JP2683239B2 - Curve interpolation generator - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a curve interpolation generation processing device for obtaining interpolation points from a control point sequence by an interpolation curve and connecting these interpolation points to generate the curve. [Prior Art] A conventional curve interpolation generation processing device will be described below by taking a cubic spline function in a two-dimensional coordinate space as an example of an interpolation function. FIG. 5 is a diagram showing a processing outline of a conventional curve interpolation generation processing device, and FIG. 6 is a diagram showing control points and curve shapes generated by interpolation in the conventional curve interpolation generation processing device in a two-dimensional coordinate space. . P1, P2, ..., P7 shown in FIG. 6 indicate solid lines connecting control points and control point sequences, which are curves generated by interpolation by a cubic spline function described later. The curve C in the two-dimensional XY space can be generally expressed by the following function. C: f (X, Y) = 0 where X is the X coordinate of the curve C, Y is the Y coordinate of the curve C, and f is a function representing the shape of the curve C. One method of expressing the curve C is an interpolation method using a cubic spline function. The cubic spline function is a function suitable for a smooth curve expression in which differential coefficients up to quadratic are continuous at control points and are used in the field of CAD and the like. The control points taken along the curve C are P1 (X1, Y1), P2 (X2, Y2), ..., Pi
Letting (Xi, Yi), ..., Pn (Xn, Yn), the expression of the curve C by the cubic spline function is as follows. X (t) = A0 + A1t + A2t 2 + A3t 3 Y (t) = B0 + B1t + B2t 2 + B3t 3 herein, t is 0TTi: a parameter that varies in the range of (Ti constant), when t = 0 X (t) = Xi, When Y (t) = Yi t = Ti X (t) = Xi + 1, Y (t) = Yi + 1 (i = 1,2, ..., n-1) Also, A0, A1, A2, A3 and B0, B1, B2, B3 are constants.
These constants are the coordinate values of the control points P1, P2, ..., Pn and the tangent vector values (first derivative) or the second derivative of the curve end points (start point) P1 and (end point) Pn. It is determined by giving conditions. As terminating conditions, the tangent vectors of the starting point P1 and the ending point Pn and the second derivative are respectively expressed in simplified expressions as P1 ′, Pi ″ and P
Let n ′ and Pn ″ be free conditions (when P1 ″ = Pn ″ = 0), periodic appropriate conditions (combination of P1 ′ = Pn ′, P1 ″ = Pn ″), antiperiodic conditions (P1 ′ = − Pn) ′, P1 ″ = − Pn ″), and fixed conditions (when the values of P1 ′ and Pn ′ are commanded to specific values). Specifically, using the cubic spline function, the solid line 20 in FIG.
In order to generate a curve as shown in 2, the position coordinates of the control points P1, P2, ..., P7 and the termination conditions as described above at the end points P1, P7 are first set as shown in the flowchart of FIG. Given, the curve between each control point is represented by a cubic spline function. Next, the shape of the generated curve is confirmed by displaying the curve generated by a display device or the like. If the shape of the curve does not fit, correct the position coordinates of the control point that seems to be inappropriate and then repeat 3
The curve shape between the control points is expressed by the quadratic spline function. In Fig. 6, the curve generated by the cubic spline function under the same termination condition when the position of the control point P4 is changed to P4 'is the dotted line 21.
Shown in 2. The above modification is repeated until the shape of the curve fits. Thus, in the conventional curve interpolation generation processing device, as shown in FIG. 5, when the generated curve shape does not fit the intended curve shape, the position coordinates of the control points in the curve section that is not fitted are simply Was corrected, and the curve shape was calculated again by the interpolation function using the corrected position coordinates. Therefore, not only the curved parts of the sections on both sides of the control point whose position coordinates were corrected, as is clear from FIG. There is a problem in that the shape of the entire curve is affected by the correction of the position coordinates of the control points. This problem is that when interactively generating a shape curve of an object using a graphic display using an interpolation function, changing the position of the control point of the non-fitted part of the generated curve to fit the entire curve well. On the contrary, when trying to do so, it appears as a phenomenon that the part that has been fitted well until now does not fit.
