| Area of Mathematics: | Computational and Applied Mathematics (ECAM) |
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| Semester: | 7o | ||
| Course ID: | 72405 | ||
| Course Type: | Elective | ||
| Teaching hours per week: | Theory: 3 | Practice: 0 | Laboratory: 0 |
| ECTS : | 5 | ||
| Eclass: | |||
| Instructors: | |||
Fractal sets and their geometry: Similarity, dimensions, dynamic system, iterated function system, complex analytic dynamics, Julia sets and the Mandelbrot set, computational methods for their construction and graphical representation in two- and three-dimensions. Design and analysis of geometric data processing algorithms: Geometric spaces and algebraic point representation, lines, curves, planes, surfaces, etc. geometric duality, space subdivisons and surface arrangements, the Zone theorem and its applications, Davenport – Schinzel sequences, applications, convex hull of points and algorithms for finding it, Voronoi diagrams and Delaunay triangulations, ways of computing them, proximity problem solutions, point and arrangement triangulations, applications, range searching techniques: subdivision trees, techniques based on random samples such as ε – net and ε – approximation, parametric searching, applications in robotics, computer vision, graphic and artificial design.
- de Berg Mark, Cheong Otfried, van Kreveld Marc and Overmars Mark, Computational Geometry: Algorithms and applications, 3rd ed., Springer-Verlag, Berlin and Heidelberg, 2008
- Peitgen Heinz-Otto, Jürgens Hartmut and Saupe Dietmar, Fractals for the classroom, Part One and Part Two, Springer-Verlag, New York, 1992
- Preparata F.P. and Shamos M. I., Computational Geometry: An introduction, Springer-Verlag, New York, 1985
- O’Rourke J., Computational Geometry in C, 2nd ed., Cambridge University Press, New York, 1998
