发表机构
Technische Universität Berlin（柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究推导了缠绕数的梯度，实现了表面表示到体素表示的可微分转换，可高效解决网格相交、可制造性形状设计及三维空间平铺等优化问题。
AI 中文摘要
不同的形状表示方式适用于不同的计算任务。表面表示（尤其是网格）常用于建模，而体积表示则适用于空间查询，如相交检测或包含性判断。基于体积属性通过梯度下降优化表面表示时，需要体积相对于其边界表面的导数。我们推导了缠绕数的该梯度，并证明其可针对规则网格（体素表示）上采样的体积值以及基于顶点集（三角形网格）的表面参数高效计算。这为多种优化问题提供了高效解决方案。我们通过三个示例展示该方法的实际应用：变形网格以解决相交问题、可通过带锯从三个方向切割制造的形状，以及接近三维空间平铺的形状。
英文摘要
Different shape representations facilitate different computations. Surface representations, in particular meshes, are often used for modeling, whereas volume representations are useful for spatial queries such as intersection or containment. Optimizing a surface representation based on a volumetric properties by gradient descent requires the derivatives of the volume relative to its bounding surface. We derive this gradient for winding numbers and show that it can be efficiently computed for volumetric values sampled on a regular grid (voxel representation) and surface parameters based on vertex sets (triangle meshes). This enables an efficient solution for a variety of optimization problems. We demonstrate the practical use of this approach at the examples of deforming meshes to resolve intersections, being manufacturable by cutting with a bandsaw from three directions, and creating shapes that are close to tiling 3D space.
Journal refSIGGRAPH Conference Papers 2026. Article No.: 22
