JPS61213902A - Nc device with automatic three-dimensional programming function - Google Patents

Abstract

PURPOSE:To obtain the same effect even for a free curved surface with evaluation in a real space while making the most of advantages of a CSG (Constructive Solid Geometry) system by storing a memory with shape data described in Polish notation in order and thus reducing the necessary memory capacity. CONSTITUTION:Shape data 20 on CSG basis uses function information on a surface which indicates a border and free curved surface data 23 is processed in a shape extraction processing part 40 together with space information from a process 44 corresponding to an application and further stored in a shape information stack area 46 together with information of an enciphered shape process 41. In this stack area 46, information on all primitive is stored. The store part of the shape data is arranged into one shape data in reverse Polish notation without being divided into body structure data and enciphered shape data, and the shape extraction processing part 40 judges the enciphered shape data 41, an operation code, or a free curved surface 45 and stores it in the shape information stack area 46, and entire shape information TS is outputted from this area 46.

Description

DETAILED DESCRIPTION OF THE INVENTION (Technical Field of the Invention) The present invention relates to a numerical control (NC) device having a three-dimensional automatic programming function.

(Technical background of the invention and its problems) Conventional cAIl (Computer Aided De
sign) and CAM (Computer Aided
When defining a shape in a manufacturing system, it is customary to express it by combining simple shapes that can be expressed by mathematical formulas, and the principle of logical operation (set operation) is used as the method of combination. 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, using a free-form surface defined by a school of fish, and a combination of the two. However, because conventional set operations are difficult for free-form surfaces, when generating machining data by processing a shape that contains a mixture of mathematically expressed shapes and free-form surfaces, separate algorithms are required for each shape. The current situation is that it must be processed using .

Shape processing of molds, etc. is performed using NC (Numerical Go).
When trying to realize this using a CAD/CAM concept that focuses on machining, it is necessary to have 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 cutting 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 free-form surface into B-Reps (B-Reps) by determining the data structure of the free-form surface.
The process is unified by recognizing it as a secondary Repre-sentation. However, in the case of B-Reps, C5G (Const'
The data structure is more complex than that of 5-solid geometry), and the processing is complicated. Therefore, if a set operation is to be implemented as a CAM function, it will be difficult to satisfy the above-mentioned requirement specification (2). 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, and there are two main methods for creating a mathematical model: ESC or B-Reps. The model is a three-dimensional space divided into two by a curved surface, that is, one side of the half-space region, which creates a closed point set region in the three-dimensional space as a three-dimensional object shape model. gives the topological relationship such as one point per side and two curved surfaces of the object, and the geometric information of one vertex per side and one curved surface which are the elements of the topological relationship, and creates a closed two-dimensional manifold in three-dimensional space to calculate the shape of the three-dimensional object. In addition, in consideration of actual shape processing, it is assumed that shapes with a valence of more than 1 in the Z-axis direction (overhanging shapes, etc.) will not be processed, and the area where the shape exists is converted into a boundary curved surface. If the Z-axis is fixed in one direction from , the set operation can be realized by comparing the Z-axis of each basic shape A and B, as shown in Figure 1.In other words, in the case of logical sum, the maximum value of the Z value , and in the case of logical product, the desired shape can be obtained by selecting the minimum value.However, it is difficult to process shapes that violate the assumptions stated in 1.E, and in the strict sense it is a set operation. However, in the case of C9G, the data structure is simple, and judging from the processing method, high-speed processing is considered 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)=0. Therefore, the curved surface has a data structure of one point group 2 as shown in FIG. 2, and the curved surface 1 can be expressed in detail by interpolating between the points of the fish school 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. That is, as shown in FIG. 3, the detailed expression of the curved surface l uses parameters interpolated in the parameter space (U coordinate system), and interpolation into the real space of the XYZ coordinate system is performed. This means that the curved surface 1 is expressed 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 an element in CAD or CAM, the relationship with other elements such as a spherical shape or a mathematical surface such as a plane must be investigated, but this obviously cannot be analyzed in real space. However, due to the above-mentioned problems, it is extremely difficult to handle free-form surfaces, which is the second drawback.

