Reproduce “Variational Barycentric Coordinates” on OpenResearch
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About this paper
Ana Dodik, Oded Stein, Vincent Sitzmann, Justin Solomon
The authors introduce VBC, a method for tuning valid cage coordinates so detailed meshes follow moving cages. A neural field blends triangle-based coordinate systems, and users optimize the resulting weights for a deformation. In one soft-body simulation fit, joint cage-and-weight optimization lowers MAE from 0.0088 to 0.0029, but this result is limited to that tested setup and practical pruning restricts choices.
Key insights
- The feasible set of barycentric coordinates at any point is a convex polytope whose extreme points are simplex-coordinate vectors, yielding a universality characterization for the unpruned representation.
- Constraint preservation is achieved through the parameterization itself rather than penalty terms, while pruning interior-containing simplices enforces the Lagrange property at cage vertices.
- Different objectives produce distinct behavior: Dirichlet coordinates are smoother and less local, TV coordinates are more localized, and ARAP refinement favors more rigid-looking deformations.
Summary by alphaXiv.
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