# Computational Geometry - Fall 2020-2021

**Fall 2020-2021**

**0368-3173-01**

**Course hours**: Monday, 16:10-19:00

**Recitation: **Wednesday, 18:10-19:00

**Location: **Zoom

**Instructor**: Dan Halperin , danha@tauex.tau.ac.il

**Teaching Assistant**: Michal Kleinbort, balasmic@post.tau.ac.il

**Grader**: Tomer Even, tomereven@mail.tau.ac.il

The course covers fundamental algorithms for solving geometric problems such as computing convex hulls, intersection of line segments, Voronoi diagrams, polygon triangulation, and linear programming in low dimensional space. We will also discuss several applications of geometric algorithms to solving problems in robotics, GIS (geographic information systems), computer graphics, and more.

### Bibliography:

The main textbook of the course is:

*Computational Geometry: Algorithms and Applications *(CGAA), 3rd edition by M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf.

A bibliographic list for the course

### Slides:

I will often use slides that accompany the main textbook of the course.The slides are by Marc van Kreveld and they can be found

at the following site: Geometric Algorithms

### Assignments, Examination and Grade:

The standard assignments will account for 10% of the final grade, in case they improve the final grade.

The grade in the final exam will account for the remaining 90% of the grade in the course.

**Exam(ple), **pdf file, traditional style

**Exam(ple), **pdf file, new covid-19 style; example first page of answers, pdf file

About halfway through the course (probably earlier), we will present a **programming assignment**.

This year's programming assignment is Multi Robot Coordination as described in the Computational Geometry Challenge 2021. We will use the same input and output format. More details on the assignment will be provided soon.

We encourage you to submit the programming assignment as well. This is not mandatory.

If however you do submit it, then your grade breakdown will be 10% the standard assignments,

15% the programming assignment, and 75% the final exam. Here as well,

the assignments grades will be counted toward the final grade only if they improve it.

The assignments will appear here.

Assignment no. 1 file , due: November 9th, 2020.

Assignment no. 2 file , due: November 23rd, 2020.

Programming assignment (pdf file), due: January 17th, 2021, 23:59; see additional information.

Assignment no. 3 file , due: December 14th, 2020.

Assignment no. 4 file , due: January 4th, 2021.

Assignment no. 5 file , **optional**; if you wish to have your assignment checked, submit by January 14th, 2021.

### Course Summary:

Below you'll find a very brief summary of what was covered in class during the semester.

This should not be taken as a complete description of the course's contents.

For an outline of the course, see for example, the course summary in the Spring 2020 computational geometry course.

Motivation and techniques. A slow convex hull algorithm. Graham's O(n log n) algorithm (Chapter 1 in CGAA). (slides1.) Lower bound. Gift-wrapping algorithm for computing the convex hull, Jarvis's March (Preparata-Shamos, Section 3.3.3).