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. That is, as shown in FIG. 4, even if linear interpolation is performed on the parameter space, distortion occurs on the curved surface -F. If this interpolation is the tool path, then A and B in real space.
The pitch (big feet) of the tool shown in Figure 1 is not constant, being wide in some places and narrow in others, and this phenomenon greatly affects machining efficiency. Next, considering the processing process, it is natural to designate a specific area A' and create a section I for only that part, as shown in FIG. but,
When specifying the area, the real space (A') and the parameter space (
It is difficult to correspond to A'').° to the cutting area is specified in real space, but it is impossible (analytically) to correspond to it in parameter space (A''). Furthermore, when the curved surface is extremely curved as shown in FIG. 6, if conventional parameter interpolation is performed, a tool trajectory neck as shown in the left figure will be generated. However, during machining, there is a requirement to generate a tool trajectory TT' 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-Reps will be described with reference to FIG.

For example, when assuming a three-dimensional shape 200 as shown in FIG. 8, the shape data inputted by the shape data input device 10 is converted into boundary elements 201 to 209 constituting the solid as shown in FIG. 9 through predetermined arithmetic processing. When decomposed, object structure data 21 indicating the connection relationship of each element, and mathematical shape data 2 indicating the vertex coordinates of each element, the equations of the 9 sides, and the equations of the 9 surfaces.
It is separated and organized into 2. When the three-dimensional shape 200 has a free-form surface, it has free-form surface data 23 that can be expressed by a school of fish and an interpolated surface as described above, but the free-form surface data 23 of B-Reps necessarily includes intersection line data. Must. The shape data 20 obtained in this way is combined with machining information 31 such as the tool radius, tool feed direction, cutting speed, machining area, etc. to the mathematical shape processing unit 30.
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, C
Perform screen display processing (101) on a display device such as RT,
Generate a tool trajectory for NO machining (102),
It is also possible to perform mass property calculation processing (103) to obtain object properties related to material, size, etc.

In this way - Raps decomposes 3D shapes etc. into boundary functions, so the amount of shape data increases, and it is also possible to define shapes that cannot exist geometrically, or There is a drawback that a mistake in inputting an element 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 FIG. contains information about the surface indicating the boundary. Therefore, the three-dimensional shape in FIG. 8 is the shape element (primitive) 210 to 212 in FIG.
If primitive 210 is subtracted from the shape obtained by adding primitives 211 and 212, three-dimensional shape 200 is obtained.
becomes. As described above, since the C5G system requires function information indicating boundaries, the conventional C8G cannot handle free-form surface data.

It is not included in the shape data 20 either. The shape data 20 is sent to the shape extraction processing section 40, which 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 synthesized in the numerical and mathematical shape processing 41, and the synthesized mathematical shape ss
p is set operation 4 together with object structure data 21
2, the overall shape information TS is generated.

This overall shape information TS is subjected to screen display processing (101).

The trajectory of the NC tool is generated (102), the mass property calculation process (103) is performed, and the one-hedral intersection line calculation process (102) is performed.
104), the application information 5t-34 indicating the processing corresponding to these application eyes is output, and the spatial information S is output in the processing corresponding to the application 43.
It is converted to P. As described above, since the conventional GSG does not handle free-form surfaces as the shape data 20, it has the disadvantage that it cannot be applied to shapes that include free-form surfaces.

Furthermore, when expressing, for example, the diagonal line shape in FIG. 12 with the shape data 20 using GSG, the object structure data 21 is
=B-A+C-D, 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, and a rectangle is expressed by lengths of long sides and short sides, and the data length differs depending on the shape. For this reason, it is necessary to prepare the longest memory area X^ of the shape to be preformed as the memory area for storing the mathematically expressed shape data, and the shape with a smaller amount of data than the longest memory area HA is input. In this case, an empty blank area BM will occur,
The disadvantage is that it wastes memory area.

