JPH0724076B2 - Intersection line extraction method in CAD / CAM system - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Technical Field of the Invention) The present invention relates to CAD (computer Aided Design) and CAM (Com
puter Aided Manufacturing) is related to the method of extracting the intersection line of the shape model having the free-form surface shape and the mathematical expression shape of the automobile, fluid equipment, home appliances, OA equipment, etc.

(Technical background of the invention and its problems) When the shape machining of dies and the like is to be realized by using the concept of CAD / CAM mainly for NC (Numerical Control) machining, the machining operator can quickly It is important to have a function that can sufficiently reflect the operator's know-how such as changing the tool path. Considering this point, when considering the shape processing system, it is necessary to satisfy the following requirements (1) to (3).

The shape definition function and the tool path generation function are completely separated. The tool path can be automatically generated in real time. The mathematical expression and the free-form surface shape can be processed by the same processor. What is possible Easy to connect with CAD system Compact system software By the way, shape modeling constructs a mathematical model of a three-dimensional object inside a computer and processes it into a form suitable for the required problem. , Is to be expressed externally. Therefore, a mathematical model must first be created, and the two methods of CSG or B-Reps described above mainly exist as the creation of the mathematical model.

First, the CSG-based model is one side of a three-dimensional space divided into two by a curved surface, that is, a set of half-space regions creates a closed point set region in the three-dimensional space as a three-dimensional object shape model. . Here, the three-dimensional object shape can be modeled as a subset of the three-dimensional Euclidean space. Since the model represents a physical object, it is a subset of a three-dimensional space with the inside closed. Now, let S (X) be the closed area of the three-dimensional space corresponding to the given object, and let S be this point set, then S = {X: XεS (X)} ... (1) can do. Since S (X) is a closed region, it can be considered as a set of half-space regions, and S can be further expressed by a set operation with some subsets. S is decomposed into a subset of Si (i = 1, 2, ..., N), and S is sequentially constructed by a set operation φi using these subsets. It is assumed that the set operation φi used here is a sum, product and difference set operation. This way Can be expressed as S. If φi is a union operation, Pi = φ
(Pi−1, Si) = SiUPi−1, Pi = φi for intersection operation
(Pi−1, Si) ＝ Si∩Pi−1, if the difference set operation (~ Is the complement operation). Suppose that Si is represented by the product of several subsets, and the inside of Si is closed. That is, Si = Si1∩Si2∩ ... ∩Sim …… (3) is set. When Sij in equation (3) is associated with the half-space region, we can write Sij = {X: fij (X) ≧ 0} (4), and thus the three-dimensional object shape can be expressed as a mathematical model in the half-space region. It was In shape modeling, one or some of Sij (j = 1,2, ..., m), which is a subset of Si, represents an analytically characteristic half-space region, and the rest closes this half-space region. Often used for. The characteristics of Si are used in the name of Si, and the types of Si prepared in advance are called primitives.

On the other hand, B-Reps gives topological relations such as points, edges, and curved surfaces of an object and geometric shape information of vertices, edges, and curved surfaces which are elements of the topological relation, and creates a closed two-dimensional manifold in three-dimensional space. This is a shape model of a three-dimensional object.

When defining shapes in conventional CAD and CAM systems, CS
A method of expressing a combination of simple shapes that can be expressed by a mathematical formula such as G is customary, and the principle of logical operation (set operation) is used as the method of combination.

However, in the case of a die shape, it may not be possible to define all with a combination of shapes that can be expressed by mathematical expressions. Actually, in many cases, a shape that can be expressed by a mathematical expression is used as a part of the desired shape, and in addition, a free-form surface defined by a point group is used and expressed by a combination of the two.

Here, a free-form surface is a curved surface whose surface shape cannot be mathematically expressed,
For example, it is a curved surface that cannot be expressed by an expression such as F (x, y, z) = 0. Therefore, the curved surface is the point group 2 as shown in FIG.
Has a data structure, and between points of point group 2 is, for example, Co
The surface 1 can be expressed in detail by interpolating with the ons expression or Bezier expression. Furthermore, since the free-form surface has a complicated shape,
All the interpolated surface expressions are expressions with parameters displayed. Specifically, considering a two-dimensional point sequence (node; node) as shown in FIG. 17, for convenience, there are innumerable curves that pass through the nodes 2A to 2C without fail and smoothly connect them. A curve formula that defines one curve is indispensable from the curve group. Assuming that the number of nodes is n, it is possible to obtain a curve formula that satisfies the above-mentioned condition with a polynomial of degree (n-1). However, as the degree of the polynomial becomes higher, the curve oscillates due to the Langer effect, and this effect is mitigated by using a low-order polynomial that connects the nodes part by part. This is local interpolation or spline interpolation. The spline interpolation expresses a space between nodes with a low-order polynomial, and when the number of nodes is n, the formula (n-1) is obtained.
The connectivity of all equations can be easily maintained by matching the end conditions of adjacent equations on the node.

