JPS60173680A - Curved surface forming system - Google Patents

Abstract

PURPOSE:To control the shape of curved surface simply by controlling freely movement of characteristic curve along controlling curves. CONSTITUTION:A characteristic curve 1 is deformed and moved along controlling curves 2, 3 to make both ends of the characteristic curve 1 conform simultaneously to PiQi. Combination of parallel shifting, rotational shifting and similarity conversion (enlarging and reducing) is enough as the method of deformation and shifting. In the section Pi, Pi+1 and section Qi, Qi+1, a point of correspondence is determined to make the ratio of interior division of arc length of controlling curves 2, 3 equal, and deformation and shifting of the characteristic curve 1 are made in similar way as above-mentioned. Thus, the characteristic curve 1 can be deformed and shifted to pass the designated point of correspondence (Pi, Qi)i=1, n simultaneously, and a smooth curved surface can be formed.

Description

[Detailed Description of the Invention] [Field of Application of the Invention] The present invention relates to a method for generating a three-dimensional curved surface, and is suitable for generating a curved surface intended by a designer for displaying a curved surface in a drawing, outputting it to a printer, etc. Concerning curved surface control methods. [Background of the Invention] A method similar to the method of generating a curved surface by moving a characteristic curve along a control curve is the Coons interpolation method. However, this interpolation method has the disadvantage that in order to generate a wide curved surface, it is often necessary to divide the curved surface and additionally input the necessary curves. [Object of the Invention] An object of the present invention is to enable designation of a point on a control curve to control the movement of a characteristic curve, and to easily display a curved surface shape on a CR1 display printer or plotter, or in graphic processing. The goal is to provide a method that can control the [Summary of the invention] The outline of the invention will be explained with reference to FIG. If both ends of the characteristic surface @l are placed on the control curves 2 and 3 and the characteristic curve is deformed and moved in the direction of A, a curved surface can be generated by the trajectory. The two points on the control curve on which both ends of the characteristic curve 1 ride are called corresponding points. Conventionally, there has been a problem in that the user cannot freely specify these corresponding points, so the intended curved surface shape cannot be obtained. Therefore, in this method,
Add a function that allows you to freely specify corresponding points on the control curve 2.3 using an input device such as a tablet or stylus pen. Assume that the corresponding points 1 p i Qf )+-+, * are specified as shown in FIG. At this time, characteristic curve 1
The characteristic curve 1 is deformed and moved along the control curves 2 and 3 so that both ends of P i Q,i coincide with each other at the same time. The only necessary deformation movement method here is a combination of parallel movement, rotation movement, and similarity transformation (enlargement, #i small). Also P
In the il P 141 section, Qi, Q i + 8 sections, corresponding points are determined so that the arc length internal division ratios of control curve 2.3 are equal, and the deformation movement of characteristic curve 1 is performed in the same manner as above. conduct. This allows the specified corresponding point (P+
, Qi)t-+, - can be transformed and moved so that a smooth curved surface can be generated. [Embodiment of the Invention] This system will be explained in detail with reference to FIG. Necessary characteristics 4
11, control 4M12,3, and the corresponding point (Pi. Q, +) t −+ r m are assumed to have already been specified. The following calculations are performed based on the flow shown in FIG. [υ Calculation of the corresponding points Points on the control curve 2.3 on which both ends of the characteristic surface @1 are Po, Q
o. Further, an arbitrary point on the control curve 2 is defined as P, and a corresponding point Q on the control curve 2 of P is determined as follows. (1) If P matches the specified corresponding point Pi, set it as "Qi". (2) In cases other than (1), first find the piPL to which P belongs.
+ interval is determined (step 201). Next, C step 2 calculates the arc length tl (P+, P) from Pt to P.
02n. Here from Qi Q i Q +. If the arc length to any point in the 0 interval is At (Qi. Q, ) (step 203), then point Q7 is a point that satisfies (step 204). By the methods (1) and (2) above, the corresponding point Qf on the control curve 3 for any point P on the control curve 2 can be found. It is also possible to perform the reverse operation of explicitly giving Q and subtracting P. (9) Generation of the curve connecting the corresponding points P and Q To determine the surface shape, the curve C (P
, Q). If you move P, CiP, Q
) is a group of curved lines and should be considered as a curved surface. P
, Q; CIP, Q; t)
(There are many curve parameters). Cip,
One method of generating Q;t) from the characteristic surface 4i11 (denoted as Co(t)) will be described. Let the vector representations of P, Q, Pi, and Qi be P, Q, P, , Qi, respectively, and Qo Pot−Qi Pl
Overlay on. Let the rotation matrix be RFP, (J). 1 (, (C step 205 where P, Ql is a rotation matrix of the axis rotation perpendicular to Qo P. and Qi P+). In this case, CIP, Q; t) can be given as follows.
Step 206) +Cr+(t)-Pa) This curve is (1) CIPo, QO; tt=Co(t)(
2) It is clear that CIP, Q; 01=P, CIP, Q; IJ=Q is satisfied. Therefore, the entire group of curves C' P * Q i [) created by applying P is a curved surface that satisfies the corresponding point indication. The above is a detailed explanation of this method. Next, referring to FIGS. 3 and 4, a processing device that implements this method and its operation will be explained. FIG. 3 shows the overall configuration of the processing device, and FIG. 4 shows the operation flow of the curved surface generating device 104 shown in FIG. The operation will be explained below. It is assumed that the graphic nice play 106 displays a characteristic curve and a control curve necessary for generating a curved surface, and that its III line theta is stored inside the curved surface generating device 104. First, corresponding points are designated on the corresponding 11 curves using the stylus pen 1o1 and the input control device 102. The corresponding point data is converted into coordinate data by the input control device 103 and transferred to the curved surface generation device of the curved surface generation device 104. In the curved surface generation 5cio4, 2o1゜202.203,204 shown in FIG. 4 is based on the method of α] described above.
processing is performed. As a result, corresponding points are determined for all points on the two control curves. Next, the above (5
) Processes 205 and 206 are performed to generate a curved surface. Since the curved surface is represented by a grid-like school of fish, 2o6 generates a school of fish. This fish school position data is transferred to the display control device 105 and displayed on the graphic display 106. The above is an explanation of the operation. [Effects of the Invention] According to the present invention, since the movement of the characteristic curve along the control curve can be freely controlled, there is an effect that the shape of the curved surface can be easily controlled. The effect will be explained below using a simple example. Fifth
As shown in the figure, the characteristic curve 11 (circular arc) and the control surface Ifs1
2.13 is given. Figure (a) is a plan view, and figure (b) is a perspective view. FIG. 6(a) shows a plan view of the movement of characteristic curve 1 when corresponding points are not designated. That is, the characteristic curve] l is 11', 11" 11///
move to. Figure (b) is a perspective view thereof. Same figure (
C) shows AA' cut (2). This cross-sectional shape 14 is
It deviates slightly from a perfect circular arc (indicated by point @15). Next, using the present invention, attempt is made to designate corresponding points so that the hA' cross section becomes a complete arc. For this purpose, (a) in Figure 7,
As shown in the plan view and perspective view of (b), Pal + Ql
It is sufficient to designate a corresponding point at the position l. The result is the same figure (C)
The long cross section 14 shown in the BB' cross section is a complete circular arc. As can be seen from the above examples, the curved surface generation method that allows corresponding point designation has the ability to control the curved surface. Therefore, there is an effect that the user's intention can be easily reflected in the curved shape.

