Deformable Triangle Splatting: Flexible Primitives for Real-Time Radiance Field Rendering

2026-07-24

AI Summary

Existing 2D primitive-based radiance field methods struggle to efficiently model curved or concave structures due to their reliance on convex boundary representations. This work proposes deformable triangle primitives that introduce K learnable scalar displacement control points along each edge, enabling non-convex boundary expression while preserving the planar geometric definition of the original triangle. We formulate a differentiable rasterization pipeline in barycentric coordinate space and integrate a winding number test with a learnable window function to achieve view-consistent, smooth opacity transitions. Our approach is the first to endow triangle primitives with non-convex deformation capabilities, significantly enhancing geometric expressiveness without compromising real-time rendering efficiency. Experiments demonstrate that our method outperforms existing non-voxel primitive approaches across diverse real-world scenes, achieving superior visual quality and generalization.

Abstract

Recent radiance field methods represent scenes with 2D primitives that offer surface alignment and efficient rasterization, from Gaussian disks to triangles, yet all rely on convex boundaries: curved and concave structures demand excessive primitives. We introduce Deformable Triangle Splatting, which augments each triangle with $K$ control points per edge, each parameterized by a single learnable scalar displacement that shifts the boundary inward or outward, enabling non-convex shape representation while preserving the three base vertices that define the 3D plane. To render these non-convex primitives differentiably, we design a rasterization pipeline in the triangle's barycentric coordinate space, ensuring view-consistent rendering. A winding number test determines whether each pixel lies inside the deformed primitive, and a window function controlled by two learnable parameters, sharpness and corner smoothness, together with a per-primitive scalar opacity, produces the smooth opacity transition from interior to boundary. Validation is done in a variety of real-world scenes, outperforming recent works based on non-volumetric primitives in terms of visual quality and versatility while still achieving competitive rendering efficiency.

Problem

• radiance field rendering
• non-convex shapes
• 2D primitives
• surface representation
• real-time rendering

Innovation

• Deformable Triangle Splatting
• non-convex primitives
• differentiable rasterization
• barycentric coordinate space
• winding number test