JPH01112384A - Curve interpolation forming system - Google Patents

Abstract

PURPOSE:To easily form a curve and to correct a form by calculating the form only of a curved segment by the use of the tangential vector of both the end points of the form corrected curved segment. CONSTITUTION:After the position coordinate of a control point considered to be improper included in the blocks P3-P5 for correcting the form of the curve is corrected, the corrected block is defined to be a new curve forming block to apply the position coordinate of a control point 4' included in the curve forming segment and the tangential vector value stored in the control points P3-P5 in both the end points of the curve forming block and calculate the curve form of the corrected block by an interpolating function again under a fixed termination condition. Thereby, even when the position coordinate of the control point of the corrected block is changed, the curve form except the corrected block can not be changed but the curve can be smoothly connected at both end points of the corrected block.

Description

Detailed Description of the Invention [Technical Field to which the Invention Pertains] The present invention relates to a curve interpolation generation method in which (111 intervening points are obtained from a sequence of control points by an interpolation curve, and the curve is generated by connecting these interpolation points. Regarding.

[Conventional technology]

Hereinafter, a conventional curve (1 (i) interval generation method will be explained using a cubic spline function in a two-dimensional coordinate space as an example of an interpolation function.

FIG. 5 is a diagram showing the processing 4Pi of the conventional curve interpolation generation method, and FIG. 6 is a diagram showing control points and interpolated curve shapes in the conventional curve interpolation generation method in a two-dimensional coordinate space.

PI, P2. shown in FIG. ......, l) 7 is a control point.

A solid line connecting a series of control points indicates a curve generated by interpolation using a cubic spline function, which will be described later.

A curve C in a two-dimensional xy space can generally be expressed by the following function.

C: r (X, Y) = 0 where X is the X coordinate of curve C, and Y is YI of curve C! - indicates the function representing the shape of the song 'KfAC.This song,
One method for expressing 〒ll is an interpolation method using a cubic spline function. The cubic spline function is a function suitable for expressing a smooth curve in which differential coefficients up to the second order are continuous at control points, and is used in fields such as CAD. The control point taken along the curve C is Pl (X1
, Yl), P2 (X1, P2, Y2), -, Pi
(Xi, Yi), -, Pn (Xn, Yn), then 3
The expression of the curve C using the second spline function is as follows.

X (shi)=AO+Alt+A2t2+Δ3tlY (
L)=[30+Blt+B2t2+B3t3 here, t
is a parameter that changes within the range O<t<,'ri (Ti: constant).

When L=Q, X (L)=Xi.

Y (L) =Yi When t=Ti, X (L) =X r + 1, Y(
L)=Y i+1 (i = 1. 2. =...-..., n-
1) Also, AO, At, A2. A3 and BO, r31
゜B2. B3 is a constant. These constants are the control point P1. P2. ....., the coordinate value of Pn and the end point (start point) Pi of the curve and (end point) 1) Specify the tangent vector value (first derivative coefficient) or second derivative coefficient at n: P: Ending property Determined by giving.

As a terminal condition, the tangent vector and the quadratic distribution coefficient of the starting point 1) 1 and the ending point 1) n are each expressed as Pi'
, PI'' and Pn', Pn'' ■ Free condition (when Pi°' = Pn'' = 0)
2 ■ Periodic conditions (Pbi -Pn', Pi''.

= Pn”).

■ Anti-periodic conditions (Pio=-Pn', PI"=-
Pn”).

■ There is a fixed condition (when specifying specific values for Pl' and Pn').

Specifically, using a cubic spline function, the solid line 20 in Figure 6 is
In order to generate a curve as shown in FIG. 5, first, control points PI, P2.・・・
..., r) Given the position coordinates of 7 and the termination conditions as shown above at the end points P1 and P7, the curve between each control point is expressed by a cubic spline function. Next, by displaying the generated curve on a display device,
Check the shape of the generated curve. If the shape of the curve does not fit, the position coordinates of the control points that are considered inappropriate are corrected, and then the curve shape between the control points is expressed again using a cubic spline function. The position of control point P4 is shown in Figure 6.
A dotted line 212 indicates a curve generated by a cubic spline function under the same termination condition when the angle is changed to 4°. Repeat the above modifications until the shape of the curve fits.

