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

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

- If you would like to enroll in this course, and cannot do so through quest, just send me email. The course is open to all UWaterloo students (grad, undergrad, non-CS).
- Classes start the week of September 6, 2022.
- Announcements through the term will be posted on Piazza

**Time and Place:** Classes are scheduled for Monday and Wednesday 9:30-10:50 AM,
DC 2568. Classes will be given live in zoom.
The first class is Wednesday September 7.

**Office Hours:** Tuesdays 1-2 pm and Thursdays 3-4 pm in zoom (same link as the lectures). The times may be revised as the term progresses.

**Credit:**

- 5 assignments (50%)
- a project (50%). Pick some topic that interests you and is relevant to the course; explore some aspect of it. You may attempt original research or report on some papers (one paper deeply or a few papers less deeply). You must do a written report (25%) and a class presentation (25%). 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 as pdf in email. You may scan handwritten solutions but please make sure they are easy to read.

Due |
||

Assignment 1 pdf tex | ||

Assignment 2 pdf tex | Wednesday Oct. 5 | |

Assignment 3 pdf tex | Wednesday Oct. 19 | |

Assignment 3 pdf tex | Wednesday Oct. 19 | |

Assignment 4 pdf tex | Wednesday Nov. 2 | |

Assignment 5 pdf tex | Wednesday Nov. 23 (a week later if your presentation is Nov. 21 or 23) |

**Topics:**

- polygon triangulation
- visibility and guarding
- convex hulls
- linear programming
- planar point location and range searching
- Voronoi diagrams and Delaunay triangulations
- surface reconstruction
- arrangements and duality
- shortest paths, motion planning
- curves, trajectories, Frechet distance
- spanners, routing, networks

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

available online in the UW library - [Zurich]
*Geometry: Combinatorics & Algorithms Lecture Notes* - [Handbook]
*Handbook of Discrete and Computational Geometry*(3rd edition), edited by Goodman, O'Rourke, Toth, CRC Press, 2017.

available online in the UW library - others (less accessible)
- [O'Rourke]
*Computational Geometry in C*(second edition), J. O'Rourke, Cambridge University Press 1998. - [Devadoss-O'Rourke]
*Discrete and Computational Geometry,*Satyan L. Devadoss and Joseph O'Rourke, Princeton University Press, 2011. - wikipedia's list of CG books

- [O'Rourke]

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

- ACM Digital Library

- the computational geometry pages from MathWorld
- CGAL Computational Geometry Algorithms Library
- David Eppstein's Geometry Junkyard and Geometry in Action
- Graphics Gems

Note that you may need to use a pdf viewer to use the links in the slides.

L01 | W Sep 7 | final slides | Every polygon can be triangulated. The Art Gallery Theorem. |

L02 | M Sep 12 | final slides | O(n log n) time triangulation algorithm via trapezoidization and plane sweep. |

L03 | W Sep 14 | final slides | Partitioning polygons (We'll do polyhedra next time.). |

L04 | M Sep 19 | final slides | Partitioning Polyhedra and Convex Hulls in the Plane |

L05 | W Sep 21 | final slides | More on Convex Hulls |

L06 | M Sep 26 | final slides | Convex Hull in 3D and Beyond |

L07 | W Sep 28 | final slides | Linear Programming |

L08 | M Oct 3 | final slides | Planar Point Location and Range Searching |

L09 | W Oct 5 | final slides | Voronoi diagrams |

L10 | M Oct 17 | final slides | Voronoi diagrams, continued. |

L11 | W Oct 19 | final slides | Delaunay Triangulations, continued. |

L12 | M Oct 24 | final slides | Triangulations |

L13 | W Oct 26 | final slides | Triangulations, continued |

L14 | M Oct 31 | final slides | Arrangements |

L15 | W Nov 2 | final slides | Arrangements, continued |

L16 | M Nov 7 | final slides | Shortest Paths |

L17 | W Nov 9 | final slides | Motion Planning |

L18 | M Nov 14 | final slides | Curves, Trajectories, Frechet distance |

L19 | W Nov 16 | final slides | Spanners, Routing, Networks |

**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.