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：我们提出了一种密集RGB-D SLAM系统，采用可微分三角形作为三维地图表示。尽管三维高斯溅射已成为新视角合成的主流方法，但三角形仍是传统渲染硬件、游戏引擎以及需要显式几何的下游任务（如模拟、碰撞检测和编辑）的标准基元。最近的离线方法已证明，通过对一组带姿态图像进行Delaunay三角剖分，可以将无结构的"三角形汤"优化为逼真网格。基于这一见解，我们提出了首个采用三角形溅射的密集SLAM系统，通过在线可微分渲染三角形汤实现追踪与建图。地图可通过受限Delaunay三角剖分实时转换为连通网格，从而支持网格变形与碰撞检测等新型在线功能。在Replica和TUM-RGBD数据集上，我们的系统在三维几何方面超越基线方法，相机追踪精度达到同等水平，并实现了基于网格的在线场景编辑。