An algorithm for trimming of parametric surface based on operation of two dimensional loops

Since a parametric surface is defined by a mapping from 2 D parametric space to 3 D space ,trimming of a parametric surface is equivalent to changing only the valid parameter region of the surface with the same mapping.By presenting a strict and comprehensible definition of union,difference and intersection of two intersecting loops in the parametric region of a parametric surface, and designing a set of stable and robust corresponding algorithm, the 3 D problem is converted into 2 D one, hence perfectly realize the trimming of parametric surface.