Construction of Manifolds via Compatible Sparse Representations

Manifold is an important technique to model geometric objects with arbitrary topology. In this article, we propose a novel approach for constructing manifolds from discrete meshes based on sparse optimization. The local geometry for each chart is sparsely represented by a set of redundant atom functions, which have the flexibility to represent various geometries with varying smoothness. A global optimization is then proposed to guarantee compatible sparse representations in the overlapping regions of different charts. Our method can construct manifolds of varying smoothness including sharp features (creases, darts, or cusps). As an application, we can easily construct a skinning manifold surface from a given curve network. Examples show that our approach has much flexibility to generate manifold surfaces with good quality.