the edge constituting the composite curve is equal to or less than the minimum error range δ for handling, and FIG. As shown in the figure, the logical product of the vertex error sphere 2 having a radius of tolerance λ centered on the vertex 1 and the outside of the edge geometric curve is the effective edge geometric curve 3, and the vertex of the composite curved surface and its composite The distance between the edge of the edge of the face constituting the curved surface and the end point of the geometric curve is equal to or smaller than the tolerance λ, and the distance between the vertices is equal to or greater than the tolerance λ. There are no other vertices, the minimum radius of curvature of the curve and the surface is greater than or equal to the tolerance λ, and the geometric curve of the edge defining the faces of the composite surface is the modulus of the geometric curve of the faces on both sides of the edge. The error in the linear distance is In the embodiment, since the bonding of the curved surfaces is also performed as described later, the error range τ _ef is larger than twice the error range τ _cs for the convergence calculation or equal to or less than the error range τ _ef , and any two valid edges of the effective edge As shown in FIG. 1B, it is assumed that the geometric curves are apart from each other via one vertex by a minimum distance τ _ee which is larger than or equal to twice the error range τ _ef or more.

In the case where two edges connected to each other via one vertex intersect at a position near the vertex and less than the minimum distance τ _ee and another edge intersects, two intersections are formed. Generates one of the intersections as a vertex, sets the new vertex as an end point of the two edges and the other edge, and sets a distance between the new vertex and the original vertex by the original two. Instead, they are connected by one edge.

As described above, according to the error graphic model in which the three kinds of base tolerances λ, τ _ef and τ _ee are determined,
As shown in FIG. 1 (c), since the geometric curves of the two effective edges are smaller than the minimum distance τ _ee , the edges around the face intersect as shown in FIGS. 11 (a) and 11 (b). The occurrence of a situation can be systematically eliminated, and the geometric normality of the face can be guaranteed. It is possible to prevent the processing from becoming impossible due to the failure of the algorithm.

However, as shown in FIG. 2, if it is attempted to eliminate the case of self-intersection where the central portions of the geometric surfaces of a plurality of faces constituting a single solid intersect with each other, a large calculation time is required. Will be consumed,
The elimination of such self-intersection is not planned in the method of this embodiment, but is handled at the responsibility of the operator of the CAD apparatus. It is also assumed that the figures handled by the method of this embodiment are monovalent when viewed from a certain direction unless errors are taken into account, and this is also handled by the operator.

As shown in FIG. 3 (a), when the distance between two edges is less than the tolerance λ and the edge of the face which is more than the minimum distance τ _ee is subdivided, As shown in FIG. 3B, a figure in which the subdivided edges have a common vertex can be obtained. And FIG.
As shown in (b), when the topological figure is within the frame of the error figure model, it is determined that the figure is normal.

Here, the above-mentioned graphic operator is created by combining each of the topological operators with a geometric operator, and the surface three-dimensional coexistence modeler of the above-mentioned CAD apparatus is a cell complex model (the inventor of the present invention firstly). On the theoretical basis of a paper published in the Journal of the Japan Society of Precision Engineering in August 1991, “Topological Model and Set Operation of a Surface Solid Coexistence Modeler”, a complex formation and complex deletion as shown in FIG. Six types of phase operators, called cell operators, are used: cell subdivision and cell reassembly as shown in FIGS. 6B to 6D, and complex subdivision and complex connection as shown in FIG. From the above, the above-mentioned graphic operators are represented by the complex generation a excluding the complex deletion, the cell subdivision b, the cell submergence c, and the complex subdivision d among the cell operators.
And the following five types of cell operators corresponding to the complex connection e. Here, the composite curve and the composite surface refer to shells (connected bodies) having one-dimensional and two-dimensional phase data, respectively.

That is, as for the complex generation a, a graphic operator (a-1) for generating a composite curve (ends of the curves to be connected are the same) by connecting the curves passing through the specified end points.
A graphic operator (a-2) for generating a composite curve from an edge sequence that does not self-intersect in a composite surface, and a graphic operator (a-3) for generating a composite curve by intersecting two composite surfaces, A graphic operator (a-4) that generates a composite curve by projecting a composite curve onto a composite surface, and a graphic operator (a-5) that generates a two-dimensional phase sweep body such as a tabsill surface, a draft surface, and a fillet surface )
And create.

