Using Local Optimization in Surface

Local optimization is used to set the free parameters in a triangular surface tting scheme resulting in surfaces with better shape While some of the free parameters can be set to match curvature information other free parameters are independent of this information Introduction A large number of local parametric triangular surface schemes have been developed over the past fteen years see MLL Man for a survey of such schemes These schemes are local in that changes to part of the data only a ect portions of the surface near the changed data Surprisingly all of these schemes exhibit similar shape defects On closer inspection it is seen that these schemes all have a large number of free pa rameters that are set using simple heuristics By manually adjusting these parameters one can improve the shape of the surfaces Man One way to improve automatically the shape of the constructed surfaces is to use global optimization Here global optimization refers to using all the data to construct any portion of the surface Several authors have used such schemes to improve the shape of the constructed surfaces but usually at a high computational cost due to the global nature of the solution CG MS In this paper I will investigate using local optimization to set the free parameters in a local triangular split domain polynomial surface interpolation scheme More precisely given a triangle of data this scheme constructs three triangular parametric polynomial patches each of which interpolates two of the positions and normals at the three vertices Further the patches meet each other with G continuity and if used to ll a triangular polyhedron the resulting surface will also be G Local optimization is Local optimization in surface tting