Weighted progressive interpolation of Loop subdivision surfaces

Abstract

This paper proposes a weighted progressive method for constructing a Loop subdivision surface interpolating a given mesh. The convergent rate of the weighted progressive interpolation can be controlled by adjusting the weight of the iteration. For different weights in the available range, the limit meshes are the same as that of the reverse solution by directly solving a linear system. The theoretical value for the optimal weight is given based on the smallest eigenvalue of the collocation matrix. An appropriate value of the weight is assigned based on both theoretical analysis and numerical experiments.