An Entropy Satisfying Boundary Layer Surface Mesh Generation

Abstract

A method is presented to generate surface boundary layers. The novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front. In particular, concave situations are enforced to respect the entropy satisfying solution. Local solutions of the offset of edges in the planes and triangles in the three dimensional space are also given, showing the relationship between normal computation, distance extrusion, and the generalized Voronoi diagram. The boundary layer mesh generation is cast as a weak solution of the Eikonal equation computed locally, layer by layer, to mimic the hyperbolic character of the Eikonal equation, augmented by a possibly nonbijective mapping between layers. This provides a theoretical framework to rely on for practical answers such as configurations where the adjacent topologies to a boundary layer may be curved, or at least not aligned with the offset direction, or if the boundary layer mesh must be generated as a mapping between the first and last layer or as a composition of mappings for each layer. Numerous examples illustrate the potential of the proposed solution.