In the case of a curved surface, a curved surface expression is set with a curved surface surrounded by four nodes as one unit (called a patch), and the continuation of them is the same as in the above-described two-dimensional case (though three-dimensional consideration is required). It is sufficient to have sex on the boundary of the patch. As the curved surface formula, one of the Coons formula, the Bezeir formula, and the B-Spline patch is generally used. The Coons interpolation formula is for the curved surface P (u, v) as shown in FIG. However, F0 (t) = 2t3−3t2 + 1, G0 (t) = t3−2t2 + t F1 (t) = − 2t3 + 3t2, G1 (t) = t3−t2, and this Coons interpolation formula is a vector that does not exist in the real space coordinate system. It is an expression. The Coons interpolation formula uses a parametric expression method. As for the relationship between the parametric space and the real space, parameters interpolated in the parameter space (uv coordinate system) of the curved surface 1 as shown in FIG. 3 are used to interpolate the XYZ coordinate system into the real space. This means that the curved surface 1 is represented by the parameter space, and it is impossible to recognize the existence of the curved surface only in the real space. When such a curved surface is added as one element of CAD or CAM, it is necessary to investigate the relationship with other elements such as a mathematical surface such as a spherical shape or a plane, but this is clearly an analysis in real space. However, it is very difficult due to the above-mentioned problems, which is a drawback in handling free-form surfaces. That is, CS
In G, it can be said that the recognition of mathematical surfaces such as spheres and planes is possible if it is possible to identify the position of any point in the real space with respect to those surfaces. Since the parameter expression is used, the point on the curved surface can be specified, but it is impossible to analyze the positional relationship between the arbitrary point on the real space and the free curved surface.

Therefore, the conventional set operation in CSG must be performed only between the shapes in the mathematical expression, and when processing the shape that mixes the shape in the mathematical expression and the shape in the free-form surface to generate the machining data, On the other hand, it is the current situation that a separate algorithm must be used for processing.

On the other hand, in FIG. 3, each boundary line (side) of the curved surface 1 corresponds to each boundary line of the rectangular area 3 indicating the curved surface area in the parameter space. This is to cause the following phenomenon. That is, as shown in FIG. 4, even if linear interpolation is performed on the parameter space, the distortion occurs on the curved surface. If this interpolation is used as the tool locus, the pitches (pick feeds) of the tools shown in A and B in the real space will not be constant, but will be wide at some places and narrow at some places, and this phenomenon will greatly affect machining efficiency. Will end up. Next, considering the machining process, it is naturally conceivable to designate a specific area A'as shown in FIG. However, even when specifying the area, the real space (A ′) and the parameter space (A ″)
It is difficult to deal with. Although the processing area A'is specified in the real space, it is impossible (analytically) to associate it with the parameter space (A "). Further, as shown in FIG. If a conventional parameter interpolation is performed, the tool locus TT as shown in the left figure is generated, but during machining, there is a demand for the tool locus generation TT 'as shown in the right figure. Is not possible with conventional parameter interpolation.

From the above background, studies are currently underway to incorporate free-form surface equations into modeling for the purpose of expanding the functions of CAD that have been developed mainly for shape modeling. The structure is judged and the free-form surface is recognized as B-Reps (Boundary Representation) to unify the processing.

Here, a conventional system example using B-Reps will be described with reference to FIG.

For example, assuming a three-dimensional shape 200 as shown in FIG. 8, the shape data input by the shape data input device 10 is subjected to predetermined arithmetic processing in boundary elements 201 to 209 forming a solid as shown in FIG. While being decomposed, the object structure data 21 showing the connection relation of each element and the mathematicized shape data 22 showing the vertex coordinates of each element, the side equation, and the surface equation are separated and arranged. When the three-dimensional shape 200 has a free-form surface, it has the free-form surface data 23 that can be represented by the point group and the interpolated surface as described above, but the free-form surface data 23 of B-Reps necessarily includes intersection line data. Must be one.
The shape data 20 thus obtained is the tool radius,
Along with the processing information 31 such as the tool feed direction, cutting speed, and processing area, it is input to the formulating shape processing unit 30 and the tracking processing of the data pointer is performed. In other words, since the B-Reps has boundary information of shape elements, if this boundary is tracked with dot information, the screen display processing (10
It is possible to perform (1), generate a tool path for NC machining (102), and perform mass property calculation processing (103) for obtaining object characteristics related to material, size, and the like.

