JPS61210480A - Formation data memory and processing system in cad/cam system - Google Patents

Abstract

PURPOSE:To effectively use a memory and to perform the division of an area with respect to a free curved surface by judging whether a reverse Polish described formation data is a mathematical formation data, an operation code or the free curved surface. CONSTITUTION:The storing section of a formation data is adjusted to one reverse Polish described formation data 24 without dividing into an object structure data and a mathematical formation data. In a formation extract processing section 40, is is judged whether it is a mathematical information data 41, an operation code 42A or a free curved surface 45 and stored in a formation information stack area 46A. In this stack area 46A, all primitive informations are stored. The stored primitives are set and operated based on the object structure data 21 to obtain all formation information TS. A method for inputting a formation is easy to be understood by human beings intuitively and desired to be rich in representation ability. In this invention, the combination of an input by the primitive and a set operation is employed.

Description

[Detailed Description of the Invention] (Technical Field of the Invention) This invention is based on CAD (Computer Aided
Design) and CAM (Computer Aid)
This paper relates to a shape data storage/processing method in ed Manufacturing.

(Technical background of the invention and its problems) When defining shapes in conventional CAfl and CAM systems, it is customary to express them by combining simple shapes that can be expressed by mathematical expressions. The principle of operation code is used. However, in the case of a mold shape, it may not be possible to define everything by a combination of shapes that can be expressed mathematically. In reality, there are many shapes that are expressed by using a shape that can be expressed mathematically as part of the desired shape, and a free-form surface defined by a school of fish, and a combination of the two. However, conventional set operations for free-form surfaces Because of this difficulty, when generating machining data by processing a shape that contains a mixture of mathematically expressed shapes and free-form surface shapes, it is currently necessary to process each shape using a separate algorithm. It is.

NO (Numerical C) performs shape processing of molds, etc.
When trying to realize this using the C^guchi/CAM concept, which is mainly based on on-rol machining, it is necessary to provide functions that allow the machining operator to sufficiently reflect the operator's know-how, such as the ability to quickly change the tool path at the machining site. It is important to have it. When considering the shape change system in consideration of this point, it is necessary to satisfy the following requirements (1) to (4).

■The shape definition function and the tool path generation function are completely separated.■It is possible to automatically generate tool paths in real time.■The same processor can process mathematical shapes and free-form shapes.■A combination thereof. Possibility of set operations ■ Easy connection with CAD system ■ Compact system software In order to expand the functionality of CAD, which has been developed mainly for shape modeling, we have developed a free-form surface model for modeling. Research is currently underway to incorporate the data structure of free-form surfaces into B-Reps (B-Reps).
The process is unified by recognizing it as a secondary representation. However, in the case of B-Repg, C5G (Constr
The data structure is more complex compared to uctive 5 solid geometer 7), and the processing is complicated.
Set operation is a function of CAM.

If we try to realize this, it will be difficult to satisfy the above-mentioned requirement specification (■). Shape modeling involves constructing a mathematical model of a three-dimensional object inside a computer, processing it into a form suitable for the required problem, and expressing it externally. Therefore, a mathematical model must first be created.

The above-mentioned C5G or B-Rep is used to create the mathematical model.
There are mainly two methods of s. As a result, aS
The model based on G is one side of a three-dimensional space divided into two by a curved surface, that is, a collection of half-space regions,
It creates a closed point set viewing area in a three-dimensional space as a three-dimensional object shape model, and B-Reps is a topological relationship such as one point per side of an object and one curved surface, and an element of the topological relationship such as one vertex per side and one curved surface. gives the geometrical information.

This method creates a closed two-dimensional manifold in a three-dimensional space and uses it as a shape model of a three-dimensional object. Also, in consideration of actual shape processing, it is assumed that shapes with a valence of more than one in the Z-axis direction (overhanging shapes, etc.) will not be processed, and if the shape is fixed in one direction along the Z-axis from the region boundary curved surface where the shape exists. ,
As shown in FIG. 1, the set operation can be realized by comparing the Z axes of each of the basic shapes A and B. That is, a desired shape can be obtained by selecting the maximum value of the Z value in the case of logical sum, and selecting the minimum value in the case of logical product. However, it is difficult to process shapes that violate the above assumptions, and it cannot be said that set operations are realized in the strict sense.On the other hand, in the case of C5G, the data structure is simple, and the processing method Judging from this, it is thought that high-speed processing is possible.

Here, a free-form surface is a curved surface whose shape cannot be expressed mathematically.
For example, it is a curved surface that cannot be expressed by a formula such as F(x, y, z)C0. Therefore, as shown in FIG. 2, the curved surface 1 can be expressed in detail by having a school of fish 2 as a data structure and interpolating between the points of one point group 2 using, for example, the Coons equation or the Bezier equation. Furthermore, since the free-form surface has a complicated shape, all interpolated surface equations are expressed as parameters. In other words, as shown in Figure C3, the detailed expression of the curved surface l uses parameters interpolated in the parameter space (U coordinate system), and interpolates to the real space of the xYz coordinate system. It means that it is expressed in space, and it is impossible to recognize the existence of a curved surface only in real space. When such a curved surface is added as an element in CAD or CAM, it is necessary to investigate the relationship with other elements such as a spherical shape or a mathematical surface such as a plane, but this is obviously not an analysis in real space. However, due to the above-mentioned problems, it is extremely difficult and a drawback in handling free-form surfaces.

