JPH09147127A - Free-form curve generating method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily generate and correct a smooth free-form curve by generating an intermediate shape between shapes before and after a knot of a B-spline curve is deleted. SOLUTION: Two B-spline curves 1 and 3 are equalized in the numbers of knots and control points by inserting knots into the B-spline curves 1 and 3 as many as required (S105). Then, a new control point P0 is generated on the straight line connecting corresponding control points of the two curves 1 and 3 at the position of the rate of an inputted parameter, and a curve 4 is formed from a new control point group. The curve 1 is inputted (S101), a smooth curve 2 is temporarily generated by removing knots from the curve 1 (S102), and knots are inserted again without changing the shape of the curve 2 to generate the curve 3 (S103). Then, the user inputs the parameter (S104) and control points of the curves 1 and 3 are interpolated to generate a curve 4 in an intermediate shape (S105).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for generating a free curve, and more specifically, a two-dimensional or three-dimensional CG system or a CAD system capable of handling a free curve such as Bezier curve or B-spline curve. Regarding

[0002]

2. Description of the Related Art Conventionally, E. Cohen, T. Lyche, and RFRiesen
feld.Discrete B-splines and subdivision technique
s in computer aided geometric design and computer
graphics. Computer Graphics and Image Processing, 1
4 (2): 87-111, 1980 and the like, a method is proposed in which knots are inserted in a B-spline curve to increase the number of knots and control points without changing the shape of the curve.

Lyche, T. Morken, K. Knot removal f
or parametric B-spline curves and surfaces.Comput
In er Aided Geometric Design 4 (1987) 217-230 and the like, conversely, a method of deleting a knot of a B-spline curve to reduce the number of control points of the curve and generating a smoother curve has been proposed.

By using the above-mentioned method, the data amount of the B-spline curve can be reduced, and the point sequence can be approximated to the B-spline curve. In addition, FIG.
Knot P of the part where the swell of the curve as shown in
2 by deleting as shown in FIG.
As shown in (B), unnecessary waviness of the B-spline curve can be eliminated.

[0005]

According to the conventional method, as shown in FIG.
As shown in, the shape of the B-spline curve existed in only two states, before and after removing the knots. For this reason, the constraint was large for use in the design of curved shapes.
Further, since the user cannot confirm the process of changing the shape, it is difficult to grasp the portion where the shape has changed.

The present invention has been made to solve the above problems by providing a method for generating an intermediate shape between the shape before the knot of the B-spline curve is deleted and the shape after the knot is deleted. It is a thing.

[0007]

According to the invention of claim 1, the knots of two curves and the number of control points are inserted by inserting as many knots as necessary for the two input B-spline curves. And then generate a new control point at the position of the ratio of the input parameters on the straight line connecting the corresponding control points of the two curves, and generate a curve from the new control point group. It is characterized by.

According to a second aspect of the present invention, in the first aspect of the invention, two B-spline curves input and two smoother curves obtained by removing arbitrary knots from the curves are input. It is characterized by doing.

According to a third aspect of the present invention, an operation equivalent to that of the first aspect is performed using a Bezier curve, that is, the curves in the two Bezier curves are appropriately divided to form a curve of two curve strings. Are equalized, and then a new control point is generated at the position of the ratio of the input parameters on the straight line connecting the control points of the corresponding Bezier curves of the two curve strings, and the new control point group It is characterized in that a curve sequence is generated more.

According to the invention of claim 4, in the invention of claim 3, the operation equivalent to that of claim 2 is performed by using a Bezier curve, that is, one inputted Bezier curve sequence and its curve sequence are It is characterized in that two curve sequences, which are smooth curve sequences represented by a smaller number of Bezier curves, are input.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a diagram showing the flow of processing of the present invention. First, in step S101, a curve 1 for deleting knots is input. Curve 1 has rational or non-rational B
-Enter the spline curve. Next, step S102
The curve 2 in which the knot P is deleted from the curve 1 is temporarily generated. The knot to be deleted may be automatically determined according to the purpose, or may be directly specified by the user. Next, in step S103, the knot P deleted in step S102 is inserted into the curve 2. The result is a curve 3 whose shape is equal to curve 2 and whose number of control points and knots are equal to curve 1.

