JPS62237507A - Creating method for curved surface - Google Patents

Abstract

PURPOSE:To create a curved surface satisfying the size of specified adjacent curved surfaces while considering relation to the adjacent curved surfaces by considering the four specified adjacent curved surfaces and satisfying the size of the curves of a specified section. CONSTITUTION:A spacial curve satisfying the specified size is formed by dividing the spacial curve into sectional curves and two curved surfaces are created by two opposed spacial curves. Then the two curved surfaces are superposed to create a curved surface considering the relation to the adjacent curved surfaces. When four spacial curves constituting the curved surface are specified, the curved surface having the spacial curves satisfying the specified size can be created while considering the relation to the adjacent curved surfaces.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a curved surface creation method used when NC processing a curved surface whose cross-sectional shape at key points is strictly specified by the design of an antenna or the like. .

"Cheap bow fr" FIG.
), (2) are cross sections, (ta), (2a) are cross section curves (3), (4), (5) are intermediate cross sections, (5a)
is the midsection curve.

Next, the above-mentioned conventional curved surface creation method will be explained.

The surface is generated according to the following steps.

■Two given cross sections (referred to as given cross sections) (1), (2
) to generate multiple intermediate sections between them.

■ Cross-sectional curve existing on given sections (1) and (2) (referred to as given section curve) (la), From (2a), intermediate cross-sectional curve (4a) existing in each intermediate section generated in ■
, (5a)... is generated.

■Intermediate section curve (4a) for many intermediate sections.

If (5a)... is determined, a curved surface is generated as a continuation of the group of intermediate cross-sectional curves.

From the above, the core of the conventional technology is generation of an intermediate cross section and generation of an intermediate curve on the intermediate cross section.

[Problems to be Solved by the Invention] As described above, the conventional curved surface generation method is configured based on the generation of an intermediate section curve, so the meaning of the intermediate section with respect to the four section curved surfaces constituting the curve is unclear. There have been problems such as the inability to take into account the relationship between clear and adjacent curved surfaces, and the inability to handle complex curved surfaces, resulting in the risk of cutting other curved surfaces during machining.

In addition, given section curves must exist on a plane, and spatial curves cannot be handled.

This invention was made to solve the above-mentioned problems. Given four cross-sectional curves constituting a curved surface, a curved surface having a cross-sectional curve that satisfies specified dimensions can be created by considering the relationship with adjacent curved surfaces. The purpose of this invention is to obtain a method for creating curved surfaces that can be created using spatial curves.

[Means for Solving the Problems] The surface creation method according to the present invention divides a space curve into a plurality of piecewise curves, expresses each of them using a normal polynomial, and connects them to create two space curves that face each other, By superimposing them, an expression for the desired curved surface is created and the curved surface is generated.

[Operation] In this invention, a space curve that satisfies specified dimensions is generated by dividing a space curve into piecewise curves, and the relationship with adjacent curved surfaces is taken into account by creating two curved surfaces using two opposing space curves and overlapping them. By combining these four spatial curves constituting the curved surface, a curved surface having a spatial curve that satisfies specified dimensions is created by considering the relationship with adjacent curved surfaces.

[Embodiment] An embodiment of the present invention will be described below with reference to the drawings. In Fig. 1, (6), (7), (8), and (9) are space curves that connect piecewise curves usually expressed as polynomials, and Q (11 is the created surface P (u, Yu). ,(
11) is a curved surface P created by two opposing space curves (6) and (7).
Surface P 1u created by two space curves (8) and (9)
(u, w), aa, α4) are parameters,
It has a range of 0≦u, tw≦1, and arbitrary uC, WC. However, by giving 0≦tlc, I'IC≦1, one point on the curved surface is determined as P (u, stomach).

Also, in Fig. 2, (goods) and α4) are the boundary conditions in the direction that crosses the spatial curves (8) and (7), respectively.

Note that symbols P, C, and Q represent vectors.

(a) Next, a method for creating a curved surface will be explained. Curved surface αQ
P (u, stomach) is P (u, tv) - a (u, w) - Plw (u,
w)◆ β (u, w) ・PLu (u, w) 0≦u,
Create using W≦1. The meaning of this is that a curved surface is defined by the superposition of two curved surfaces Plu(u, W) and Plu(u, u) as shown in FIG. Here, α(u
, W) and β(U, W) are given the following conditions.

a (u, w) + β (u, w) = 1 Here, the feature of this invention is not to create the above method, but to
The space curve (
6), (7), (8), and (9) are usually expressed as a connection of piecewise curves expressed as polynomials, and Plu(u, w)
The objective is to create a curved surface by a combination of two methods: creating Plw (u, w) and creating P (u, w) using the above method. In addition, α(U, W), β(U
, W), the formula used by Brown * is shown below.

* (R,E, BarnhtliBrown, 1.M,
Klucewicz: A New Twist in
Computer Aided Geometric
Design, Computer Graphics
andImage Processing, 8 (1
978)) (b) Next, Plu(u,w) and I'1r(
Two methods of creating curved surfaces (u, w) will be shown. Since the two surface generation methods are the same, PIII
I (IJ, 19) is shown.

Plu(u,u) is created by the following equation.

plu (u, w) = HO, 0 (11) ・C (0,
w)”l(o, + (u) ・C(1,w)+L,o(
uicu(0,w)+L,+(u)・C(1,w)0≦
U, stomach ≦ 1) 1 o, o (u) - 2t' - 3t2 + 1Ho, t
(u)"-2t3-3t'' +, o(u)-t3-2t'*t H+, +(u)-t3-t' The above equation is called a loft curved surface. As is clear from FIG. 2, the relationship with adjacent curved surfaces is reflected by Cu(0°w)Q [phase] and Cu(1,w)C4).