[Brief explanation of drawings]

Figure 1 is a diagram showing an overview of this method, Figure 2 is a diagram to explain the surface generation method using this method, Figure 3 is a diagram of the equipment configuration for realizing this method, and Figure 4 The figure is a processing flow of the curved surface generation device, and FIGS. 5 to 7 are explanatory diagrams showing the effect of the curved surface control ability of this method. 1.11... Characteristic surface image, 2, 3, 12.13... Control curve, P, Q... Corresponding points at arbitrary positions on control curves 2 and 3, PiQi... Control curve 2 .3 Corresponding points indicated on C(P, Q,; t)...Characteristic curve 1 as P. 3rd day 4th day (α) (of// 6th day

Claims (1)

[Claims] Both ends of the characteristic curve are 1st. In the method in which movement is constrained on the second control curve and a curved surface is generated by the locus formed by the characteristic curve, the first. The same number of points (Pi) I-11++ (Q, J) J=+, - are specified on the second control curve, and the end point on the first control curve of the characteristic curve is (Ps).
+*11°, the characteristic curve is moved so that the end point on the second control curve passes through point Qk that is paired with Pk, and If the end point of does not coincide with any point of (Pi) l*1111, put that point between (Pi) +, 1
．． - two points of and paired with those points (QJ
) by using the two points j + I + - to find a point on the second control curve that is paired with the non-matching point, and moving the characteristic curve to pass through the non-matching point and the determined point,
A curved surface generation method characterized by controlling the curved surface shape.