Precise evaluation of uniform Doo-Sabin surfaces

Using eigenanalysis of uniform Doo-Sabin subdivision surfaces, parameterization approaches for two types of Doo-Sabin subdivision surfaces are developed, and evaluation methods for values and derivatives of Doo-Sabin surfaces at arbitrary parameters are presented by means of non-iterative approaches. Generalized basis functions for Doo-Sabin surfaces are also derived. Thus, the prejudice is disproved further that subdivision surfaces cannot be evaluated precisely.