The relationship between a conventional three-dimensional automatic programming system and an HC device is such that an NC programmer creates NC command information for a workpiece and passes the information to a machine tool operator as an NC command tape. In such a process, corrections to the NC commanded tape must be made back to the NO program level. In this case, the machining techniques possessed by the machine tool operator cannot be fully reflected on the IC command data creator. Also, NCs with complex shapes
Since the amount of instruction tape is extremely large, there are also problems in its handling. Furthermore, in general, there are almost no 3D automatic programming systems that have accurate geometric information of the workpiece internally, and as a result, the degree of freedom in generating tool paths is low, and it is not always possible to achieve the optimum machining pattern. It wasn't.

(Objective of the invention) This invention was made in view of the circumstances mentioned in -.
In order to make full use of the know-how (know-how) and to facilitate the handling of information media, we have developed a three-dimensional method that takes advantage of the C8G method and achieves the same effect as when evaluating free-form surfaces in real space. An object of the present invention is to provide an NC device incorporating an automatic programming function.

(Summary of the Invention) The present invention provides a shape data input device that also uses a free-form surface as an object, and calculates the distance of arbitrary position data to a function expressing the shape of real space and parameter space. The 3D automatic programming function consists of a shape extraction processing section that performs set operations using data, and a tool trajectory generation processing section that generates a tool trajectory based on the overall shape information output from this shape extraction processing section. It is equipped with an NC device.

(Embodiment of the invention) Figure 14 shows an example of a system for realizing the method of the invention.
Shape data 2 by CSG is shown in correspondence with the figure.
As 0, function information of a surface indicating a boundary is used, and the free-form surface data 23 does not include boundary data. Then, the free-form surface data 23 is processed in the shape extraction processing unit 4θ together with the spatial information from the application-compatible processing 44,
Furthermore, it is stored in the shape information stack area 48 together with the information of the mathematical shape processing 41. This stack area 48 stores information on all primitives. The stored primitives are subjected to a set operation 42 based on the object structure data 21 to obtain overall shape information TS. 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, the set operation is also called a Boo 1ean Operation, and performs a result calculation on two spatial regions of shapes already defined by primitives, sweeps, or the like. Generally, three types of operations are used: sum, difference, and product.
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 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 a 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 figure (A)
It is represented by I to CB3 and a width W perpendicular to this plane.

In addition, a cylinder is expressed by the center and radius of the base circle, a unit vector in the axial direction, and the height, and a 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 UV force direction boundary line 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 Borland notation is stored in the memory in order, so that the required memory capacity is not wasted. 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 Fig. 8, it is organized into one shape data 24 written in reverse Borland, and the shape extraction processing unit 40 judges whether it is mathematical shape data (41), operation code (42^), or free-form surface (45). Then, it 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 46A. The shape data 24 written in reverse Borland 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 "B'°,""A゛°"C" and "
Mathematical shape data is described in D''.

Such shape data 24 written in reverse Borland is
Input as shown in Fig. 17 (P=B-A+C-B) 11
Compiler processing 12, which is general computer software processing, is applied to the data to obtain shape data 24 written in reverse Borland. If such a storage method is used, the shape data is stored in order from the beginning of the memory area HA, so there is no need to waste memory due to blank areas. Shape data can be input and stored in order within the memory area HA.

FIG. 17 is an example in which the shape data 24 written in reverse Borland is obtained all at once in the compiler processing 12, but the shape data 24 is obtained sequentially according to the flow shown in FIG.
You can also get First, store "P" in memory to indicate that the input shape is P! 31)
, when the mathematical shape data of shape B is input (step S2), the data is converted into a format suitable for internal processing of the computer (step S3) and stored in memory (step S4). Then the operation code (
-) is input (step S5), the mathematical shape data of shape A is input, data is converted, and the result is stored in memory (steps 56 to S8). After that, the operation code (-) is stored in the memory (step S8), then the operation code (+) is input (step 510), and the mathematical shape data of shape C is input (step 511), and similarly. Data is converted and the result is stored in memory (step S12゜513
), the operation code (re) is stored in memory (
Step 514), an operation code (-) is input (step 515), the mathematical shape data of the shape is input (step 51B), the result is stored in memory after data conversion, and the operation code (-) is input.
is input and ;” is input (step Sl?~52
0) and shape data 24 as shown in FIG. 17 are generated and stored in a memory for shape data input.

