Anisotropic Green Coordinates

Anisotropic Green Coordinates (AGC) add a directional twist to classic cage-based deformation. Instead of treating space as uniformly responsive, the method uses an anisotropic Laplace equation, letting deformation strength vary with the orientation of the cage and the chosen anisotropy matrix.

For game teams, the practical appeal is finer control over shape editing and rig-adjacent deformation workflows. The formulation works in both 2D and 3D, preserves basic properties like linear reproduction and translation invariance, and has closed-form expressions in both cases, which makes it easier to reason about and potentially integrate into tooling or offline deformation pipelines.

The authors also derive gradients and Hessians, then plug AGC into a local-global optimization setup for variational deformation and ARAP-style shape manipulation. That means the technique is not just a static coordinate system; it can support iterative editing workflows where artists want flexible, controllable deformations without losing structural stability.

A notable takeaway is that anisotropy can be used deliberately as a design knob. The deformation effect becomes stronger when a cage face normal aligns with the larger-eigenvalue direction of the anisotropy matrix, which could matter for anyone building authoring tools, mesh editing systems, or procedural deformation features that need more expressive, targeted control.