  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 $\mu$-basis
and the order of a singular point is also discussed.
