TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization

TL;DR

TetWeave presents a scalable, differentiable isosurface representation that jointly optimizes an unstructured tetrahedral grid and a directional signed distance, constructed on-the-fly from a point cloud via Delaunay triangulation. By introducing edge-aware directional SDFs encoded with spherical harmonics and extracting surfaces with Marching Tetrahedra, TetWeave achieves watertight, 2-manifold meshes with improved adaptivity and memory efficiency. The approach is reinforced by regularizers (ODT and triangle fairness) and a resampling-based adaptive meshing strategy, plus a multi-stage optimization pipeline that balances global structure with high-frequency details. Applications to multi-view reconstruction, mesh compression, and geometric texture generation demonstrate strong reconstruction quality, efficient memory usage, and robust performance across challenging shapes, highlighting TetWeave’s potential as a practical unstructured mesh representation for gradient-based optimization.

Abstract

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.

Figures (20)

• Figure 1: Illustration of our mesh extraction pipeline, which begins with a point cloud where each point is associated with a signed distance value. The process starts by generating a tetrahedral grid through Delaunay triangulation. Next, active edges are identified, and a directional signed distance is computed for each active point using spherical harmonics (Sec. \ref{['sec:directional_sdf']}). The final mesh is extracted using the Marching Tetrahedra algorithm (Sec. \ref{['sec:mesh_extraction']}). Our method iteratively refines the randomly initialized point cloud, distributing points to closely align with the target shape (Sec. \ref{['sec:resampling']}), which ensures scalability and adaptability. In this figure, only a portion of the point cloud and Delaunay Triangulation is displayed to enhance clarity.
• Figure 2: Contrary to FlexiCubes shen2023flexicubes, our method is guaranteed free from self-intersections.
• Figure 3: Storing a single SDF value at each point can lead to inaccurate surface reconstruction (left), where a directional distance encoded as spherical harmonics allows our method to place mesh vertices differently on each tetrahedral edge, resulting in a more accurate shape reconstruction (right).
• Figure 4: We compare the reconstructed meshes with and without the use of directional signed distance (spherical harmonics). Using spherical harmonics enhances detail preservation, particularly for shapes with complex topology, where a single grid point can influence multiple parts of the shape.
• Figure 5: Comparison of reconstructed meshes with and without the use of the fairness loss. We show that incorporating a simple fairness loss improves tessellation quality without compromising shape fidelity.

Theorems & Definitions (1)

• proposition 1