Here’s the video to go along with our paper, Smooth Shape-Aware Functions with Controlled Extrema, that we’ll present at SGP 2012.
Posts Tagged ‘eth zurich’
I put up a project page for our new paper that we’ll present at SGP (Symposium of Geometry Processing) this month. The paper’s called, “Smooth Shape-Aware Functions with Controlled Extrema” and it’s a collaboration between me, my advisor, Olga Sorkine and my ex- officemate at NYU Tino Weinkauf, who’s now at MPI in Saarbrucken.
Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multi scale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but also increasing oscillation, immediately releasing the maximum principle. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing.
My colleagues, Ilya Baran, Ladislav Kavan, Jovan Popović, Olga Sorkine, and I have just submitted the camera ready version of paper “Fast Automatic Skinning Transformations” to be presented at ACM SIGGRAPH 2012. I’ve put up a fast automatic skinning transformations page where you can find the preprint version of the article, videos and more to come.
Skinning transformations are a popular way to articulate shapes and characters. However, traditional animation interfaces require all of the skinning transformations to be specified explicitly, typically using a control structure (a rig). We propose a system where the user specifies only a subset of the degrees of freedom and the rest are automatically inferred using nonlinear, rigidity energies. By utilizing a low-order model and reformulating our energy functions accordingly, our algorithm runs orders of magnitude faster than previous methods without compromising quality. In addition to the immediate boosts in performance for existing modeling and real time animation tools, our approach also opens the door to new modes of control: disconnected skeletons combined with shape-aware inverse kinematics. With automatically generated skinning weights, our method can also be used for fast variational shape modeling.
Update: The full resolution version of the above teaser.
Update: The accompanying video (with narration)