Next, the specific processing steps of the set operation in the B-Reps representation will be described. Now
As shown in Fig. 13 (A), there are two solids B1 and B2.
1 and B2 each have 6 faces, 12 sides and 8 vertices. That is, for B1: F1 = 6, E1 = 12, V1 = 8, H1 = 0, R1 = 0, B1 = 1 For B2: F2 = 6, E2 = 12, V2 = 8, H2 = 0, R2 = 0 , B2 = 1 However, F = face, E = side, V = vertex, H = hole, R = hole contour (Rin
g), B = solid.

Becomes This satisfies the Euler-Poincare formula V-E + F-R + 2H-2B = 0 (5) which is a necessary condition for the polyhedron. For these two solids B1 and B2,
As shown in Figure (B), the shape B3 shown in Figure (C) is created by taking the sum of them, and for this shape B3, F3 = 11, E3 = 24, V3 = 16, H3 = 0, R3 = 1, B3 = 1, which also satisfies Euler Poincaré's formula. That is, "B1" = (8,12,6,0,1), "B2" = (8,12,
When "B3" = "B1" + "B2" in 6,0,0,1) "B3" = (16,2
4,11,0,1,1) required to be “τ” ＝ (0,0, −1,1,0, −1) where each component is (v, e, f, r, h , b) need to be implemented. The process of "τ" is a process of deleting one solid and one surface to create one hole contour. In this way, from R1 = 0, R2 = 0 to R3 = 1, R
Shows the outline of a hole, but this shows the line of intersection between solids without a doubt. This means that in order to perform the set operation in the topology model (connection relation model), it is only necessary to find a symmetrical intersection line between the solids. Also, FIGS. 14 to 16
The figure shows an example of a primitive set operation, and FIG. 14 shows how the shape model P3 is created by the sum of the primitives P1 and P2. FIG. 15 shows how the shape model P6 is created by the difference between the primitives P4 and P5, and FIG. 16 shows how the shape model P9 is created by the product of the primitives P7 and P8.

In the B-Reps described above, the solid shape and the like are decomposed into boundary functions, so the number of shape data increases and a shape that cannot exist geometrically is defined. However, there is a drawback in that a shape that cannot be three-dimensional is input due to a mistake in inputting a shape element.

In the case of B-Reps, CSG (Constructive Solid Geom
Since the data structure is more complicated than that of etry) and the processing is complicated, it is difficult to satisfy the above-mentioned required specifications when trying to realize the set operation as a function of CAM.

By the way, in consideration of the actual shape processing, assuming that a shape having a valence of 1 or more (such as an overhanging shape) is not processed in the Z-axis direction, and fixing the region where the shape exists from the boundary curved surface in one direction of the Z-axis, As shown in FIG. 1, the set operation can be realized by comparing the Z axes of the basic shapes A and B with each other. That is, in the case of logical sum, select the maximum Z value,
In the case of logical product, a desired shape can be obtained by selecting the minimum value. However, it is difficult to process a shape that violates the above assumption, and it cannot be said that the set operation is realized in a strict sense.

Finally, the conventional system example by CSG has a configuration as shown in FIG. 10, the shape data input from the shape data input device 10 is separated into object structure data 21 and formulated shape data 22, and these The data includes information on the surface indicating the boundary. Therefore, the solid shape in FIG. 8 is decomposed into the shape elements (primitives) 210 to 212 in FIG. 11, and the primitive 210 is added to the shape added with the primitives 211 and 212.
Subtracting will give a three-dimensional shape 200. As described above, since the CSG system needs the function information indicating the boundary, the conventional CSG cannot handle the free-form surface data and is not included in the shape data 20 either. The shape data 20 is sent to the shape extraction processing unit 40, and the spatial information SP corresponding to the application-corresponding processing (43) such as display and tool locus generation is input to generate three-dimensional overall shape information TS. That is, the formulated shape data 22 and the spatial information SP are combined by the formulated shape processing 41, and the combined formulated shape SSP is subjected to the set operation 42 together with the object structure data 21 to generate the overall shape information TS. This whole shape information TS is subjected to screen display processing (101), generation of NC tool locus (102), mass property calculation processing (103), face intersection line calculation processing (104), and Application information S1 to S4 indicating processing corresponding to these applications
Is output, and spatial information is processed in application-compatible processing 43.
Converted to SP.