In this way, in the conventional curve interpolation generation method, as shown in FIG. After correcting the position coordinates, the curve shape was calculated again using the interpolation function using the corrected position (n coordinates, so as is clear from Figure 6, the curved portion of the section on both sides of the control point whose position coordinates were corrected) In addition, there was a problem in which the shape of the two-curve body was affected by the correction of the position coordinates of the control points. When generating a curve, when trying to fit the entire curve by changing the position of the control points of the unfitted part of the generated curve, the part that was well fitted until now ends up being fitted. It appears as a phenomenon of disappearing.For this reason.

Conventionally, when expressing a curve by interpolation using an interpolation function, specialized knowledge is required to determine the control points, and the interpolation function itself is difficult to use as a method for generating curve interpolation.

[Purpose of the invention]

An object of the present invention is to solve such problems and provide an easy-to-use curve interpolation generation method.

[Structure and operation of the invention]

The present invention calculates and stores tangent vector values at control points in advance when generating one curve, and when modifying the shape of the generated curve, the control points (
Using the new position coordinates of column) and the memorized tangent square values at the control points that are both end points of the curve section, calculate the curve shape only for the curve section with the fixed termination condition. The most important feature of the conventional one-track interpolation generation method is that the shape of only the curve section is calculated using the tangent vectors at both end points of the curve section, which are corrected by IV. are different.

Hereinafter, a curve interpolation generation method using an interpolation function in a two-dimensional space will be explained based on the drawings.

FIG. 1 is a diagram showing a processing outline of an embodiment of the curve interpolation generation method according to the present invention, and FIG. 2 is a diagram showing an example of a curve generated according to the present invention.

Specifically, in order to generate a curve as shown by the solid line 402 in FIG. 2 using an interpolation function, first, as shown in FIG. 1, the control points P1.2. . . . , position coordinates of Pl, end points Pi, 0 at P7; i Given the termination conditions as described above, the curve between each control point is expressed by an interpolation function. At this time, the tangent vector value at each control point is calculated and stored. A cubic spline function can be used as the interpolation function at this time. Next, the shape of the generated curve 5 is confirmed by displaying the generated curve on a display device or the like. If the shape of the curve does not fit, correct the position coordinates of the control points that are considered inappropriate in the section where the shape of the curve should be corrected (correction section), and then update the 112 correct section. As a curve generation section, the position coordinates of the control point included in the curve generation section and the tangential vector value which is the storage of the control point at the point 0;:j of the curve generation section are given, and the fixed path 5iii conditions (i.e.,
The curve shape of the correction section is calculated again using the interpolation function under the termination condition that specifies the tangent hexagonal value at the end point.

At this time, tangent vector values at each control point in the correction section are calculated and stored. Because it operates in this way, even if the control point position coordinates of the correction section are changed, the shape of the curve outside the correction section does not change, making it possible to connect smooth curves at both end points of the correction section. shall be. If the shape of the curve does not fit, the above operation can be repeated.

Figure 2 shows the curve generated by the interpolation function according to the method of the present invention when the position of the control point P4 is changed to P4', as indicated by the dotted line 41.
Shown as 2. As is clear from the results of the conventional method shown in FIG. 2, in the present invention the control points are changed from P4 to P4'
Even if the position is changed to l), there is no change in the shape of the curve between 1 and 23 and the curve between P5 and P7.

In FIGS. 1 and 2, the explanation was given using the example of modifying one control point, but even in the case of modifying multiple control points (i.e., a control point sequence), the modified position coordinates of the control point sequence, Using the position coordinates and tangent vectors at the previous control point and the next control point in the control point sequence, find the position between the previous control point and the next control point in the control point sequence. It is obvious that it is possible to modify the shape of only the curved section in the same way.

FIG. 3 is a diagram showing the structure of an embodiment of the curved sleeve gap generation method according to the present invention. 501 is a conversation terminal bag 71 for inputting data and command information for various processes; 502 is a graph ink display for displaying generated curves, etc.;
04 is a data storage device that records the positional pressure of control points (votes, tangent vector values, termination condition 1 curve shape, etc.); A curve generation arithmetic device that generates a curve, and 5o3 a control device that controls the device and the overall processing.

Reference numeral 506 denotes a hub (or communication line) that connects the devices.

