A fast mesh parameterization algorithm based on 4-point interpolatory subdivision

In this paper we present a novel fast mesh parameterization algorithm based on subdivision scheme. First, an algorithm of approximating a given triangular mesh by the 4-point interpolatory subdivision is proposed, then a mesh parameterization method is developed based on the subdivision surface approximation algorithm. The novel mesh parameterization method is a generalization of the chordal parameterization to surface case, and it is more computationally efficient than previous methods because it obviates any computation of linear system of equations. Some numerical experiments show the efficiency of the novel algorithm.