Exact Evaluation of NURSS at Arbitrary Parameter Values

Convergence and continuity analyses as well as exact evaluation of non-uniform subdivision surfaces at arbitrary parameter values have been very difficult because the subdivision matrix varies at each iteration step, unlike uniform subdivision surfaces. Using eigenanalysis and convergence properties of non-uniform subdivision surfaces that have been given by authors recently, a parameterization approach for non-uniform subdivision surfaces is developed, and an evaluation method for values and derivatives of non-uniform Catmull-Clark surfaces at arbitrary parameters is presented by means of a non-iterative approach. Generalized basis functions for non-uniform Catmull-Clark surfaces are derived. Thus we further disprove the prejudice that non-uniform subdivision surfaces cannot be evaluated exactly.