**Proceedings of Symposia in Applied Mathematics**

Volume: 76;
2020;
140 pp;
Softcover

MSC: Primary 53; 52; 65;

**Print ISBN: 978-1-4704-4662-8
Product Code: PSAPM/76**

List Price: $118.00

AMS Member Price: $94.40

MAA Member Price: $106.20

**Electronic ISBN: 978-1-4704-6003-7
Product Code: PSAPM/76.E**

List Price: $118.00

AMS Member Price: $94.40

MAA Member Price: $106.20

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# An Excursion Through Discrete Differential Geometry

Share this page *Edited by *
*Keenan Crane*

Discrete Differential Geometry (DDG) is an emerging discipline at the
boundary between mathematics and computer science. It aims to
translate concepts from classical differential geometry into a
language that is purely finite and discrete, and can hence be used by
algorithms to reason about geometric data. In contrast to standard
numerical approximation, the central philosophy of DDG is to
faithfully and exactly preserve key invariants of geometric objects at
the discrete level. This process of translation from smooth to
discrete helps to both illuminate the fundamental meaning behind
geometric ideas and provide useful algorithmic guarantees.

This volume is based on lectures delivered at the 2018 AMS Short
Course “Discrete Differential Geometry,” held January
8–9, 2018, in San Diego, California.

The papers in this volume illustrate the principles of DDG via
several recent topics: discrete nets, discrete differential operators,
discrete mappings, discrete conformal geometry, and discrete optimal
transport.

#### Readership

Graduate students and researchers interested in discrete differential geometry and its applications.

# Table of Contents

## An Excursion Through Discrete Differential Geometry

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Discrete Laplace operators 112
- Discrete parametric surfaces 1930
- Discrete mappings 4152
- 1. Triangulations and discrete mappings 4152
- 2. Convex combination mappings 4354
- 3. Proof of homeomorphism 4859
- 4. Part (i) 4960
- 5. Part (ii) 4960
- 6. Part (iii) 5162
- 7. Variational principle 5162
- 8. Approximation of conformal mappings 5263
- 9. Surface to surface mappings 5364
- 10. Other Euclidean cone surfaces 5465
- 11. Convex combination in higher dimensions 5566
- Acknowledgments 5667
- References 5667

- Conformal geometry of simplicial surfaces 5970
- Optimal transport on discrete domains 103114
- Back Cover Back Cover1154