Course: Geometric Modeling
Code: 3ФЕИТ08002
ECTS points: 6 ЕКТС
Number of classes per week: 3+0+0+3
Lecturers: Assoc. Prof. Dr. Vesna Andova, Asst. Prof. Dr. Sanja Atanasova
Course Goals (acquired competencies): After finishing this course, the student should adopt the basic concepts of affine geometry and its application in modeling curves and surfaces, as well as fractals and iterative functional systems. The student should develop an ability for analytic thinking, critical observations, and learning ability.
Course Syllabus: Basic concepts, metric spaces, Hausodorff metrics. Elements of affine geometry. Affine transforms. Fractals: classical fractals and selfsimilarity. Hausdorff measure and dimension. Other dimensions for fractals. Iterative functional systems (IFS). Hatchinson operator. Collage theorem. Algorithms for generating fractals. Julia sets and Mandelbrot sets. Relation between IFS and dynamical systems. Application. Basic models of curves. Bezier model ant its properties. B-splines and cubic splines. NURBS. Application of geometric modeling and using software.
Literature:
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Required Literature |
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No. |
Author |
Title |
Publisher |
Year |
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1 |
M. Barnsley | Fractals everywhere | Academic Press, INC | 1998 |
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2 |
K. J. Falconer | Fractal Geometry. Mathematical foundations and Applications | John Wiley and Sons | 1990 |
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3 |
D. F. Rogers | An introduction to NURBS | Birkhäuser | 2007 |
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Additional Literature |
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No. |
Author |
Title |
Publisher |
Year |
|
1 |
J. Gallier | Geometric Methods and Applicationс For Computer Science and Engineering | Springer | 2011 |
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2 |
G.Farin | Curves and Surfaces for GACD | Academic press, San Diego, CA | 2002 |
