Local barycentric coordinates

Zhang, Juyong; Deng, Bailin; Liu, Zishun; Patanè, Giuseppe; Bouaziz, Sofien; Hormann, Kai; Liu, Ligang

Abstract

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.

Citation

Zhang, J., Deng, B., Liu, Z., Patanè, G., Bouaziz, S., Hormann, K., & Liu, L. (2014). Local barycentric coordinates. ACM Transactions on Graphics, 33(6), 1-12. https://doi.org/10.1145/2661229.2661255

• Journal Article Type: Conference Paper
• Acceptance Date: Sep 18, 2014
• Publication Date: Nov 19, 2014
• Deposit Date: Apr 20, 2016
• Publicly Available Date: Apr 20, 2016
• Journal: ACM transactions on graphics
• Print ISSN: 0730-0301
• Electronic ISSN: 1557-7368
• Publisher: Association for Computing Machinery (ACM)
• Peer Reviewed: Peer Reviewed
• Volume: 33
• Issue: 6
• Article Number: ARTN 188
• Pages: 1-12
• DOI: https://doi.org/10.1145/2661229.2661255
• Keywords: Barycentric coordinates; Total variation; Locality; Smoothness; Shape deformation; Image warping
• Public URL: https://hull-repository.worktribe.com/output/436599
• Publisher URL: http://dl.acm.org/citation.cfm?doid=2661229.2661255
• Additional Information: © ACM, 2014. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in PUBLICATION, {VOL33, ISS6, November 2014} http://doi.acm.org/10.1145/2661229.2661255