Speaker: Michael Rabinovich, ETH Zurich

Tuesday June 4th, 1:00pm, in BC 420
Title: Discrete Orthogonal Geodesic Nets

We present a discrete theory and a set of computational tools for modeling developable surfaces. The basis of our theory is a discrete model termed discrete orthogonal geodesic nets (DOGs). Our model is simple, local, and, unlike previous works, it does not directly encode the surface rulings.
We prove and experimentally demonstrate strong ties to smooth developable surfaces, as well as theorems relating DOGs to other nets in discrete differential geometry. We further develop a set of tools to effectively deform DOGs. We prove that generically the shape space of DOGs is a smooth manifold of a fixed dimension, implying that DOGs are smoothly deformable, and we show how to navigate the shape space by computing tangents on this shape space. We navigate the DOG shape space using a novel DOG Laplacian operator together with a Willmore flow objective, and we prove the convergence of both to their smooth equivalent under sampling. We apply our tools to develop the first interactive editing system for developable surfaces that supports arbitrary bending, stretching, cutting, (curved) folds, as well as smoothing and subdivision operations.

Michael is PhD student in the Interactive Geometry Lab at ETH Zurich, under the supervision of Prof. Olga Sorkine-Hornung. His thesis focus on developing concepts in discrete differential geometry into simple and efficient shape modeling algorithms, with a focus on developable surfaces.