Most of our work is in some form or another focussed on Digital
Geometry Processing (DGP) in the broadest sense of the word,
covering the entire pipeline from acquisition to reconstruction,
parameterization, (re)meshing, editing, simulation, and compression,
including new user interfaces for the creation of digital geometry.
We are actively developing the theoretical foundations of this new
area as well as building prototype implementations to test out our
ideas and learn how to build efficient representations and algorithms.
Below is a short, high level description of some of the ongoing research thrusts. More detail can be found on the publications page.
|Theoretical foundations of smooth subdivision||The limit surface of a given subdivision scheme is determined by the mask, i.e. the local neighborhood, and the weights used. In earlier work we have focused on full characterizations of smooth subdivision schemes (Butterfly Subdivision, Denis Zorin's PhD thesis, Smoothness of Stationary Subdivision on Irregular Meshes). More recently we have characterized the suitability of subdivision basis functions for use in the Subdivision Element Method (SEM) and explored generalized constructions for alternating primal/dual quadrilateral schemes of arbitrary order. Ongoing work focusses on building dual schemes for triangle based subdivision and surface approximation through subdivision. Personnel: Ilja Friedel, Adi Levin, Nathan Litke, Peter Oswald, Peter Schröder, Denis Zorin.|
|Semi-regular remeshing, mesh extraction, and compression||The most powerful algorithms (by far!) for Digital Geometry Processing are based on semi-regular meshes, i.e., meshes which are regular almost everywhere. Often meshes constructed from measurements are not semi-regular and need to be remeshed, a major focus of our ongoing work (beginning with the MAPS paper and continuing through Normal Meshes and the most recent Hybrid Meshes). Of course, ideally one would like to create semi-regular meshes directly. Typically this means extracting such meshes from sampled distance volumes. Such a technique will have a great impact on scientific and medical computing applications which we are actively pursuing. Often the data is noisy leading to interesting problems such as how to remove topological noise. Once the data is in semi-regular form very powerful compression algorithms can be applied (check out the software). Going beyond processing individual meshes we are also working on the application of classical signal processing ideas to entire sets of surfaces. Personnel: Mathieu Desbrun, Igor Guskov, Andrei Khodakovsky, Emil Praun, Peter Schröder, Wim Sweldens, Zoë Wood.|
|Subdivision for Modeling, Simulation, and Design||Subdivision surfaces are appearing in more and more places from commercial modeling systems to high end movie production because they are so useful in geometric modeling, simulation, and engineering design. Many issues need to be addressed to move this agenda forward. On the modeling end we are working on trimming, surface-surface intersection (closely related to collision detection), topological modeling, and interactive variational modeling. For simulation scalable adaptive solvers are needed and difficult issues such as collision response need to be resolved; both are areas we are currently working in. Personnel: Jeff Bolz, Ilja Friedel, Eitan Grinspun, Michael Holst, Petr Krysl, Nathan Litke, Patrick Mullen, Peter Schröder.|
|Human Factors in Geometric Modeling||Building free-form geometry with traditional modeling tools is very difficult and cumbersome. In particular, for purposes of rapid ideation and artistic creation traditional tools are useless. To address this issue we are exploring the use of semi-immersive environments, props, and the human body for the direct creation of free-form geometry. In collaboration with DesignWorks/USA we have developed Surface Drawing using the Responsive Workbench and continue to evolve this new paradigm. Personnel: Jim Barry, Gary Fitzgerald, Cici Koenig, davidkremers, Andy Logan, Michael Pruett, Steven Schkolne, Peter Schröder.|
Copyright © 1997-2001 Peter Schröder