Simplification of surface mesh using Hausdorff envelope

This paper presents a new method for surface mesh simplification. Given an initial surface mesh (denoted as reference mesh), the goal is to reduce the number of mesh elements while preserving the geometric approximation as well as the shape quality of the resulting mesh. Two tolerance areas with respect to the reference mesh have been introduced to preserve the geometry of the surface. The reference mesh is then simplified and optimized (in terms of shape quality) so that the resulting mesh belongs to these tolerance areas. Several examples of surface meshes are provided regarding different application areas in order to assess the efficiency of the simplification method.