# Computing quasiconformal folds

arXiv: https://arxiv.org/abs/1804.03936 · HTML: https://mlsanity.com/paper/1804.03936/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

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

- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Free-Boundary Quasiconformal Maps via a Least-squares Operator in Diffeomorphism Optimization](https://mlsanity.com/paper/2511.11679/) (2025)
- [Deep Learning-Based Quasi-Conformal Surface Registration for Partial 3D Faces Applied to Facial Recognition](https://mlsanity.com/paper/2405.09880/) (2024)
- [Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration](https://mlsanity.com/paper/2602.01589/) (2026)

## Abstract (arXiv)

We propose a novel way of computing surface folding maps via solving a linear PDE. This framework is a generalization to the existing quasiconformal methods and allows manipulation of the geometry of folding. Moreover, the crucial quantity that characterizes the geometry occurs as the coefficient of the equation, namely the Beltrami coefficient. This allows us to solve an inverse problem of parametrizing the folded surface given only partial data but with known folding topology. Various interesting applications such as fold sculpting on 3D models and self-occlusion reasoning are demonstrated to show the effectiveness of our method.