A direct approach for Loop subdivision surface offset approximation

A novel and direct approach for Loop subdivision surface offset approximation is proposed. Instead of solving a linear equation system previously, the main idea is to convert the Loop subdivision surface offset approximation into updating the vertices of original triangular mesh iteratively by using progressive interpolation (PI) method. Generated smooth subdivision surfaces interpolate the original mesh control points and preserve the sharp features. Then triangular mesh offset method can be utilized to obtain Loop subdivision surface offset approximation. The proposed method has the advantages of both local and global methods. The meshes considered here can be either closed or open. Some typical examples are illustrated to demonstrate the efficiency of the proposed approach in the end.