Triangle splatting: radiance fields represented by triangles

Methodology Our rendering pipeline uses 3D triangles as primitives, each defined by three learnable 3D vertices, color, opacity, and a smoothness parameter \( \sigma \). The triangles are projected onto the image plane using a standard pinhole camera model with known intrinsics and extrinsics. Instead of binary masks, we introduce a smooth window function that softly modulates the triangle's influence across pixels. This function is derived from the 2D signed distance field (SDF) of the triangle, which measures the distance from a pixel \( \mathbf{p} \) to the triangle’s edges. The signed distance field \( \phi(\mathbf{p}) \) is defined as the maximum of three half-plane distances: \( \phi(\mathbf{p}) = \max\left( L_1(\mathbf{p}),\; L_2(\mathbf{p}),\; L_3(\mathbf{p}) \right) \) where each half-space function is defined as: \( L_i(\mathbf{p}) = \mathbf{n}_i \cdot \mathbf{p} + d_i \) with \( \mathbf{n}_i \) denoting the outward-facing unit normal of the \( i \)-th edge, and \( d_i ... Read full article.