B-splines Based Subdivision Surfaces Parameterization

The quadrilateral subdivision surface parameterization algorithm is widely used in the gaming and film industry. However, current algorithms do not effectively balance the speed and quality of parameterization. To tackle this problem, a B-spline-based subdivision surface parameterization algorithm is proposed. In this algorithm, the input subdivision surface is first transformed into a piecewise B-spline surface. Then, the spline surface is parameterized section by section using optimized geometric distortion. In cases where the subdivision surface has numerous subdivisions, the algorithm utilizes patch concatenation to parameterize the merged surface. Unlike grid-based parameterization methods that are defined in the piecewise linear space, the proposed method reduces the number of control grids used as optimization variables. This approach results in a parameterization mapping defined in the spline space, ensuring C² continuity within each patch. Compared to existing methods, the algorithm demonstrates faster convergence, lower overall distortion in parameterization results, effective reduction of seam count through merging strategies, and improved quality of the parameterization outcomes.