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 o...

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Bibliographic Details
Published in:Computer graphics forum Vol. 29; no. 5; pp. 1517 - 1524
Main Authors: Manson, Josiah, Schaefer, Scott
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.07.2010
Subjects:
Boundaries
Computer based modeling
Computer graphics
Derivatives
Exact solutions
I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Boundary representations
Image coding
Least squares method
Mathematical analysis
Mathematical models
Polygons
Studies
Two dimensional
ISSN:0167-7055, 1467-8659
Online Access:Get full text
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Summary: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.
Bibliography:istex:AFE9380D382146B82C8F03C1AA1EB5533D350E4E
ark:/67375/WNG-FQN9JKD9-C
ArticleID:CGF1760
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2010.01760.x