Abstract: Abstarct Based on the criterion of Extending-Delaunay triangulation for the arbitrary plane domain with multi-island，a general triangulation algorithm for Trimmed surface is proposed．The triangulation is performed completely in parametric space，so that the procedure run fast and reliable．The algorithm can prevent cracks between patches and surfaces easily．This algorithm is successfully applied to the HUSTCADM for the shading and manufacturing of Trimmed surface．