Computational geometry: Schedule and links
Some useful links:
Here is a detailed schedule of the class, to be updated as the
semester progresses:
Wed 9/1
- Topics: Introduction. Basic setup. Warm-up: Finding collinear points.
- Resources:
- Project 0: Setup
[due
Monday 9/6 by class]
Mon 9/6
- Topic: Finding the closest pair of points.
- Resources:
Wed 9/8
- Topics: Geometric primitives (area of a triangle, collinear, left-of, segment intersection).
- Resources:
- Reading: O'Rourke 1.3-1.5 (geometric primitives)
- Project 1: Closest pair
[due
end of week 3, Sun 9/19]
Week 3, 4 [ 9/13, 9/15, 9/20 , 9/23]
- Topics: Geometric primitives (area of a
triangle, collinear, left-of, segment intersection).
Convex hull in 2D: Properties, algorithms (gift wrapping, Quickhull, Graham scan, Andrew's monotone chain, incremental, divide-and-conquer) and lower bound.
- Resources:
- Project 2: Hull2d with Graham's
scan [due
end of week 5, Sun 10/3 ]
Week 5 [Sept 27, 29]
- Topics: Convex hull in 3D: gift wrapping, incremental, divide-and-conquer.
- Resources:
- Project 3: Hull3d
[due end of week 7, Sun 10/17 ]
Week 6 [Oct 4, 6]
- Topics: The line-sweep technique. Orthogonal
line segment intersection. Bentley-Ottman sweep.
- Resources:
Mon Oct 11: fall break
Week 7, 8 [Oct 13, 18, 20]
- Topics: 2D space partition data structures (grids, kd-trees, range trees). Range searching.
- Resources:
- Project 4: kd-trees [due end of week 9]
Week 9, 10 [Oct 24, 27, Nov 1, 3]
- Topics: Art gallery problems. Definition and properties. Fisk's sufficiency proof. Point-in-polygon tests and ray crossings.
- Resources:
- Project 5: Fun in an
art gallery [due week 12]
Week 11 [Nov 8, 10]
- Topics:Polygon triangulation: Properties.
Polygon triangulation in quadratic time via ear removal. An O(n lg n)
triangulation algorithm via trapezoidalization and partition into
monotone mountains.
- Resources:
Week 12 [Nov 15, 17]
Week 13 [Nov 22, 24]
- Topics: THANKSGIVING BREAK
- Resources: Happy Thanksgiving everyone!
- Project: Eat, sleep, relax.
Week 14, 15 [Nov 29, Dec 1, 6, 8]
- Topics: Approximate motion planning.
- Resources:
- Project 7: Heuristical motion planning [final demo: December 15th, 1:30pm, Searles 126]
- More links:
- Search-based planner: Incremental ARA*: An incremental anytime search algorithm for moving-target search by Sun, Uras, Koenig and Yeoh, 2012
- RRT planner:
RRT-Connect: An efficient approach to single-query path planning by Kuffner and LaValle |
wiki page | RRT: Progress and prospects, LaValle, Kuffner, 2000
- PRM planner:
slides |
Latombe slides |
Probabilistic roadmaps for path planning in high dimensional configuration spaces by Kavraki, Svestka, Latombe and Overmars
| A comparative study of probabilistic roadmap planners by Geraertz and Overmars
- A survey of motion planning and control techniques for self-driving urban vehicles by Paden, Cap, Yong, Yershov and Fraziolli, 2016.
- Nice visualization of search algorithms
- Darpa grand challenge 2007
- CMU Planning techniques spring 2017 by Maxim Likhachev
- Some people/groups: CMU Boss | USC Koenig | Stanford Latombe |
UNC GAMMA group
(Dinesh Manocha) |
UIUC LaValle | ...
- Code: Motion strategy library | MPK Motion planning kit
- lastlecture.pdf
Last modified: Mon Nov 1 13:04:24 EDT 2021
