Polynomial-Based Non-Uniform Ternary Interpolation Surface Subdivision on Quadrilateral Mesh

For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence continuity are demonstrated. Following subdivision, surface on regular quadrilateral meshes proposed by applying the tensor product method. Analyses were conducted updating rules of parameters, proving that limit continuous. In this paper, we present novel method to generate new virtual edge points face extraordinary mesh. We also provide numerical examples assess validity various methods.