Figure 3 also shows a map of the curved surface l that exists in the real space into the parameter space, and each boundary line (side) of the curved surface l
correspond to each boundary line of the rectangular area 3 indicating the curved surface area on the parameter space. This causes the phenomenon shown below. In other words, as shown in Figure 4, even if linear interpolation is performed on the parameter space, it will be distorted on the curved surface.
If this interpolation is used as a tool trajectory, the pitch (big feed) of the tool shown in A and B is not constant in real space,
Considering the process of zero-order machining, where it is wide in some places and narrow in others, and this phenomenon greatly affects the machining efficiency, we can designate a specific area A' as shown in Figure 5. Of course, partial machining of only one part can be considered. However, when specifying the area, the real space (Ao) and the parameter space (Ao)
”).The machining area A° is specified in real space, but it is difficult to correspond to it in parameter space (
A”) is impossible (analytical), and furthermore, if the curved surface is extremely curved as shown in Figure 6, if conventional parameter interpolation is performed, the tool trajectory front as shown in the left figure will occur. However, during machining, there is a requirement to generate a tool trajectory T?' as shown in the figure on the right, and such a tool trajectory is not possible with conventional parameter interpolation.

Next, an example of a conventional system using B-Raps will be described with reference to FIG.

For example, when assuming a three-dimensional shape 20G as shown in Figure f58, the shape data input by the shape data input device 10 is decomposed into boundary elements 201 to 209 constituting the solid as shown in Figure 9 through predetermined arithmetic processing. At the same time, it is separated and organized into object structure data 21 indicating the connection relationship of each element, and mathematical shape data 22 indicating the equation of one side of the vertex coordinate of each element and the equation of two sides. When the three-dimensional shape 20G has a free-form surface, it has free-form surface data 23 that can be expressed by the school of fish and interpolated surface as described above, but B-Raps
The free-form surface data 23 must necessarily include intersection line data.The shape data 20 obtained in this way includes the tool radius, tool feed direction, cutting speed,
Along with machining information 31 such as machining area! l [The data is input to the formulated shape processing unit 30 and data pointer tracking processing is performed. In other words, since B-Reps has boundary information of shape elements, if this boundary is tracked using dot information, screen display processing (101) can be performed on a display device such as a CRT.
l, generate tool trajectory for NC machining (102
), or perform mass property calculation processing (103) to obtain object properties related to material, size, etc. Since such B-Reps are decomposed into functions of three-dimensional isoelectric boundaries, the amount of shape data increases, and shapes that cannot exist geometrically may be defined. There is a drawback that a shape element input error may result in inputting a shape that cannot be created in 3D.

On the other hand, a conventional system example using C5G has a configuration as shown in No. 10, in which the shape data input from the shape data input wave filO is separated into object structure data 21 and mathematically expressed shape data 22, and these data are contains information about the surface indicating the boundary. Therefore, the three-dimensional shape of FIG. 8 is the shape element (primitive) 210 to 2 of FIG. 11!
2, and subtracting the primitive 210 from the shape obtained by adding the primitives 211 and 212 yields the three-dimensional shape 20.
It becomes 0. In this way, since the C5G system requires function information that indicates boundaries, the conventional C8G cannot handle free-form surface data, and the shape data 20, which is not included in the shape data 20, is processed through shape extraction processing. Part 4
0 and inputs spatial information SP corresponding to application-compatible processing (43) such as display and tool trajectory generation to generate three-dimensional overall shape information TS. That is, the mathematical shape data 22 and the spatial information SP are combined in a mathematical shape processing 41, and the combined mathematical shape SSP is subjected to a set operation 42 together with the object structure data 21, thereby generating the overall shape information TS. be done. This overall shape information T
S is subjected to screen display processing (101), NC tool trajectory generation (102), mass property calculation processing (
103) and surface intersection line calculation processing (100), application information S1 to S4 indicating processing corresponding to these applications is output, and converted into spatial information SP in processing corresponding to the application 43. In this way, Since the conventional C9G does not handle free-form surfaces as the shape data 20, it has the disadvantage that it cannot perform calculations on shapes that include free-form surfaces.

Furthermore, when using CSC to express, for example, the diagonal line shape in FIG. 12 with the shape data 20, the object structure data 2! is expressed as pms-a+c-o, and the mathematical shape data 22
is described as shown in FIG. Here.

The mathematical shape data of a circle is expressed by center point coordinates and radius,
A rectangle is expressed by the lengths of its long and short sides, and its data length varies depending on the shape. For this reason, it is necessary to prepare the longest memory area HA of the expected shape as the memory area for storing the mathematically expressed shape data of the shape data, and it is necessary to prepare the longest memory area HA of the expected shape. In this case, there is a problem that an empty blank area BM is generated and the memory area is wasted.

