M.S. in Computer Science
California Institute of Technology
Contact Information
Email: am@caltech.edu
Fax: +1 (626) 792 4257
Mail Code 256-80, Caltech
Pasadena, CA 91125, USA
M.S. in Computer Science
California Institute of Technology
Contact Information
Email: am@caltech.edu
Fax: +1 (626) 792 4257
Mail Code 256-80, Caltech
Pasadena, CA 91125, USA
Patrick Mullen, Alexander McKenzie, Yiying Tong and Mathieu Desbrun.
ACM Transactions on Graphics (SIGGRAPH). August 2007, San Diego, USA.
We present a purely Eulerian framework for geometry processing of surfaces and foliations. Contrary to current Eulerian methods used in graphics, we use conservative methods and a variational interpretation, offering a unified framework for routine surface operations such as smoothing, offsetting, and animation. Computations are performed on a fixed volumetric grid without recourse to Lagrangian techniques such as triangle meshes, particles, or path tracing. At the core of our approach is the use of the Coarea Formula to express area integrals over isosurfaces as volume integrals. This enables the simultaneous processing of multiple isosurfaces, while a single interface can be treated as the special case of a dense foliation. We show that our method is a powerful alternative to conventional geometric representations in delicate cases such as the handling of high-genus surfaces, weighted offsetting, foliation smoothing of medical datasets, and incompressible fluid animation.
Supplemental Video (divx)
Alexander McKenzie, Eugene Vendrovsky and Junyong Noh.
Journal of Computing Science and Engineering, March 2008.
Terrain reconstruction from images is an ill-posed, yet commonly desired task when integrating visual effects into live-action photography. Such surfaces are used for choreography of a scene, casting physically accurate shadows of CG elements, and more. In this technical report we discuss a novel moving Radial Basis Function (RBF) approach to generating landscapes from extremely noisy point cloud datasets---obtained via limited resolution techniques such as optical flow based vision algorithms applied to live-action plates, or LIDAR scans of the actual filming location---in the absence of high quality geological survey data that may prove difficult to obtain. In these scenarios, our algorithm offsets the tremendously laborious task of modeling such landscapes by hand, automatically generating excellent results within minutes for a typical tracking shot.
Supplemental Video (divx)
Alexander McKenzie, Santiago V. Lombeyda and Mathieu Desbrun.
Proceedings of EuroVis. June 2005, Leeds, UK. Pages 29-35.
Scientific computing is an increasingly crucial component of research in various disciplines. Despite its potential, exploration of the results is an often laborious task, owing to excessively large and verbose datasets output by typical simulation runs. Several approaches have been proposed to analyze, classify, and simplify such data to facilitate an informative visualization and deeper understanding of the underlying system. However, traditional methods leave much room for improvement.
In this article we investigate the visualization of large vector fields, departing from accustomed processing algorithms by casting vector field simplification as a variational partitioning problem. Adopting an iterative strategy, we introduce the notion of vector "proxies" to minimize the distortion error of our simplification by clustering the dataset into multiple best-fitting characteristic regions. This error driven approach can be performed with respect to various similarity metrics, offering a convenient set of tools to design clear and succinct representations of high dimensional datasets. We illustrate the benefits of such tools through visualization experiments of three-dimensional vector fields.