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Judging or setting weight steady-state of rational Bézier curves and surfaces.

Authors :
Cai, Hong-jie
Wang, Guo-jin
Source :
Applied Mathematics: A Journal of Chinese Universities; Dec2014, Vol. 29 Issue 4, p391-398, 8p
Publication Year :
2014

Abstract

Many works have investigated the problem of reparameterizing rational Bézier curves or surfaces via Möbius transformation to adjust their parametric distribution as well as weights, such that the maximal ratio of weights becomes smallerthat some algebraic and computational properties of the curves or surfaces can be improved in a way. However, it is an indication of veracity and optimization of the reparameterization to do prior to judge whether the maximal ratio of weights reaches minimum, and verify the new weights after Möbius transformation. What's more the users of computer aided design softwares may require some guidelines for designing rational Bézier curves or surfaces with the smallest ratio of weights. In this paper we present the necessary and sufficient conditions that the maximal ratio of weights of the curves or surfaces reaches minimum and also describe it by using weights succinctly and straightway. The weights being satisfied these conditions are called being in the stable state. Applying such conditions, any giving rational Bézier curve or surface can automatically be adjusted to come into the stable state by CAD system, that is, the curve or surface possesses its optimal parametric distribution. Finally, we give some numerical examples for demonstrating our results in important applications of judging the stable state of weights of the curves or surfaces and designing rational Bézier surfaces with compact derivative bounds. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
10051031
Volume :
29
Issue :
4
Database :
Complementary Index
Journal :
Applied Mathematics: A Journal of Chinese Universities
Publication Type :
Academic Journal
Accession number :
99886529
Full Text :
https://doi.org/10.1007/s11766-014-3231-1