Multi-degree reduction of tensor product Bézier surfaces with conditions of corners interpolations
- 35 Downloads
This paper studies the multi-degree reduction of tensor product Bézier surfaces with any degree interpolation conditions of four corners, which is urgently to be resolved in many CAD/CAM systems. For the given conditions of corners interpolation, this paper presents one intuitive method of degree reduction of parametric surfaces. Another new approximation algorithm of multi-degree reduction is also presented with the degree elevation of surfaces and the Chebyshev polynomial approximation theory. It obtains the good approximate effect and the boundaries of degree reduced surface can preserve the prescribed continuities. The degree reduction error of the latter algorithm is much smaller than that of the first algorithm. The error bounds of degree reduction of two algorithms are also presented.
Keywordscorner interpolation multi-degree reduction approximation tensor product surfaces
Unable to display preview. Download preview PDF.
- 14.Hu Shimin, Zheng Guoqin, Sun Jiaguang, Approximate degree reduction of rectangular Bézier surfaces, Journal of Software, 1997, 4(4): 353–361.Google Scholar
- 16.Chen Guodong, Wang Guojin, Multi-degree reduction of Bézier curves with conditions of endpoint interpolations, Journal of Software (in Chinese), 2000, 11(9): 1202–1206.Google Scholar
- 17.Fox, L., Parker, I. B., Chebyshev Polynomials in Numerical Analysis, London: Oxford University Press, 1968Google Scholar