# MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement

arXiv: https://arxiv.org/abs/2412.08484 · HTML: https://mlsanity.com/paper/2412.08484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 56 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 15 of 15)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [GEOMetrics: Exploiting Geometric Structure for Graph-Encoded Objects](https://mlsanity.com/paper/1901.11461/) (2019)

## Abstract (arXiv)

Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh refinement that leverages reference geometry to correct deformed or degraded meshes. We formulate the problem as a second-order cone program where vertex positions are optimized to align with target geometry while enforcing smoothness through convex edge-length regularization. MeshCone performs geometry-aware optimization that preserves fine details while correcting structural defects. We demonstrate robust performance across 56 diverse object categories from ShapeNet and ThreeDScans, achieving superior refinement quality compared to Laplacian smoothing and unoptimized baselines while maintaining sub-second inference times. MeshCone is particularly suited for applications where reference geometry is available, such as mesh-from-template workflows, scan-to-CAD alignment, and quality assurance in asset production pipelines.