As described above, in CSG, it is possible to recognize mathematical surfaces such as spherical shapes and planes if it is possible to identify the position of any point in real space with respect to those surfaces. Since the free-form surface is parameterized, the point on the surface can be specified, but it is impossible to analyze the positional relationship between any point in the real space and the free-form surface.

As described above, the conventional CSG does not handle the free-form surface as the shape data 20, so there is a drawback that the application cannot be applied to the shape including the free-form surface.

On the other hand, in the case of CSG, the data structure is simple, and it is considered that high-speed processing is possible depending on the processing method.

Therefore, from the above points, it is desired to develop a processing method that can perform set operations including free-form surfaces in the CSG method.

On the other hand, in addition to the above description, when only a predetermined shape of a curved surface is processed, when a roundness R is added to the intersection of two curved surfaces, or when chamfering is performed, an intersection line of two curved surfaces Need to know. The intersection line is a straight line in the case of a plane and a plane, but is generally a complicated curve. In addition, it is very difficult to find the intersection line of various basic shape elements such as a mathematically-formable curved surface and a free-form surface. In particular, finding the intersection line of a free-form surface and a free-form surface that can be mathematically expressed is a difficult problem because the data structure of the free-form surface is basically different from that of the free-form surface. ing. Conventionally, the mathematical expression curved surface data is once converted into the same data structure as the free curved surface data, and then the intersection line is obtained. However, there is a drawback in that another step of data conversion has to be performed and the amount of data increases.

(Object of the Invention) The present invention has been made under the circumstances described above.
An object of the present invention is to provide a surface intersection line extraction method in a CAD / CAM system that enables the intersection line calculation to be performed with the same algorithm for a free-form surface shape and a mathematical expression shape while making use of the advantages of the CSG method. .

(Summary of the Invention) The present invention provides an input device to which shape data and object structure data are input, a shape extraction processing unit that performs a set operation using the shape data and the object structure data, and a shape extraction processing unit. In a CAD / CAM system including an application processing unit that performs screen display processing based on the output overall shape information, in the CAD / CAM system, as the shape data, the mathematical expression shape data and / or the parameter space that represents the mathematical expression shape in the real space. Input the free-form surface data that represents the free-form surface shape, and if there are a plurality of the above-mentioned mathematical expression shape data and / or the above-mentioned free-form surface data, any two shape data of them are extracted and the extracted shape data is used. By the convergence calculation, the surface normal vector from an arbitrary position on the surface represented by one shape data to the surface represented by the other shape data Repeating a process of obtaining the distance seek, when the magnitude of said distance becomes zero of the arbitrary 2
It is assumed that the surfaces represented by the two shape data intersect each other and that the arbitrary position exists when the magnitude of the distance becomes zero on the intersection line formed by the intersecting surfaces. The intersection line is extracted, and the set operation is performed using the shape data representing the extracted surface intersection line.

(Embodiment of the Invention) FIG. 12 shows an example of a system for realizing the method of the present invention in correspondence with FIG. First, the shape data input device 10
Enter more shape data. It is desired that the shape input method be intuitively understandable by humans and that the expression ability be rich. Here, a combination of input by a primitive and set operation is used. Since complex shapes are created step by step, modification operations such as deformation, addition and deletion of shapes also play a major role in constructing shapes.

The input by the primitive is a method in which a simple figure such as a rectangular parallelepiped or a cylinder is registered as a basic shape, and this is taken out as needed.

As the shape data 20 by the CSG, the function information of the surface indicating the boundary is used, and the free-form surface data 23 does not include the boundary data.

Then, when one of the application processes such as the screen display process 101 is executed, the data S1 and the like from the process are input to the processes 43 and 44 corresponding to the application. The process 43 corresponding to the application sends it as SP1 to the mathematical shape processing 41. Application-aware process 44 SP it
2 is sent to the free-form surface calculation processing 45. Formulation and shape processing 41
Evaluates and determines each data of the formulated shape data 22 based on SP1, and stores the result in the shape information stack area 46. On the other hand, the free-form surface evaluation calculation processing 45 makes an evaluation / judgment based on SP2 for each data of the free-form surface data 23, and stores the result in the shape information stack area 46. The evaluation / determination in the mathematical expression shape processing 41 and the free-form surface evaluation calculation processing 45 will be described in detail later.
The set operation 42 has a shape information stack area 46.
Based on the object structure data 20, the set operation is performed on the evaluation results of the individual shape data stored in. The resulting TS is returned to the application processing such as the screen display processing 101.

