Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces
Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces
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DOI：
10.1016/j.jsc.2011.12.029
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发表时间：
2012-06
期刊：
影响因子：
--
通讯作者：
Xuhui Wang;Falai Chen
中科院分区：
文献类型：
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作者：
Xuhui Wang;Falai Chen
Steiner 曲面是没有基点的二次参数化曲面。为了使Steiner曲面更适用于计算机辅助几何设计和几何建模，本文讨论了利用移动曲面技术对Steiner曲面进行隐式化、参数化和奇点计算。对于隐式化，我们证明参数变量中存在两个总度数为一的线性独立移动平面。由此可见，Steiner 曲面的隐式方程可以表示为 3×3 行列式。斯坦纳表面的反演公式和奇点也可以很容易地从移动平面计算出来。对于参数化，我们首先以隐式形式计算斯坦纳曲面的奇点。基于奇点，我们可以找到一些特殊的移动平面，从中可以检索斯坦纳曲面的二次参数化。
A Steiner surface is a quadratically parameterizable surface without base points. To make Steiner surfaces more applicable in Computer Aided Geometric Design and Geometric Modeling, this paper discusses implicitization, parameterization and singularity computation of Steiner surfaces using the moving surface technique. For implicitization, we prove that there exist two linearly independent moving planes with total degree one in the parametric variables. From this fact, the implicit equation of a Steiner surface can be expressed as a 3×3 determinant. The inversion formula and singularities for the Steiner surface can also be easily computed from the moving planes. For parameterization, we first compute the singularities of a Steiner surface in implicit form. Based on the singularities, we can find some special moving planes, from which a quadratic parameterization of the Steiner surface can be retrieved.