JPH01116884A - Sectional data forming method - Google Patents

Abstract

PURPOSE:To enable representing a three dimensional sectional curve in a representing form, two-dimensionally similar to the conventional drawing method by parallel movement converting and rotating movement converting free curve data representing the three dimensional sectional curve and converting a coordinate on a prescribed reference plane. CONSTITUTION:A free curved surface SC is cut on a desired cutting plane SP to obtain the free curve data representing the sectional shape (c) of the free curved surface SC, and the free curve data is parallel displacement converted and rotating movement converted, thereby, sectional data representing the sectional form of the free curved surface SC on the prescribed reference surface SST. Namely, if the quantity of the rotating movement conversion and the quantity of the parallel displacement conversion are selected to desired values and the free curve data representing the sectional shape of the free curved surface SC is coordinate converted on the prescribed reference surface SST, the two dimensionally represented free curve can be obtained on the reference surface SST, and the sectional data representing the sectional shape of the free curved surface SC represented according to the representing form of the conventional drawing method can be obtained.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

A. Industrial field of application B. Overview of the invention C. Conventional technology Problems to be solved by the invention E. Means for solving the problems (Fig. 1) F. Effects (Fig. 1)
Figure) G Example (Figures 1 to 7) Effects of the invention
(computer aided design), or CAM (c.

mputer aided manufacturer
This method is suitable for use in creating data representing the cross-sectional shape of a free-form surface generated in g) or the like, which is cut at a desired cross section.

B. Summary of the Invention The present invention is a method for creating cross-sectional data, by rotating and translating free curve data obtained in a three-dimensional space, thereby converting a cross-sectional shape expressed in accordance with the expression format of a conventional drafting method. cross-sectional data can be obtained.

C Conventional technology For example, when designing the shape of an object with a free-form surface using a CAD method (geometric mode
ling), -Finally, the designer specifies multiple points in the three-dimensional space through which the curved surface should pass, and calculates the boundary surface 891m connecting the specified multiple points by a computer using a desired vector function. , to create a curved surface expressed in a so-called wire frame. It is thus possible to form a large number of framework spaces surrounded by boundary curves.

The boundary curve network formed in this way itself represents the rough shape that the designer is trying to design, and it can be expressed as a curved surface (hereinafter referred to as a patch) by a parametric vector function using the boundary curves surrounding each framework space. By performing an interpolation operation on the surface (called 2D), it is possible to generate a free-form surface (which cannot be defined by a two-dimensional function) that is designed by the designer as a whole.

Problems that the invention aims to solve By the way, in reality, designers' design work usually involves repeating local corrections to move step by step closer to the shape that the designer envisions. Even the free-form surfaces generated in this way are usually repeatedly modified to approximate the shape envisioned by the designer.

In such cases, if the cross-sectional shape of the free-form surface obtained by cutting the free-form surface at a desired cross section can be visually confirmed, it is thought that the correction work of the free-form surface can be simplified.

Furthermore, at that time, if it is possible to visually confirm the cross-sectional shape from the direction perpendicular to the cross-section, as in the case of expressing cross-sectional shapes in conventional drafting methods, it is possible to visually confirm the external shape of the free-form surface in the same way as in conventional design work. It is thought that the shape can be easily visually confirmed and the correction work can be further simplified.

Furthermore, when cutting a product with the external shape of the free-form surface, or processing a mold etc. of a product with the external shape of the free-form surface, it is necessary to check the finished shape of the product, mold, etc. Even in such a case, if the cross-sectional shape of the free-form surface can be expressed in accordance with the expression format of the conventional drafting method, the work of confirming the finished shape can be simplified, which is convenient in practice.

The present invention has been made in consideration of the above points, and aims to propose a cross-sectional data creation method that can express the cross-sectional shape of a free-form surface according to the expression format of conventional drafting methods.

E Means for Solving the Problem In order to solve this problem, in the present invention, the free-form surface Sc is cut at a desired cutting surface Sr to obtain free-form curve data representing the cross-sectional shape C of the free-form surface S, By subjecting the free curve data to translational translation and rotational translation, cross-sectional data representing the cross-sectional shape crt of the confessional curved surface SC on a predetermined reference plane SSt is obtained.

By selecting desired values for the F-action rotational movement conversion amount and the parallel translation conversion amount, and performing coordinate transformation on the free curve data representing the cross-sectional shape GTt of the predetermined reference plane S and the free-form surface S on the air, the reference plane SS is obtained. ? A free curve expressed two-dimensionally above can be obtained, and thus cross-sectional data representing the cross-sectional shape of the free-form surface SC expressed in the expression format of the conventional drafting method can be obtained.

