Moving Least Squares Coordinates

We propose a new family of barycentric coordinates that have closed-forms for arbitrary 2D polygons. These coordinates are easy to compute and have linear precision even for open polygons. Not only do these coordinates have linear precision, but we can create coordinates that reproduce polynomials of a set degree m as long as degree m polynomials are specified along the boundary of the polygon. We also show how to extend these coordinates to interpolate derivatives specified on the boundary. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling--Boundary representations

• Type: Journal
• Year: 2010
• Where: CGF
• Authors: Josiah Manson, Scott Schaefer
• Keywords: Arbitrary 2D Polygons, Barycentric Coordinates, CGF 2010, Open Polygons