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# Geometry, Imaging and Computing

## Volume 2 (2015)

### Number 2

### Hooke’s Optimization for 3D triangular mesh

Pages: 109 – 131

DOI: http://dx.doi.org/10.4310/GIC.2015.v2.n2.a2

#### Authors

#### Abstract

A new framework for mesh optimization, the Filtered Hooke’s Optimization, is proposed. With the notion of the elasticity theory, the Hooke’s Optimization is developed by modifying the Hooke’s law, in which an elastic force is simulated on the edges of a mesh so that adjacent vertices are either attracted to each other or repelled from each other, so as to regularize the mesh in terms of triangulation. A normal torque force is acted on vertices to guaranteed smoothness of the surface. In addition, a filtering scheme, called the Newtonian Filtering, is proposed as a supplementary tool for the proposed Hooke’s Optimization to preserve the geometry of the mesh. Numerical simulations on meshes with different geometry indicate an impressive performance of our proposed framework to significantly improves the mesh triangulation without noteworthy distortions of the mesh geometry.