For this reason, in the past, when the curve was interpolated by the interpolation function, specialized knowledge was required in the way of the control points, and the interpolation function itself was difficult to use as a method for generating the curve interpolation. . [Object of the Invention] An object of the present invention is to solve such a problem and to provide an easy-to-use curve interpolation generation processing device. [Configuration and Operation of the Invention] In the present invention, the tangent vector value at a control point is calculated and stored in advance when a curve is generated, and when the shape of the generated curve is corrected, Using the new position coordinates of the control point (column) and the stored tangent vector values at the control points that are the end points of the curve section, the curve shape is calculated only for the curve section under a fixed termination condition. This is the most significant feature, and differs from the conventional curve interpolation generation processing device in that the shape of only the curved section is calculated by using the tangent vectors at both end points of the curved section whose shape is corrected. Hereinafter, a curve interpolation generation processing device using an interpolation function in a two-dimensional coordinate space will be described as an example with reference to the drawings. FIG. 1 is a diagram showing a processing outline of an embodiment of a curve interpolation generation processing device according to the present invention, and FIG. 2 is a diagram showing an example of a curve generated according to the present invention. To specifically generate a curve as shown by the solid line 402 in FIG. 2 using an interpolation function, first, as shown in FIG. 1, the position coordinates of the control points P1, 2, ... Then, the above-mentioned termination condition in P7 is given and 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 is confirmed by displaying the curve generated by a display device or the like. If the shape of the curve does not fit, the position coordinates of the control points that are considered to be inappropriate and are included in the section (correction section) in which the shape of the curve should be corrected are corrected, and then the correction section is newly updated. As the curve generation section, the position coordinates of the control points included in the curve generation section and the stored tangent vector values of the control points at both end points of the curve generation section are given to give a fixed termination condition (that is, a tangent vector at the end point). Under the end condition for specifying the value), the curve shape of the modified section is calculated again by the interpolation function. Then, the curved shape of the correction section and the non-correction portion are combined. At this time, the tangent vector value at each control point in the correction section is calculated and stored. Since it operates in this way, even if the control point position coordinates of the correction section are changed, it is possible to keep the curve shape other than the correction section unchanged, and it is possible to connect smooth curves at both end points of the correction section. To do. If the shape of the curve does not fit, the above operation can be repeated. FIG. 2 shows a curve generated by the interpolation function in the processing apparatus of the present invention when the position of the control point P4 is changed to P4 ', which is indicated by a dotted line 412.
Indicated by As is apparent from the comparison with the result of the conventional processing apparatus shown in FIG. 2, in the present invention, even if the control point is changed from P4 to P4 ', the curve between P1 and P3 and P5 and P7. There is no change in the shape of the curve sandwiched between. In FIGS. 1 and 2, the correction of one control point is described as an example, but even in the case of correction of a plurality of control points (that is, a control point sequence), the correction position coordinates of the control point sequence, It is sandwiched between the control point one before and the control point one after the control point sequence by using the position coordinates and the tangent vector at the control point one before and one control point after the control point sequence. It is obvious that the shape modification of only the curved section can be done in the same way. FIG. 3 is a diagram showing the configuration of an embodiment of the curve interpolation generation processing device according to the present invention. 501 is a conversation terminal device for inputting data and command information for various processes, 502 is a graphic display for displaying a generated curve, etc., 504 is storage of position coordinates and tangent vector values of control points, end conditions, curve shape, etc. 505 is a data storage device, 505 is a curve generation calculation device that generates a curve using an interpolation function by giving position coordinates of a control point sequence and a generation curve end condition, and 503 is a control device that controls the device and the overall processing Reference numeral 506 is a bus (or communication line) that connects the devices. To make it work, after initializing,
Based on the instruction of 3, the number of control points, each position coordinate, and the end condition are first input from the conversation terminal 501, and the control device
Data is stored in the data storage device 504 via 503. The data storage format may be such as to hold tangent vectors corresponding to respective control points as shown in FIG. The control device 503 instructs the curve generation calculation device 505 to read the number / position coordinates of the control points and the termination condition stored in the data storage device 504, calculate the curve shape, and calculate the curve shape data and the curve shape. The tangent vector value at each control point obtained in the calculation process is stored in the data storage device 504 via the control device 503. The controller 503 has a graphic display 5
02 is instructed to read the curve shape data from the data storage device 504 and display the curve. If the operator sees the curved shape displayed on the graphic display 502 and determines that the curved shape does not partially fit, the operator inputs the predetermined information from the conversation terminal 501 to the controller 503 to that effect. To notify. After this, the controller 5
Based on an instruction from 03, a control point or a control point sequence to be corrected in a position included in a curved section (correction section) not fitted by the conversation terminal 501 (this is defined as Pi to Pi + j;
i, j is a number) information (for example, i, i + j in the above case), and the corrected position coordinates of the corrected control point (column) are input (in this case,
It does not matter if the position coordinates are not changed in part of the correction section). The control device 503 writes the input correction section control point number i, i + j as the curve generation section control point number, and writes the correction position coordinates of the control point (column) Pi, ..., Pi + j to the corresponding address of the data storage device 504. . When the control device 503 instructs the curve generation calculation device 505 to calculate the curve shape of the correction section, the curve generation calculation device 505 reads the curve generation section control point numbers i, i + j from the data storage device 504, and based on this, the control points. Pi-1, Pi, ..., Pi + j, Pi + j + 1 (i-
Position coordinates of 1 ≧ 1, i + j + 1 ≦ 7) and control point Pi−
The tangent vector values of 1 and Pi + j + 1 are read, and the control point Pi-1 and the control point Pi + j are set as fixed end conditions (that is, the end condition that specifies the tangent vector value at the end point).
