# Developability Approximation for Neural Implicits through Rank Minimization

arXiv: https://arxiv.org/abs/2308.03900 · HTML: https://mlsanity.com/paper/2308.03900/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 42 references that are in the map.
- First posted on arXiv 7 Aug 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Cubic Stylization](https://mlsanity.com/paper/1910.02926/) (2019)
- [Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications](https://mlsanity.com/paper/1503.01444/) (2015)
- [Natural Boundary Conditions for Smoothing in Geometry Processing](https://mlsanity.com/paper/1707.04348/) (2017)
- [Discrete Geodesic Nets for Modeling Developable Surfaces](https://mlsanity.com/paper/1707.08360/) (2017)
- [Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces](https://mlsanity.com/paper/1808.07560/) (2018)
- [Low-Rank Factorization for Rank Minimization with Nonconvex Regularizers](https://mlsanity.com/paper/2006.07702/) (2020)
- [Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces](https://mlsanity.com/paper/2103.00239/) (2021)

## Built on by (most cited first, 3 of 3)

- [FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models](https://mlsanity.com/paper/2506.16627/) (2025)
- [A Finite Difference Approximation of Second Order Regularization of Neural-SDFs](https://mlsanity.com/paper/2511.08980/) (2025)
- [As-Rigid-As-Possible Regularization for Implicit Surfaces](https://mlsanity.com/paper/2608.15933/) (2026)

## Abstract (arXiv)

Developability refers to the process of creating a surface without any tearing or shearing from a two-dimensional plane. It finds practical applications in the fabrication industry. An essential characteristic of a developable 3D surface is its zero Gaussian curvature, which means that either one or both of the principal curvatures are zero. This paper introduces a method for reconstructing an approximate developable surface from a neural implicit surface. The central idea of our method involves incorporating a regularization term that operates on the second-order derivatives of the neural implicits, effectively promoting zero Gaussian curvature. Implicit surfaces offer the advantage of smoother deformation with infinite resolution, overcoming the high polygonal constraints of state-of-the-art methods using discrete representations. We draw inspiration from the properties of surface curvature and employ rank minimization techniques derived from compressed sensing. Experimental results on both developable and non-developable surfaces, including those affected by noise, validate the generalizability of our method.