For the cell subdivision b, a graphic operator (b
-1), a point operator projected onto the edge of the composite surface and the figure operator (b-2) added as a vertex, and when the edge of the composite surface intersects the vertex error sphere of the vertex of another figure, A graphic operator (b-3) that adds the center of the vertex error sphere to the edge as the vertex, and when the vertex error sphere of the vertex intersects the edge, the geometric curve of the edge is formed at a point inside the vertex error sphere. Divided, a figure operator (b-4) that connects the edges topologically to the vertices, and a composite curve generated by the figure operators (a-3) and (a-4) as an edge sequence Create a graphic operator (b-5) to be added to the composite surface.

For the cell merging c, a graphic operator that performs the inverse operation of the graphic operators (b-1), (b-2), and (b-3)
(c-1) and a graphic operator (c-2) that deletes an edge sequence between adjacent faces having the same geometric surface, and for the complex subdivision d, the complex curve at the vertex of the complex curve And a graphic operator (d-2) that divides the composite surface in the edge sequence of the composite surface, and has the same end point for the complex connection e Graphic operator (e-1) that connects two compound curves and the above graphic operator
A graphic operator (e-2) that combines the composite surface with the edge sequence added by (b-3) and the composite surface subdivided by the graphic operator (d-2) in any combination, When the distance from the peripheral edge is equal to or less than the error range τ _ef and the end point of the geometric curve of the edge connected to the corresponding vertex exists inside the vertex error spherical surface of the vertex, the two composite surfaces are joined. And the geometric operator (e-3) to be created.

Here, the graphic operators (a-1), (b-1) to (b
-4), (c-1), (c-2), (d-1), (d-2), (e-1), (e-3) Since a normal figure is created, the other figure operators will be further described. In the case of the figure operator (a-2), the end point of the geometric curve 4 as shown in FIG. (B), a geometric curve 5 is generated by the graphic operator (a-1) as shown in FIG.
Can be operated without causing the problem of error by combining with the graphic operator (e-1). If the angle formed by the two geometric curves 4 of the edge is more than a certain degree, the curves 5 having a radius of curvature of λ or more generated so as not to go out of the vertex error spherical surface are connected to each other. The geometric curves 4 can be connected without making them tangent discontinuous.

In the case of the graphic operator (a-3), the intersection between the complex surfaces is calculated by the edge advance method. In the edge advance method, as shown in FIG. The two faces F ₁ and F ₂ are selected, the intersection line E is obtained by calculating the intersection between them, and when the calculation is completed, the next set is searched for, and the process proceeds in the same manner. Specifically, when performing the cross calculations, first, one of the valid geometric curve of the edge E ₁ of the face F ₁ try to project to the other face F _2, the one face F ₁ and the other face examine the relationship between the F _2.

[0034] Then, the investigation absent one valid edge E ₁ of the face F ₁ of the two face chosen by over other face F _2, as shown in FIG. 7 (a) ,
Intersection of the case, the valid edge geometric curve of E ₁ and the face F ₂ of the face F ₁ geometrical curve valid edge E ₁ of the face F ₁ of the one crosses the other geometric curved face F ₂ And make it vertex V _1, and their faces F ₁ ,
The intersection between the geometrical surfaces of F ₂ is calculated, and the geometric curve of the intersection line is obtained, and is set as the intersection line edge E. Note that the graphic operator (a
(3-3), when performing the division and join operation of the combination of the graphic operators (b-5) and (e-2) and the addition operation of the edge sequence of the graphic operator (b-5). Vertices of the compound curve
In (b-3), an edge is added to the edge of the composite curved surface as necessary.

Here, the valid edge E ₁ and the intersection line edge E of the face F ₁ are, as shown in FIG. 7B, symbols e ₁ and e in the figure where they exactly intersect as geometric data. In order to ensure that the intersection line E intersects the vertex error sphere 2 of the vertex V _{1 in} the normal direction from the indicated position in the error range τ _ef , the error range of the effective edge geometric curve is required. between τ _ef and the tolerance λ, which is the radius of the vertex error sphere 2,
There must be a relationship of λ ≧ 2τ _ef . Considering that two vertices should be created when the face whose width is the minimum distance τ _ee and another face intersect at a right angle, the tolerance λ should be λ = τ _ee .

