35.679 S96 List of lectures, RPI, Computational Geometry

1. W1-17-96
  • Handouts 1 and 2.
  • Course intro.
  • Brief history of geometry: Euclid, Descartes, Euler, Peano.
  • Isosceles triangle paradox.
2. M1-22-96
  • Lee & Preparata thru locus method.
3. W1-24-96
  • Lee & Preparata ctd thru divide and conquer.
  • Sweep line edge intersection in detail, with heaps and tree rotation.
  • Recurrence relations.
4. M1-29-96
  • Lee & Preparata ctd into intersections.
  • Intro to Megiddo & Dyer linear time LP.
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.
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.
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.
8. M2-12-96
  • Lee & Preparata ctd into Voronoi diagrams.
  • Refs to Preparata and Shamos.
9. W2-14-96
  • Number of polytopes of the generalized tetrahedron, cube, octahedron types.
  • Voronoi properties and applications.
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
11. M2-26-96
  • Show xvoronoi slides.
  • GPS.
  • Using reduction to convex hull to do K-nearest neighbor Vord.
12. W2-28-96
  • Vords ctd.
  • Vords for interpolation of scattered data (Gold).
  • Handout 4.
13. M3- 4-96
  • Handouts 6 to 8.
  • Vords on other metrics.
  • Randomized search tree.
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.
15. M3-18-96
  • More points from Fortune's paper
  • My uniform grid paper
16. W3-20-96
  • Handouts 10, 13, 14, 15.
  • discuss my Steensel paper.
  • discuss my hidden surface papers.
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.
16. W3-27-96
  • Faculty job market.
  • Guibas & Stolfi paper: topology, quadedges, etc.
  • Handouts 16 to 19.
17. M4- 1-96
  • More geometry videos.
  • Break early for Vollmer Fries talk by Moog.
18. W4- 3-96
  • Wesley papers on fleshing out wireframes and projections.
19. M4- 8-96
  • Handouts 20 and 21.
  • Simulation of Simplicity.
  • Guest lecture :-) Mandlebrot on fractals.
20. W4-10-96
  • Handout 22.
  • Las Vegas Linear Programming.
  • Chazelle-Edelsbrunner edge intersection.
21. M4-15-96
  • continue Chazelle-Edelsbrunner edge intersection.
  • Numerical computations (start).
22. W4-17-96
  • TBP survey.
  • Handouts 23 to 26.
  • Robust geometry ctd.
23. M4-22-96
    Handout 27.
  • Robust geometry concl.
24. W4-24-96
    Terrain visibility.
25. M4-29-96
    Handouts 28 to 30.
  • Terrain compression.
  • State of computational geometry.
26. W5-1-96

Up to 35.679
Last updated: 18 April 96

Wm. Randolph Franklin, ECSE Dept, Rensselaer Polytechnic Institute, wrf@ecse.rpi.edu