JPS6273306A - Interpolating method for three-dimensional curved surface - Google Patents

Abstract

PURPOSE:To resolve intersection between a ridgeline connecting shape element connection point on a boundary curve and interpolated curves by creating an interpolated curve on a basis of interpolated points on the boundary line operated for individual divided shape elements of boundary curves facing each other. CONSTITUTION:A computer 10 reads in definitions of boundary line and definitions of correspondence described with a part program and decodes them. The computer 10 decodes them to create boundary curves in accordance with program data and discriminates a correspondence method on a basis of correspondence designating data and operates interpolated points on a pair of boundary lines facing each other. The connection processing between interpolated points facing each other is performed for each of boundary curved facing each other after this operation, and intersection coordinate values of boundary curves are operated as interpolated values of a three-dimensional curved surface. When operation is completed, interpolated value data is stored in a disc device 12.

Description

DETAILED DESCRIPTION OF THE INVENTION <Industrial Application Field> The present invention relates to a method for interpolating a three-dimensional curved surface, and more specifically, a method for dividing at least a pair of opposing boundary curves into an equal number of shape elements each consisting of a circular arc or a line segment. The present invention relates to a three-dimensional curved surface interpolation method for interpolating a three-dimensional curved surface surrounded by four possible boundary curves.

<Prior art> In the conventional interpolation method for three-dimensional curved surfaces, the method shown in FIG.
As shown in , a pair of opposing boundary curves BL1 and BL3
．． Points where the distance ratio m:n is equal on BL2 and BL4 are interpolated points Pli and P2i on the boundary curve BLI-BLA.
, P3i, and P4i, and connect corresponding interpolation points on a pair of opposing boundary curves with an interpolation curve to create an interpolation curve ■L1 that connects the boundary curves BLI and BL3, and a boundary curve BL2. The coordinate values of the intersection with the interpolation curve rL2 connecting with BL4 are derived as the interpolation values of the three-dimensional curved surface.

<Problems to be Solved by the Invention> When a pair of opposing boundary curves have similar shapes, an interpolated curve can be formed between the pair of boundary curves in a shape close to the ideal by the interpolation method described above. If the pair of boundary curves are not similar, a preferable interpolation curve cannot be formed. For example, as shown in FIG. 9(b), a pair of opposing boundary curves BLI.

Each BL3 has a shape that is a combination of a line segment and a circular arc, but if the positions of the boundary points DPI and BP2 between the line segment and the circular arc are significantly different, if an interpolated curve is created using the conventional method, the boundary curve The interpolation curve IL formed between BLI and BL2 is a point BPI.

It is formed so as to intersect with the ridge line connecting points BF2, and when an interpolation point is derived based on this, there is a problem that the shape of the ridge line connecting points BPI and BP2 is distorted.

<Means for Solving the Problems> The present invention calculates the coordinates of interpolation points on the boundary curves for each divided shape element on a pair of opposing boundary curves, and Interpolation points are connected with interpolation curves, and the coordinates of the intersections between these multiple interpolation curves and the multiple interpolation curves formed on the remaining pair of boundary curves are calculated as the interpolation point coordinates of the three-dimensional surface. It is characterized by the fact that

<Operation> On a pair of opposing boundary curves having the same number of shape elements such as arcs and line segments, each shape element P
For each Ell-PE 22, interpolation points are derived by dividing the shape element into the number equal to the number of corresponding shape elements of the opposing boundary curve. Then, an interpolation curve is formed between the interpolation points (corresponding points) on the pair of boundary curves derived in this way. Thereafter, the coordinates of the intersection with the interpolated curve formed between the remaining pair of boundary curves are derived. By performing interpolation in this way, a shadow of the interpolated curve IL is formed between a pair of boundary curves composed of the same number of shape elements, as shown in FIG. ~Do not cross the ridge line connecting BP2. Therefore, the interpolation points obtained by the above method can interpolate the shape near the ridgeline into a shape close to the ideal.

<Example> Embodiments of the present invention will be described below based on the drawings.

In FIG. 2, IO is a computer forming the main body of the automatic programming device. This computer 10 is connected not only to a magnetic disk device 12 but also to a CRT terminal 13 via an interface IFI.
A printer 15 and a tape puncher 16 are connected via an interface IF2.

Next, the interpolation operation in the apparatus having the above configuration will be explained. First, the computer 10 reads the definition of the boundary curve and the definition of the correspondence described by the part program and decodes it by the processing of steps (30) and (31) shown in FIG.

In this example, when the article W has a shape having a top surface and a bottom surface, the bottom surface and the top surface of the article W are defined as reference cross sections SCI and SC2, as shown in FIG. The four mutually orthogonal cross sections represented by interpolated cross sections SC3 and S
They are defined as C4, SC5, and SC6. In the part program shown in FIG. 6, lines up to the 33rd line are programs that define these cross sections.

