On Wachspress pentagonal patches

On Wachspress pentagonal patches

Wachspress quadrilateral patches have been recently studied from the point of view of applications to surface modelling in CAGD [1], [3], [4]. Some more applications for defining barycentric coordinates for arbitrary polygons have also been presented in [5] [9]. The purpose of the present paper is to introduce non-negative Wachspress rational basis functions for surface modelling on pentagonal ...

Gradient Bounds for Wachspress Coordinates on Polytopes

We derive upper and lower bounds on the gradients of Wachspress coordinates defined over any simple convex d-dimensional polytope P . The bounds are in terms of a single geometric quantity h∗, which denotes the minimum distance between a vertex of P and any hyperplane containing a non-incident face. We prove that the upper bound is sharp for d = 2 and analyze the bounds in the special cases of ...

Wachspress Elements for Topology Optimization

Traditionally, standard Lagrangian-type finite elements, such as linear quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these conventional elements exhibit the well-known "checkerboard" pathology in the iterative solution of topology optimization problems. A feasible alternative to eliminate such long-standing prob...

Discretizing Wachspress kernels is safe

Barycentric coordinates were introduced by Möbius in 1827 as an alternative to Cartesian coordinates. They describe points relative to the vertices of a simplex and are commonly used to express the linear interpolant of data given at these vertices. Generalized barycentric coordinates and kernels extend this idea from simplices to polyhedra and smooth domains. In this paper, we focus on Wachspr...

On Some Hexagonal and Pentagonal Nets