For example, the screen display process 101 will be described. In order to display the overall shape, it is only necessary to be able to determine whether or not an arbitrary point in the real space is inside or outside the overall shape. Therefore, regarding the coordinate information from the screen display device 101, the mathematical expression shape processing 41 is performed for each shape data.
Alternatively, the free-form surface evaluation calculation processing 45 evaluates whether it is inside or outside, that is, which half space side, and performs a set operation on the evaluation result based on the object structure data 21, so that the coordinate position is the entire shape. Can be determined to be inside or outside. To display the outline of the entire shape, it is sufficient to search for a coordinate position having an evaluation value of 0, not on the inside or outside.

Next, the processing in the free-form surface evaluation calculation processing 45 will be described in detail. That is, this is a process of evaluating which side of a half space a certain coordinate position of a free-form surface is divided into.

Therefore, as shown in FIG. 19, it is calculated what kind of positional relationship the coordinate values (x, y, z) specified in the real space have with respect to the curved surface 1 that is parameterized (u, v). To do. The calculation method uses a convergence calculation. The outline of the convergence calculation will be described below, and then the details thereof will be described.

The basic concept of half-space domainization is the realization of evaluation in the space of free-form surfaces. Now, as shown in FIG. 20, a point P is assumed above the free curved surface, and a distance from an arbitrary point N on the curved surface 1 to a given point P is E. When this distance E is calculated for all infinite positions existing on the curved surface 1 and the points on the curved surface 1 having the same value of the distance E are connected, as shown in FIG.
A contour line of distance E can be drawn above. FIG. 22 shows a diagram in which this is represented by the E axis and the system u and v axes on the curved surface. This is a distance function from the curved surface 1 to the given point P, and this function is set to Ψ (u, v). Then, for this function, the curved surface 1
When the directional differential coefficient is obtained for the above u direction, Becomes Let θ1 be the unit vector and θ1 be the angle formed by grad Ψ. To get Similarly for v direction To get Now, to find the minimum value of this potential function, The following conditions must be met. Also, Therefore, if | ▽ Ψ | ≠ 0, cos θ1 = 0, cos θ2
Must be = 0. Therefore, θ1 = 90 °, θ2 = 90 °
Becomes Here, since θ is an angle between each direction on the curved surface and grad Ψ, E, which minimizes the potential function value, is the distance from the point P to the point P in the surface normal direction.

The minimum potential value indicates the shortest distance of a given point to a curved surface, which is a value for spatially evaluating a curved surface expressed parametrically. The surface interpolation formula is (u,
v) then the potential value is Ψ (u, v) ＝ ｜ － (u, v) ｜ ・ ・ ・ (12), and considering the direction of potential generation, (u, v) ＝ － (u , v) …… (13). Now find the point on the surface that gives the minimum potential value
Given u1, v1, the potential vector is (u1, v1) ＝ − (u1, v1) …… (14). Since the surface normal on u1, v1 that gives the minimum potential matches the direction of (u1, v1), let the surface normal vector of u1, v1 be S = (u1, v1) ··· (15) The sign of the potential can be determined by
As a result, the orientation of the half-space region can be performed.

Parameter value on the surface with the smallest potential (u1, v1)
By calculating, the half-space area can be divided into the free-form surface.

The parameter value (u1, v1) should be obtained based on the above, but it is impossible to analytically obtain (u1, v1), so it is necessary to use a search method. That is, the search initial position (u0, v0) is set on the curved surface, and the minimum value is −grad Ψ (u0, v0) for Ψ (u0, v0) at that time.
It is understandable that it is in the v0) direction.

here Therefore,-▽ Ψ =-| ▽ Ψ | cosθ1- | ▽ Ψ | cosθ2 (17). This is (-| ▽ Ψ | cosθ1, − | ▽ Ψ | cosθ
2) It shows that there is a desired solution in the direction. Here, since Ψ (u0, v0) is obviously the distance from the given point P, the position to be obtained next is u1 = −Ψ (u0, v0) ｜ ▽ Ψ | cos θ1 + u0 v1 = −Ψ (u0, v0) ｜ ▽ Ψ | cos θ2 ＋ v0 …… (18) Here, assuming that = (u, v), the above equation (18) is generally expressed as follows: i = −Ψ (i−1) ▽ Ψ (i−1) + i−1.
You can write (19). Ψ (i-1) is the search step, − ▽ Ψ (
i-1) indicates the search direction. The next search position is obtained by this formula, and S = (-(i) · = S (is the surface normal) for each search position.
0) should be monitored. When S≈1 or S≈−1
Xi is the minimum potential position.

