Computational Geometry | Faculty of Technical Sciences

Subject: Computational Geometry (17.DOM54L)

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)
Doctoral Academic Studies	Engineering Animation (Year: 1, Semester: Summer)

General information:

Category	Scientific-professional
Scientific or art field	Applied Computer Science and Informatics Teorijska i primenjena matematika
ECTS	10

Enabling students to develop abstract thinking and acquire knowledge about computational geometry.

To use the acquired knowledge in engineering subjects and in practice, postulate and solve mathematical models in engineering subjects using the knowledge about computational geometry.

Introduction (Euclidean, projective, affine and analytical geometry). Geometric Searching. Convex Hulls. Fundamental Algorithms. Variants and Generalizations. Intersections. Geometry of Rectangles. Fuzzy Computational Geometry. Computer Graphics and Geometric Modeling. Geometric algorithms of pattern recognition.

Lectures. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. In addition to lectures there are regular consultations. The students can take partial exams during the course. A part of the course material (which represents a unit of course subject matter) is presented orally and submitted as a written seminar paper. The oral part of the final examination is eliminatory. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Authors	Title	Year	Publisher	Language
Preparata, F.P., Shamos, M.I.	Computational Geometry: an Introduction	1985	Springer-Verlag, New York	English
Valentin E. Brimkov (Editor), Reneta P. Barneva (Editor)	Digital Geometry Algorithms: Theoretical Foundations and Applications to Computational Imaging (Lecture Notes in Computational Vision and Biomechanics)	2012	Springer	English
Agoston, M.K.	Computer Graphics and Geometric Modeling: Mathematics	2005	Springer-Verlag, London	English
De Berg, M. et al.	Computational Geometry: Algorithms and Applications	2008	Springer, Berlin	English
Agoston, M.K.	Computer Graphics and Geometric Modeling: Implementation and Algorithms	2005	Springer-Verlag, New York	English

Course activity	Pre-examination	Obligations	Number of points
Project defence	Yes	Yes	10.00
Practical part of the exam - tasks	No	Yes	25.00
Theoretical part of the exam	No	Yes	40.00
Term paper	Yes	Yes	20.00
Lecture attendance	Yes	Yes	5.00