论文/arXiv 2610.23173·12 天前

Structural Affinity：一种用于连贯的基于笼的形状设计的算法

针对 CBD 优化中的网格畸变，提出 Structural Affinity 双笼耦合方法，并在三类形状设计任务中验证。

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• 本体 SDK 与控制

原文链接：Structural Affinity: An Algorithm for Coherent Cage-Based Shape Design（arXiv 2610.23173 · 发布日期：2026-10-16）

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

针对 CBD 优化中的网格畸变，提出 Structural Affinity 双笼耦合方法，并在三类形状设计任务中验证。

核心要点

• 现有 CBD 正则化多为软约束，会与任务目标竞争，未直接改变形变参数化。
• 方法用均值坐标预计算亲和矩阵，将内控制笼绑定到更粗的外控制笼。
• 亲和矩阵使控制柄位移传播到邻近控制柄，减少笼自交与网格畸变，并仅增加线性开销。
• 在协同设计、神经形变迁移和翼形优化中，多个诊断指标显示形变更规则。

验证范围与局限：验证范围为机器人控制-形态协同设计、源到目标神经形变迁移和气动翼形优化任务。

英文摘要 (Abstract)

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 overhead at deformation time. Across robotic control--morphology co-design, source-to-target neural deformation transfer, and aerodynamic wing shape optimization, Structural Affinity produces more regular deformations and substantially reduces reliance on hand-designed structural loss terms. We report consistent gains on three complementary diagnostics: the cotangent Laplacian, a proxy for surface smoothness; cage distortion, capturing whether control handles move coherently; and surface roughness, which measures undesirable oscillation in wing geometry.

作者：Aviraj Newatia, Shengan Yang, Hantao Zhong, Rika Antonova

来源

本页事实对应的公开页面，以原文为准。

1. arXiv 2610.23173：Structural Affinity: An Algorithm for Coherent Cage-Based Shape Design访问 2026-10-21