alubiw@uwaterloo.ca, DC 2334, (519) 888-4567, ext. 34449

**Contents:**
Organization,
Course Outline,
Assignments,
Resources,
Lectures,
Project,
Presentation Schedule

- Announcements will be posted on Piazza
- Classes start on Thursday September 6.

**Time and Place:** Tuesday and Thursday,
1:00 -- 2:20 pm. DC 2568.

**Credit:**

- 5 assignments (50%)
- a project (50%). Pick some topic that interests you and is relevant to the course; explore some aspect of it; read a few papers; and survey them. You must do a written report and a class presentation. I will suggest possible topics.

**Collaboration policy:**
The work you hand in must be your own.
The value of the assignment is in doing it yourself.
Acknowledge any sources (human or non-human) you have used.
You may discuss the assignment questions verbally with others, but you should come away from these discussions with no written or electronic records and you must acknowledge the discussion.
If you use an electronic source or a research article, again, read it, then close it, then compose your solution and acknowledge your source.
Write your solutions in your own words, from your own head.
Any assistance received (from human or nonhuman sources) that is not given proper citation may be considered a violation of the university policies.

Assignments should be handed in (on paper) in class.

Due |
||

Assignment 1 pdf | Thursday Sept. 20 | |

Assignment 2 pdf | Thursday Oct. 4 | |

Assignment 3 pdf | Thursday Oct. 25 | |

Assignment 4 pdf | Thursday Nov. 8 | |

Assignment 5 pdf | Thursday Nov. 22 (or the following Tuesday if your presentation is Nov. 20 or 22) |

**Topics:**

- polygon triangulation
- convex hulls
- Voronoi diagrams and Delaunay triangulations
- arrangements and duality
- linear programming
- geometric data structures, search problems
- motion planning, shortest paths

- [CG]
*Computational Geometry: Algorithms and Applications,*(third edition) M. de Berg, M. van Kreveld, M. Overmars, O. Schwarzkopf, Springer, 2008.

There should be copies in the bookstore. - [CGinC]
*Computational Geometry in C*(second edition), J. O'Rourke, Cambridge University Press 1998. - [D&CG]
*Discrete and Computational Geometry,*Satyan L. Devadoss and Joseph O'Rourke, Princeton University Press, 2011.

- the computational geometry pages from MathWorld
- CGAL Computational Geometry Algorithms Library
- David Eppstein's Geometry Junkyard and Geometry in Action
- Joseph O'Rourke's comp.graphics.algorithms FAQ
- Graphics Gems

- Computing Research Repository for Computational Geometry (arXiv)
- Google Scholar
- Computational Geometry journals
- Computational Geometry conferences
- Symposium on Computational Geometry
- Canadian Conference on Computational Geometry
- European Symposium on Computational Geometry
- Fall Workshop on Computational Geometry (no proceedings)

- ACM Digital Library

L01 | Th Sep 6 | notes | slides | Every polygon can be triangulated. The Art Gallery Theorem. |

L02 | Tu Sep 11 | notes | slides | O(n log n) time triangulation algorithm via trapezoidization, and randomized version. |

L03 | Th Sep 13 | notes | slides | Partitioning polygonal regions and polyhedra. |

L04 | Tu Sep 18 | notes | slides | Convex Hulls in the Plane |

L05 | Th Sep 20 | notes | slides | Convex Hulls in 3D and higher |

Tu Sep 25 | guest lecture by Ahmad Biniaz | |||

L06 | Tu Oct 2 | notes | slides | More on Convex Hull -- randomized incremental algorithm |

L07 | Th Oct 4 | notes | slides | Voronoi diagrams and Delaunay triangulations |

L08 | Th Oct 11 | notes | slides | Voronoi diagrams and Delaunay triangulations continued |

L09 | Tu Oct 16 | notes | slides | Algorithms for Voronoi diagrams and Delaunay triangulations |

L10 | Th Oct 18 | notes | slides | End of Delaunay triangulation algorithm. Triangulations. |

L11 | Tu Oct 23 | notes | slides | Triangulations, continued. |

L12 | Th Oct 25 | notes | slides | Medial axis, Straight skeleton. Start of Arrangements. |

L13 | Tu Oct 30 | notes | slides | Line Arrangements |

L14 | Th Nov 1 | notes | slides | Planar Point Location |

L15 | Tu Nov 6 | notes | slides | Shortest Paths |

L16 | Th Nov 8 | slides | Motion Planning |

**Academic Integrity:** In order to maintain a culture of academic integrity, members of the University of Waterloo community are expected to promote honesty, trust, fairness, respect and responsibility.

[Check www.uwaterloo.ca/academicintegrity for more information. ]

**Grievance:** A student who believes that a decision affecting some aspect of his/her university life has been unfair or unreasonable may have grounds for initiating a grievance. Read Policy 70 - Student Petitions and Grievances, Section 4. When in doubt please be certain to contact the department's administrative assistant who will provide further assistance.

**Intellectual Property:**
Students should be aware that this course contains the intellectual property
of their instructor, TA, and/or the University of Waterloo. Intellectual
property includes items such as:

- Lecture content, spoken and written (and any audio/video recording thereof);
- Lecture handouts, presentations, and other materials prepared for the course (e.g., PowerPoint slides);
- Questions or solution sets from various types of assessments (e.g., assignments, quizzes, tests, final exams); and
- Work protected by copyright (e.g., any work authored by the instructor or TA or used by the instructor or TA with permission of the copyright owner).

Course materials and the intellectual property contained therein, are used to enhance a student's educational experience. However, sharing this intellectual property without the intellectual property owner's permission is a violation of intellectual property rights. For this reason, it is necessary to ask the instructor, TA and/or the University of Waterloo for permission before uploading and sharing the intellectual property of others online (e.g., to an online repository). Permission from an instructor, TA or the University is also necessary before sharing the intellectual property of others from completed courses with students taking the same/similar courses in subsequent terms/years. In many cases, instructors might be happy to allow distribution of certain materials. However, doing so without expressed permission is considered a violation of intellectual property rights.

Please alert the instructor if you become aware of intellectual property belonging to others (past or present) circulating, either through the student body or online. The intellectual property rights owner deserves to know (and may have already given their consent).

**Note for Students with Disabilities:**
The AccessAbility office, located in Needles Hall Room 1401,
collaborates with all academic departments to arrange appropriate
accommodations for students with disabilities without compromising
the academic integrity of the curriculum. If you require academic
accommodations to lessen the impact of your disability, please
register with AccessAbility Services at the beginning of each academic term.