The above theory will be specifically described.

As shown in FIG. 23, the curved surface 1 is represented by two parameters u and v, and the position vector of the point arbitrarily specified in the real space. Let P. Now, assuming that the initial parameter value is (Pu, Pv) and the position vector (Pu, Pv) on the curved surface 1, the vector is =-(Pu, Pv) ... (21), and for this vector == ∂ / ∂u × ∂ / ∂v (22) / || ≈ / || (23), || is the shortest distance from the curved surface 1 to an arbitrary point.

Next, parameters (Pu, P
The method of obtaining v) is explained. Figure 24 shows the parameters (Pu,
Pv) shows a tangent plane 1A of the curved surface 1 at which points tangent vectors exist in the u and v directions. This tangent plane 1A
Calculating ′ by projecting the vector onto, calculate the vector direction by ′ ＝ (×) × …… (24), and then calculate ′ ＝ || sinθ ′ / | ′ ｜ …… (25) Can be sought by. Then, for this vector ', it exists on the tangent plane 1A.
The component in the u, v direction tangential vector (u, v) direction is calculated. In the calculation, each direction component is TU, TV, and u
If the angle between the x-axis and the x-axis, and v and the y-axis is θ, Ψ, TU = V ′ × cos θ−Vy sin θ (26) TV = −V ′ × sin Ψ−Vy cos Ψ (27). It can be said that the parameter moved from the initial parameter by the amount of the parameter corresponding to the TU and TV is a curved surface position that may further satisfy the above equation (23). This parameter is calculated as follows: PUnew = PU + TU / DU (28) PVnew = PV + TV / DV (29) where DU and DV are the boundary lengths of the curved surfaces in the u and v directions. Based on this result, we return to equation (20) again,
This process is repeated until the expression (23) is satisfied. (twenty three)
|| that satisfies the expression represents the distance from the surface. However, as it is, it is not clear which direction the surface is facing, so it is necessary to determine the polarity described below.

Therefore, the above equation (23) is Against V ' As shown below, when the opening angle of and 'is 90 ° or more, AN is negative, and when it is 90 ° or less, AN is positive. Since and ′ are almost on the same straight line, AN ≈ 1; same direction as the surface normal vector −1; opposite direction to the surface normal vector, and the evaluation function value is Then, the evaluation function can determine whether the shape is inside or outside.

As the handling of the evaluation function at the surface boundary, there is a range of areas to which the evaluation function can be applied. The evaluation function is represented by the distance in the surface normal direction of the surface expressing the shape with respect to an arbitrary scan point. Therefore, there is an applicable range as shown in FIG. However, when performing the calculation of the evaluation function, (2
The results of Eqs. 8) and (29) may fall outside this range.
Since this position does not exist on the curved surface 1, it is impossible to set a surface normal to the scan point from that position, and special consideration must be given to the handling of the evaluation function outside the region.

Here, the vector shown in FIG. 28 is used as the evaluation vector. That is, with respect to the surface normal 6 perpendicular to the boundary line 5 of the patch 4, a vector orthogonal to the boundary line 5 is considered, and the vertical direction vector is set as the evaluation vector.
When such an evaluation vector is used, the evaluation function approximates the distance from the patch curved surface 4 as shown in FIG. 29, but also the vertical relationship (front-back relationship) with respect to the surface 4. The calculation method is (28) and (29) above.
It is determined where the result of the expression belongs to the areas A to H shown in FIG. This is a region determination on the parameter space. For this judgment, prepare a relation (4) for each boundary line such that F (u, v) ≤ 0 that makes the region expressing the inside of the shape negative in the parameter space, and compare all the values. Can be done easily. Next, as shown in FIG. 31, the intersection point IP of the straight line and the shape boundary that can be obtained from the previous search position P1 in the parameter space and the result P2 of the above equations (28) and (29) is obtained. . The straight line formula is Therefore, the intersection IP can be easily obtained. Based on this parameter, the processing for obtaining 'again is performed. If the result P2 of the equations (28) and (29) is out of the area even after this processing, the boundary line and the scan point are searched as shown in FIG. 32, and ′ · = 0 ...... The polarities for obtaining the u and v parameters such that (45) and for obtaining the evaluation function value as shown in Fig. 27 are the same as above. In addition,
FIG. 32 shows a vector ′ between the point (u, v) on the boundary line 5 and the scan point SC, and a tangent vector at the point (u, v). The method of obtaining the result of equation (45) is as shown in FIG.