-1- The shape data 24 written in reverse Borland and stored in the memory as described above is processed by the shape extraction processing unit 40, and the entire shape information T is stored in the shape information stack area 4BA.
Store S. Figure 18 shows this situation.
Information is transferred in order from the first address of the shape data 24,
Mathematical shape data (41), operation code (
42A) or free-form surface (45) is determined,
The shape information stack area 48A has three areas ARI~
It is divided into AR3. First, when information indicating that the shape is P is transferred, this is determined and stored in the area API (state 5TI), and then the mathematical shape data B is transferred and stored in the area AR2 (state 5T2). )
. After that, the next mathematical shape data A is transferred and stored in area AR3 (state 5T3), and the operation code (-) is transferred to area AR2 (B
-A) is calculated, and the result Sl is stored in area AR2 (state ST4). When the next mathematical shape data C is transferred, it is stored in area AR3 as shown in gsT5, and then the operation code (+) is transferred, so that the result S1 of area AR2 and the mathematical form data of area AR3 are stored. C is added, and the result (S1+C) is stored in area AR2 (state JfR3TB). After that, the mathematical shape data D is transferred and stored in area AR3 (state ST?), and the operation code (-)
is transferred, (S2-If) is calculated and stored in area AR2 (state gsr8), and when "=" is transferred, (S2-If) is calculated and stored in area ARI as in state ST9.
D), that is, P=B-A+C-D is stored. As a result, the entire shape information of the input shape data P is stored in the shape information stack area dEiA.

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 lifted object be 5(X), and let this point set be S, then S
It can be expressed as = (X: Xe 5(X)) - (1). Since 5(X) is a closed region, it can be considered as a collection of half-space regions, and S can be further expressed by set operations using several subsets.

Decompose S into 5l (i=1.2...+") subsets, and sequentially perform set operation φ on S using these subsets.
Consists of l. It is assumed that the set operation φ1 used here is a sum, a product, and a difference set operation. In this way, S can be expressed as (i=2.3...,n). If φl is a union operation, PL=
φ(Pi-1, 9t)=Si U Pi-1, if it is an intersection set operation, Pi=φ+ (P+-+, Si)='5u
lP+-+, if it is a difference set operation, Pj=φ+(P+-++
Si) =P+-+-S+=P+-+nS+ (~ is a complementary set operation). Let us represent Si as a product of several subsets and close the interior of Sl. That is, S+=S++ n 5ull-fl Si-・-
Put it as ・・・(3). When Sij in equation (3) is made to correspond to the half-space region, S+j= (X: flJ(X)≧O)...
...-(4), and thus the three-dimensional object shape could be expressed as a mathematical model using a half-space region. In shape modeling, SIJ (j”L 2*
. 91 features of this Sl
Each type of Si 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 solid openings 1.82, and the solid Bl
, B2 each have 6 faces, 12 edges, and 8 vertices. That is, for B1: F1=8. E1=12. V+ =8. H1=0. R1=
0. Regarding B+ = IB2.

F2=JE2=12. V2=8. H2=0. R2=0.
Bz = square, F-plane, E = edge, v = vertex, ■-hole,
R-Ring, B-Stereo.

bawl. This satisfies the Euler-Poincaré equation (5), which is a necessary condition for a polyhedron. For these two solids B1 and B2,
Overlap as shown in Fig. 20 (B) and its shape B3
For F3=11. E3=24. V3=18. H3=0
．． R3=1. B3=1, which also satisfies the Euler-Poincaré equation. In other words, “B+” = (8
, 12, 6, 0, 1).

