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Local barycentric coordinates

Zhang, Juyong, Deng, Bailin ORCID:, Liu, Zishun, Patanè, Giuseppe, Bouaziz, Sofien, Hormann, Kai and Liu, Ligang 2014. Local barycentric coordinates. ACM Transactions on Graphics 33 (6) , 188. 10.1145/2661229.2661255

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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 all control points. Thus a local change in the value at a single control point will create a global change by propagation into the whole domain. In this context, we present a family of local barycentric coordinates (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. Our experiments show that LBC provide more local and finer control on shape deformation than previous approaches, and lead to more intuitive deformation results.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords: barycentric coordinates, total variation, locality, smoothness, shape deformation, image warping.
Publisher: Association for Computing Machinery (ACM)
ISSN: 0730-0301
Date of First Compliant Deposit: 2 May 2017
Last Modified: 24 Apr 2024 08:14

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