Tiling space and slabs with acute tetrahedra

We show it is possible to tile three-dimensional space using only tetrahedra with acute dihedral angles. We present several constructions to achieve this, including one in which all dihedral angles are less than 74.21 , and another which tiles a slab in space. 1 Problem definition Triangulations of two and three-dimensional domains find numerous applications in scientific computing, computer graphics, solid modeling and medical imaging. Most of these applications impose a quality constraint on the elements of the triangulation. Among the most popular quality criteria for elements [5] are the aspect ratio (circumradius over inradius), the minimum dihedral angle, and the radius-edge ratio (circumradius over shortest edge). However, many other quality criteria have been considered, including maximum dihedral angle. Bern et al. for instance, studied nonobtuse triangulations [3, 6], where domains are meshed with simplices having no obtuse angles. In this paper, we consider a slightly stron...

• Type: Journal
• Year: 2004
• Where: COMGEO
• Authors: David Eppstein, John M. Sullivan, Alper Üngör
• Keywords: Acute Dihedral Angles, Applied Computing, COMGEO 2004, Dihedral Angle, Minimum Dihedral Angle