B2” = (8, 12, 8, 0, 0, 1) and “B5
1T = “mouth 1”, “when B2 pa, pa B3” = (
1B, 24.11.0.1.1)" = (0, 0, -1, 1, 0, -1) However, each component is (v + e, t, r + h + b) processing must be performed. The processing τ°" is a process of erasing one of the nine three-dimensional surfaces and creating one hole outline. In this way, R1=0. Since R2=O becomes R3=1, R is defined as a hole outline, which clearly indicates an 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. Also, the 21st
23 to 23 show examples of the set operation of primitives, and FIG. 21 shows how a shape model P3 is created by the sum of primitives P1 and R2. FIG. 22 shows how the shape model P6 is created by the difference between the primitives P4 and R5, and FIG. 23 shows how the shape model P8 is created by the product of the primitives P7 and R8.

By the way, a free-form surface is usually represented by a school of fish on a curved surface, and as shown in FIG. 2, the entire shape of the curved surface is expressed by connecting the school of fish 2 smoothly. 2 as shown in Figure J-124
Considering a dimensional point sequence (node), node 2
Although there are countless curves that always pass through A to 2G and connect smoothly, a curve equation is required that defines one curve from among these curves. When the number of nodes is n, a curved expression that satisfies the above condition 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 reduced by using a low-order 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 when the number of nodes is n, an equation (n-1) is obtained. Total connectivity can be easily maintained by matching the endness of adjacent expressions on nodes.

In the case of a curved surface, one unit (
It is sufficient to set a surface equation as a patch (referred to as a patch) and provide continuity on the boundary of the patch in the same way as in the two-dimensional case described above (however, three-dimensional consideration is required). The curved surface formula is
Generally, Coons equation, Bezeir equation, B-3pl
I'm using one of the ine patches. The Coons correction formula is as follows for the curved surface P(u, v) as shown in Fig. 25: P(u, v) = ...... (6) However, Fo(t) = 2t1- 3t2+1. Go(t)4
3-2t2+tF+ (t)=-2t3+3t2,
G+ (t)=t3-t2, and this Coo
The ns compensation formula is a vector formula that does not exist in the real space coordinate system. Further, the Coons compensation formula uses a parametric expression method, and while this parametric expression can simply express a complex expression, it has the drawback that the relationship between the parametric space and the real space cannot be made clear. In other words, the parameters given to the equation in parametric space cannot be evaluated at all in real space; the object exists in three-dimensional space and must 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.

To explain the free-form surface evaluation method of this invention with reference to the drawings, as shown in Fig. 26, coordinate values (x, y, z) specified in real space are expressed as parameters (u, v). The positional relationship with respect to the curved surface 1 is calculated. The calculation method uses convergence calculation,
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, a point P is assumed above the free-form surface, and a distance E from an arbitrary point N on the curved surface 1 to four points P is assumed. If we calculate this distance E for all the infinitely many arbitrary positions on the curved surface 1 and connect the points on the curved surface l where the distance #E has the same value, we will find the distance E on the hole curved surface 1 as shown in Figure 28. We can draw a contour of distance E. this,
FIG. 28 shows a diagram representing the E axis and the system U and v axes of the curved surface. This is a distance function from the curved surface 1 to a point P,
Let this function be ψ(u, ma). Then, the directional differential coefficient of this function with respect to the U direction of the 10 curved surface 1-1- is calculated as follows. With U as a unit vector, gradψ
Letting the angle formed by 01 be obtained. Similarly, obtain the information for the V direction. Now, when finding the minimum value of this potential function, it is necessary to satisfy the following condition. Also, if 1ψ1≠0 because ・・・・・・・・・(11), then aOSθ1=o.

It is necessary that COSθ2=0. Therefore, θ1=90°
, θ2=80°. Here, since 0 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, and is a value for spatially evaluating a parametrically expressed curved surface. The surface interpolation formula is Q(u
, v), then the potential value is ψ(u, v)J P-Q(u, v) I ---
(12), and further considering the direction in which the potential is generated, ψ (u, v) = P - Q (u, v) ... =
-...C13) Now, if the point on the curved surface that gives the minimum potential value is Ma1, the potential vector is as follows. Since the surface normal of ul+VI-L that gives the minimum potential value and the direction of ψ(ul, v+) match, +1
1. Letting the surface normal vector of Vl be n, S=ψ(u+
, v+) on −−−−−−−・−(I5
), the sign of the potential can be determined and, as a result, the orientation of the half-space region can be determined.

