Abstract
The present studies on the extension of B-spline mainly focus on Bezier methods and uniform B-spline and are confined to the adjustment role of shape parameters to curves. Researchers pay little attention to nonuniform B-spline. This paper discusses deeply the extension of the quasi-uniform B-spline curves. Firstly, by introducing shape parameters in the basis function, the spline curves are defined in matrix form. Secondly, the application of the shape parameter in shape design is analyzed deeply. With shape parameters, we get another means for adjusting the curves. Meanwhile, some examples are given. Thirdly, we discuss the smooth connection between adjacent B-spline segments in detail and present the adjusting methods. Without moving the control points position, through assigning appropriate value to the shape parameter, C1 continuity of combined spline curves can be realized easily. Results show that the methods are simple and suitable for the engineering application.
Highlights
B-spline methods are very popular in computer-aided geometric design and associated fields because of their distinct advantages
Some other methods have been presented for representing curves and surfaces
In order to improve the flexibility of product design, researchers give further consideration to introduce shape parameters
Summary
B-spline methods are very popular in computer-aided geometric design and associated fields because of their distinct advantages. Researchers paid attention to extension of traditional B-spline methods They mainly concentrated on Bezier curves [13], quadratic and cubic uniform B-spline curves [14–19]. Uniform B-splines can represent overall continuity closed curves and surfaces They use spaced knots; the spline does not interpolate the first and last control points. The designers can locate more the two end points of the curve and achieve smooth connection between adjacent B-spline segments It has more practical significance for us to study extension of nonuniform B-spline curves and surfaces. We focus on discussions about how to realize C1 continuity between adjacent B-spline segments by only adjusting the value of the shape parameters without changing the position of the control points. Results show that the methods given by this paper are simple and suitable for the engineering application
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