Sciweavers

COMGEO
2004
ACM

Tiling space and slabs with acute tetrahedra

13 years 11 months ago
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...
David Eppstein, John M. Sullivan, Alper Üng&o
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMGEO
Authors David Eppstein, John M. Sullivan, Alper Üngör
Comments (0)