By finding the parameter values (ul, ma1) on the curved surface with the minimum potential, it is possible to divide the free-form surface into half-space regions. However, since it is impossible to find (u4.v+) analytically, it is necessary to find it using a search method. In other words, it is understood that when the initial search position M (uo, Ma 0) is set on the curved surface 2, the minimum value is in the -grad ψ (UO * Ma 0) direction with respect to ψ (uo, Ma 0) at that time. can.

・・・・・・・・・(16) ψ Here, □=1ψl cas O, so 1ψ= ・・・・・・・・・(17) This is (-1ψl cos θ1.-1ψI
This indicates that there is a desired solution in the cos θ2) direction. Here, ψ(UO, Ma0) is clearly the distance from the 4 points P, so the next position to be found is Lll''-ψ(uo,
vo)・1ψl cos O+ + u.

v+”-ψ(uo+Ma0)・1ψl Co502+Ma0
・・・・・・・・・(18) Here, if we take X-(u, v),
) formula can generally be written as ・・・・・・・・・(18). ψ(X+-+) is the search step, −ψ(Xi
−+) indicates the search direction. Use this formula to find the next search position, and for each search position 5=(P Q(X+)
)・n=S (n is the surface normal) should be monitored.

xl when S#l or S≠-1 is the position of the minimum potential.

As shown in FIG. 30, the curved surface 1 has two parameters U,
It is represented by 2 = S (u, v), and P is 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 the curved surface 1 is C=S (Pu, Pv) - (20), and the vector V at this time is V = P-C... (21), and for this vector V, IVI is the shortest distance from the curved surface l to any point. Next, a method for determining parameters (Pu, Pv) that satisfies the above equation (23) will be explained. Figure 31 shows the tangent plane IA of the curved surface l at the parameter (Pu, Pv) point.
, and tangent vectors exist in each of the u and v directions on the tangential plane IA. Calculating V' by projecting the vector ■ onto this tangent plane IA, we get V' = (nXV) X n
--Calculate the direction of the vector by (24), and then calculate V'= IV l sjnθ・V' /
l V'l can be obtained by calculating (25). And this vector V
, the tangent vector (Tu) in the U and V directions existing on the tangent plane IA.

Tma) Calculate the direction component. The calculation is as follows, where each direction component is TU and TV, and the angles between Tu and the X-axis, and between Tma and the y-axis are θ and ψ.TU=V'x case -Vy sin O・-・-
・(2B) TV=-V'x sinψ-Vy cosψ
・Dan・(27) becomes. It can be said that the parameters that are shifted from the initial parameters by a corresponding parameter amount based on TU and TV indicate the curved surface position that is more likely to satisfy the above equation (23). Calculation of this parameter is as follows: PUnew - PU + TU, where DI and DV are the boundary line lengths of the curved surface in the U and M directions of the surface.
/DU・--C28)PVnew=
PV + TV / DV = - (29). Based on this result, return to equation (20) again and (23
) This process is repeated until the formula is satisfied. IVI that satisfies equation (23) represents the distance from the surface. but,
As it is, it is not clear whether the surface is the front or the back, so 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, the point C on the curved surface 4A is expressed as parameters u and v.

C= S (u, v) x ” 5t (u, v) y
= 5y(u, ri 0≦U≦1 z=Sz(u,v) 0≦V≦1 ・・・・・・・・・(30) Let P be any point on the scan line 7, and A search starting point is determined at a patch, and if the parameter values of this search starting point are ul and vl, then the distance vector between the starting point and an arbitrary point is determined.

V=P-C...(32) For this V vector, If it holds true, IVI is the value of the evaluation function.