G example An embodiment of the present invention will be described in detail below with reference to the drawings.

As shown in FIG. 1, in this embodiment,
Free-form surface S with three-dimensional expansion in the y direction and two directions
, on a predetermined reference plane SST (hereinafter referred to as cross-sectional data) is obtained.

That is, as shown in FIG. 2, the arithmetic processing device moves from step SP1 to step SP2, and after receiving the designation of the free-form surface Sc from which the cross section is to be obtained in accordance with the designer's input operation,
Next, the process moves to step SP3, and a plane (hereinafter referred to as a cutting plane) SP that cuts the free-form surface Sc is generated.

In this embodiment, one desired point on the three-dimensional space and the direction from the point, two desired points on the three-dimensional space, or three desired points on the three-dimensional space are input to the arithmetic processing device. A cutting plane S is generated by .

That is, when a desired point on a three-dimensional space and a direction from the point are specified and input, the cutting plane Sp passes through the specified point and has a normal vector n in the specified input direction from the point. , and if two points are specified and input, a cutting plane S having a normal vector n in a direction that passes through the first input point and connects the two points is generated.

If three points are further specified, a cutting plane SP passing through the three points is generated.

Subsequently, the arithmetic processing device proceeds to step SP4, and approximates the cross-sectional curve C with a Bezier equation 33-dimensional empty curve.

That is, as shown in FIG. 3, deformation control points P are placed on the cross-sectional curve G at predetermined intervals. 14, and set the relevant deformation control point P
A cross-sectional curve C is divided into multiple curve segments KSG using DM.
Divide into.

Each curve segment KsG is a parametric spatial curve 1? expressed by the following formula % Formula % (1) Expressed as (t).

Here, t is calculated by the following formula between the reference control point P0, which is one deformation control point P9.4, and the reference control point P3, which is the other deformation control point PDM, in the direction along the curve segment Ksc. It is a parameter that changes from the value O to the value l as expressed by the % formula % (2).

In this way, the curve segment KSG expressed by the cubic Bezier equation is changed to the reference control point P0 by the shift operator E.
By specifying two control points P and P2 between expressed.

Here, the shift operator E has the following relationship with the control point P on the curve segment KSG as shown in the following equation (4). Therefore, by expanding equation (1) and substituting the relationship in equation (4), we get the following equation R(t)=(1t+tE)3Pa=((1-t
)+ 3 (1-t)”E+ 3 (1-t)E”+
E') p.

=(1-t)3P(1+3(1-t)"EPO+3(
1-t)E"P6+E31'.

= (1-t)3p, +3 (1-t)2pt+3(1
-t) Pt+P.

・・・・・・(6) As a result, equation (3) is obtained.

Thus each curve segment on the cross-sectional curve C)KSG is (
3) Four control points p, , p, , p, , based on Eq.
p3, thus the reference control point P0
and two control points P between 23, and P2 as a free-form surface S,
By selecting a desired value according to the cross-sectional shape of , the curve segment KSG can be represented by the coordinate data of the reference control points P0 and P3 and the control points Pl and P2.

Therefore, the cross-sectional curve C can be expressed based on the coordinate data (hereinafter referred to as free curve data) of the control points P0 to P4 of each curve segment KSG.

After obtaining the free curve data, the arithmetic processing device then proceeds to step SP5 and calculates the centroid P from the cross-sectional curve C.

Next, the arithmetic processing device moves to step SP6, calculates the distance from the centroid P to the origin O between xyzy, moves the centroid P to the origin 0 based on the calculation result, and calculates the amount of movement by The data is divided into components in the X-axis direction, y-axis direction, and z-axis direction and stored in a parallel movement buffer and a parallel reverse movement buffer as parallel movement conversion data.

Therefore, as shown in FIG. 4, if the free curve data is translated in parallel based on the parallel translation data stored in the translation translation buffer, the centroid P of the cross-sectional curve C will be at the origin O.
A three-dimensional spatial curve CTI can be obtained by translating the cross-sectional curve C so that it matches the .

Conversely, if the free curve data of the three-dimensional spatial curve CTI is subjected to parallel translation transformation based on the parallel translation transformation data stored in the parallel translation buffer, the cross-sectional curve C can be obtained from the three-dimensional spatial curve G71.

Subsequently, the arithmetic processing device moves to step SP7 and performs the fifth
As shown in the figure, a direction vector nT representing the same direction as the normal vector n of the cutting plane S is set at the origin O, and the inclinations φ and θ of the direction vector n7 with respect to the X axis and the z axis are obtained. After that, based on the inclinations φ and θ, the directional vector n7 is rotated about the origin O so that the direction of the directional vector nTO matches the positive direction of the two axes.

