Semester Offering: InterSem
 

To provide students with an introduction to both the theory and applications of the discipline of computational geometry which is concerned with the solving of computational problems arising from geometric questions. Essential theory and algorithms will be covered and content will be motivated by practical problems. Implementations of geometric algorithms in a high-level language will be covered. Course will be seminar-style.

 

Geometric Algorithms and Analysis. Geometric Data Structures. Convex Hull Theory and Computation. Segment Intersection. Polygon Triangulation. Geometric Linear Programming. Voronoi Diagrams. Delaunay Triangulation. Point Location. Motion Planning. Binary Space Partition. Special Topics.

 

Data Structures and Algorithms, or Instructor Consent.

 

I.          Convex Hulls
1.     Properties
2.     Algorithms
3.     Handling Degeneracy and Robustness
4.     Applications Domains

II.        Line Segment Intersections
1.     Algorithms
2.     Plane Sweep Method
3.     Doubly-Connected Edge List
4.     Application Domains

III.       Polygon Triangulation
1.     Properties
2.     Algorithms
3.     Applications Domains
        
IV.       Linear Programming
1.     Geometric View of Linear Programming
2.     Two-variable Linear Programming: Intersecting Half-Planes
3.     Incremental Linear Programming
4.     Randomized Linear Programming: Backward Analysis
5.     Linear Programming in Higher Dimensions

V.        Voronoi Diagrams
1.     Properties
2.     Algorithms
3.     Application Domains

VI.       Delaunay Triangulation
1.    Point Set Triangulation
2.   Properties: Delaunay Triangulation as Dual of the Voronoi Diagram
3.     Algorithms
4.     Application Domains 

VII.     Point Location
1.     Trapezoidal Maps
2.     Randomized Incremental Algorithms

VIII.    Robot Motion Planning
1.     Work space and Configuration Space
2.     Point Robots
3.     Motion Planning Techniques

IX.       Binary Space Partition
1.     Properties     
2.     Painter’s Algorithm
3.     Construction

X.        Special Topics
1.     According to interest.

 

M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf: 
Computational Geometry: Algorithms and Applications (2nd Edition), Springer Verlag, 2000.

 

J-D. Boissonnat and M. Yvinec:
Algorithmic Geometry, Cambridge University Press, 1998.

K. Mulmuley:
Computational Geoemetry: An Introduction through Randomized Algorithms, Prentice Hall, 1998.

J. O’Rourke:
Computational Geometry in C (2nd Edition), Cambridge University Press, 1998.

F. P. Preparata and M. I. Shamos:
Computational Geometry: An Introduction, Springer-Verlag, 1991.

 

International Journal of Computational Geometry and Applications, World Scientific.

Computational Geometry: Theory and Applications, Elsevier.

 

The final grade will be computed from the following constituent parts:

Assignments (30-40%),
Programming projects (30-40%) and
Presentations (30-40%).

Open/closed-book examination is used for both mid-semester and final exam.