Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation

A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.