The evaluation of scan line 7 is as shown in FIG. (3
Equation 3) is a calculation of the cross product of the tangent vector in the U direction and the tangent vector in the ma direction with the parameter ul+ma1, which becomes the surface normal vector n. As in the two-dimensional case, (34)
Since the formula cannot be satisfied once, we move on to the next procedure. This process is a process of projecting V onto the tangential plane 4S, and the tangential plane 4S is a plane on which the u and v tangent vectors of the coordinate system consisting of the U, ma tangent vector and normal vector n exist. The projection process onto the tangential plane 4S is as shown in FIG. That is, by calculating the following, the direction of the projected vector can be calculated, and then the magnitude of Vo is determined. The calculation is calculated by . Regarding the ■ asked here, Tu.

Determine the Tu and Tv acid components for the Tv and n coordinate systems, respectively. Here, the t, Tu, and Tv axes are not necessarily x, y,
Since it does not match the z-orthogonal coordinate system, coordinate transformation processing is required. The procedure for coordinate transformation is based on the process of aligning the normal vector with the Z-axis. Assuming that the parameters θ and ψ are known for n as shown in Figure 35, around the Z-axis, Next, if we calculate the following around the Y axis, n will match the Z axis. At this time, the relationship between the Tu and Tv coordinate systems on the X-Y plane is the third
The result is shown in Figure 6. Next, find such a function. V
If the components of o are (Vx, Vy, Vz), then Tu@,
The minutes are Tu = Vx cogθ −Vy sinθ ・・
...(38), Tv acid component, Tv = -Vx sinψ+Vy cosψ...
...-(40). Based on the values calculated using equations (39) and (40), a point shifted from the initial parameters ul and ma1 by a parameter corresponding to this value is more likely to satisfy equation (34). It can be said to be the location.

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

If the boundary line lengths in the V direction are Du and Dma, then

Incidentally, the polarity of the evaluation function is data necessary for determining whether a solid formed by surfaces is inside or outside the shape. 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 →→ for Vo that satisfies Equation 2 (23), as shown below, AM is negative when the opening angle between n and Vo is 80° or more, and AN is positive when it is 90° or less. becomes. Also, since n and V" exist on almost the same straight line -L, AN slope is 1. Same direction as the surface normal vector -1;
The direction is opposite to the surface normal vector, 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 as a distance in the normal direction of the surface representing the shape with respect to an arbitrary scan point. Therefore, there is an applicable range as shown in FIG. 37. However, when calculating the evaluation function, the above (2B
) and (29) 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 surface 4, although approximately, as shown in Figure 39, and also clarifies the military relationship (front and back relationship) with respect to surface 4. become The calculation method is to determine which of the castles A to H shown in FIG. 40 the results of the above equations (28) and (28) belong to. This is area determination on the Hahara meter space. This determination is based on F(u,v)≦0, which makes the region representing the inside of the shape negative on the parameter space.
This can be easily done by preparing four functions for each boundary line) and comparing all their values. Next, the fourth
As shown in FIG. 1, the intersection point IP of the straight line and the shape boundary, which can be obtained from the previous search position MPl on the parameter space and the result P2 of equations (28) and (28) above, is found. Since the equation of the straight line is, the intersection point IP can be easily determined. Based on this parameter, the process of determining Vo is performed again. If the result P2 of equations (28) and (29) is still outside the area even after this process, search is performed for the boundary line and scan point as shown in FIG. 42, and V"・T=0・・・・・・・・・(4
5) The polarity of determining the U and V parameters and determining the evaluation function value as shown in FIG. 37 is the same as described above. In addition, in FIG. 42, the distance between the point (U, V) on the boundary line 5 and the scan point SC is represented by a vector V', and the tangent vector at the point (u, ma) is represented by T. and,(
The method for obtaining the result of equation 45) 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 below. 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 device 300.