(Object of the invention) This invention was made under the above circumstances,
The purpose of this invention is to provide a storage and processing method for shape data in a CAD/CAM system that takes advantage of the advantages of the C'3G method and achieves the same effect as when evaluating free-form surfaces in real space. Our goal is to provide the following.

(Summary of the Invention) The present invention uses a shape data input device that also targets free-form surfaces, calculates the distance of arbitrary position data to a function expressing the shape of real space and parameter space, and uses object structure data of the above shape. C, which has a shape extraction processing section that performs a set operation, and a display section that displays the shape based on the overall shape information output from the shape extraction processing section.
The shape data input by the shape data input device in the AD/CAM system is stored in the shape data memory in reverse Polish notation, and the free-form surface data is also stored in vector representation, and the shape data written in reverse Polish is expressed mathematically. A determination is made as to whether it is shape data, an operation code, or a free-form surface, and the overall shape information is obtained in the shape information stack area according to the reverse Polish memory data.

(Embodiment of the invention) Figure 14 shows an example of a system for realizing the method of the invention.
This is shown in correspondence with the figure, and the function information of the surface indicating the boundary is used as the shape data 20 according to CSa <, the free-form surface data 23 does not include boundary data, and the free-form surface data 23 is subjected to shape extraction processing. This information is processed in the unit 40 together with the spatial information from the process 44 corresponding to the applicator 1, and is further stored in the shape information stack area 4B together with the information from the mathematical shape process 41. This stack area 4B
stores all primitive information. The stored primitives are subjected to a set operation 42 based on the object structure data 21 to obtain overall shape information 15. A shape input method that is easy for humans to intuitively understand and has rich expressive capabilities is desired, and here a combination of input using primitives and set operations is used. Complex shapes are created step by step, so changing operations such as deforming, adding, and deleting shapes also play a major role in constructing shapes. The primitive input is a rectangular parallelepiped.

This is a method in which a simple figure such as a cylinder is registered as a basic shape, and this is extracted as needed. Further, a set operation is also called a Boa 1ean Operation, and is a set operation that performs a set operation on two spatial regions of shapes already defined by primitives, sweeps, or the like. Generally, three types of operations are used: sum, difference, and m.
In some cases, inversion (Negative) is used instead of difference. By repeatedly applying such set operations, complex shapes can be obtained.

As mentioned above, when the shape data is divided into the object a structure data 21 and the mathematically expressed shape data 22, the memory capacity of the shape data storage section becomes redundant and is wasted. In the above, the two-dimensional shape was explained, but the mathematical shape data of one sphere is expressed by the center coordinates and radius, and the rectangular parallelepiped is expressed by the 15th
Three points CB that define one surface as shown in the figure (^)
It is represented by I to GB3 and a width W perpendicular to this plane.

In addition, one cylinder is expressed by the center and radius of the base circle, the unit vector in the axial direction, and the height, and the cone is expressed by the center CPI and radius r of the base circle, and the unit in the axial direction, as shown in Figure 15 (B). It is expressed by the vector N, the height H, and the inclination angle θ of the slope, and the free-form surface is expressed by the number of fish schools 2 on the boundary line in the U-ma direction as shown in FIG. When such a three-dimensional shape is taken into account, the redundancy of the memory capacity of the shape data storage section becomes even greater. Therefore, in the present invention, the shape data described in reverse Polish notation is stored in the memory in order, so as not to waste the required memory capacity. That is, in this invention, the shape data storage section is not divided into object structure data and mathematically expressed shape data;
As shown in Figure B, the shape data is organized into one shape data 24 written in reverse Polish, and the shape extraction processing unit 40 determines whether it is mathematical shape data (41), an operation code (42A), or a free-form surface (45). , is stored in the shape information stack area 48A using a method described later, and the entire shape information TS is output from this shape information stack area 48A. The shape data 24 described in reverse Polish is, for example, the second
In the case of the shape shown in the figure, the format is shown as 24 in FIG. 17, and the mathematical shape data is written in B'', "A", C", and "D".

Such reverse Polish-described shape data 24 is
Input as shown in Figure 17 (P-B-A◆C-D) I
1 is subjected to compiler processing 12, which is general computer software processing, to obtain shape data 24 written in reverse Polish. If such a storage method is used, the shape data will be stored in order from the beginning of the memory area MA.

Shape data can be inputted and stored in order within the memory area X^ without creating a blank area or wasting the memory.

