Developable Approximation via Isomap on Gauss Image.

Abstract

We propose a novel method to generate developable approximations for triangular meshes. Instead of fitting the Gauss image using a geodesic circle in the local neighborhood, we apply a nonlinear dimensionality reduction method, called Isomap, to use a general curve on the sphere for fitting. This brings us a larger space to represent the Gauss image in the local neighborhood as a 1D structure. Specifically, each triangle is assigned a target normal after local fitting; then, we deform the mesh to approach the target normal globally. By iteratively performing fitting and deformation, we obtain the developable approximation. We demonstrate the feasibility and effectiveness of our method over various examples. Compared to the state-of-the-art methods, our results exhibit a higher fidelity to the input mesh while possessing more prominent and visually distinct undevelopable seam curves.