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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.

### Prerequisite(s)

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.       <

### Textbook

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

### Journals

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.

### Reference books

International Journal of Computational Geometry and Applications, World Scientific.

Computational Geometry: Theory and Applications, Elsevier.

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