As a result of the above investigation, as shown in FIG.
Distance D between the two face F _1, one geometric curve and the other active edge E ₁ of the face F ₁ of geometric curved face F ₂ of the F ₂ (E _1, F ₂₎ is the error range tau _ef Less than (D (E ₁ , F ₂ ) <
In the case of τ _ef ), a part of the entire geometric curve of the effective edge E ₁ that is smaller than the error range τ _{ef is} defined as the geometric curve of the intersection line edge E of the two faces F ₁ and F ₂ , On the other hand,
As shown in FIG. 9, the other face F ₃ into two face F _1, F _2, in the case where F ₄ are connected, the two face F _1, F ₂ of each of the valid edge E ₁ , the distance between the geometric curves of E ₂ is less than the minimum distance τ _ee , the geometric curve of the valid edge E ₁ of _one of the two faces F ₁ , F ₂ of the face F ₁ The distance D (E ₁ , F ₂ ) from the geometrical surface of the other face F ₂ to which the other face F ₄ is connected, and the geometric curve of the effective edge E ₁ of the _one face F ₁ , The distance D (E ₁ , F ₄ ) from the geometrical surface of the other face F ₄ connected to the other face F ₂ is less than the error range τ _ef (D (E ₁ , F ₂ ) <τ _ef and D (E ₁ , F ₄ ) <
In the case of τ _ef ), a part of the entire geometric curve of the effective edge E ₁ that is smaller than the error range τ _{ef is} defined as the geometric curve of the intersection line E of the two faces F ₁ and F ₂ .

However, since the above equation is not always satisfied, the above equation is not always satisfied, that is, the above two distances D
If any one of (E ₁ , F ₂ ) and D (E ₁ , F ₄ ) is equal to or _larger than the error range τ _ef , the intersection calculation between the remaining two faces is performed by taking into account the subsequent graphic operation. Find the intersection line edge.
For example, if the faces F ₁ and F ₄ are left as a result of the split join operation, the intersection line between the faces F ₁ and F _{4 is} calculated as described above regardless of the distance to the faces F ₂ and F _3. To find the intersection line edge.

In the modeler of the CAD apparatus used in this embodiment, the entire shell including two intersecting faces is erased from the live shell, which is a set of figures to be displayed on the screen, and from the operation result screen. Since it is expressed as a non-manifold that forms a hierarchy along with the procedure of the graphic operation, including a dead shell, which is a set of figures, the two distances D (E ₁ , F ₂ ), D If any _{one of} (E ₁ , F ₄ ) is greater than or equal to the error range τ _{ef and} the intersection line edge is obtained by calculating the intersection between the two faces remaining on the screen, the topologically identical intersection line edge, For the vertices, the intersection of the two remaining faces of the live shell displayed as a figure is used. For the vertices, the newly calculated geometric data is used, while the intersection of the dead shell not displayed as a figure is used. For vertices The original face edges, to keep the geometric data of the vertex, when the shape recovery, the original face that had been stored in a dead shell edge, geometric curve vertices used. This makes it possible to reliably restore the original figure when performing the shape restoration for correcting the shape in the error figure model.

Further, when the intersection line is closed in one face or passes through the vertex of one face, the intersection is performed in the same manner as described above in the case shown in FIG. The line edge can be found, where the figure
As shown in 10, by the vertex error sphere 2 between the two vertices V _2, V ₃ having the one or both of the two face F _1, F ₂ have a common point, the two face F _1, F ₂ Are passed through the vertex error sphere 2, a composite curve passing through the two vertices V ₂ and V ₃ is defined as a cross line E.

In the case of the graphic operator (a-4), by performing the same method as in the graphic operator (a-3), a composite curve can be generated by projection. In the case of the graphic operator (a-5), when generating a two-dimensional phase-swept body, an edge is determined by calculating the intersection of geometric surfaces on both sides, and a face that is defined first and connected to it In some cases, the error does not exceed the error range τ _ef .

Further, in the case of the graphic operator (b-5), since the two vertices are apart from each other by the radius λ of the vertex error sphere, only one corresponding vertex can be searched. If it is tied, there will be no topologically and geometrically inconsistent figures, and even in the case of the figure operator (e-2), the distance between the edge to be combined and the face will be within the error range _τef . Since the corresponding vertices are formed at a distance within the range of the tolerance λ, the figure calculation can be performed without any trouble. Note that the value to be set for the error range τ _ef differs depending on the type of graphic operation required for the shape modeler. In this embodiment, there are cases where independently created complexes are combined (surfaces are joined together). , Τ _ef ≧ τ _cs +
τ _ss, that is, τ _ef ≧ 2τ _cs . For reference, in this embodiment, each tolerance and error range are represented by τ _cs
= 0.002 mm, τ _ef = 0.004 mm, τ _ee = 0.010 mm, λ = 0.
By setting the value to 010 mm, extremely high stability is achieved.