Figure 17 shows compiler processing! In this example, the shape data 24 written in reverse polish is obtained all at once in step 2, but the shape data 24 is obtained sequentially according to the flow shown in FIG.
You can also get First, in step Sl), store "P" indicating that the input shape is P in the memory.
When the mathematical shape data of shape B is input (step S2
), the data is converted into a format suitable for the internal processing of the computer (step S3), and stored in the memory (step S00).Next, an operation code (-) is input (step S5), and the mathematical shape data of shape A is stored. is input and data is converted, the result is stored in the memory (steps S8 to S8), and then the operation code (-) is stored in the memory (step S8).
), then the operation code (÷) is input (step 5IG), the mathematical shape data of shape C is input (step 5ll), the data is similarly converted, and the result is stored in memory (step S12゜). 513), the operation need is stored in the memory (step 5114), the operation code (-) is input (step 515), the mathematical shape data of the shape is input (step 5ill), and after the data is converted. The result is stored in memory, the operation code (-) is input, and axis=" is input (step SIT~92).
0) and shape data 24 as shown in FIG. 17 are generated and stored in a memory for shape data input.

The shape data 24 written in reverse Polish and stored in the memory as described above is processed by the shape extraction processing unit 40 and the entire shape information TS is stored in the shape information stack area tEIA.
Store. FIG. 18 shows this process. Information is transferred in order from the first address of the shape data 24, and the information is transferred to the mathematical shape data (41), the operation code (41), and the operation code (41).
2A) or free-form surface (45), and the shape information stack area 48A is divided into three areas ARI-A.
It is divided into R3. First, when information indicating that the shape is P is transferred, this is determined and stored in area ARI (state 1sT1), and then mathematical shape data B is transferred and stored in area AR2 (state 71ST2). )
After that, the next mathematical shape data A is transferred and stored in area ^R3 (state 8-3), and the operation code (-) is transferred to store (B in area AR2).
-A) is calculated, and the result Sl is stored in the area AR2 (state 7!1ST0, when the next mathematical shape data C is transferred, it is stored in the area AR3 as shown in state s!3T5 and the first By transferring the operation code (ri), the result Sl of area ^R2 and the mathematical shape data C of area AR3 are added, and the result (St+C)
is stored in area AR2 (state 57B), then the mathematical shape data D is transferred and stored in area AR3 (state Hs〒7), and the operation code (-) is transferred (S2-D ) is calculated and stored in area AR2 (state 5T8), and -=" is transferred to area ARI (S2
- 口), that is, P=B-A+G-D is stored. As a result, the entire shape information of the input shape data P is stored in the shape information star 7 querier 48A. Therefore, the memory capacity of the shape information stack area 48A can also be reduced.

By the way, a three-dimensional object shape can be modeled as a subset of a three-dimensional Euclidean space. Since a model represents a physical object, it is a subset of a closed three-dimensional space. Now, let the closed region of the three-dimensional space corresponding to the given object be 5(X), and let this point set be S, then S = (X: )l 5(X))...
It can be expressed as ...(1). Since 5(X) is a closed region, it can be thought of as a collection of half-space regions.

S can be further expressed by set operations using several subsets. S to S'1 (i scale 1, 2...on
) into subsets, and sequentially construct S using these subsets by set operation φ1. It is assumed that the set operations φ used here are sum, product, and difference set operations. In this way, S can be expressed as. If φt is a union operation, PL−
1φ(Pt-+, 5t)=St U P+-! , intersection set operation nara jfP+ = φI(P+-r, 5i)
= Si j'1P1-+, if it is a difference set operation, Pi-φ
+(P+-+, Si) =Pt-+-5t=Pt-+
1”1st (Let ~ be the complementary set operation), Sl
Let us express it as a product of several subsets and close the interior of Si. Namely.

Si = S++ n 5tzn"・fl Sts
--(3) and SIJ in equation (3) corresponds to the half-space region, 5tj= (X: flj(X) ≧Q) ・
... (4) can be written, and in this way the shape of a three-dimensional object can be expressed as a mathematical model using a half-space region. In shape modeling, Sij (j-1,
2゜..., intestine) represents a characteristic half-space region analytically, and the rest are often used to close this half-space region, and define the features of this Si as St Each type of St prepared in advance is called a primitive.

Next, a description will be given of the processing steps that a topology model set operation undergoes. Now, Figure 20 (A
), there are two solids Bl, 82, and the solid Bl
+82 each has 6 faces, 12 edges, and 8 vertices,
That is, for B1: Fl-8, EI-12, V1s8. Hl-0, R+-0
, B1-lB2: F2-8. B2-12. V2-8. B2-0. R2-0
, B2-straight, F-plane, E-side, to-vertex, H-hole,
R-Ring, B-Stereo.

This satisfies the Euler-Poincaré equation (5), which is a necessary condition for a polyhedron. For these two solids B and B2,
By overlapping them as shown in i2G diagram (B) and taking the sum, a shape B3 shown in the same diagram (C) is created, and for this shape B3, B3-11. B3-24. v3=18. H1*Q,
R3-1,63m1, which also satisfies Euler-Poincaré's equation, tail, sumari, "81" = (8,
12,8,O,I).

