We present a dense RGB-D SLAM system using differentiable triangles as the 3D map representation. While 3D Gaussian Splatting has emerged as the leading method for novel-view synthesis, triangles remain the standard primitive for traditional rendering hardware, game engines, and downstream tasks requiring explicit geometry such as simulation, collision, and editing. Recent offline methods have demonstrated that an unstructured 'triangle soup' can be optimised into a photorealistic mesh via Delaunay triangulation across a set of posed images. Building upon this insight, we present the first dense SLAM system to employ Triangle Splatting to perform both tracking and mapping through online differentiable rendering of a triangle soup. The map can be converted into a connected mesh on-the-fly via restricted Delaunay triangulation, enabling new online capabilities such as mesh deformation and collision checking. On Replica and TUM-RGBD, our system outperforms baselines on 3D geometry, matches the camera-tracking accuracy, and enables online mesh-based scene editing.

翻译：我们提出一种密集RGB-D SLAM系统，采用可微三角形作为3D地图表示。尽管3D高斯溅射已成为新视角合成的主流方法，三角形仍是传统渲染硬件、游戏引擎以及需要显式几何的后续任务（如仿真、碰撞检测和编辑）的标准图元。近期离线方法已证明，通过在一组姿态图像上执行Delaunay三角剖分，可以将非结构化的"三角形网格"优化为照片级逼真网格。基于这一洞见，我们首次提出采用三角形溅射的密集SLAM系统，通过在线可微渲染三角形网格同时实现追踪与建图。该地图可通过受限Delaunay三角剖分实时转换为连通网格，从而支持网格变形和碰撞检测等在线功能。在Replica和TUM-RGBD数据集上，我们的系统在3D几何重建方面优于基线方法，相机追踪精度与现有方法持平，并支持基于网格的在线场景编辑。