The above is the evaluation method for the free-form surface in the free-form surface evaluation calculation processing 45.

Since the free-form surface can be evaluated as described above, the line of intersection between two free-form surfaces as shown below can be obtained. As shown in FIG. 25, two curved surfaces 4A and 4B
The scan line 7 is set on one of the surfaces, and the evaluation method based on the above method is used for points on the line 7. At this time, the relationship between the evaluation function calculated by this evaluation method and the scan line is as shown in FIG. 26, and the position where the evaluation function becomes 0 is the intersection of the scan line 7 and the surface 4A, and all scans are performed. When this intersection is obtained for the line 7, the intersection group represents the intersection between the curved surfaces 4A and 4B.

The above processing is the same as in the mathematical expression shape processing 41.

Extraction of the intersection line will be described in detail with reference to the flowchart of FIG. The extraction of the surface intersection line is performed in the surface intersection line calculation process 104 shown in FIG. 12, and the position vector on the scanning line on one curved surface is given to the process 43 corresponding to the application. The scan line is set in the parameter space.

First, consider two curved surfaces 4A and 4B as shown in FIG. 25. For example, a start scan line 7A starting from SSP is set at the boundary line on the curved surface 4B (step S1), and the points on the curved surface 4B are described above. Parameters are interpolated by the method (step S2). Then, the surface normal vector from the curved surface 4A is calculated for the point on the curved surface 4B (step S3), and it is determined whether or not the magnitude of the vector is zero (step S4). The point on the curved surface 4B is moved along the scanning line 7A in accordance with the size of (step S7), and the process returns to step S2. If the magnitude of the vector is zero, it is stored in the memory as the intersection line coordinates (step S5), and it is determined whether or not the whole surface of the curved surface 4B is completed (step S6).
If the entire surface is not completed, the next scanning line 7B is set (step S8) and the process returns to step S2.

Here, the processing shown in FIG. 34 will be described with reference to FIG. The curved surface 4A shown in FIG. 25 is stored in the free curved surface data 23 via the shape data input device 10. Therefore, the surface intersection line calculation process 104 first generates a search point Sn by parameter interpolation using the curved surface 4B that generates a scanning line. The search point Sn is passed to the process 44 corresponding to the application.
The application-compatible processing 44 performs input switching corresponding to a plurality of applications (101 to 104),
Therefore, the search point Sn is SP2 and the free-form surface evaluation calculation process 4
Passed to 5. In the free-form surface evaluation calculation processing 45, the processing by the search method described above is performed. That is, the search point SP
The normal vector from the curved surface 4A to 2 is obtained and passed to the shape information stack area 46. Shape data in this case
Since only one curved surface is possible in 20, the data in the shape information stack area 46 is passed to the set operation 42 and is obtained as a result TS. Curved line calculation processing 10
4 finds the next search point based on this TS. And
The above processing is repeated until the value of TS, that is, the magnitude of the vector becomes 0, and when it becomes 0, the same processing is performed for the next scanning line.

On the other hand, if a plurality of curved surfaces are stored in the shape data 20, the free curved surface evaluation calculation process for each curved surface 45
The processing result in (1) is once stored in the shape information stack area 46. That is, the evaluation calculation process is performed on all curved surfaces. When the processing for all curved surfaces is completed, the processing of the set operation 42 is performed. This is because when a plurality of curved surfaces are combined to form one object, as shown in FIGS. 11, 14, 15, and 16, for example,
The processing is to obtain a normal vector from the object. That is, it is a process of selecting the most suitable one to be used as a normal vector for each of the individual curved surfaces.
In addition, how the individual curved surfaces are combined
It is described as the object structure data 21 in the shape data 20.

