用动态四面体网格实现可优化的高质量网格提取
TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization
- 动态构建Delaunay四面体网格，联合优化网格位置与方向距离场
- 输出网格无孔洞、无自交，内存随顶点数近线性增长
- 适合需要高精度、低存储的3D重建与几何生成任务
我们提出TetWeave，一种用于基于梯度的网格优化的等值面表示方法，同时优化用于Marching Tetrahedra的四面体网格位置和每个点上的新型方向符号距离场。TetWeave通过Delaunay三角剖分实时构建四面体网格，相比预定义网格更具灵活性。生成的网格保证为封闭、二维流形且无自交。该灵活性支持在重建误差高的区域自适应重采样，并可在不牺牲重建精度的前提下提升网格平滑性。由此得到的自适应网格质量高、内存占用少，优化参数极少。因此，TetWeave相对于输出网格顶点数呈现近线性内存增长，显著优于预定义网格。我们展示了TetWeave在计算机图形学与视觉中的广泛应用，包括多视角3D重建、网格压缩和几何纹理生成。
原文摘要 · Abstract (English)
We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh - a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation.
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