To operate this, after initial setting, the control device 50
3, the number of control points, their respective position coordinates, and termination conditions are inputted from the conversation terminal 501 and stored in the data storage device 504 via the control device 503. The data storage format may be, for example, as shown in FIG. 4, in which tangent vectors are held corresponding to each control point. Control device 5
03 instructs the curve generation operation 'T, 1 device 505 to read out the number of control points, position coordinates, and termination conditions recorded in the data storage device 504 1a, calculate the 1 curve shape, and store the curve shape data and The control device 503 calculates the tangent vector value at each control point obtained in the process of calculating [gamma] of the curve shape.
The information is stored in the data storage device 504 via the . The control device 503 instructs the graphic display 502 to read the curve shape data from the data recording tα device 504 and display one curve. If the first author looks at the curved shape displayed on the graph ink display 502 and determines that some of the curved shapes are not correct, he/she can use conversation O.
: from 501 to predetermined 11'? By manually inputting +ta, the controller 503 is notified of this fact. After this, the conversation is based on instructions from the control device 503 ◇
: is the curve section that is not fitted from the end 501 (r13
control point or control point sequence (this is referred to as PixPi+j: l+J is a number) information (for example, i, i+j in the above case) whose position is to be corrected in the corrected control point (sequence), The corrected position coordinates are manually entered (at this time, it is okay even if the position coordinates are not changed in part of the 5 correction sections).

The control device 503 receives the input correction section control point number 12i.
+j is the curve generation section control point number, and the corrected position coordinates of the control points (column) Pi, . . . , Pi+J are loaded into the corresponding address of the data recording device 504.

When the control device 503 instructs the curve generation calculation bag E 505 to calculate the curve shape of the correction section, one curve generation calculation device 50
5 reads the curve generation section control unit point numbers i and ++j from the data storage device 504, and based on these, controls the control points Pi.
1, Pi,..., Pi→-j, Pi+j+1
The position coordinates of (i-1≧1, i+j+l≦7) and the tangent vector values of the control points Pi-1 and Pi+j+l are read out, and the end condition is a fixed condition (i.e., the end point that specifies the tangent vector value at the end point). control point Pi-
1 and the control point Pi+j+l. Based on the completion of the curve shape calculation from the curve generation calculation device 505, the a,lH]n device 503 reads out the already calculated curve shape data from the data storage device 504, The curve shape data is replaced with the curve shape data of the correction section newly calculated by the curve generation calculation device 505, and the data is recorded in the tq device 504.
The curve shape data of the correction section is reread t0 (the "replacement" of the curve shape data of this correction section is performed by the curve generation calculation unit 50 according to the shape data format and according to the instructions of the control device 503.
5 to the data storage device 504). Also, the control points Pi, .

The tangent vector value of Pi→−J is obtained from the data Hito a device 50.
4. Store it in the corresponding position. After this, the control device 503
commands the graphic display 502 to read out the curve shape data from the data storage device 504 and display one curve.

Thereafter, the normal operation of the curve (1) is repeated until one operator determines that the curve shape is appropriate.

In the above description, control points (columns) Pi, which modify one position when modifying a part of the generated curve, are used.

Control point Pi-1゜Pi before and after Pi+j
Control using +j+1 tangent vector? ffU point Pi-1
I explained how to modify the curve sandwiched by the control points Pi+j+1, but the control points (column) Pi that corrects the two positions...
..., control points P m1 before and m2 after Pi+j
i-ml (i-ml top 1).

Control point Pi-ml and control point Pi+j+rr1 using the tangent vector of Pi+j+m2 (i+j+m2≦7)
2 can also be corrected as follows.

The process of first generating a curve and displaying the curve on the graph ink display is similar to the above description.

If the operator looks at the curved shape displayed on the graph ink display 502 and determines that some of the curved shape is not properly fitted, the operator can control the curved shape by inputting predetermined information from the conversation terminal 501. The 1n device 503 is notified of this fact. Thereafter, based on an instruction from the control device 503, the conversation terminal 501 selects a control point or a control point sequence (Pi to P i + j ) information (e.g. i
, i+j), the corrected position coordinates of the control point (column) (in this case,
It does not matter if the position coordinates may not be changed in part of the correction section) and the new curve generation section control point number 1
-m1→-1, 1-1-j+m2-1 is manually generated. The control device 503 receives control point (column) information i that should be manually corrected.
, i + j, then control point Pi,...
Record the corrected position coordinates of Pi+j and the curve generation section control point numbers 1-m1+1 and i+j+rn2-1 as data 41.
Each is written to the corresponding address of the device 504. When the control device 503 instructs the curve generation calculation device 505 to calculate the curve shape of the correction section, the 1-curve generation calculation device 505 retrieves the curve generation section control point number 1-m1 from the data storage device 504.
+1. i+j+m2-1 is read, and based on this, the control points Pi-m1, Pi-ml+1 . −, Pi+j+m2
-1 , P i + j + m 2 (i m
1≧1, i+j+m2≦7) and the tangent vector values of the control points Pi-ml and Pi+j+m2 are read out, and the control points are set with a fixed condition as the terminal condition (i.e., a terminal condition that specifies the tangent vector value at the terminal point). Pi-
The shape of the curve sandwiched between ml and the control point Pi+j+m2 is calculated.

