An acyclicity theorem for cell complexes ind dimension

LetC be a cell complex ind-dimensional Euclidean space whose faces are obtained by orthogonal projection of the faces of a convex polytope ind+ 1 dimensions. For example, the Delaunay triangulation of a finite point set is such a cell complex. This paper shows that the in_front/behind relation defined for the faces ofC with respect to any fixed viewpointx is acyclic. This result has applications to hidden line/surface removal and other problems in computational geometry.