B2" - (8, 12, 8, 0, 0, 1) "83" -
61", 1B2", B3"~(1B, 24.11
．． 0.1.1) - (0, 0, -1, 1, 0, -1) However, each component needs to undergo the processing of (Ma*e+Er+h*b). The processing of "τ" is the processing of erasing one solid surface and creating one hole outline.In this way, R, -0, R2
From the mackerel 0, R3-If becomes R3-If, so R is a hole outline, which definitely indicates the intersection line between two solids. This means that in order to perform a set operation in a topology model (connection relationship model), it is sufficient to find a line of intersection between symmetric solids. Further, FIGS. 21 to 23 show examples of primitive set operations, and FIG. 21 shows how a shape model P3 is created by the sum of primitives PI and F2. FIG. 22 shows how the shape model PG is created by the difference between the primitives P4 and F5, and FIG. 23 shows how the shape model P9 is created by the product of the primitives P7 and F8.

By the way, a free-form surface is usually represented by a school of fish on a curved surface, and as shown in Figure 2, the entire shape of the curved surface is expressed by smoothly connecting the school of fish 2. Considering (node:mode), node 2^
Although there are curves that always pass through ~2C and connect smoothly, a curve equation that defines one curve from among these curves is required. Letting the number of nodes be n,
A curve equation that satisfies the above conditions can be obtained using a (+-1) degree polynomial. However, the higher the degree of the polynomial, the more the curve oscillates due to the Langer effect, and this effect can be alleviated by using a low-degree polynomial that connects the nodes one part at a time. This is local interpolation or spline interpolation. Spline interpolation expresses the distance between nodes using a low-order polynomial, and if the number of nodes is n, then (n-1)
We will obtain the formula. The connectivity of the entire system can be easily maintained by matching the ends of adjacent systems on the 7th wire.

In the case of a curved surface, one unit (
For the 0-surface equation, all you need to do is set the surface equation as a batch (called a batch) and maintain continuity on the boundary of the patch in the same way as in the 2-dimensional case described above (however, 3-dimensional consideration is required).
In general, Coons equation, Bezeir equation, B-3
I am using one of the pline patches. Coon
The s Kikuma equation is P(u, ma)- for the curved surface P(u, ma) as shown in Fig. 25. However, Fo(t) = 2t''- 3t'+1.Go(t)at
3-2t2+tF+(t)g-2t3+3t2.
(+(t) is given by t3-L2, and this Goons interpolation formula is a vector formula that does not exist in the real space coordinate system. Also, the above Coons interpolation formula uses a parametric expression method, and this parametric expression Although it is possible to express complex expressions simply, it has the disadvantage that the relationship between the parametric space and the real space cannot be made clear, that is,
Parameters given to an expression in parametric space cannot be evaluated at all in real space. Objects exist in three-dimensional space and need to be evaluated within that space.

Although free-form surfaces seen in mold shapes and shapes that can be expressed mathematically exist in the same coordinate system, they are discussed in completely different spaces. Therefore, in this invention, the free-form surface is handled in the same space as the mathematically expressed shape.

The free-form surface evaluation method of this invention will be explained with reference to the drawings. As shown in the m2B diagram, coordinate values (x, y, z) specified in real space are expressed as parameters (U, curved surface 1 The calculation method uses convergence calculation, and an outline of the convergence calculation will be described below, and then its details will be explained.

The basic concept of half-space regionalization is the realization of evaluation in the space of free-form surfaces. Now, as shown in Fig. 27, suppose a point P is above the free-form surface, and let E be the distance from any point N on the surface l to 4 points P. By calculating this distance E for all positions and connecting points on the curved surface 1 where the distance E takes the same value, it is possible to draw equigrades of the distance E on the two curved surfaces 1 as shown in FIG. 28. this,
Figure 28 shows a diagram expressed by the E axis, the system U on the curved surface, and the ma axis. This is a distance function from the curved surface l to the four points P, and this function is denoted as ψ (u, ma), and , If we calculate the directional differential coefficient for this function in the U direction on one curved surface l, we will get the following.If U is a unit vector, and the angle formed by gradψ is θI.

get. Similarly, obtain the information for the V direction. Now, if we want to find the minimum value of this potential function.

It is necessary to meet the following conditions. Moreover, if 1ψ1≠O, then it is necessary that aOSθ1-0°COjθ2-0. Therefore, θ18300
, θ2 becomes 90°. Here, since θ is the angle formed by each direction on the curved surface and gradψ, E, which takes the minimum potential function value, is the angle between the 4 points P in the surface normal direction toward the 4 points P.
The distance between

The minimum potential value indicates the shortest distance between four points on a curved surface.
, ma), then the potential value is ψ(u, v)=I P−Q(u, v) l =(
12), and further considering the direction in which the potential is generated, ψ (u, v) = P - Q (u, v)...
・”・(13) Now, if the point on the curved surface that gives the minimum potential value is ul+ma!, then the potential vector is ψ(u+, v+)=P −Q(u+, v+) ・
...-C14), which gives the minimum potential value u
The direction of the surface normal of l+l and ψ(ul, maI) is the same, so if the surface normal vector of ul and ma1 is n, then S=
ψ (old, ma+) conflict n ・・・・・・・・・
By performing (15), the sign of the potential can be determined, and as a result, the direction of the half-space castle can be determined.

