Optimization of mesh quality with preserving surface characteristics and features

In this paper, we introduce a new approach to surface mesh improvement problem. In contrast to previous methods we do not tend to preserve new mesh vertices on the original discrete surface. Instead our technique keeps mesh nodes very close to a smooth or piecewise-smooth surface approximated by an initial mesh. As a result, the algorithm is able to improve mesh quality while preserving essential surface characteristics and features. Proposed approach can be applied iteratively not only to polygonal meshes but also to 2D and 3D curves that allows to treat sharp edges and surface boundaries. We demonstrate Effectiveness of our method using various triangular and quadrilateral meshes.