# title
A Family of Barycentric Coordinates for Co-Dimension 1 Manifolds with Simplicial Facets

# abstract
2019 The Author(s) Computer Graphics Forum  2019 The Eurographics Association and John Wiley  &  Sons Ltd. Published by John Wiley  &  Sons Ltd. We construct a family of barycentric coordinates for 2D shapes including non-convex shapes, shapes with boundaries, and skeletons. Furthermore, we extend these coordinates to 3D and arbitrary dimension. Our approach modifies the construction of the Floater-Hormann-Ks family of barycentric coordinates for 2D convex shapes. We show why such coordinates are restricted to convex shapes and show how to modify these coordinates to extend to discrete manifolds of co-dimension 1 whose boundaries are composed of simplicial facets. Our coordinates are well-defined everywhere (no poles) and easy to evaluate. While our construction is widely applicable to many domains, we show several examples related to image and mesh deformation.

# keywords[]
Center Dot Computing Methodologies -> Shape Modeling