After generating the curve, display the graphic display 502 again.
It is the same as the above explanation up to the point where it is displayed. From then on,
The curve correction operation is repeated until the operator determines that the curve shape is appropriate.

Although the above description has been made using an example of application to a two-dimensional coordinate space, the present invention can be generally applied to an N-dimensional coordinate space.

〔Effect of the invention〕

As explained above, according to the present invention, even if the position coordinates of some control points (columns) are corrected after calculating the curve shape using the interpolation function from the control points specified by − degrees, the cough correction control Any other system except points? 7 [The curve shape does not change between one point or the change can be kept small. Therefore, it is easy to generate curves and modify shapes conversationally, and it is also possible to directly apply interpolation functions to curve shape representations without special knowledge. .

[Brief explanation of the drawing]

FIG. 1 is a diagram showing a processing overview of an embodiment of the curve interpolation generation method of the present invention, FIG. 2 is a diagram showing an example of a curve generated by the present invention, and FIG. Fig. 4 is a diagram showing an example of the data storage format of the data storage device 504, Fig. 5 is a diagram showing an outline of the processing of the conventional curve interpolation generation method, and Fig. 6 is a diagram showing the processing outline of the conventional curve interpolation generation method. FIG. 201, 401... Control point 1 202, 402... Interpolation generation curve. 211, 411... Correction control point. 212, 412... Modified interpolation generation curve. Patent applicant Nippon Telegraph and Telephone Corporation

Claims (2)

[Claims] (1) A sequence of control points P1, P2, etc. on or near the curve to be expressed in the N-dimensional coordinate space.
・In the curve interpolation generation method, which generates the curve or an approximate curve of the curve by taking Pe, and interpolating the points located between the control points using an interpolation function from these control point sequences, When modifying a part of the shape, among the tangent vector values of each control point calculated using the control point sequence position coordinates of the curve and the curve end conditions at the start point P1 and end point Pe of the control point sequence, Control points or control point sequences Pi, Pi+1, . . . , one control point Pi-1 (i-1≧1) before Pi+j and one control point included in the section of the curve that needs to be corrected Later control point P
a first means for storing a tangent vector value at i+j+1 (i+j+1≦e); and a control point or control point sequence Pi, P that requires the correction.
The corrected position coordinates of i+1, ..., Pi+j and the control points Pi-1, Pi stored by the first means
Using the tangent vector value of +j+1, control point Pi-1,
A curve interpolation generation method comprising: second means for modifying the curve shape of a curve section sandwiched by Pi+j+1. (2) A sequence of control points P1, P2, etc. on or near the curve to be expressed in the N-dimensional coordinate space.
..., a curve generated in a curve interpolation generation method that generates the curve or an approximate curve of the curve by taking Pe and interpolating the points located between the control points using an interpolation function from a sequence of control points. When modifying a part of the shape of the curve, among the tangent vector values of each control point calculated using the control point sequence position coordinates of the curve and the curve termination conditions at the start point P1 and end point Pe of the control point sequence. , control points or control point sequences Pi, Pi+1, etc. included in the section where the position coordinates of the control points of the curve need to be corrected.
, control point Pi-m1 (i-m1≧
1) and m2 subsequent control points Pi+j+m2(i+j+
a third means for storing tangent vector values at m2≦e); and control points or control point sequences Pi-m1, Pi-m of the curve.
1+1, ......, Pi-1 and Pi+j+1,
A fourth means for storing the position coordinates of Pi+j+2, . . . , Pi+j+m2; Corrected position coordinates and control points or control point sequences Pi-m1, Pi-m1+1, . . . stored by the fourth means
・, Pi-1 and Pi+j+1, Pi+j+2,...
..., the control point Pi-m1 and the control point P using the position coordinates of Pi+j+m2 and the tangent vector values of the control points Pi-m1 and Pi+j+m2 stored by the third means.
A curve interpolation generation method comprising: fifth means for modifying the curve shape of the section sandwiched by i+j+m2.