The shape of the curve sandwiched by +1 is calculated. Based on the completion of the curve shape calculation from the curve generation calculation device 505, the control device 503
Reads out the already calculated curve shape data from the data storage device 504, and replaces the curve shape data sandwiched between the control points Pi-1 and Pi + j + 1 with the curve shape data of the correction section newly calculated by the curve generation calculation device 505. Data storage
It is stored again in the curve shape data of 504 ("replacement" of the curve shape data of this correction section is performed by writing directly from the curve generation arithmetic unit 505 to the data storage unit 504 according to the instruction of the control unit 503 according to the form of the shape data. You can also do this). Further, in the curve generation calculation device 505, the control points Pi ,.
The tangent vector value of Pi + j is stored in the corresponding position of the data storage device 504. Thereafter, the control device 503 instructs the graphic display 502 to read the curve shape data from the data storage device 504 and display the curve. After that, the curve correcting operation is repeated until the operator determines that the curve shape is appropriate. In the above explanation, when modifying a part of the generated curve,
The control point (column) whose position is to be corrected is sandwiched between the control point Pi-1 and the control point Pi + j + 1 by using the tangent vector of the control point Pi-1 and Pi + j + 1 before and after Pi, ..., Pi + j. The method of modifying the curve has been explained, but the control points (rows) Pi, ..., Pi + j that modify the position are control points Pi one m1 before and two m2 after.
-M1 (i-m1 ≧ 1), Pi + j + m2 (i + j + m2 ≦ 7) using the tangent vector Pi-m1 and control point Pi + j + m2
If you want to modify the curve sandwiched between, you can do the following. The procedure is the same as the above description until the curve is first generated and then displayed on the graphic display. If the operator sees the curved shape displayed on the graphic display 502 and determines that the curved shape does not partially fit, the operator inputs the predetermined information from the conversation terminal 501 to the controller 503 to that effect. To notify. After this, based on an instruction from the control device 503, the control point or control point sequence (Pi
-Pi + j) information (for example, i, i + j), corrected position coordinates of the control point (column) (at this time, the position coordinates may not be changed in part of the corrected section) and a new curve generation section Input the control point number i-m1 + 1, i + j + m2-1. Based on the input control point (column) information i, i + j to be corrected, the control device 503 determines that the control point Pi ,.
The corrected position coordinates of + j and the curve generation section control point numbers i-m1 + 1 and i + j + m2-1 are written to the corresponding addresses of the data storage device 504, respectively. When the control device 503 instructs the curve generation calculation device 505 to calculate the curve shape of the correction section,
The curve generation calculation device 505 reads the curve generation section control point numbers i-m1 + 1, i + j + m2-1 from the data storage device 504,
Based on this, control points Pi-m1, Pi-m1 + 1, ..., Pi + j +
The position coordinates of m2-1, Pi + j + m2 (i-m1≥1, i + j + m2≤7) and the tangent vector value of control points Pi-m1 and Pi + j + m2 are read, and the fixed condition (that is, the tangent vector value at the end point is specified) as the termination condition. Under the terminating condition), the shape of the curve sandwiched between the control point Pi-m1 and the control point Pi + j + m2 is calculated. Generate curves and then graphic display 502 again
The description up to the point is the same as that described above. Since then
The curve correcting operation is repeated until the operator determines that the curve shape is appropriate. In the above, the application to the two-dimensional coordinate space has been described as an example, but the present invention can be generally applied to the N-dimensional coordinate space. [Effect of the Invention] According to the present invention as described above, even if the position coordinates of some control points (columns) are corrected after the curve shape is calculated from the once specified control points by the interpolation function. The curve shape does not change or can be suppressed to be small between the control points other than the modified control point. For this reason, it is easy to interactively generate a curve and modify the shape, and it is possible to intuitively apply the interpolation function to the curve shape expression without special knowledge.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing a processing outline of an embodiment of a curve interpolation generation processing device of the present invention, FIG. 2 is a diagram showing an example of a curve generated by the present invention, and FIG. Is a diagram showing a configuration of an embodiment of the present invention, FIG. 4 is a diagram showing an example of a data storage format of a data storage device 504, FIG. 5 is a diagram showing a processing outline of a conventional curve interpolation generation processing device, FIG. 6 is a diagram showing a curve shape generated by a conventional processing device. 201,401 …… Control point, 202,402 …… Interpolation generation curve, 211,411 …… Modified control point, 212,412 …… Corrected interpolation generation curve.

