Publications

Variational Green and Biharmonic Coordinates for 2D Polynomial Cages

SIGGRAPH 2025

Publication date: July 27, 2025

Élie Michel, Alec Jacobson, Siddhartha Chaudhuri, Jean Thiery

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We present closed-form expressions for Green and biharmonic coordinates with respect to polynomial curved 2D cages, enabling reliable cage-based image deformation both to and from a curved cage. We further provide closed-form expressions for first- and second-order derivatives of these coordinates with respect to the encoded position. This enables the use of variational solvers for interacting with the 2D shape at arbitrary points while keeping the fast decoding strength of cage-based deformation, which we illustrate for a variety of elastic deformation energies.

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Research Area:  Adobe Research iconGraphics (2D & 3D)