Medial Axis Construction in Three Dimensions and its Application to Mesh Generation

Abstract

An algorithm for the construction of the medial axis of a three-dimensional body given by a triangulation of its bounding surface is described. The indirect construction is based on the Delaunay-triangulation of a set of sample points on the bounding surface. The point set is refined automatically so as to capture the correct topology of the medial axis. The computed medial axis (or better medial surface) is then used for hex-dominant mesh generation. Quad-dominant meshes are generated on the medial subfaces first and extruded to the boundary of the body at both sides. The resulting single cell layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided prismatic cells. The resulting volume mesh is orthogonal at the boundary and ‘semi-structured’ between boundary and medial surface. Mixed cell types (tets, pyramids, degenerate hexahedra) may result along the medial surface. An advancing front algorithm (paving) is used for meshing the subfaces of the medial surface. Development of the mesh generator has not been fully completed with respect to degenerate parts of the medial axis. First medium-complexity bodies have been meshed, however, showing moderate meshing times.