# Spherical Conformal Parameterization of Genus-0 Point Clouds for Meshing

arXiv: https://arxiv.org/abs/1508.07569 · HTML: https://mlsanity.com/paper/1508.07569/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2015.

## Built on by (most cited first, 11 of 11)

- [Flatten Anything: Unsupervised Neural Surface Parameterization](https://mlsanity.com/paper/2405.14633/) (2024)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
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- [QIS : Interactive Segmentation via Quasi-Conformal Mappings](https://mlsanity.com/paper/2402.14695/) (2024)
- [FlexPara: Flexible Neural Surface Parameterization](https://mlsanity.com/paper/2504.19210/) (2025)
- [A shallow physics-informed neural network for solving partial differential equations on surfaces](https://mlsanity.com/paper/2203.01581/) (2022)
- [Adaptive area-preserving parameterization of open and closed anatomical surfaces](https://mlsanity.com/paper/2111.04265/) (2021)
- [Circular Quasiconformal Deturbulence: Geometry-Based Restoration from Multiple Turbulent Frames](https://mlsanity.com/paper/2504.13432/) (2025)
- [Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems](https://mlsanity.com/paper/2511.01911/) (2025)
- [Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration](https://mlsanity.com/paper/2602.01589/) (2026)
- [SeamFlow: Structure-Aware Flow Matching on Edge Probabilities for Artist-Like UV Unwrapping](https://mlsanity.com/paper/2609.04751/) (2026)

## Abstract (arXiv)

Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh structure on point clouds. This task can be simplified with the aid of a parameterization. In particular, conformal parameterizations are advantageous in preserving the geometric information of the point cloud data. In this paper, we extend a state-of-the-art spherical conformal parameterization algorithm for genus-0 closed meshes to the case of point clouds, using an improved approximation of the Laplace-Beltrami operator on data points. Then, we propose an iterative scheme called the North-South reiteration for achieving a spherical conformal parameterization. A balancing scheme is introduced to enhance the distribution of the spherical parameterization. High quality triangulations and quadrangulations can then be built on the point clouds with the aid of the parameterizations. Also, the meshes generated are guaranteed to be genus-0 closed meshes. Moreover, using our proposed spherical conformal parameterization, multilevel representations of point clouds can be easily constructed. Experimental results demonstrate the effectiveness of our proposed framework.