Deformable Triangle Splatting (DETRIS)

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 (DETRIS), which augments each triangle with K control points per edge, each 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 primitives differentiably, we design a rasterization pipeline in the triangle's barycentric coordinate space, ensuring view-consistent rendering: a winding-number test classifies pixels as inside/outside, and a smooth distance-based window controlled by learnable sharpness and corner smoothness produces the opacity. DETRIS outperforms recent non-volumetric primitives in visual quality and versatility while remaining competitive in rendering speed.

Method

Overview. A sparse SfM point cloud initializes one triangle per point. Each triangle is projected and mapped to a canonical barycentric frame; K control points per edge displace the boundary along edge normals, producing a deformable piecewise-linear contour. The deformed polygon is rendered with a winding-number inside test, a polynomial smooth-minimum distance field with corner smoothness δ, a power-law opacity window σ, and SH color — all composed via front-to-back α-blending and optimized end-to-end.

Live Demo — Deform a Primitive

Drag the control points to deform the boundary, or the vertices to move the triangle. Try the presets to form non-convex shapes — exactly what a single DETRIS primitive can learn. Canvas fill uses the non-zero winding rule, just like our rasterizer.

Control points per edge (K): 3

Sharpness (σ): 2.0

Corner smoothness (δ): 0.10

Presets:

show opacity falloff

One Primitive, Many Shapes

A single deformable triangle (K=3) fits convex and non-convex targets that rigid triangles cannot represent and Gaussians cannot render with sharp edges. Hover to compare target vs. ours.

Results

Ours vs. Triangle Splatting

Drag the divider. Our deformable primitives resolve fine structures where rigid triangles show tessellation artifacts.

What the deformations contribute

Full model vs. the same model with all control-point displacements zeroed (rigid). The signal concentrates at fine boundaries.

Real-time fly-throughs

Camera paths rendered through trained DETRIS scenes.

Counter

Bicycle

Stump

Treehill

BibTeX

@inproceedings{JimenezAgudo2026Deformable,
  title     = {Deformable Triangle Splatting: Flexible Primitives for
               Real-Time Radiance Field Rendering},
  author    = {Jiménez-Ayguadé, Oriol and Agudo, Antonio},
  booktitle = {European Conference on Computer Vision (ECCV)},
  year      = {2026},
}