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Digital geometry processing with discrete exterior calculus

Published: 21 July 2013 Publication History

Abstract

An introduction to geometry processing using discrete exterior calculus (DEC), which provides a simple, flexible, and efficient framework for building a unified geometry-processing platform. 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. Compared to previous SIGGRAPH courses, this course focuses heavily on practical aspects of DEC, with an emphasis on implementation and applications.
The course begins with the core ideas from exterior calculus, in both the smooth and discrete setting. Then it shows how a large number of fundamental geometry-processing tools (smoothing, parameterization, geodesics, mesh optimization, etc.) can be implemented quickly, robustly, and efficiently within this single common framework. It concludes with a discussion of recent extensions of DEC that improve efficiency, accuracy, and versatility.
The course notes grew out of the discrete differential geometry course taught over the past five years at the California Institute of Technology, for undergraduates and beginning graduate students in computer science, applied mathematics, and associated fields. The notes also provide guided exercises (both written and coding) that attendees can later use to deepen their understanding of the material.

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ZIP File (a7-crane.zip)
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Part 1 (crs218_01.mp4)
Part 2 (crs218_02.mp4)
Part 3 (crs218_03.mp4)
Part 4 (crs218_04.mp4)

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cover image ACM Conferences
SIGGRAPH '13: ACM SIGGRAPH 2013 Courses
July 2013
860 pages
ISBN:9781450323390
DOI:10.1145/2504435
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 21 July 2013

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