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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
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| 8:35 |
Introduction
- Motivation
- Preview -- Think Discrete Differential - Not Purely Discrete Nor
Purely Differential Schröder
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| 9:15 |
Didactic Example in 1D and 2D
- Curves in 1D as polyline
- Meshes in 2D
Grinspun
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| 9:35 |
Geometry Processing
Mesh Parameterization
Desbrun+Schröder
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| 10:15 |
Break
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| 10:30 |
What Can We Measure?
- Simplicial Complexes
- Integral Geometry
- Geometric Measure Theory
- Discrete Measures => Simpler Implementation
Grinspun and Schröder
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| 11:20 |
Discrete Shells
- Principal Curvatures
- Discrete Shape Operator Applications
Grinspun
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| 12:15 |
Lunch
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| 1:30 |
Barycentric Coordinates and Whitney Forms
Desbrun
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| 2:15 |
Discrete Fluids
Desbrun and Schröder
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| 3:15 |
Break
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| 3:30 |
Surfaces From Circles
Schröder
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| 4:20 |
Meshing
Desbrun
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Wrap-up & Questions
All
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