Meshing volumes with curved boundaries

Abstract This paper introduces a three-dimensional mesh generation algorithm for domains whose boundaries are curved surfaces, possibly with sharp features. The algorithm combines a Delaunay-based surface mesher with a Ruppert-like volume mesher, resulting in a greedy scheme to sample the interior and the boundary of the domain simultaneously. The algorithm constructs provably-good meshes, it gives control on the size of the mesh elements through a user-dened sizing eld, and it guarantees the accuracy of the approximation of the domain boundary. A notable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line segment intersects the boundary. This makes the algorithm generic enough to be applied to domains with a wide variety of boundary types, such as implicit surfaces, polyhedra, level-sets in 3D gray-scaled images, or point-set surfaces. Key words Mesh generation, reconstruction,...

• Type: Journal
• Year: 2010
• Where: EWC
• Authors: Steve Oudot, Laurent Rineau, Mariette Yvinec
• Keywords: Algorithm, Domain Boundary, EWC 2010, Mesh Generation Algorithm