Claims (1)

(57) [Claims] A control point sequence P1, P2, ..., Pe is set on or near the curve to be represented in the N-dimensional coordinate space, and the points located between the control points are interpolated from these control point sequences by an interpolation function. In the curve interpolation generation processing device for generating the curved line or the approximated curve of the curved line, the control point sequence position coordinates of the curved line and the starting point P1, of the control point sequence
Using the curve end condition at the end point Pe and a curve generation arithmetic unit that generates a curve between the control points so that the curve between the control points is represented by an interpolation function, When correcting a part of the shape, the control point sequence position coordinates of the curve and the tangent vector value of each control point calculated using the curve termination condition at the start point P1 and the end point Pe of the control point sequence Of the control point sequences Pi, Pi + 1, ..., Pi + j included in the section of the curve that needs to be modified, the control point Pi-1 (i-1 ≧ 1) before and the control point one after The data storage device stores a tangent vector value at Pi + j + 1 (i + j + 1 ≦ e), and a control device that controls the curve generation calculation device and the data storage device, and the control device is a control that requires the correction. Point Pi, Pi ＋
1, ..., Pi + i after correction, and the tangent vector values of the control points Pi−1, Pi + j + 1 stored by the data storage device are configured to be supplied to the curve generation calculation device, and the curve generation The arithmetic unit is configured to generate a curve shape of a curve section sandwiched between the control points Pi−1, Pi + j + 1 as a correction curve based on the supplied position coordinates and the tangent vector value. Generation processing device. 2. A control point sequence P1, P2, ..., Pe is set on or near the curve to be represented in the N-dimensional coordinate space, and the points located between the control points are interpolated from these control point sequences by an interpolation function. In the curve interpolation generation processing device for generating the curve or the approximate curve of the curve, the position coordinates of the control point sequence Pi, Pi + 1, ..., Pi + j of the curve and the start point P1, the end point Pe of the control point sequence A curve generation arithmetic unit for generating a curve between the control points is provided so that the curve between the control points is represented by an interpolation function using the curve end condition and one of the shapes of the generated curves. When correcting the part, among the tangent vector values of each control point calculated using the control point sequence position coordinates of the curve and the curve termination condition at the start point P1 and the end point Pe of the control point sequence, of the curve Correct the position coordinates of control points Control point sequence Pi, Pi + 1, ...
..., control point Pi-m1 (i-m1 ≧ m1) before Pi + j
1) and the control point after m2 pieces Pi + j + m2 (j + j + m2 ≦
e) storing the tangent vector value and controlling the sequence of control points Pi-m1, Pi-m1 + 1, ..., Pi-1 and Pi + j + of the curve.
1, Pi + j + 2, ..., Pi + j + m2 is provided with a data storage device for storing the position coordinates and a control device for controlling the curve generation operation device and the data storage device, and the control device needs to correct the position coordinates. The corrected position coordinates of the control point sequence Pi, Pi + 1, ..., Pi + j and the control point sequence Pi-m1, Pi-m1 + 1, ..., Pi-1 and Pi + j +
1, Pi + j + 2, ..., Pi + j + m2 position coordinates and tangent vector values of the control points Pi-m1, Pi + j + m2 are configured to be supplied to the curve generating and calculating device, and the curve generating and calculating device is provided A curved line interpolation generation processing device, which is configured to generate a curved shape of a section sandwiched between the control point Pi-m1 and the control point Pi + j + m2 as a corrected curve by the respective position coordinates and the tangent vector value. .