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14. Discrete Differential Geometry: An Applied Introduction


Full-Day, Sunday, 31 July, 8:30 am - 5:30 pm
Room 501AB
Level: Intermediate

An introduction to fundamentals of discrete differential geometry. This new and elegant area of mathematics has exciting applications, as this course demonstrates in practical examples of surface fairing, parameterization, cloth/shell simulation, and fluid flow.

Prerequisites


A basic background in vector calculus and familiarity with triangle meshes.

Intended Audience


Graduate students, researchers, and application developers who seek a unified understanding of the mathematics underlying common geometry-processing operations and how these fundamentals apply to problems such as Laplacian smoothing, surface fairing using prescribed curvature flow, remeshing, conformal parameterization, cloth/shell simulation, and fluid flow.

Organizer


Eitan Grinspun
Columbia University

Lecturers


Mathieu Desbrun
Peter Schröder
California Institute of Technology



Schedule



8:30 Welcome

All

8:35 Introduction
- Motivation
- Preview -- Think Discrete Differential - Not Purely Discrete Nor

Purely Differential Schröder

9:15 Didactic Example in 1D and 2D
- Curves in 1D as polyline
- Meshes in 2D

Grinspun

9:35 Geometry Processing
Mesh Parameterization

Desbrun+Schröder

10:15 Break
10:30 What Can We Measure?
- Simplicial Complexes
- Integral Geometry
- Geometric Measure Theory
- Discrete Measures => Simpler Implementation

Grinspun and Schröder

11:20 Discrete Shells
- Principal Curvatures
- Discrete Shape Operator Applications

Grinspun

12:15 Lunch
1:30 Barycentric Coordinates and Whitney Forms

Desbrun

2:15 Discrete Fluids

Desbrun and Schröder

3:15 Break
3:30 Surfaces From Circles

Schröder

4:20 Meshing

Desbrun

  Wrap-up & Questions

All

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