Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator positions in stable configurations, which can lead to locally uneven surface geometry. We present VoroLight, a differentiable framework that promotes controlled Voronoi degeneracy for smooth surface reconstruction. Instead of optimizing generator positions alone, VoroLight associates each Voronoi surface vertex with a trainable sphere and introduces a sphere--intersection loss that encourages higher-order equidistance among face-incident generators. This formulation improves surface regularity while preserving intrinsic Voronoi properties such as watertightness and convexity. Because losses are defined directly on surface vertices, VoroLight supports multimodal shape supervision from implicit fields, point clouds, meshes, and multi--view images. By introducing additional interior generators optimized under a centroidal Voronoi tessellation objective, the framework naturally extends to volumetric Voronoi meshes with consistent surface--interior topology. Across diverse input modalities, VoroLight achieves competitive reconstruction fidelity while producing smoother and more geometrically regular Voronoi surfaces. Project page: https://jiayinlu19960224.github.io/vorolight/

翻译：沃罗诺伊图天然生成凸形、水密且拓扑一致的胞腔，使其成为三维形状重建的有吸引力的表示方法。然而，标准可微沃罗诺伊方法通常优化稳定配置下的生成器位置，可能导致局部曲面几何不均匀。我们提出VoroLight，一种可微框架，通过促进受控的沃罗诺伊退化实现平滑曲面重建。VoroLight不单独优化生成器位置，而是将每个沃罗诺伊曲面顶点与可训练球体关联，并引入球体交集损失，该损失鼓励面邻接生成器间的高阶等距性。这种公式在保持水密性和凸性等沃罗诺伊固有性质的同时改善曲面规则性。由于损失直接定义在曲面顶点上，VoroLight支持来自隐式场、点云、网格和多视图图像的多模态形状监督。通过在质心沃罗诺伊镶嵌目标下优化额外内部生成器，该框架自然扩展到具有一致曲面-内部拓扑的体沃罗诺伊网格。在多种输入模态下，VoroLight在保持竞争性重建保真度的同时，生成更平滑且几何更规则的沃罗诺伊曲面。项目页面：https://jiayinlu19960224.github.io/vorolight/