inf562 | computational geometry - polytechnique · the wordle of computational geometry our...
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![Page 1: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/1.jpg)
INF562 — Computational Geometry
from Theory to Applications
Steve Oudot
Luca Castelli Aleardi
c© O. Devillers
c© J.-P. Pons
![Page 2: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/2.jpg)
c© P. Raman
The Wordle of Computational Geometry
![Page 3: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/3.jpg)
c© P. Raman
The Wordle of Computational Geometry
our itinerary
![Page 4: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/4.jpg)
c© P. Raman
The Wordle of Computational Geometry
our itinerary
![Page 5: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/5.jpg)
Course Outline
1. Fundamentals I — Convex hulls, triangulations
2. Fundamentals II — Delaunay triangulations I
3. Fundamentals III — Delaunay triangulations II, arrangements
4. Geometric aspects of graph theory I — Graph embeddings
5. Geometric aspects of graph theory II — Graph separators
6. Curve and surface reconstruction — with guarantees, multiscale
7. Proximity Problems — nearest neighbor(s) in high dimensions
8. Geometric Approximation I — Travelling Salesman Problem
9. Geometric Approximation II — Convex geometry, center points
![Page 6: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/6.jpg)
2D convex hull
and their generalizations
Voronoi of line segments
Fundamentals of Computational Geometry
Power diagram
Voronoi diagram Delaunay triangulation
Line arrangements
![Page 7: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/7.jpg)
c© R. Ghrist, A. Muhammad
Embeddings of geometric planar graphs
Schnyder drawing of a triangulation
Application to sensor networks
application to greedy routing
circle packing
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Multiscale
Reconstruction
scan + reconstruction
c© Stanford shape repository
![Page 9: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/9.jpg)
Multiscale
Reconstruction
scan + reconstruction
c© Stanford shape repository
![Page 10: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/10.jpg)
Multiscale
Reconstruction
scan + reconstruction
c© Stanford shape repository
c© Guibas, Oudot
multiscale
![Page 11: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/11.jpg)
Multiscale
Reconstruction
scan + reconstruction
c© Stanford shape repository
c© Guibas, Oudot
multiscale
![Page 12: INF562 | Computational Geometry - polytechnique · The Wordle of Computational Geometry our itinerary. Course Outline 1.Fundamentals I | Convex hulls, triangulations 2.Fundamentals](https://reader034.vdocument.in/reader034/viewer/2022052103/603dd79005f41851485839fe/html5/thumbnails/12.jpg)
2
37
5
1
0.2 8
17
Euclidean TSP (Travelling Salesman Problem)
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2
37
5
1
0.2 8
17
opt
|opt| = 36.2
Euclidean TSP (Travelling Salesman Problem)
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1
1
Euclidean TSP (Travelling Salesman Problem)
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1
1
level 1
level 2
level 3
Euclidean TSP (Travelling Salesman Problem)
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1
1
level 1
level 2
level 3
c© S. Arora
Euclidean TSP (Travelling Salesman Problem)
|opt| ≤ |T | ≤ (1 + ε)|opt|