Experimental lower bounds for three simplex chirality measures in low dimension.
David Avis · Canadian Conference on Computational Geometry · 2004
molecules may be modeled as simplicial complexes in , with an overall chirality measure formed by considering the chirality measures of the constituent -simplices (tetrahedra). Discussions at the 2001 Bellairs Winter Workshop on Computational Geometry led to the proposal of three candidate chirality measures for tetrahedra—the intersection, (convex hull of) union, and inflation measures—though the question of which is superior was not resolved. A definitio n of each of these measures follows (see also Fig. 2). For a polytope , let denote the content (“hypervolume”) of and let denote the convex hull of . For a -simplex , and a given chirality measure , let be a rigid motion that maximizes . The intersection measure for is defined as