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Graph."],"published-print":{"date-parts":[[2014,11,19]]},"abstract":"<jats:p>Barycentric coordinates yield a powerful and yet simple paradigm to interpolate data values on polyhedral domains. They represent interior points of the domain as an affine combination of a set of control points, defining an interpolation scheme for any function defined on a set of control points. Numerous barycentric coordinate schemes have been proposed satisfying a large variety of properties. However, they typically define interpolation as a combination of<jats:italic>all<\/jats:italic>control points. Thus a<jats:italic>local<\/jats:italic>change in the value at a single control point will create a<jats:italic>global<\/jats:italic>change by propagation into the whole domain. In this context, we present a family of<jats:italic>local barycentric coordinates<\/jats:italic>(LBC), which select for each interior point a small set of control points and satisfy common requirements on barycentric coordinates, such as linearity, non-negativity, and smoothness. LBC are achieved through a convex optimization based on total variation, and provide a compact representation that reduces memory footprint and allows for fast deformations. 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