Computer Aided Geometric Design
An intuitive framework for real-time freeform modeling
ACM SIGGRAPH 2004 Papers
As-rigid-as-possible shape manipulation
ACM SIGGRAPH 2005 Papers
Image deformation using moving least squares
ACM SIGGRAPH 2006 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM SIGGRAPH 2008 papers
Transfinite mean value interpolation
Computer Aided Geometric Design
Variational harmonic maps for space deformation
ACM SIGGRAPH 2009 papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Biharmonic diffusion curve images from boundary elements
ACM Transactions on Graphics (TOG)
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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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. © 2012 Wiley Periodicals, Inc.