Furthermore, the amount of movement when the direction vector n1 is rotated is separated into component data (hereinafter referred to as rotational movement conversion data) with the X-axis, y-axis, and z-axis as rotation centers, and the rotational movement is Based on the transformation data, a rotational movement transformation matrix that rotationally transforms the coordinate data so that the direction vector nT coincides with the two axes, and a reverse rotational movement transformation matrix that rotationally transforms the coordinate data in the opposite direction are formed. .

Therefore, if the free curve data (Fig. 4) that has been subjected to translation transformation so that the centroid P coincides with the origin 0 is rotationally transformed using the rotational transformation matrix, then as shown in Figure 6, The free curve data on the xy plane SS formed by the axes and y axes can be rotated and translated, and a three-dimensional spatial curve CpTt representing the cross-sectional curve C can be obtained on the reference plane SST formed by the xy plane. be able to.

Conversely, the three-dimensional spatial curve C expressed on the reference plane Sll
If the free curve data of 7□ is inversely rotated and translated using the inverse rotational shift transformation matrix, from the three-dimensional space curve t, c t□ on the reference element surface S, a, the centroid P becomes the origin O. A three-dimensional space curve CTt (FIG. 4) of the cross-sectional curve C that is translated and transformed so as to match can be obtained.

The arithmetic processing device proceeds to step SP8 and creates cross-sectional data of a three-dimensional free curve representing the cross-sectional shape of the cross-sectional curve C on the reference plane S, 7 formed by the xy plane based on the above-described conversion procedure.

That is, after the free curve data representing the cross-sectional curve G is translated in parallel based on the translational translation data stored in the translational translation buffer, it is then subjected to rotational translation using the rotational translation matrix.

Thus, the reference plane S8 consisting of the xy plane. Free curve data (hereinafter referred to as cross-sectional data) obtained by translating and rotating the above can be obtained (Fig. 6), and if a three-dimensional free curve is expressed based on the cross-sectional data, , it is possible to obtain a three-dimensional free curve expressed two-dimensionally on the xyy plane (that is, the coordinate data in two directions has a fixed value at 0).

Therefore, based on the cross-sectional data on the xyy plane, image data having a two-dimensional spread can be obtained, and if the image data is output to a plotter, for example,
A two-dimensional image similar to that obtained by cutting a free-form surface at a desired cross section and visually observing the cross-sectional shape from a direction perpendicular to the cross section can be obtained.

In this way, in the two-dimensional image, the cross-sectional shape of the free curve can be expressed in the same expression format as the conventional drafting method, so that correction work and checking work of molds, etc. can be further simplified.

Furthermore, in this case, by performing the translation transformation based on the centroid P and the normal vector n, and then performing the rotation transformation, the cross-sectional shape can be easily obtained by simply inputting the cutting plane. Overall, the designer's modification work can be simplified.

That is, the arithmetic processing unit moves to step SP9 to determine whether or not to output to the plotter, and if a positive result is obtained here, the processing unit proceeds to step 5pio (preferably outputs two-dimensional XY coordinates to the plotter based on the cross-sectional data). After outputting the image data represented by the system, the process moves to step SPI.1.

In this manner, it is possible to obtain a two-dimensional image in which the cross-sectional shape of the free-form surface is expressed using the conventional drawing method through the blocks.

On the other hand, if a negative result is obtained in step 5PIO, the process moves to step 5PII, where it is determined whether or not to display graphics.

If a positive result is obtained here, the process moves to step 5P12, where two-dimensional image data is output to the graphic device, and then the process moves to step 5PL3.

In this way, it is possible to obtain a two-dimensional image representing the cross-sectional shape of a free-form surface in the expression format of the conventional drafting method through the graphics device.

On the other hand, if a negative result is obtained in step 5PII, the process moves to step 5P13, where it is determined whether or not to perform correction work.

If the designer corrects the cross-sectional shape, a positive result is obtained, and the process moves to step 5P14 to correct the cross-sectional data represented on the xy plane.
Move on to 15.

On the other hand, if a negative result is obtained in step 5P13, the arithmetic processing unit moves to step 5PI5 and determines whether or not to reconstruct the free-form surface based on the cross-sectional data represented on the reference planes S and T. I do.