By finding the parameter values (ul, maI) on the curved surface with the minimum potential, it is possible to divide the free-form surface into half-space regions. However, analytically (U+, Mar)
Since it is impossible to find, it is necessary to find it using a search method. In other words, the initial position of the search on the curved surface! ! (uo,
It can be understood that the minimum value is in the -gradψ (UO+Ma0) direction with respect to ψ(UO+Ma0) at that time.

・・・・・・・・・(18) ψ Here, □Full 17ψl cosO, so 1ψ proverb −u−+ 7ψl cos O+ −v−1ψI cos
θ2・・・・・・(17) This becomes (-1ψl cas 01.-IψI
cos 172) indicates that there is a desired solution in the direction. Here, ψ(UO+ma0) is clearly the distance from the 4 points P, so the next position to be found is ul-1-ψ(u
o*va)−+ψI cas O+ +u.

Vl snow −ψ(”o+voll maψl cas
O2+ v.

・・・・・・・・・(1 day) Here, if X = (u, ma), the above (1B)
The formula is generally: X1=-*()l-+)・w! (XI-+) +X+-
+・・・・・・・・・(19) It can be written as: ψ()l−+) is the search step, −ψ(XI
−+) indicates the search direction. Find the next search position using this formula, and for each search position, S・(P-Q(XI))
・Just monitor n=S (n is the surface normal), S#
1 or 3#-1 is the position where the potential is minimum.

As shown in Figure 30, one curved surface 1 has two parameters:
It is expressed as ``ma'' and shown as 2〇 *S (u, ma).

Let P be the position vector of an arbitrarily specified point in real space.

Now, if the initial parameter values are (Pu, Pv), the position vector C on one curved surface L is C-5 (Pu, Pv) - - = (20), and the vector V at this time is V -P-C ......(21), and for this vector ■, n - aC/ au X aC/ av - (2
2) n/Inl#V/IVI
-C23), IVI will be described as a method for finding parameters (Pu, Pv) that satisfy the above equation (23) at the 0th order, which is the shortest distance from the curved surface l to an arbitrary point. FIG. 31 shows the tangent plane IA of the curved surface l at the parameter (Pu, Pv) point, and tangent vectors exist on the tangent plane IA in the U and M directions. When calculating V′, which is the vector V projected onto this tangent plane IA, V′=(nXV
) X n = · - (24) to calculate the direction of the vector, and later V' = IV l sin
θ・V'/l V'l can be obtained by calculating (25), and
With respect to this vector V°, U that exists on the tangent plane IA
, calculate the component in the direction of the tangent vector (Tu, Tma) in the Ma direction. The calculation is as follows: TIJ-V'x case -V7 sIn
O----・・-(28) TVs-V'x gin
* -Vy cas ψ=...-(27) Based on this TU, TV, the parameters shifted from the initial parameters by an amount of parameters commensurate with the TU and TV will make the above equation (23) more It can be said that this indicates a curved surface position that may be satisfied. To calculate this parameter, let DO and DV be the boundary line lengths of the curved surface in the U and M directions of the surface, then PUnow = PU - TU / 1
10...(28) PV
new = PV +TV / roV
. . . (29) is performed. Based on this result, return to equation (20) again and repeat this process until equation (23) is satisfied. IVI that satisfies equation (23) represents the distance from the first surface. Since it is not clear which direction is the front or the back, it is necessary to perform polarity determination, which will be described later.

The above has been explained using a general vector equation, but to explain it with a more specific example, the evaluation function when obtaining data with properties similar to those shown in Fig. 31 is the tangent plane 4S shown in Fig. 32. is the distance vector n in the direction of the surface normal. Here, point C on one curved surface 4A is expressed by parameters U and Ma.

(30) Let P be an arbitrary point on the scan line 7, set a search start point on the patch to be scanned, and let the parameter value of this search start point be ult.

Next, find the distance vector between the starting point and any point.

V=P-C...(32) For this V vector.

If holds true, 1v1 is the value of the evaluation function.

The evaluation of scan line 7 is as shown in FIG. (
Equation 33) is an explant calculation of the tangent vector in the U direction and the tangent vector in the ma direction with the parameter uLmar, which becomes the surface normal vector n. As in the two-dimensional case, (34)
Since the formula cannot be satisfied in one go, we move on to the first procedure. This process is a process of projecting V onto the tangential plane 4S, and the tangential plane 4S is a plane in which U, the ma-tangent vector of the coordinate system consisting of the ma-tangent vector and the normal vector n exist. The projection process onto the tangential plane 4S is as shown in FIG. Namely.

By calculating , the direction of the projected vector can be calculated, and then the magnitude of this V' is determined. The calculation is given by. Regarding V obtained here, Tu.

Find the Tu and T components for the D and n coordinate systems, respectively. Here, since the Tu and D axes do not necessarily coincide with the X, LZ orthogonal coordinate system, coordinate transformation processing is required.

