ABSTRACT
The Sliver Theorem states that, given a Delaunay mesh covering R3 whose tetrahedra have good radius-edge ratios, we can eliminate the worst slivers by assigning appropriate weights to the vertices. There are two hurdles in applying sliver exudation to finite domains. The first is domain conformity: if we increase the weight of a vertex to remove a sliver, some nearby subsegment or subpolygon may be removed as well. Loosely speaking, strongly weighted vertices can punch holes in the domain boundaries. The second is that a finite domain undercuts one of the premises of sliver exudation: that a sliver cannot be weighted Delaunay if its orthoball grows too large. If a sliver rests against the boundary of the domain’s convex hull, its orthoball can grow arbitrarily large without ever enclosing a vertex.
