System and method for generating smooth low degree polynomial spline surfaces over irregular meshes

摘要

A system and method for modeling smooth free-form shapes using B-splines over irregular meshes, in a simple and efficient manner, to generate a display of aesthetically pleasing shapes is disclosed. A low degree parametric polynomial representation is generated. As a result, techniques for surface-surface or ray-surface intersection are faster and more robust than possible with existing techniques. In accordance with the present invention, an input mesh M0 is initially simplified by isolating irregularities and constraining geometry. First, the input mesh M0 is subjected to general refinement, whereby a new mesh M1 is constructed, which in turn is subjected to constrained refinement, whereby another new mesh M2 is constructed. After the general and constrained refinement steps, the mesh M2 is broken up into a set of "quad-nets" corresponding to each of its vertices. Finally, these quad nets are used as local geometry, over which, 4 cubic B+E,acu e+EE zier triangles are constructed.