Next, in step S104, the user inputs a real number parameter t. Usually, the value of t is set according to the movement of a mouse or dial connected to the computer. Next, in step S105, a curve 4 having an intermediate shape between the curves 1 and 3 is generated according to the parameter t input in step S104. That is, the corresponding control points of the curve 1 and the curve 3 are connected by a straight line, and the control point of the curve 4 is generated from the control point of the curve 1 at the position P ₀ having a ratio of t: 1−t. When the curve 1 is in the rational form, the weights of the control points are also values interpolated at the same ratio. As a result, the shape of the curve 4 is equal to the curve 1 when t is 0, approaches the shape of the curve 3 as t increases, and is equal to the curve 3 when t is 1.

Next, in step S106, the user sets the curve 4
Check the shape of and enter if you are satisfied with the shape. If the shape is not satisfactory, step S10 is performed again.
Return to step 4 and input parameters. When satisfied, the curve 4 at this point is output in step S107. Normally, the determination until the user takes some action is set to No, and the shape of the curve 4 is continuously changed according to the movement of the mouse or dial. Note that the operations from step S103 to step S105 correspond to claim 1, and step S1
The operation of 01 and step S102 corresponds to claim 2.

Although the input in step S101 is limited to the B-spline curve in FIG. 1, the input is Bez.
The same operation can be performed with an ier curve.
That is, in step S101, the Bezier curve sequence 1 in which a plurality of Bezier curves are connected is input, and then, in step S102, the plurality of Bezier curves in the curve sequence 1 are represented by one Bezier curve, thereby obtaining the number of curves. Is temporarily generated, and the Bezier curve in the curve sequence 2 is divided again in step S103 to obtain a smooth curve having the same number of curves as the original curve sequence 1. Column 3 may be generated. In step S105, the control points of the Bezier curves corresponding to the curve sequence 1 and the curve sequence 3 may be interpolated to generate the curve sequence 4 having an intermediate shape. The input is Bez
The operation from step S103 to step S105 when it is an ier curve sequence corresponds to claim 3, and step S
The operation of 101 and step S102 corresponds to claim 4.

[0015]

According to the above-described method of generating a free curve, it becomes possible to generate an intermediate shape between the shape before deleting the knots of the B-spline curve and the shape after deleting the knots. The present invention can be applied to two-dimensional and three-dimensional CA.
If it is realized by the D system or the CG system, the degree of freedom of the shape when smoothing the curve is increased, and since the process of changing the shape can be easily confirmed, the design and the design can be easily performed.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining a flow of processing according to the present invention.

FIG. 2 is a diagram for explaining deletion of knots on a spline curve.

Claims (4)

[Claims] 1. The number of knots and control points of two curves is made equal by inserting as many knots as necessary for the two input B-spline curves, and then the two curves are equalized. A method for generating a free curve, characterized in that a new control point is generated at a position of a ratio of input parameters on a straight line connecting the corresponding control points, and a curve is generated from the new control point group. 2. The two input curves, one input B-spline curve and a smoother curve obtained by removing arbitrary knots from the input curve, are input.
Free curve generation method described in. 3. Bezier in two Bezier curves
The number of curves in the two curve series is made equal by dividing the r-curve appropriately, and then the corresponding Be of the two curve series is
A free curve generation method characterized in that a new control point is generated at a position of a ratio of input parameters on a straight line connecting control points of a zier curve, and a curve string is generated from the new control point group. 4. A two-curve sequence, one input Bezier curve sequence and a smooth curve sequence represented by a smaller number of Bezier curves, is input. The free curve generation method according to Item 3.