# BG-Triangle: B'ezier Gaussian Triangle for 3D Vectorization and Rendering

arXiv: https://arxiv.org/abs/2503.13961 · HTML: https://mlsanity.com/paper/2503.13961/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 69 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Builds on (most cited first, 30 of 33)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [IBRNet: Learning Multi-View Image-Based Rendering](https://mlsanity.com/paper/2102.13090/) (2021)
- [Scaffold-GS: Structured 3D Gaussians for View-Adaptive Rendering](https://mlsanity.com/paper/2312.00109/) (2023)
- [Mip-Splatting: Alias-free 3D Gaussian Splatting](https://mlsanity.com/paper/2311.16493/) (2023)
- [NeRV: Neural Reflectance and Visibility Fields for Relighting and View Synthesis](https://mlsanity.com/paper/2012.03927/) (2020)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [Deferred Neural Rendering: Image Synthesis using Neural Textures](https://mlsanity.com/paper/1904.12356/) (2019)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [Mini-Splatting: Representing Scenes with a Constrained Number of Gaussians](https://mlsanity.com/paper/2403.14166/) (2024)
- [Editable Free-viewpoint Video Using a Layered Neural Representation](https://mlsanity.com/paper/2104.14786/) (2021)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [NeRFactor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination](https://mlsanity.com/paper/2106.01970/) (2021)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [Unsupervised Training for 3D Morphable Model Regression](https://mlsanity.com/paper/1806.06098/) (2018)
- [NeuTex: Neural Texture Mapping for Volumetric Neural Rendering](https://mlsanity.com/paper/2103.00762/) (2021)
- [A Learned Representation for Scalable Vector Graphics](https://mlsanity.com/paper/1904.02632/) (2019)
- [Neural Point Catacaustics for Novel-View Synthesis of Reflections](https://mlsanity.com/paper/2301.01087/) (2023)
- [Human Performance Modeling and Rendering via Neural Animated Mesh](https://mlsanity.com/paper/2209.08468/) (2022)
- [Inverse Path Tracing for Joint Material and Lighting Estimation](https://mlsanity.com/paper/1903.07145/) (2019)
- [Vectorization and Rasterization: Self-Supervised Learning for Sketch and Handwriting](https://mlsanity.com/paper/2103.13716/) (2021)
- [Deep Surface Light Fields](https://mlsanity.com/paper/1810.06514/) (2018)
- [Deep Vectorization of Technical Drawings](https://mlsanity.com/paper/2003.05471/) (2020)

## Built on by (most cited first, 4 of 4)

- [Duplex-GS: Proxy-Guided Weighted Blending for Real-Time Order-Independent Gaussian Splatting](https://mlsanity.com/paper/2508.03180/) (2025)
- [Radiant Triangle Soup with Soft Connectivity Forces for 3D Reconstruction and Novel View Synthesis](https://mlsanity.com/paper/2505.23642/) (2025)
- [Difix3D-W: Distractor-Free Few-Shot 3D Gaussian Splatting in the Wild](https://mlsanity.com/paper/2604.27422/) (2026)
- [3DGS3: Joint Super Sampling and Frame Interpolation for Real-Time Large-Scale 3DGS Rendering](https://mlsanity.com/paper/2605.11489/) (2026)

## Abstract (arXiv)

Differentiable rendering enables efficient optimization by allowing gradients to be computed through the rendering process, facilitating 3D reconstruction, inverse rendering and neural scene representation learning. To ensure differentiability, existing solutions approximate or re-formulate traditional rendering operations using smooth, probabilistic proxies such as volumes or Gaussian primitives. Consequently, they struggle to preserve sharp edges due to the lack of explicit boundary definitions. We present a novel hybrid representation, B'ezier Gaussian Triangle (BG-Triangle), that combines B'ezier triangle-based vector graphics primitives with Gaussian-based probabilistic models, to maintain accurate shape modeling while conducting resolution-independent differentiable rendering. We present a robust and effective discontinuity-aware rendering technique to reduce uncertainties at object boundaries. We also employ an adaptive densification and pruning scheme for efficient training while reliably handling level-of-detail (LoD) variations. Experiments show that BG-Triangle achieves comparable rendering quality as 3DGS but with superior boundary preservation. More importantly, BG-Triangle uses a much smaller number of primitives than its alternatives, showcasing the benefits of vectorized graphics primitives and the potential to bridge the gap between classic and emerging representations.