Researchers in the Graphics and Geometric Computing Laboratory recently have made significant achievements on digital manifold structure construction. The work has been published in the top journal in computer graphics, ACM Transactions on Graphics, and will be presented at the 43rd International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 2016). The homepage of the project is as follows:

http://staff.ustc.edu.cn/~lgliu/Projects/2016_ToG_SparseManifold/default.html

Manifold is an important technique to model geometric objects with arbitrary topology. We propose a new approach for constructing manifolds with sparse optimization. The local geometry for each chart is sparsely represented by a set of atom functions, consisting of shape functions and polynomials. A global optimization is proposed to guarantee compatible sparse representation in the overlapping regions of different charts. Our method can construct manifolds of varying smoothness including sharp features. Examples have shown that our approach has much flexibility to generate manifold surface with good quality. This work is the first to successfully introduce sparse representation in manifold surface construction.

The first author, WANG Ruimin, a PhD student, and the corresponding author, Prof. LIU Ligang, are both from the School of Mathematical Sciences

This work is supported by the National Natural Science Fund for Excellent Young Scholars of China, the Young Scientists Fund of the National Natural Science Foundation of China, and the One Hundred Talent Project of the Chinese Academy of Sciences.

(School of Mathematical Sciences)