We present a differentiable representation, **DMesh**, for general 3D triangular meshes. **DMesh** considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates the domain based on *Weighted Delaunay Triangulation* (WDT), and formulate probability of faces to exist on our desired mesh in a differentiable manner based on the WDT. This enables **DMesh** to represent meshes of various topology in a differentiable way, and allows us to reconstruct the mesh under various observations, such as point cloud and multi-view images using gradient-based optimization.

DMesh is an explicit shape representation that encodes every information into

Then, we determine

Therefore, we optimize the

DMesh handles

Therefore, it admits

DMesh is very general representation, which can handle

Even though there are slight perturbations to the vertex positions, DMesh can restore

In the point cloud rendering, the color of each point represents its real value.

Note that some points disappear because they lose weights and thus

Since we already have sample points, we can use their subset to initialize our mesh.

Therefore, it

Note that connectivity keeps changing mainly due to

In our formulation, we can consider

When we give a larger coefficient for the point orientations, the reconstructed mesh usually gave more favorable results (left).

Interestingly, when we set the coefficient to a large value, we could also observe a compact mesh that aligns with geometric features well (right).

```
@misc{son2024dmesh,
title={DMesh: A Differentiable Representation for General Meshes},
author={Sanghyun Son and Matheus Gadelha and Yang Zhou and Zexiang Xu and Ming C. Lin and Yi Zhou},
year={2024},
eprint={2404.13445},
archivePrefix={arXiv},
primaryClass={cs.CV}
}
```