Adaptive fitting algorithm of progressive interpolation for Loop subdivision surface

Subdivision surface and data fitting have been applied in data compression and data fusion a lot recently. Moreover, subdivision schemes have been successfully combined into multi-resolution analysis and wavelet analysis. This makes subdivision surfaces attract more and more attentions in the field of geometry compression. Progressive interpolation subdivision surfaces generated by approximating schemes were presented recently. When the number of original vertices becomes huge, the convergence speed becomes slow and computation complexity becomes huge. In order to solve these problems, an adaptive progressive interpolation subdivision scheme is presented in this article. The vertices of control mesh are classified into two classes: active vertices and fixed ones. When precision is given, the two classes of vertices are changed dynamically according to the result of each iteration. Only the active vertices are adjusted, thus the class of active vertices keeps running down while the fixed ones keep rising, which saves computation greatly. Furthermore, weights are assigned to these vertices to accelerate convergence speed. Theoretical analysis and numerical examples are also given to illustrate the correctness and effectiveness of the method.

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.