The coordinate transformation procedure is based on the process of matching the normal vector with the Z axis, and as shown in FIG. 35, 0.
Assuming that the parameter ψ is known, if we calculate the following around the Z-axis and then around the Y-axis, n will match the Z-axis. At this time, the relationship between the D-u and T-ma coordinate systems on the X-Y plane is the third
It will be as shown in Figure B. Tu in this kind of relationship,
Next, find each component of Vo for the T coordinate system. V
If the components of l are (Vx, Vy, Vz), then TLI
J&min.

Tu = Vx cosO-Vy s1nθ ・-
---・(39), Tv acid component.

Tv −−Vx sin ψ 10 V7
cos ψ −・−・−−(40), (3
Based on the values calculated using formulas 9) and (40), the initial parameters Ill
, it can be said that a point shifted from Ma1 is a position that is more likely to satisfy equation (34).

Calculation of the position of the new parameter U of the patch.

If the length of the boundary line in the ma direction is nu and D ma, then it is sufficient to perform the process as follows.

By the way, the polarity of the evaluation function is the degree data necessary for determining whether the shape of the solid formed by one surface is inside or outside. This polarity is preferably negative within the shape and positive outside the shape, and the basis for determining the inside and outside of a shape expressed by a surface is the relationship with the surface normal. Here, a method is used to determine the polarity based on the opening angle between the surface normal and the evaluation vector.

When calculating the value of Vo that satisfies the above formula (23), as shown below, when the opening angle between n and Vo is 80° or more, AM is negative, and when it is 80° or less, AM is positive. . Further, since n and Vo exist on almost the same straight line, the following equation is obtained, and if the evaluation function value is taken, it becomes an evaluation function that can determine whether the shape is inside or outside.

When handling evaluation functions at surface boundaries, there is a range of areas to which evaluation functions can be applied. The evaluation function is expressed by the distance in the normal direction of the surface representing the shape with respect to an arbitrary scan point, so there is an applicable range as shown in FIG. 37. However, when calculating the evaluation function, the above (28
) and (28) may fall outside this range.

Since this position does not exist on the curved surface 1, it is impossible to establish a surface normal to the scan point from this position, and special consideration must be given to the handling of evaluation functions outside the area.

Here, a vector E as shown in FIG. 38 is assumed to be an evaluation vector. In other words, consider a vector perpendicular to the boundary line 5 with respect to the surface normal 6 perpendicular to the boundary line 5 of the patch 4,
The vertical vector is defined as the evaluation vector E. When such an evaluation vector E is used, the evaluation function clarifies the distance from the patch curved surface 4, although only approximately, as shown in Fig. 38, and clarifies the superior military relationship (front and back relationship) with respect to the blood clot 4. do. The calculation method is (28) and (
29) Determine to which region the result of the equation belongs among the regions A to H shown in FIG. 40. This is region determination on the parameter space. This determination can be made by preparing four functions for each boundary line such that F (u, ma) ≦ O such that the area representing the inside of the shape is negative in the parameter space, and comparing all of their values. As shown in FIG. 41, the previous search position P on the parameter space is
1, and the intersection point IP between the straight line and the shape boundary, which can be found from the result P2 of equations (28) and (28) above, is found.

Since the equation of the straight line is M1□u+□ (44) uOu・, the intersection point IP can be easily determined. The process of calculating Vo is performed again based on this parameter. If the result P2 of equations (28) and (28) is still outside the area even after this process, the boundary line and scan point are calculated as shown in Fig. 42. The polarity of the evaluation function value shown in Fig. 37 is determined by performing a search and finding the U and ma parameters such that Vo ・ T = O (45). is the same as In addition, the fourth
In Figure 2, the distance between the point ("+ma) on the boundary line 5 and the scanning point SC is represented by a vector V°, and the tangent vector at the point (u, ma) is shown by T. Then, (45) The method for obtaining the result of the equation is as shown in FIG.

By evaluating the free-form surfaces using the method described above, it is possible to find the line of intersection between two free-form surfaces as shown in the first order. As shown in FIG. 32, a scan line 7 is set on one of the two curved surfaces 4A and 4B, 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 Figure 33, and the position O of this evaluation function is the intersection of scan line 7 and surface 4A, and all scan If this intersection point is found for the line 7, the group of intersection points will represent the line of intersection between the curved surfaces 4A and 4B.

FIG. 44 shows the flow of processing when the above-mentioned tool trajectory generation function is incorporated into the NC system [300].

Normal processing reads the NC information of the paper tape 307 (3
03) The character image data representing the NC information is converted into binary (304).

