Shape approximation via sparse optimization

A novel sparse optimization based shape approximation method to represent a 3D model using planar pieces was introduced, which enables a designer specified reasonable and fixed number of planes to be obtained. The method first gives a L₀ minimization algorithm to optimize the face normal of the input model and then updates the vertex position based on filtered normal information. Next, a simple clustering method was proposed to obtain a clustering model. To this end, a boundary vertex gradient minimization algorithm was developed for solving a global energy function to represent the input model. A large number of experiments show the validity of the model and algorithm as well as the stability of the algorithm when solving mesh simplification problems in dynamic environments.