Normal processing reads the HC information on the paper tape 307 (3
03) The data of the character image 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. When the tool path generation function 302 is incorporated into the NC device 300, there are advantages such as being able to directly output binary data and not requiring analysis of command information since it is a continuous linear interpolation process, which can be expected to speed up the processing. . For this reason, it is effective for the NC device 300 to have a tool trajectory generation function, and the shape data
01 to generate the tool path TP and perform servo processing (3
08) Then, processing can be performed according to the input shape data. Please familiarize yourself with the above-mentioned shape extraction processing section 40.
If it is incorporated into the NC device 300 as the tool trajectory generation processing 302, the entire shape information TS that has been set operated can be
can be used as the tool path TP. In this case, the amount of NC command information required when machining a complex shape is enormous, and its handling becomes a problem.
01 is available in a very compact quantity and is easy to handle. Further, FIG. 45 shows an example of the hardware configuration of the NC device 300, and there are two possible connections between the tool trajectory generation processing section 312 and the conventional NC control section. 1
The first method is to take full advantage of the advantage of locating the tool path generation processing section 312 internally.
A RAM 311 that can be used in common by O310 is provided, and information is mutually transmitted via this RAM 311.

According to this, there is no loss time during data transfer, and high-speed processing is possible. The other is an interface 31 between the conventional NC control unit and the broken line in the figure.
This is a method of connecting by providing 3. When this method is used, the processing speed includes the influence of the data transfer speed, so the overall processing speed becomes slower.

In the example shown in FIG. 44, the shape data 3Ql is directly processed (302) to generate the tool trajectory in the E-mount M300, but as shown in FIG. It is also possible to determine whether the command information is NC information or shape data and to sort it when reading the command information.

The present invention is an NC device in which a machining condition input function, a tool trajectory simulation function, and a tool trajectory generation function are incorporated into the NC device, by removing the shape data input function of an automatic programming system. The NC program accurately creates geometric information of the workpiece using the shape modeling system described above. If necessary, create machining conditions that take the machining process into consideration. Geometric information of the workpiece and processing condition information are used as information to the NC device. Compared to NC command data, this information does not become enormous even if the shape becomes complicated, and handling of the information becomes very easy. Upon receiving this information, the machine tool operator checks the machining using the tool trajectory simulation function within the NC device. Then, if necessary, the processing conditions are corrected. Since this invention has a correction function, there is no need to go back to the NC programmer level for this type of correction, and the machining know-how of the machine tool operator can be reflected on the spot, making it possible to realize machining with a high degree of freedom. can. The automatic programming system uses the reverse Borland notation structure for the data structure, and for handling free-form surfaces, the basic system is a system that uses a normal vector creation algorithm and its functions are incorporated into the NC device, but other automatic programming systems However, the above effects can be sufficiently obtained.

(Effects of the Invention) As described above, according to the NC device of the present invention, when MO processing is performed using automatic programming, the
N
This problem can be solved by incorporating an automatic programming function into the C device.

[Brief explanation of drawings]

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 the real space and the parameter space, and Figure 7 is a diagram for explaining the relationship between the real space and the parameter space.
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 CSG.
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 19 are diagrams for explaining the generation and processing of shape data described in reverse Borland, 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 26 to 31 are diagrams for explaining the s-compensation formula, Figures 26 to 31 are diagrams to explain the principle of evaluation of free-form surfaces according to the present invention, and Figures 32 to 36 are diagrams showing specific examples of free-form surfaces according to the present invention. Figures 37 to 43 are diagrams to explain the polarity determination method for free-form surfaces, and Figures 44 and 45 are blocks showing specific application examples to the NC device. FIG. 48 is a block diagram showing yet another example. l...Curved surface, 1^...Tangential plane, 2...Fish school (node), 3...Rectangular area, 4...Patch, lO...
Shape data input device, 20... Shape data, 30...
- Mathematical shape processing section, 31... Processing information, 40...
Shape extraction processing unit, 41... Mathematical shape processing, 42...
・Set operation, 43. 44... Application compatible processing, 45... Free-form surface evaluation calculation processing,
46... Shape information stack area, 200... Three-dimensional shape, 300... NC device. Drawing nY! L (:)・No change in content) % l Figure % 2 Figure B also 9 Figure l1 Figure Chopsticks 26 Figure stone 29 Figure 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 tool path generation unit that generates a tool path based on the overall shape information output from the shape extraction processing unit. An NC device with