Discrete Differential Geometry course notes (siggraph2005).pdf

Preface
This volume documents the full day course Discrete Differential Geometry: An Applied Introduction pre-
sented at SIGGRAPH ’05 on 31 July 2005. These notes supplement the lectures given by Mathieu Desbrun,
Eitan Grinspun, and Peter Schr¨piling contributions from: Pierre Alliez, Alexander Bobenko,
David Cohen-Steiner, Sharif Elcott, Eva Kanso, Liliya Kharevych, Adrian Secord, John M. Sullivan, Yiy-
ing Tong, Mariette Yvinec.
The behavior of physical systems is typically described by a set of continuous equations using tools such
as geometric mechanics and differential geometry to analyze and capture their properties. For purposes
putation one must derive discrete (in space and time) representations of the underlying equations.
Researchers in a variety of areas have discovered that theories, which are discrete from the start, and have
key geometric properties built into their discrete description can often more readily yield robust numerical
simulations which are true to the underlying continuous systems: they exactly preserve invariants of the
continuous systems in the putational realm.
A chapter-by-chapter synopsis The course notes anized similarly to the lectures. Chapter 1
presents an introduction to discrete differential geometry in the context of a discussion of curves and cur-
vature. The overarching themes introduced there, convergence and structure preservation, make repeated
appearances throughout the entire volume. Chapter 2 addresses the question of which quantities one should
measure on a discrete object such as a triangle mesh, and how one should define such measurements. This
exploration yields a host of measurements such as length, area, mean curvature, etc., and these in turn
form the basis for various applications described later on. Chapter 3 gives a concise summarization of
curvature measures for discrete surfaces, paving the way for the discrete treatment of thin shell mechanics
developed in Chapter 4. Continuing with the