Finite element simulation of a 3-D information, despite having enormous significance and applications, could not get its due. Because of the complexity in the formulation of the basis functions, this topic is not much researched. In this paper, we propose a simple formulation of the Wachspress coordinates over a 3-D domain, where each node is considered to be of order 3(i.e. 3 planes do intersect at each node). The concept of barycentric coordinates for a polyhedron was proposed by Wachspress(1975), but being dependent on the Exterior Triple Points (ETPs), the computation of denominator function (adjoint) was quite intricate. Inspired by the simple recursive relation proposed by Dasgupta (2003), and with the help of a property which is being explored in this paper that,”for a polyhedron, wedge functions corresponding to the consecutive nodes which are linear on the common face, attain the same value at the mid point of the edge joining them”, a simple recursive relation has been derived in this paper. The entire analysis has been experimented over the convex hexahedron.
L. Powar, Pournima; Tiwari, Rishabh; and Narayan Mishra, Vishnu
"Interpolants for linear approximation over convex Polyhedron,"
Information Sciences Letters: Vol. 9
, Article 4.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol9/iss3/4