Keenan Crane

COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK

Digital Geometry Processing with Discrete Exterior Calculus

SIGGRAPH 2013 Lecturers: | Fernando de Goes, Keenan Crane, Mathieu Desbrun, Peter Schröder |

SGP 2013 Lecturers: | Etienne Vouga, Keenan Crane |

This course provides an introduction to geometry processing using discrete exterior calculus (DEC). DEC provides a simple, flexible, and efficient framework within which one can build a unified platform for geometry processing. The course provides essential mathematical background as well as a large array of real-world examples. It also provides a short survey of the most relevant recent developments in digital geometry processing and discrete differential geometry.

Course material has been used for semester-long courses at Caltech (2011, 2012, 2013, 2014), Columbia University (2013), and RWTH Aachen University (2014), as well as special sessions at SIGGRAPH (2013) and SGP (2012, 2013, 2014).

These notes grew out of a Caltech course on discrete differential geometry (DDG) over the past few years. Some of this material has also appeared at SGP Graduate schools and a course at SIGGRAPH 2013. Peter Schröder, Max Wardetzky, and Clarisse Weischedel provided invaluable feedback for the first draft of many of these notes; Mathieu Desbrun, Fernando de Goes, Peter Schröder, and Corentin Wallez provided extensive feedback on the SIGGRAPH 2013 revision. Thanks to Mark Pauly's group at EPFL for suffering through (very) early versions of these lectures, to Katherine Breeden for musing with me about eigenvalue problems, and to Eitan Grinspun for detailed feedback and for helping develop exercises about convergence. Thanks also to those who have pointed out errors over the years: Mirela Ben-Chen, Nina Amenta, Chris Wojtan, Yuliy Schwarzburg, Robert Luo, Andrew Butts, Scott Livingston, Christopher Batty, Howard Cheng, Gilles-Philippe Paillé, Jean-François Gagnon, Nicolas Gallego-Ortiz, Henrique Teles Maia, Joaquín Ruales, Papoj Thamjaroenporn, and all the students in CS177 at Caltech, as well as others who I am currently forgetting!

@inproceedings{Crane:2013:DGP,
author = {Keenan Crane, Fernando de Goes, Mathieu Desbrun, Peter Schröder},
title = {Digital Geometry Processing with Discrete Exterior Calculus},
booktitle = {ACM SIGGRAPH 2013 courses},
series = {SIGGRAPH '13},
year = {2013},
location = {Anaheim, California},
numpages = {126},
publisher = {ACM},
address = {New York, NY, USA},
}

Source

C++— | several fundamental geometry processing algorithms (parameterization, smoothing, geodesic distance, ) implemented in a single unified DEC framework. |

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