# Computational Geometry - Fall 2017/2018

**0368-3173-01**

Monday, 16:00-19:00, Melamed 006

**Instructor**: Dan Halperin , danha@post

**TA:**Michal Kleinbort, balasmic AT post.tau.ac.il

**Grader**: Shahar Shamai, shasha94@gmail.com

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.

### Prerequisites:

### 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

### Bibliography:

The main textbook of the course is:

*Computational Geometry: Algorithms and Applications *(CGAA), 2nd or 3rd edition by M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf.

A bibliographic list for the course

### 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, to be held on Wednesday, February 22nd, 2017, will account for the remaining 90% of the grade in the course.

About halfway through the course, we will present a **programming project**.

We encourage you to submit the programming project 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 project, and 75% the final exam. Here as well,

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

There is an option to do the project in pairs, in which case its weight will be only 10% for each student of the pair instead of 15%.

The assignments will appear here.

Assignment no. 1 file , Part I due: November 13th, 2017. Part II due: November 20th, 2017.

Submission guidelines

Assignment no. 2 file , due: December 4th, 2017.

Assignment no. 3 file , due: December 25th, 2017.

Programming assignment (pdf file), due: January 11th, 2018, 23:55.

Additional Information

Assignment no. 4 file , due: January 21th, 2018 (updated due date).

Assignment no. 5 file , not for submission.

### 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. "Slides X" refers to the relevant set of slides from Geometric Algorithms.

For an outline of the course, see for example, the course summary in the 2010 computational geometry course.

- 23.10.17
- What is Computational Geometry?

Course outline, motivation and techniques. A slow convex hull algorithm. Orientation (Side-of-line) test. Graham's O(n log n) algorithm (Chapter 1 in CGAA). Lower bound. (Slides 1.) - 30.10.17
- Gift-wrapping algorithm for computing the convex hull.

Output sensitive algorithm to compute the intersections of line segments: Bentley Ottmann's plane sweep; handling degeneracies (CGAA, Chapter 2). (Slides 2a.)

Recitation: Problems about convex polygons. - 6.11.17
- The doubly-connected edge list (DCEL). Map overlay and applications (CGAA, Chapter 2).

The Douglas-Peucker algorithm for line simplification. - 13.11.17
- Polygon triangulation and art gallery problems - Part I: combinatorial bounds and properties (O'Rourke's book CG in C, Chapters 1 and 2, and in CGAA, Chapter 3). Part II: Triangulating a monotone polygon (CGAA, Chapter 3) and decomposing a polygon into monotone polygons via trapezoidal decomposition (O'Rourke's book, Chapter 2).

Recitation: Problems about sweep line.

**20.11.17**

*Art Gallery Theorems and Algorithms*by J. O'Rourke.

**27.11.17**

**4.12.17**

**11.12.17**

*Orthogonal range searching, range trees, handling degeneracies through composite numbers (CGAA, Chapter 5).*

**18.12.17**

**25.12.17**

**Trapezoidal maps and planar point location (CGAA, Chapter 6).**

**8.1.18**

**15.1.18**

### Forum:

We will use piazza platform for our forum discussions.

Use this link to sign up for this class: piazza.com/tau.ac.il/winter2018/cs3173