Moving Least Squares Coordinates

A family of barycentric coordinates that are defined for both closed and non-closed polygons, have polynomial precision, and can control boundary derivatives.

download pdf download preprint


  author  = {Josiah Manson and
             Scott Schaefer},
  title   = {Moving Least Squares Coordinates},
  journal = {Computer Graphics Forum (Proceedings of the Symposium on 
             Geometry Processing)},
  volume  = {29},
  number  = {5},
  year    = {2010},
  pages   = {1517--1524},


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.


download pptx presentation_SGP2010.pptx

This is the set of slides that I used in my presentation of the paper at SGP 2010.

download zip Bary2.zip

An implementation of the MLS coordinates with source code.


The images, executables, and code supplied are from the web page http://josiahmanson.com. These materials are free to use for non-commercial purposes. Any works that use materials from this web page should acknowledge Josiah Manson and the paper Moving Least Squares Coordinates. For commercial use, please contact Josiah Manson (josiahmanson@gmail.com).