Rational bases for convex polyhedra

AbstractIn Wachspress (1975) [2] rational bases were constructed for convex polyhedra whose vertices were all of order three. The restriction to order three was first removed by Warren (1996) [3] and his analysis was refined subsequently by Warren and Schaefer (2004) [4]. A new algorithm (GADJ) for finding the denominator polynomial common to all the basis functions was exposed in Dasgupta and Wachspress (2007) [1] for convex polyhedra with all vertices of order three. This algorithm is applied here for generating bases for general convex polyhedra