Structural Affinity: An Algorithm for Coherent Cage-Based Shape Design

Aviraj Newatia, Shengan Yang, Hantao Zhong, Rika Antonova

Cage-based deformation (CBD) parametrises 3D geometry through a small set of control handles, effectively enabling a variety of tasks from animation and interactive modelling to tool-based co-design, neural deformation transfer, and aerodynamic shape optimization. Many optimization approaches relying on CBD employ regularisation strategies to reduce the distortion of the deformed mesh by encouraging smooth, regular cage deformations. These techniques offer soft guidance to an optimization algorithm towards desirable deformations, but compete with the task objective rather than changing the deformation parameterization itself. In this work we introduce Structural Affinity for CBD, an explicit regularisation method which enables smooth deformations through control cages by exploiting a two-cage structure to couple cage-handle motion directly. Structural Affinity precomputes an affinity matrix using mean-value coordinates, binding the inner control-cage to a coarser outer-cage. This matrix defines how much a cage handle displacement propagates to neighbouring handles which substantially decreases and often eliminates cage self-intersections, reduces mesh distortion, and adds linear…