Developability Approximation for Neural Implicits through Rank Minimization

TL;DR

This paper presents a novel method for reconstructing approximate developable surfaces from neural implicit surfaces by using a regularization term based on second-order derivatives to promote zero Gaussian curvature, with applications in fabrication.

Contribution

It introduces a regularization approach leveraging rank minimization on second derivatives to approximate developable surfaces from neural implicit representations.

Findings

Effective in reconstructing developable surfaces

Robust to noise and non-developable surfaces

Outperforms traditional discrete methods

Abstract

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.