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Moving Least Squares Coordinates
Author(s) -
Manson Josiah,
Schaefer Scott
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2010.01760.x
Subject(s) - barycentric coordinate system , polygon (computer graphics) , log polar coordinates , bipolar coordinates , boundary (topology) , orthogonal coordinates , degree (music) , generalized coordinates , set (abstract data type) , mathematics , parabolic coordinates , computer science , geometry , mathematical analysis , telecommunications , physics , frame (networking) , acoustics , programming language
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.