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Higher Order Barycentric Coordinates
Author(s) -
Langer Torsten,
Seidel HansPeter
Publication year - 2008
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.1467-8659.2008.01143.x
Subject(s) - barycentric coordinate system , bipolar coordinates , generalized coordinates , orthogonal coordinates , log polar coordinates , cartesian coordinate system , interpolation (computer graphics) , mathematics , computer science , action angle coordinates , frame (networking) , mathematical analysis , geometry , telecommunications
In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We introduce a method to modify existing barycentric coordinates to higher order barycentric coordinates and demonstrate, using higher order mean value coordinates, that our method, although conceptually simple and easy to implement, can be used to give easy and intuitive control at interactive frame rates over local space deformations such as rotations.