SIGGRAPH ASIA 2016
Daniel Schmitter, EPFL STI LIB

Test Run • 01 November 2016 • BM 4 233

Abstract
Title: Smooth Shapes with Spherical Topology: Beyond Traditional Modeling, Efficient Deformation, and Interaction Abstract: In this talk we discuss the work that we are presenting at SIGGRAPH this year. Existing shape models with spherical topology are typically designed either in the \textit{discrete} domain using \textit{interpolating} polygon meshes or in the continuous domain using \textit{smooth} but \textit{non-interpolating} schemes such as subdivision or NURBS. Both polygon models and subdivision methods require a large number of parameters to model smooth surfaces. NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation. We present a new method to construct deformable closed surfaces, which includes the exact sphere, by combining the best of two worlds: a \textit{smooth} and \textit{interpolating} model with a continuously varying tangent plane and well-defined curvature at every point on the surface. Our formulation is considerably simpler than NURBS while it requires fewer parameters than polygon meshes. We demonstrate the generality of our method with applications ranging from intuitive user-interactive shape modeling, continuous surface deformation, shape morphing, reconstruction of shapes from parameterized point clouds, to fast iterative shape optimization for image segmentation. Comparisons with discrete methods and with non-interpolating approaches highlight the advantages of our framework.