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

arXiv cs.GR details Structural Affinity, a new cage-based deformation method aimed at making control-handle edits behave more coherently. The paper frames it as an explicit regularization technique for cage-based deformation, using a two-cage setup rather than only nudging an optimizer with soft losses.

The core idea is to precompute an affinity matrix with mean-value coordinates, binding a finer inner cage to a coarser outer cage. That matrix controls how handle motion propagates to neighboring handles, which substantially reduces cage self-intersections, lowers mesh distortion, and keeps deformation behavior more regular at runtime.

For developers, the practical appeal is that it can replace or reduce hand-tuned structural loss terms in pipelines that depend on controllable 3D deformation. The authors test it across robotic morphology co-design, source-to-target neural deformation transfer, and aerodynamic wing optimization, reporting better cotangent Laplacian, cage distortion, and surface roughness metrics.

The runtime cost is described as linear overhead during deformation, so the method is positioned as a preprocessing-heavy but interactive-friendly option. That makes it especially relevant for tools, animation, and procedural modeling systems where predictable cage behavior is often more valuable than raw flexibility.