1 research outputs found
Developability Approximation for Neural Implicits through Rank Minimization
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