| Lect | Date | Topic | Reference |
| Geometric Fundamentals |
| 1 |
08/30 |
Introduction, models |
[PS P.19-35] |
| Geometric Data Structures I |
| 2 |
09/01 |
1D Data structures: segment, interval, and priority trees
|
[dBKOS Ch5, 11] |
| 3 |
09/06 |
2D orthogonal range searching, kd trees |
[dBKOS Ch5; GO Ch36] |
| 4 |
09/08 |
quad trees, range trees, Planar point location |
[dBKOS Ch5; Ch6] |
| Intersection Detection |
| 5 |
09/13 |
Intersection detection: sweep-line, RIC |
[dBKOS Ch2] |
| 6 |
09/15 |
RIC analysis |
[dBKOS Ch6] |
| Convex Hull |
| 7 |
09/20 |
2D Convex Hull, Convex polytopes |
[PS Ch3; dBKOS Ch1; Ma Ch5] |
| 8 |
09/22 |
Convex hull in high dimensions, Guest Lecture by Thomas Mølhave |
[PS Ch3; dBKOS Ch11] |
| Proximity Problems |
| 9 |
09/27 |
Voronoi Diagram, Delaunay triangulation |
[dBKOS Ch7] |
| |
09/29 |
No class |
|
| 10 |
10/04 |
RIC for DT, generalizations of DT |
[dBKOS Ch9; Ed P.9-17] |
| 11 |
10/06 |
Applications of VD/DT |
[Ed 9-17] |
| 12 |
10/12 |
Quad trees, WSPD |
[HP, Ch 2,3] |
| 13 |
10/13 |
WSPD, Nearest neighbor searching |
[HP Ch 3,11] |
| Arrangements |
| 14 |
10/18 |
Arrangements of lines & curves, lower envelopes, zone theorem |
[dBKOS Ch8] |
| 15 |
10/20 |
Lower envelope, single cell, motion planning |
[Mat Ch 6,7; AS] |
| Triangulations |
| 16 |
10/25 |
Point-set triangulation, Delaunay refinement |
[Ed Ch2] |
| Geometric Sampling |
| 17 |
10/27 |
Random sampling, e-nets, e-approximations |
[PA Ch16] |
| 18 |
11/01 |
Geometric summaries, core sets |
[HP; AHV] |
| Geometric Data Structures II |
| 19 |
11/03 |
Geometric cuttings |
[Ma Ch4 & 6] |
| 20 |
11/08 |
Simplex range searching |
[dBKOS Ch16] |
| 21 |
11/10 |
Halfspace range reporting |
[CGL] |
| Geometric Optimization |
| 22 |
11/15 |
Linear programming, prune and search, RI algorithm |
[Clarkson] |
| 23 |
11/17 |
Geometric set cover |
[Clarkson] |
| 24 |
11/22 |
Shape matching |
|
| 25 |
11/29 |
Clustering |
|
| Dimension Reduction |
| 26 |
12/01 |
Embedding techniques |
[Ma Ch15] |