FIG. 35 shows the flow of processing when the tool path generation function as described above is incorporated in the NC device 300. In a normal process, the NC information of the paper tape 307 is read (303), and the character image data representing the NC information is converted into binary data (304). The command information is analyzed based on the binary data (305), the servo processing (306) is performed, and the output is given to the machine tool 308. Incorporating the tool path generation function 302 into the NC device 300 has the advantages that it can output binary data directly and that command information analysis is not necessary because it is a series of linear interpolations, which can be expected to speed up processing. . Therefore, it is effective that the NC device 300 has a tool locus generating function, and if the shape data 301 is input to generate the tool locus TP and the servo processing (306) is performed, machining according to the input shape data is performed. Can be done. Therefore, if the shape extraction processing unit 40 described above is incorporated into the NC device 300 as the tool trajectory generation processing 302, the overall shape information TS that has been set and operated can be used as the tool trajectory TP. In this case, it is necessary when processing complex shapes
The NC command information becomes a huge amount and its handling becomes a problem, but the shape data 301 for the tool locus generation processing (302) is a very compact amount and its handling is easy. Further, FIG. 36 shows an example of the hardware configuration of the NC device 300, and the tool path generation processing unit 312
There are two possible connections between the NC control unit and the conventional NC control unit.
One is a method of fully utilizing the advantage of placing the tool locus generation processing unit 312 inside, and this is a RAM 311 that can be commonly used by the tool locus generation processing unit 312 and the CPU 310 of the NC control unit as shown by the solid line in the figure. Is provided and information is mutually transmitted via the RAM 311. According to this, loss time at the time of data transfer is eliminated, and high-speed processing is possible. The other is a method in which an interface 313 is provided and connected to the conventional NC control unit as shown by the broken line in the figure. When this method is used, the processing speed includes the influence of the data transfer speed, so that the processing speed becomes slow as a whole.

Note that in the example of FIG. 35, the shape data 301 is directly subjected to the tool locus generation processing (302) in the NC device 300.
As shown in FIG. 37, it is also possible to input the same with the NC information to the paper tape 307, and at the time of reading the command information, determine whether it is the NC information or the shape data and distribute it.

(Effects of the Invention) As described above, according to the surface intersection line extraction method in the CAD / CAM system of the present invention, the surface intersection line can be extracted by applying a free-form surface to the CSG method.

[Brief description of drawings]

FIG. 1 is a diagram for explaining a set operation for a two-dimensional figure, FIG. 2 is a diagram showing a display example by a point group of a curved surface, FIG. 3 is a diagram showing a relationship between an XYZ real space and a uv parameter space, 4 to 6 are diagrams for explaining the relationship between the real space and the parameter space, FIG. 7 is a block diagram showing a conventional system example by B-Reps, and FIG. 8 is an example of a three-dimensional shape. FIG. 9, FIG. 9 and FIG. 11 are diagrams for explaining an example of disassembling the three-dimensional shape of FIG. 8. FIG. 10 is a block diagram showing an example of a conventional system by CSG, and FIG. A block diagram showing an example of a system to be realized, FIGS. 13 to 16 are diagrams for explaining a set operation, FIG. 17 is a diagram for explaining the interpolation of a curved surface, and FIG. 18 is a diagram for explaining the Coons interpolation formula. Fig. 19 to 2
FIG. 4 is a diagram for explaining the principle of evaluation of a free-form surface according to the present invention.FIGS. 25 and 26 are diagrams for explaining a specific evaluation of the free-form surface of the present invention. FIG. 34 is a flow chart showing the method of the present invention, FIGS. 35 and 36 are block configuration diagrams showing a concrete application example to the NC device, and FIG. 37 is a further diagram for explaining the method for determining the polarity of the free-form surface. It is a block block diagram which shows another example. 1 ... curved surface, 1A ... tangent plane, 2 ... point group (node), 3
...... Rectangular area, 4 ...... Patch, 10 ...... Shape data input device, 20 ...... Shape data, 30 ...... Formulation shape processing unit, 31 ・ ・ ・
… Processing information, 40 …… Shape extraction processing part, 41 …… Formation processing of mathematics, 42 …… Set operation, 43,44 …… Process for application, 45 …… Free curved surface evaluation calculation processing,
46: Shape information stack area, 200: 3D shape.

Claims (1)

[Claims] 1. An input device to which shape data and object structure data are input, a shape extraction processing section that performs a set operation using the shape data and the object structure data, and an entire output from the shape extraction processing section. In a CAD / CAM system equipped with an application processing unit that performs screen display processing and the like based on shape information, the free-form surface in the parameter space and / or the mathematical expression shape data that represents the mathematical expression shape in the real space as the shape data. When inputting free-form surface data representing a shape, and when there are a plurality of the above-mentioned mathematical expression shape data and / or the above-mentioned free-form surface data, two arbitrary shape data of them are taken out, and a convergence operation using the extracted shape data is performed. Obtain the surface normal vector from an arbitrary position on the surface represented by one shape data to the surface represented by the other shape data, and calculate its distance. The process of obtaining the distance is repeated, and when the magnitude of the distance becomes zero, the arbitrary 2
It is assumed that the surfaces represented by the two shape data intersect each other and that the arbitrary position exists when the magnitude of the distance becomes zero on the intersection line formed by the intersecting surfaces. An intersection line extraction method in a CAD / CAM system, characterized in that intersection lines are extracted, and the set operation is performed using the shape data representing the extracted intersection lines.