# CWF: Consolidating Weak Features in High-quality Mesh Simplification

arXiv: https://arxiv.org/abs/2404.15661 · HTML: https://mlsanity.com/paper/2404.15661/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 24 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Coverage Axis: Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2110.00965/) (2021)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [Top-Down Shape Abstraction Based on Greedy Pole Selection](https://mlsanity.com/paper/1910.08954/) (2019)
- [Surface Simplification using Intrinsic Error Metrics](https://mlsanity.com/paper/2305.06410/) (2023)
- [MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram](https://mlsanity.com/paper/2403.18761/) (2024)
- [VoroCrust: Voronoi Meshing Without Clipping](https://mlsanity.com/paper/1902.08767/) (2019)

## Built on by (most cited first, 8 of 8)

- [TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes](https://mlsanity.com/paper/2405.20283/) (2024)
- [PDT: Point Distribution Transformation with Diffusion Models](https://mlsanity.com/paper/2507.18939/) (2025)
- [MeshMosaic: Scaling Artist Mesh Generation via Local-to-Global Assembly](https://mlsanity.com/paper/2509.19995/) (2025)
- [Strips as Tokens: Artist Mesh Generation with Native UV Segmentation](https://mlsanity.com/paper/2604.09132/) (2026)
- [Autoregressive B-Rep Shape Generation with Parametric Surfaces](https://mlsanity.com/paper/2607.17093/) (2026)
- [NASM: Neural Anisotropic Surface Meshing](https://mlsanity.com/paper/2410.23109/) (2024)
- [Feature-Preserving Mesh Decimation for Normal Integration](https://mlsanity.com/paper/2504.00867/) (2025)
- [SubdivAR: Autoregressive Next-Scale Prediction for Neural Mesh Subdivision](https://mlsanity.com/paper/2606.27088/) (2026)

## Abstract (arXiv)

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.