The 35th line of the part program is a program that instructs curved surface interpolation, and this line includes a description of "CR35" that defines the association method. This mapping is a definition that specifies how to calculate interpolation points on a pair of opposing boundary curves to form an interpolation curve.As shown in Table 1, length ratio mapping, coordinate Select one of value mapping and inter-element mapping.

Table 1 Figure 7 (at, (b), (cl) indicates the difference in the interpolation curve due to the difference in mapping, Figure 7 (al) indicates the length ratio mapping, When coordinate value mapping is selected, FIG. 7(C) shows a case where element-to-element mapping is selected.

In this way, when the part program representing the designation of the boundary curve and the correspondence is decoded by the computer 10, the computer 10 creates the boundary curve from the program data, and (32) the correspondence is made based on the designation data. 33), ? Corresponding points, that is, interpolation points on a pair of opposing boundary curves are calculated using a predetermined method (35) to (37).

After this, a process of connecting opposing interpolation points (opposing points) on a pair of opposing boundary curves with an interpolation curve is performed.
After performing the calculation for each pair of opposing boundary curves, a process is performed to calculate the intersection coordinate values of these two sets of opposing boundary curves as interpolated values of the three-dimensional curved surface (38). This process is performed using a pair of reference cross sections. The process is performed using a surface surrounded by SC1, SC2 and a pair of adjacent interpolated cross sections as a unit, and when the above process is repeated four times and all processes are completed, the interpolated value data is stored in the disk device 12 (41). .

Next, a method for determining corresponding points in steps (35) to (37) will be explained.

i) Length ratio correspondence As shown in Fig. 8(a), each of the pair of opposing boundary curves BLa, BLb is divided into the same number of parts, and interpolation points on the burial mound curves BLa, BLb are derived. Then, an interpolation curve is created by connecting the opposing interpolation points. FIG. 7(a) shows an example in which facing was performed using this method.

ii) Coordinate value correspondence As shown in Figure 8 ('b), this is an interpolation point (corresponding point) on a pair of opposing boundary curves so that the coordinate value in the specified axis direction changes by a constant amount. It derives
The seventh example applied coordinate value mapping with the Z axis as the designated axis.
It is figure (b).

iii) Correspondence between elements This correspondence is a feature of the present invention, and is applicable when a pair of opposing boundary curves BLa and BLb are composed of the same number of shape elements. Note that the shape element is a basic shape element composed only of circular arcs or line segments.

The details of this element mapping process are shown in Figure 4.
First shape element PEl1. Interpolation points (corresponding points) PI on the boundary curves BLa and BLb are sequentially derived from PE21 by the aforementioned length ratio correspondence for each shape element (50) to (52).
), and the same process is performed for the remaining pair of boundary curves to calculate corresponding points.

When an interpolation curve is calculated by calculating corresponding points using this method, as shown in FIG. 7(C), the shape element connection point BP1. A ridge line connecting BP2 is clearly created.

By selecting one of the three mapping methods described above using the part program, it is possible to perform interpolation that most closely matches the requested shape of the article W.

<Effects of the Invention> As described above, in the present invention, opposing boundary curves are divided into a plurality of shape elements, interpolation points on the boundary curve are calculated for each shape element, and based on this, a pair of boundaries Since interpolation curves are created between curves, the interpolation curves do not intersect with the edges that connect shape element connection points on opposing boundary curves (this makes it possible to interpolate the vicinity of the edges into a shape close to the ideal). There are advantages.

[Brief explanation of drawings]

1 to 8 show embodiments of the present invention, with FIG. 1 being a diagram showing the interpolation method of the present invention, FIG. 2 being a block diagram of an automatic programming device to which the present invention is applied, and FIG. and the fourth
The figure is a flowchart showing the operation of the computer 10 in Figure 2, Figure 5 is a diagram showing a defined cross section, Figure 6 is a diagram showing an example of a part program, and Figure 7 is a case where a different mapping method is applied. FIG. 8 is a diagram showing a matching method, and FIG. 9 is a diagram showing a conventional method. 10... Computer, 12... Magnetic disk device, 13... CRT terminal, BLI to BL4...
Boundary curve, PEII to PE22...shape element.

Claims (1)

[Claims] (1) A three-dimensional curved surface interpolation method that interpolates a three-dimensional curved surface surrounded by four boundary curves, each of which is divisible into an equal number of shape elements, each of which is a pair of opposing boundary curves consisting of circular arcs or line segments. Then, on the pair of opposing boundary curves, the coordinates of the interpolation point on the boundary curve are calculated for each divided shape element, and the interpolation points on the opposing boundary curve are connected by an interpolation curve. Interpolation of a three-dimensional curved surface, characterized in that coordinate values of intersections between a plurality of interpolation curves and a plurality of interpolation curves formed between the remaining pair of boundary curves are calculated as interpolation point coordinate values of the three-dimensional curved surface. Method.