Tuning Subdivision Algorithms Using Constrained Energy Optimization

In this paper a method is presented to fair the limit surface of a subdivision algorithm around an extraordinary point. The eigenvalues and eigenvectors of the subdivision matrix determine the continuity and shape of the limit surface. The dominant, sub-dominant and subsub-dominant eigenvalues should satisfy linear and quadratic equality- and inequality-constraints to guarantee continuous normal and bounded curvature globally. The remaining eigenvalues need only satisfy linear inequality-constraints. In general, except for the dominant eigenvalue, all eigenvalues can be used to optimize the shape of the limit surface with our method.

• Type: Conference
• Year: 2007
• Where: IMAMS
• Authors: Ingo Ginkel, Georg Umlauf
• Keywords: Eigenvalues, IMAMS 2007, Limit Surface, Mathematics, Satisfy Linear