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Biharmonic Coordinates
Author(s) -
Weber Ofir,
Poranne Roi,
Gotsman Craig
Publication year - 2012
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.1467-8659.2012.03130.x
Subject(s) - biharmonic equation , barycentric coordinate system , bipolar coordinates , log polar coordinates , orthogonal coordinates , generalized coordinates , action angle coordinates , computer science , mathematics , domain (mathematical analysis) , computation , mathematical analysis , interpolation (computer graphics) , algorithm , boundary value problem , geometry , computer vision , motion (physics)
Barycentric coordinates are an established mathematical tool in computer graphics and geometry processing, providing a convenient way of interpolating scalar or vector data from the boundary of a planar domain to its interior. Many different recipes for barycentric coordinates exist, some offering the convenience of a closed‐form expression, some providing other desirable properties at the expense of longer computation times. For example, harmonic coordinates, which are solutions to the Laplace equation, provide a long list of desirable properties (making them suitable for a wide range of applications), but lack a closed‐form expression. We derive a new type of barycentric coordinates based on solutions to the biharmonic equation. These coordinates can be considered a natural generalization of harmonic coordinates, with the additional ability to interpolate boundary derivative data. We provide an efficient and accurate way to numerically compute the biharmonic coordinates and demonstrate their advantages over existing schemes. We show that biharmonic coordinates are especially appealing for (but not limited to) 2D shape and image deformation and have clear advantages over existing deformation methods.