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2004•Journal of Hefei University of TechnologyRequires access

C~2 4-degree continuous spline curves with the shape parameter

Liu Zhi

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Abstract

This paper deals with a class of C~2 4-degree continuous spline curves with some shape parameter. The segmented curves are all shape-preserving to the given polygon. By changing the value of the shape parameter, the approaching degree of the curves to their control polygon can be adjusted. The results have definite geometric meanings that are useful for shape modification and representation of curves. Finally, a few numerical examples illustrate that the method given in this paper is effective for CAGD.

About this research paper

What this paper is about

This paper deals with a class of C~2 4-degree continuous spline curves with some shape parameter. The segmented curves are all shape-preserving to the given polygon. By changing the value of the shape parameter, the approaching degree of the curves to their control polygon can be adjusted. The results have definite geometric meanings that are useful for shape modification and representation of curves. Finally, a few numerical examples illustrate that the method given in this paper is effective for CAGD.

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Available abstract

This paper deals with a class of C~2 4-degree continuous spline curves with some shape parameter. The segmented curves are all shape-preserving to the given polygon. By changing the value of the shape parameter, the approaching degree of the curves to their control polygon can be adjusted. The results have definite geometric meanings that are useful for shape modification and representation of curves. Finally, a few numerical examples illustrate that the method given in this paper is effective for CAGD.

Key concepts: Polygon (computer graphics), Mathematics, Shape parameter, Spline (mechanical), Degree (music), Geometric design, Family of curves, Representation (politics)

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