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邓建松

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期刊论文

Implicitization and parametrization of quadratic and cubic surfaces by μ-bases

邓建松F. Chen L. Shen and J. Deng Anhui

Computing 79, 131-142 (2007),-0001,():

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摘要/描述

Parametric and implicit forms are two common representations of geometric objects. It is mportant to be able to pass back and forth between the two representations, two processes called parameterization and implicitization, respectively. In this paper, we study the parametrization and implicitization of quadrics (quadratic parametric surfaces with two base points) and cubic surfaces (cubic parametric surfaces with six base points) with the help of μ-bases-a newly developed tool which connects the parametric form and the implicit form of a surface. For both cases, we show that the minimal μ-bases are all linear in the parametric variables, and based on this observation, very efficient algorithms are devised to compute the minimal μ-bases either from the parametric equation or the implicit equation. The conversion between the parametric equation and the implicit equation can be easily accomplished from the minimal μ-bases.

版权说明:以下全部内容由邓建松上传于   2010年08月31日 09时41分15秒,版权归本人所有。

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