Therefore, according to the calculation using the graphic operator, even if the relation between the compound surfaces is various, a curve appropriate as an intersection line between the compound surfaces in the error graphic model is smoothly and surely formed. You can ask. According to the method of this embodiment in which a figure that fits within the frame of the error figure model is generated by using such a figure operator, the error of the geometric data can be reduced without requiring a large change in the conventional modeling technique. It is possible to stabilize graphic operations with a small number of development man-hours without causing problems in calculation time and required memory.
Various graphic operations can be consistently stabilized.

Although the present invention has been described based on the illustrated example, the present invention is not limited to the above example. For example, when the above method is actually applied, the error range τ _cs , In the determination regarding at least one of the tolerance λ, the error range τ _ef and the minimum distance τ _ee , for example, when determining whether the distance between the geometric curve of the edge and the geometric curved surface of the face is smaller than the error range τ _ef In the method of calculating the length of an edge and inspecting with the midpoint as a representative, inconvenience is likely to occur when the edge is divided, for every fixed length of the edge or between the vertices of the edge, Integer n
The inspection may be performed for each of the n division points divided by the above. In this case, a valid judgment result can be obtained over the entire edge, so that inconvenience occurs when the edge is divided after the judgment. Can be prevented, and the error graphic model can be given more robustness. Although τ _ef ≧ 2τ _cs is set in the above embodiment, τ _ef ≧ τ _cs can be set when only the division and join operation is performed without performing the bonding of the curved surfaces. If it is set smaller, the stability can be further improved.

[0044]

As described above, according to the graphic operation stabilizing method of the present invention, it is possible to clarify the handling of geometric data errors without requiring a large change to the conventional modeling technique, and to reduce the calculation time and required memory. In this way, it is possible to stabilize the figure calculation with a small number of development man-hours without causing any problems.
Various graphic operations can be consistently stabilized.

Here, in the graphic operation, the error of the intersection between the geometric surfaces, the error of the projection line of the geometric curve onto the geometric surface, and the error of the two geometric surfaces being regarded as being the same,
By managing the error to the error range τ _cs or less for the convergence calculation, the geometric error of the topological model is calculated between the vertex of the composite surface and the end point of the geometric curve of the edge of the face constituting the composite surface. The distance is equal to or less than a predetermined tolerance λ,
The distance between the vertices is equal to or larger than the tolerance λ, and the error in the normal direction distance of the geometric curve of the edge that partitions between the faces of the composite curved surface with respect to the geometric curved surfaces of the faces on both sides of the edge causes the bonding of the curved surfaces. the convergence equal error range greater than or twice the error range tau _cs for calculating tau _ef less, if not performed bonding of the curved surface is larger than the error range tau _cs for the convergence calculation when performing Or less than or equal to the error range τ _ef , and the minimum distance greater than or equal to twice the error range τ _ef , unless the geometric curves of any two edges are connected to each other via one vertex. if, apart over _ee tau, in various graphical operation, when performing the operation between closely spaced graphic elements, falling into unhandled due to collapse of the algorithm by setting inconsistent tolerance It is possible to prevent.

Further, in the graphic operation, the intersection calculation between the compound curved surfaces is performed by first selecting two faces and projecting the geometric curve of the edge of one of the faces onto the other face. Investigate the relationship between one face and the other face, and if the geometric curve of the edge of the one face intersects the geometric surface of the other face based on the examined relationship, The intersection of the geometric curve or vertex of the edge and the geometric surface of the other face is set as the vertex, and the intersection between the geometric surfaces of those faces is calculated to find the geometric curve of the intersection line. of cases less than the geometric curve distance is the error range of the geometric curved surface of the other face tau _ef, the two face geometric curve of the edge And the line of intersection, the distance between the geometric curve of each edge of said two face is equal to or less than the _ee minimum distance tau, to the other face, the other face via the edges of the face are connected in case of,
The distance between the geometric curve of the edge of the one face and the geometric surface of the other face, and the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face; If both distances are less than the error range τ _ef , the edge of the one face is the intersection of the two faces, and if at least one of the two distances is greater than or equal to the error range τ _ef , In consideration of the subsequent graphic operation, an intersection line is obtained by calculating the intersection between the remaining two faces, and the vertex error spherical surfaces having the tolerance λ with the radius centered on the two vertices of the two faces are determined. By having a common point,
If the intersection of the two faces passes through their vertex error sphere, the geometric curve passing through the two vertices is taken as the intersection, and if it is performed sequentially by the method of Even when the relationship is various, a curve appropriate as an intersecting line between the compound curved surfaces in the error graphic model can be smoothly and reliably obtained.

