English

Moving Planes and Singular Points of Rational Parametric Surfaces

Numerical Analysis 2010-01-14 v2 Commutative Algebra

Abstract

In this paper we discuss the relationship between the moving planes of a rational parametric surface and the singular points on it. Firstly, the intersection multiplicity of several planar curves is introduced. Then we derive an equivalent definition for the order of a singular point on a rational parametric surface. Based on the new definition of singularity orders, we derive the relationship between the moving planes of a rational surface and the order of singular points. Especially, the relationship between the μ\mu-basis and the order of a singular point is also discussed.

Keywords

Cite

@article{arxiv.0909.2810,
  title  = {Moving Planes and Singular Points of Rational Parametric Surfaces},
  author = {Falai Chen and Xuhui Wang},
  journal= {arXiv preprint arXiv:0909.2810},
  year   = {2010}
}

Comments

13 pages

R2 v1 2026-06-21T13:46:41.719Z