Moving Planes and Singular Points of Rational Parametric Surfaces
Provides theoretical insights for algebraic geometry and geometric modeling, but is incremental in nature.
The paper establishes a relationship between moving planes and singular points of rational parametric surfaces, deriving an equivalent definition for the order of singular points and linking it to the μ-basis.
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 $μ$-basis and the order of a singular point is also discussed.