Further, the modeler of the CAD apparatus expresses the entire shell including the two intersecting faces as a non-manifold in a hierarchy in accordance with the procedure of the graphic operation. The distance between the geometric curves of the edges is equal to or less than the minimum distance τ _ee , the other face is connected to the other face via the edge of the face, and the geometric curve of the edge of the one face is And the distance between the other face and the geometric surface,
Since at least one of the distance between the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face was _{equal to} or _larger than the error range τ _ef , consideration was given to subsequent graphic calculations. Then, when the intersection line is calculated by the intersection calculation between the two remaining faces,
For topologically identical intersection lines and vertices, use the newly calculated geometric data of the edges and vertices for the intersection lines and vertices of the remaining two faces of the live shell displayed as a figure. On the other hand, the geometric data of the edges and vertices of the original face are stored for the intersection lines and vertices of the dead shell which are not displayed as figures, and when restoring the shape, the original data stored in the dead shell are stored. If the geometric data of the edges and vertices of the face is used, the original figure can be reliably restored when the shape is restored in the error figure model for correcting the shape or the like.

The determination regarding at least one of the error range τ _cs , the tolerance λ, the error range τ _ef, and the minimum distance τ _ee for the convergence calculation is performed for each fixed length of the edge, or Any integer n between the vertices of
If the determination is made for each of the n division points, a valid determination result can be obtained over the entire edge, so that inconvenience can be prevented when the edge is divided after the determination, and the error can be prevented. More robustness can be given to the graphic model.

[Brief description of the drawings]

FIG. 1A is an explanatory view showing a vertex error spherical surface and an effective edge geometric curve of an error graphic model in one embodiment of a graphic operation stabilizing method according to the present invention, and FIGS. 1B and 1C.
FIG. 9 is an explanatory diagram showing a normal face and a non-normal face determined in the embodiment, respectively.

FIG. 2 is an explanatory diagram showing a state of self-intersection not inspected by the method of the embodiment.

FIGS. 3A and 3B are explanatory diagrams showing a subdivision method for subdividing an adjacent edge in the method of the embodiment.

FIGS. 4A to 4E are explanatory diagrams respectively showing a phase operator of a modeler of a CAD apparatus that performs the method of the embodiment.

FIGS. 5A and 5B are explanatory diagrams showing a method of generating a composite curve in the method of the embodiment.

FIG. 6 is an explanatory diagram showing an edge advance method for finding an intersection line between composite curved surfaces in the method of the embodiment.

FIGS. 7A and 7B are explanatory diagrams showing a method of obtaining an intersection line edge when a geometric curve of an edge of one face and a geometric surface of another face intersect in the edge advance method. It is.

FIG. 8 is an explanatory diagram illustrating an example of a method of obtaining an intersection line edge in the edge advance method when a geometric curve of an edge of one face exists on a geometric curved surface of the other face.

FIG. 9 is an explanatory diagram showing another example of a method of obtaining an intersection line edge when the geometric curve of the edge of one face exists on the geometric curved surface of the other face in the edge advance method.

FIG. 10 is an explanatory diagram showing a method of obtaining an intersection line when two vertex error spherical surfaces of two vertices have a common point and an intersection line of two faces passes through the vertex error spherical surfaces in the edge advance method. is there.

FIGS. 11A and 11B are explanatory diagrams showing examples of figures in which contradiction occurs between phase data and geometric data.

[Explanation of symbols]

1 Vertex 2 Vertex error sphere 3 Effective edge curve δ Minimum handling error τ _cs Error range for convergence calculation λ Tolerance τ _ef Error range in the normal direction of the geometric curve of the edge to the geometric surface of the face τ _ee Minimum separation between geometric curves of edges

────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Masato Honda 2-6-32 Takashima-cho, Nishi-ku, Yokohama-shi, Kanagawa 19th floor of Nissan Yokohama Building Inside Nissan R Technology Co., Ltd. (56) References IPSJ Symposium Proceedings vol. 92 no. 5 (Graphics and CAD), pp. 95-104 Atsuyoshi Sugihara, "Phase First Method-A Method for Numerically Stabilizing Geometric Algorithms" (58) Fields investigated (Int. Cl. ⁷ , DB name) G06F 17 / 50 G06T 17/00

Claims (5)