(C) Next, the expression of the curve will be shown. In Figure 3, CI (0, w) (!9CII (0, w) (I
EI), CIII (0, w) Qη is the curve C(0,
w) This is the dividing line that constitutes (8). In the present invention, each piecewise curve is expressed by the following ordinary polynomial. In addition,
Although the number of section curves is three for convenience in FIG. 3, it goes without saying that there is no limit to the number.

A) When the piecewise curve is a line segment; C(0, w) = [Φo, 3(W) , Φ, , (
If), Φ2.3 (1”) +okuλ.Kue+<
i o<w<1i=I, II, III Q o -Ci (0,0) Q 3 =Ci (0,1) Qo and Q+ are both end points of the piecewise curve.

B) When the segmented curve is an arc; Consider the arc shown in Figure 4 in a separate room.

Let C1(0,w)・(x,y) and CI(0,w)
-[Φ,, 3 (W), Φ1.3 (W), Φ2.
It is expressed as s (W) +Φ3°Q s = C1(0,1).

Note that in both A) and B), the following formula is used for the normal polynomial of Φ.

Φo, s (W)・(1-w)3Φ1.3 (W)
-3(1-W) 2WΦ2.3 (W)-3(1-W)
l'! 2Φ s, 3(W) dust w3 The range of the parameter ω for each piecewise curve is 0≦W≦1, but it is necessary to set the range of the parameter ω to 0≦W≦1 for all 9 curves in steps (a) and (b). ), the domain of the parameter W is determined from the relationship between the segmented curve length and the length of the entire curve. For example, if the curve is composed of three segmented curves as shown in FIG. 3, the length of each segmented curve is S I , S
II, if it is 5lll, it will be as follows.

CI (0, w): O≦ω≦Sl/S C11 (0, w): SI/S≦ω≦(SI+5
11)/5CIIO,w):(SI +SIRI/S
≦ω≦1S = S I + S If + S I1
1. The parameter domain of each piecewise curve may be transformed so that it becomes the above domain.

Although the embodiments of the present invention have been specifically described, the feature of the present invention lies in the method of creating a curved surface by the combination of step (C) and steps (a), (b), and (C).

FIGS. 5(b), 5(b), and 5(c) are examples of curved surfaces generated by the present invention.

FIG. 6 is a block diagram of a curved surface generating device that implements the present invention. In the figure, α mark is a device for inputting space curves as data, and (support) is a memory, which stores input data and data created in each procedure. The holder is a piecewise curve creating device, and stores the data generated in the above procedure in a memory. 21> is Plu, P1
The w curved surface generating device a) is a Plu, P1w curved surface superimposition device, which processes the above procedure and stores the data in the memory (2). As shown in Figure 5, the curved surface is a memory (2)
For example, when processing using a multi-axis milling cutter, the data is sent to the NC data creation device and the NC
The data transfer device Cψ allows NC data to be sent to a multi-axis milling cutter for processing. The curved surface generating device shown in FIG. 6 can also be configured by a computer system. Further, in the above embodiment, a (u, u) and β (u, u) are expressed using Brown's equations, but the following equations may be used.

[Effects of the Invention] As described above, according to the present invention, there is an excellent effect that a curved surface can be created by considering adjacent curved surfaces with four limits specified and satisfying the dimensions of the specified cross-sectional curve. can get.

[Brief explanation of drawings]

FIG. 1 is a diagram illustrating the outline of curved surface generation according to an embodiment of the present invention, FIG. 2 is a diagram illustrating a method of creating two opposing curves, FIG. Figure 4 is a diagram for explaining the method of expressing circular arcs, Figures 5 (A), (B), and (C) are examples of curved surfaces generated by this invention, and Figure 6 is a curved surface that realizes this invention. A block diagram showing an example of a generation device, FIG.
FIG. 2 is a diagram showing a conventional curved surface creation method disclosed in Publication No. 09. In the figure, (1) 12) are cross-sectional views, (la), (
2a) is the cross-sectional curve, (3), (4), (5) intermediate cross-section, (5a) is the intermediate cross-sectional curve, (6), (7)
, (8) , (91C space curve, Go), (1υ
, (goods) is a curved surface, θ mark, α4) parameter, α two, (
+8), (17) is a piecewise curve, the scream is a data human device,
α mark is memory, 翺 is piecewise curve creation device, 121) is P
Lu, P 1w surface creation device, (to) Plu,
P1w is a curved surface superposition device, (to) is an NC data creation device, C4 is an NC data transfer device, and (a) is a control circuit. Note that the same reference numerals in the figures indicate the same or equivalent parts. Agent Patent Attorney Tadashi Sato Figure 1 p (u, w) ~ 10 ~ ゝ U ~ 14 II ~ Plu ('u, w) U ~ 14 12 ~ P1 w (u, w) Figure 2 11 --YU~14 Plu (tJ, W)~l l Figure 3 Figure 5 (A) (B) (C)

Claims (2)

[Claims] (1) Divide a space curve into multiple piecewise curves, express each piece as a polynomial and connect them, create two curved surfaces with two opposing space curves, and then create a curved surface by superimposing them. A curved surface creation method characterized by the following. (2) When the spatial curve is a cross-sectional curve, the curved surface is created by creating the curved surface by using each of the circular arcs and line segments constituting the cross-sectional curve as a segmented curve. Creation method.