If a positive result is obtained here, the process moves to step 5P16, and as shown in FIG. and converts it into free curve data on the original cutting plane SP. Next, the processing unit
After generating the cross-sectional curve GT3 based on the free-form curve data converted onto the cutting plane SP, the free-form surface S is reconstructed based on the cross-sectional curve C1.

Thus, by modifying the cross-sectional shape in the same manner as in the conventional drafting method, the external shape of the free-form surface can be modified more easily than in the past.

When the arithmetic processing unit completes the reconstruction of the free-form surface, it moves to step 5P17 and ends the processing procedure.

On the other hand, if a negative result is obtained in step 5P15, the process moves to step 5P17 and ends the processing procedure.

In the above configuration, the free-form surface S is set to a desired cutting plane S
By cutting at P, three-dimensional free curve data representing the cross-sectional shape is obtained.

The free curve data is translated so that the centroid P coincides with the origin O, and then the direction vector ny, which represents the same direction as the normal vector n of the cutting plane SF, is oriented in the positive direction of the two axes. The coordinates are transformed onto the reference plane SSt consisting of the xy plane.

In this way, by representing a three-dimensional free curve based on cross-sectional data consisting of free curve data whose coordinates have been transformed on the reference plane SSt, a free curve having a two-dimensional spread on the xy plane can be obtained. Based on the cross-sectional data, the cross-sectional shape can be visually confirmed from a direction perpendicular to the cross-section, in the same way as in the expression format of conventional drafting methods.

According to the above configuration, three-dimensional free curve data representing a cross-sectional curve obtained by a desired cutting plane is rotated and translated based on the centroid and normal vector, and the coordinates are set on the reference plane. By converting, it is possible to obtain a three-dimensional free curve that has a two-dimensional extent on the reference plane and represents the cross-sectional shape of the free-form surface.

By performing the rotational movement conversion and the parallel movement conversion in this manner, the cross-sectional shape can be expressed from a direction perpendicular to the cross-section, and the cross-sectional shape can be expressed in the same expression format as the conventional drafting method.

In the above-mentioned embodiment, a case was described in which the reference plane was set to the xy plane, but the present invention is not limited to this.
A reference plane may be set at a desired position in three-dimensional space as necessary.

Further, in the above-described embodiment, a case was described in which rotational movement conversion was performed with the X-axis and the X-axis as the rotation center, but the present invention is not limited to this. The rotation center axis can be selected according to the following.

Further, in the above-mentioned Φ embodiment, a case was described in which the cross-sectional shape was displayed by cutting on a plane, but the present invention is not limited to this, and the cross-section may be cut on a curved surface, for example. In this case, a free curve may be expressed on the reference plane using a perspective transformation method in addition to parallel translation transformation and rotational translation transformation.

Furthermore, in the above embodiment, a case was described in which the cross-sectional shape is output to a block and also to a graphics device, but the present invention is not limited to this. It can be widely applied to cases where the image data is output to other display devices, graphic processing devices, etc.

Furthermore, in the above embodiment, the case where the rotational movement amount and the parallel movement ■ are stored and the cross-sectional shape is corrected is described, but the present invention is not limited to this, and the present invention is not limited to this, but the case where the cross-sectional shape is simply displayed, etc. Can be widely applied.

Furthermore, in the above-described embodiment, a case was described in which the cross-sectional shape is expressed by a three-dimensional free curve expressed by the Bezier equation, but the present invention is not limited to this, and for example, a three-dimensional free curve such as a B-spline can be used. You can also express it.

H Effects of the Invention As described above, according to the present invention, free curve data representing a three-dimensional cross-sectional curve is translated and rotated, and coordinates are transformed onto a predetermined reference plane. can represent a three-dimensional free curve with a two-dimensional extent, and thus, based on the free curve,
Three-dimensional cross-sectional curves can be expressed two-dimensionally in a similar expression format to conventional drafting methods.

[Brief explanation of the drawing]

Fig. 1 is a route map representing a free-form surface in three-dimensional space, Fig. 2 is a flowchart showing an embodiment of the cross-sectional data creation method according to the present invention, and Figs. 3 to 7 are route maps for explaining the method. . C, CTl, C7□, CT, ... cross-sectional curve, n
...Normal vector, nt...Direction vector, O...Origin, P...Centroid, Sc
...Free-form surface, SP ... Cutting plane, S
St...Reference plane.

Claims (1)

[Claims] Free curve data representing the cross-sectional shape of the free curve surface is obtained by cutting the free curve surface at a desired cutting plane, and the free curve data is translated and rotated to obtain a predetermined standard. A method for creating cross-sectional data, characterized in that cross-sectional data representing the cross-sectional shape of the free-form surface is obtained on a plane.