(57) [Claims] Upon 1. A CAD apparatus for stabilizing the graphic calculation performed at each stage of the graphic operation, Rutotomoni using graphics operator combining the phase operator and geometric operators, vertices and
Phase diagram with predetermined geometric error for each of the edges
Set the shape model and operate the phase data in the graphic operation by the graphic operator
Make sure that the topological operator of
The geometrical data operation in the graphic operation is performed by the graphic operator.
The geometric operators among, characterized in that to perform as one holding in geometric error range of the graphic phase mark model after the operation, the graphic calculation stabilization method. 2. The graphic operation according to claim 1, wherein an error of an intersection between geometric surfaces, an error of a projection line of the geometric curve onto the geometric surface, and an error of assuming that the two geometric surfaces are the same are calculated. by controlling the following error range tau _cs for the geometric errors the phase graphic model has, the distance between the end points of the geometric curves of the face of the edges constituting the compound curves and vertices of compound curves Is less than or equal to a predetermined tolerance λ, the distance between the vertices is greater than or equal to the tolerance λ, and the geometric curve of the edge defining the faces of the composite curved surface is
The error of the normal direction distance of the face on both sides of the edge with respect to the geometric surface is equal to or less than twice the error range τ _cs for the convergence calculation or equal to or less than the error range τ _ef when the bonding of the surfaces is performed. If the surfaces are not bonded, the error range τ _ef is larger than or equal to the error range τ _cs for the convergence calculation, and is equal to or less than the error range τ _ef , and the geometric curve of any two edges passes through one vertex. 2. The method according to claim 1, wherein the distance is larger than twice the error range τ _ef or more than the minimum distance τ _ee which is equal to or larger than twice the error range τ _ef except when the two are connected to each other. 3. The intersection calculation between the complex surfaces in the graphic operation is performed by first selecting two faces and projecting a geometric curve of an edge of one of the faces onto the other face. Examining the relationship between the one face and the other face, based on the examined relationship, if the geometric curve of the edge of the one face intersects the geometric surface of the other face, the one face The intersection between the geometric curve or vertex of the edge of the edge and the geometric surface of the other face is set as the vertex, and the intersection between the geometric surfaces of the faces is calculated to determine the geometric curve of the edge that is the intersection line. If the distance between the geometric curve of the edge and the geometric surface of the other face is less than the error range τ _ef , the geometric curve of the edge is defined as the intersection of the two faces. When the distance between the geometric curves of the edges of each of the two faces is equal to or less than the minimum distance τ _ee and another face is connected to the other face via the edge of the face. The distance between the geometric curve of the edge of the one face and the geometric surface of the other face, and the geometric curve of the edge of the one face and the geometric surface of the other face connected to the other face _Are less than the error range τ _ef ,
The edge of the one face is defined as the intersection of the two faces, and if at least one of the two distances is equal to or _larger than the error range τ _ef , the two remaining faces are considered in consideration of the subsequent graphic calculation. The intersection line is calculated by calculating the intersection between the two faces, and the two vertices of the two faces are respectively centered.
When the vertex error spheres having a radius of the tolerance λ have a common point, when the intersection line of the two faces passes through the vertex error spheres, the geometric curve passing through the two vertices is formed. 3. The method according to claim 2, wherein the intersection is performed. 4. The modeler of the CAD apparatus expresses an entire shell including two intersecting faces as a non-manifold in a hierarchy according to a graphic operation procedure, and each of the two faces The distance between the geometric curves of the edges is equal to or less than the minimum distance τ _ee , the other face is connected to the other face via the edge of the face, and the geometric curve of the edge of the one face is And at least one of a distance between the geometric curve of the other face and a distance between the geometric curve of the edge of the one face and the geometric curve of the other face connected to the other face is the error range. Since it was τ _ef or more, considering the subsequent figure calculation, when the intersection was calculated by the intersection calculation between the remaining two faces, the topologically identical intersection line edge For the vertices, the geometric data of the newly calculated edges and vertices are used for the intersecting edges and vertices of the two remaining faces of the live shell displayed as a graphic, while the dead shell not displayed as a graphic The geometric data of the edges and vertices of the original face is saved for the intersection line edges and vertices of the original face, and the shape of the edges and vertices of the original face saved in the dead shell at the time of shape restoration 4. The method according to claim 3, wherein data is used. 5. The error range τ _cs , the tolerance λ, the error range τ _ef and the minimum distance τ _ee for the convergence calculation.
The determination regarding at least one of the above is performed at every fixed length of the edge or at every n division point obtained by dividing the vertices of the edge by an arbitrary integer n. Any of the graphic calculation stabilizing methods according to any of the above.