Summer Seminar. Lubin Fan 2011-07-07. Discrete Differential Geometry. Circular arc structures Discrete Laplacians on General Polygonal Meshes HOT: Hodge-Optimized Triangulations Spin Transformations of Discrete Surfaces. Example-Based Simulation. Frame-based Elastic Models (TOG)
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Summer Seminar
Lubin Fan
2011-07-07
Discrete Differential Geometry
Example-Based Simulation
Circular Arc Structures
Pengbo Bo1,2 Helmut Pottmann2,3 Martin Kilian2
Wenping Wang1 Johannes Wallner2,4
1Univ. Hong Kong
2TU Wien
3KAUST
4TU Graz
Helmut Pottmann
KAUST
Vienna University of Technology
Pengbo Bo
Postdoctoral Fellow
Univ. Hong Kong
Martin KilianRA
Vienna University of Technology
Wenping Wang
Professor
Univ. Hong Kong
Johannes Wallner
Professor
Graz University of Technology
Vienna University of Technology
Node complexity
A circular arc structure consists of 2D mesh combinatorics (V, E), where edges are realized as circular arcs, such that in each vertex the adjacent arcs touch a common tangent plane.
We require congruence of interior vertices, and we consider the following three cases:
A quadrilateral CAS is radius-repetitive along a flow line, if the radius of its edges is constant. It is transversely radius-repetitive for a pair of neighboring ‘parallel’ flow lines, if the edges which connect these flow lines have constant radius.
Discrete Laplacians on General Polygonal Meshes
Marc Alexa1 Max Wardetzky2
1TU Berlin
2Universitaat Gottingen
Marc Alexa
Professor
Electrical Engineering and Computer Science
TU Berlin
Max Wardetzky
Assistant Professor
Heading the Discrete Differential Geometry Lab
Universitaat Gottingen
Maximal Projcetion
—— pre-Laplacians
—— positive semi-definite
Spin Transformation of Discrete Surface
Keenan Crane1 Ulrich Pinkall2 Peter Schroder1
1California Institute of Technology
2TU Berlin
http://users.cms.caltech.edu/~keenan/project_spinxform.html
Ulrich Pinkall
Geometry Group
Institute of mathematics
TU Berlin
Keenan Crane
PhD Student
California Institute of Technology
Peter SchroderProfessor
Director of the Multi-Res Modeling Group
California Institute of Technology
for the similarity transformation λ
for the new surface
California Institute of Technology
HOT: Hodge-Optimized Triangulations
Patrick Mullen Pooran Memari Fernando de Goes Mathieu Desbrun
1University of British Columbia, Vancouver, CANADA
2University of Grenoble
3INRIA
4LJK – CNRS
Frame-based Elastic Models
Benjamin Gilles1 Guillaume Bousquet2,3,4 Francois Faure2,3,4 Dinesh K. Pai1
Guillaume Bousquet
Second year PhD student
University of Grenoble
Laboratoire Jean KuntzmannINRIA
Benjamin Gilles
Post-doctoral Fellow
Sensorimotor Systems Lab
Department of Computer ScienceUniversity of British Columbia
François Faure
Assistant Professor
University of Grenoble
Laboratoire Jean KuntzmannINRIA
Dinesh K. Pai
Professor
Sensorimotor Systems Lab
Department of Computer ScienceUniversity of British Columbia
Sparse Meshless Models of Complex Deformable Solids
Francois Faure2,3,4 Benjamin Gilles1 Guillaume Bousquet2,3,4Dinesh K. Pai1
1University of British Columbia, Vancouver, CANADA
2University of Grenoble
3INRIA
4LJK – CNRS
Guillaume Bousquet
Second year PhD student
University of Grenoble
Laboratoire Jean KuntzmannINRIA
Benjamin Gilles
Post-doctoral Fellow
Sensorimotor Systems Lab
Department of Computer ScienceUniversity of British Columbia
François Faure
Assistant Professor
University of Grenoble
Laboratoire Jean KuntzmannINRIA
Dinesh K. Pai
Professor
Sensorimotor Systems Lab
Department of Computer ScienceUniversity of British Columbia
Local compression:
Displacement function:
Shape function:
Compliance distance:
Slope of shape function:
Affine function!
RBF kernels
Our kernels
Node distribution: farthest point sampling [Martin et al. 2010]
Example-based Elastic Materials
Sebastian Martin1 Bernhard Thomaszewski1,2Eitan Grinspunt3 Markus Gross1,2
1ETH Zurich
2Disney Research Zurich
3Columbia University
Bernhard Thomaszewski
Post-doctoral Researcher
Disney Research Zurich
Sebastian Martin
RA, PhD. Student
CGL, ETH
Eitan GrinspunAssociate Professor
Computer Science Dept.Columbia University
Markus Gross
Professor
CGL, ETH
Disney Research Zurich