Barycentric coordinates yield a powerful and yet simple paradigmudto interpolate data values on polyhedral domains. They representudinterior points of the domain as an affine combination of a set ofudcontrol points, defining an interpolation scheme for any functionuddefined on a set of control points. Numerous barycentric coordinateudschemes have been proposed satisfying a large variety of properties.udHowever, they typically define interpolation as a combination ofudalludcontrol points. Thus audlocaludchange in the value at a single controludpoint will create audglobaludchange by propagation into the wholeuddomain. In this context, we present a family ofudlocal barycentricudcoordinatesud(LBC), which select for each interior point a small setudof control points and satisfy common requirements on barycentricudcoordinates, such as linearity, non-negativity, and smoothness. LBCudare achieved through a convex optimization based on total variation,udand provide a compact representation that reduces memory footprintudand allows for fast deformations. Our experiments show that LBCudprovide more local and finer control on shape deformation thanudprevious approaches, and lead to more intuitive deformation results.
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