Based on the binary data, command information is analyzed (305), servo processing (30B) is performed, and the output is given to the machine tool 308. Incorporating the tool path generation function 302 into the NO system@300 has the advantages of being able to directly output binary data and not requiring command information analysis because it is a continuous linear interpolation process, which is expected to speed up the processing. can. For this reason, it is effective for NO@ equipment 00 to have a tool trajectory generation function, and the shape data 3
01 to generate the tool path TP and perform servo processing (3
0B), processing can be performed according to the input shape data. Therefore, the shape extraction processing section 40 described above
If it is incorporated into the NC device 1300 as the tool trajectory generation process 302, the entire shape information T
S can be used as the tool path TP. In this case, the amount of NO command information required when machining a complex shape is enormous, and its handling becomes a problem.
01 is a very compact quantity and its handling is easy. Further, FIG. 45 shows an example of the hardware configuration of the NC equipment ff1300, in which the tool trajectory generation processing section 312
There are two ways to connect the conventional NO control unit. One is a method that takes full advantage of the advantage of locating the tool path generation processing section 312 internally, and this is a method in which the tool path generation processing section 312 and the CPO 310 of the NO control section use a RAM 311 that can be used in common, as shown by the solid line in the figure. established,
Information is mutually transmitted via this RAM 311. According to this, loss time during data transfer is eliminated,
High-speed processing is possible. The other method is to provide an interface 313 as shown in the dashed line in the figure to connect to the conventional NO control section.With this method, the processing speed includes the influence of the data transfer speed. Overall processing speed becomes slower.

In addition, in the example of FIG. 44, the shape data 301 t-HC
The tool trajectory generation process (302) is performed directly within the installation gi 300, but as shown in FIG.
It is also possible to determine whether the data is C information or shape data and then sort the data.

(Effects of the Invention) As described above, according to the shape data storage/processing method of the present invention, even a free-form surface based on CSa can be divided into regions, and memory can be used effectively.

[Brief explanation of the drawing]

Fig. 1 is a diagram for explaining a set operation for a two-dimensional figure, Fig. 2 is a diagram showing an example of displaying a school of fish on a curved surface, Fig. 3 is a diagram showing the relationship between the XYZ real space and the U parameter space, Figures 4 to 6 are diagrams for explaining the relationship between real space and parameter space, and Figure 7 is B-Ra.
A block diagram showing an example of a conventional system using ps, FIG. 8 is a diagram showing an example of a three-dimensional shape, and FIGS.
Figure 10 is a block diagram showing an example of a conventional system using C5G.
2 and 13 are diagrams for explaining the input of shape data, FIG. 14 is a block diagram showing an example of a system that implements the method of this invention, and FIGS. 15 (A) and (B) are representations of mathematically expressed shape data. FIG. 18 is a block diagram showing an example of a graphic data processing system according to the present invention.
Figures 7 to 18 are diagrams for explaining the generation and processing of shape data described in reverse Polish, Figures 20 to 23 are diagrams for explaining set operations, and Figure 24 is a diagram for explaining interpolation of curved surfaces. A diagram for explaining, Fig. 25, is a diagram of Coon
Figures for explaining the s interpolation formula, Figures 28 to 31 are diagrams for explaining the principle of evaluation of free-form surfaces according to the present invention, and Figures 32 to 36 are diagrams for explaining the free-form surfaces of the present invention. Figures 37 to 43 are diagrams to explain the polarity determination method for free-form surfaces. Figures 44 and 45 are block configuration diagrams showing specific application examples for MCIItfi. , No. 48v4 is a block configuration diagram showing still another example. l...Curved surface, IA...Tangential plane, 2...Fish school (node), 3...Rectangular area, 4...Batch, IO...
Shape data input device, 20... Shape data, 30...
- Mathematical shape processing unit, 31... Processing information, 40...
・Shape extraction processing unit, 41... Mathematical shape processing, 42.
...Set operation, 43.44...Application cage processing, 45...Free-form surface evaluation calculation processing, 4B...Shape information stack area, 20G...
3D shape. Applicant's agent Yu Yasugata Engraving of the three drawings (no changes to the contents) %2 drawings% 3 drawings 4) 8 figures also 9 figures! 2 Figure HA Ru 17 Figure A 18 Figure (Al mo 24 Figure Atsushi 25 Figure also 21 Figure stone 22 Figure 423 Figure 26 Figure L27 Figure Stone 2B Figure % 29 Figure also 30 Figure stone 3f Figure 34 Figure stone 35 Figure Issue 36 Diagram L 38 Diagram 39 Diagram 40 Diagram procedure amendment (method) June 28, 1985

Claims (1)

[Claims] A shape data input device that also targets free-form surfaces, and a shape extraction processing unit that calculates the distance of arbitrary position data to a function that expresses the shape in real space and parameter space, and performs a set operation using object structure data of the shape. and a display unit that displays the shape based on the overall shape information output from the shape extraction processing unit.
In the shape data storage and processing method in the M system, the shape data inputted by the shape data input device is stored in the shape data memory in reverse Polish notation, and
The free-form surface data is also stored in a vector representation, and the shape data described in reverse polish is determined whether it is mathematical shape data, an operation code, or a free-form surface, and the entire shape information is stored in the shape information stack area according to the reverse polish memory data. A CA characterized by being made to obtain
Shape data storage and processing method in D/CAM system.