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Computational Geometry and Applications

Course code: AT70.16
Credits: 3(3–0)
This course is elective

Course objectives

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.

Learning outcome

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.

Course outline

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.

Learning resources


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


International Journal of Computational Geometry and Applications, World Scientific.
Computational Geometry: Theory and Applications, Elsevier.

Reference books

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.


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.

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