| 1. | W1-17-96 |
- Handouts 1 and 2.
- Course intro.
- Brief history of geometry: Euclid, Descartes, Euler, Peano.
- Isosceles triangle paradox.
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| 2. | M1-22-96 |
- Lee & Preparata thru locus method.
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| 3. | W1-24-96 |
- Lee & Preparata ctd thru divide and conquer.
- Sweep line edge intersection in detail, with heaps and tree rotation.
- Recurrence relations.
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| 4. | M1-29-96 |
- Lee & Preparata ctd into intersections.
- Intro to Megiddo & Dyer linear time LP.
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| 5. | W1-31-96 |
- Lee & Preparata ctd into range search, with excursions:
- Intersecting convex polygons,
- Intersecting general polygons,
- Testing point inclusion in a polygon by the Jordan curve method,
- The special cases of two coincident vertices or a vertex on the other polygon's edge,
- Solving recurrence relations such as Fibonacci using powers.
- 1-D range search with segment tree
- 2-D range search: N5 and then N3 methods.
- Handout 3.
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| 6. | M2-5-96 |
- Lee & Preparata ctd thru range search, with excursions:
- 1-D data structures: binary search trees, digital search trees (tries),
- 2-D data structures: quadtrees, k-d trees.
- Refs to Preparata and Shamos
- Handout 3.
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| 7. | W2-7-96 |
- Lee & Preparata ctd thru into point location.
- Planar graph data structures, including DCEL.
- Point location methods: slab, chain.
- Refs to Preparata and Shamos.
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| 8. | M2-12-96 |
- Lee & Preparata ctd into Voronoi diagrams.
- Refs to Preparata and Shamos.
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| 9. | W2-14-96 |
- Number of polytopes of the generalized tetrahedron, cube, octahedron types.
- Voronoi properties and applications.
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| 10. | "M"2-21-96 |
- Attempt to demo xvoronoi.
- Demo U. Minn. interactive geometry.
- Voronoi diagram construction by
- divide and conquer, plus implementation problems
- reduction to convex hull in one dimension higher
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| 11. | M2-26-96 |
- Show xvoronoi slides.
- GPS.
- Using reduction to convex hull to do K-nearest neighbor Vord.
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| 12. | W2-28-96 |
- Vords ctd.
- Vords for interpolation of scattered data (Gold).
- Handout 4.
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| 13. | M3- 4-96 |
- Handouts 6 to 8.
- Vords on other metrics.
- Randomized search tree.
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| 14. | W3- 6-96 |
- Handouts 9 to 11.
- Data structures for storing all US streets on a CD.
- Fortune alg ctd.
- Triangulations in 2D and 3D: in 3D the number is variable, and
Steiner points may be necessary, and knowing whether is hard.
- Intro to Guibas and Stolfi.
- Vord by edge flipping.
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| 15. | M3-18-96 |
- More points from Fortune's paper
- My uniform grid paper
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| 16. | W3-20-96 |
- Handouts 10, 13, 14, 15.
- discuss my Steensel paper.
- discuss my hidden surface papers.
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| 15. | M3-25-96 |
- Geometry algorithms animation videos
- Decomposing a polygon into a boolean expression on the halfplanes defined by its edges, with each edge used only once.
- That can't be done in 3D.
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| 16. | W3-27-96 |
- Faculty job market.
- Guibas & Stolfi paper: topology, quadedges, etc.
- Handouts 16 to 19.
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| 17. | M4- 1-96 |
- More geometry videos.
- Break early for Vollmer Fries talk by Moog.
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| 18. | W4- 3-96 |
- Wesley papers on fleshing out wireframes and projections.
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| 19. | M4- 8-96 |
- Handouts 20 and 21.
- Simulation of Simplicity.
- Guest lecture :-) Mandlebrot on fractals.
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| 20. | W4-10-96 |
- Handout 22.
- Las Vegas Linear Programming.
- Chazelle-Edelsbrunner edge intersection.
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| 21. | M4-15-96 |
- continue Chazelle-Edelsbrunner edge intersection.
- Numerical computations (start).
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| 22. | W4-17-96 |
- TBP survey.
- Handouts 23 to 26.
- Robust geometry ctd.
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| 23. | M4-22-96 |
Handout 27.
- Robust geometry concl.
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| 24. | W4-24-96 |
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| 25. | M4-29-96 |
Handouts 28 to 30.
- Terrain compression.
- State of computational geometry.
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| 26. | W5-1-96 |
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