Medial axis construction in three dimensions and its application to mesh generation

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 in direct construction is based on the Delaunay-triangulation of a set of samp le points on the bounding surface. The point set is refined automatically s o as to capture the correct topology of the medial axis. The computed media l axis (or better medial surface) is then used for hex-dominant mesh genera tion. Quad-dominant meshes are generated on the medial subfaces first and e xtruded to the boundary of the body at both sides. The resulting single cel l layer is subdivided in direction normal to the boundary, yielding columns of hexahedral and three-sided prismatic cells. The resulting volume mesh i s orthogonal at the boundary and 'semi-structured' between boundary and med ial surface. Mixed cell types (tets, pyramids, degenerate hexahedra) may re sult along the medial surface. An advancing front algorithm (paving) is use d for meshing the subfaces of the medial surface. Development of the mesh g enerator has not been fully completed with respect to degenerate parts of t he medial axis. First medium-complexity bodies have been meshed, however, s howing moderate meshing times.