Geometric Modeling

Објавено: February 28, 2019

Geometric Modeling

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:

Required Literature

No.

Author

Title

Publisher

Year

1

M. BarnsleyFractals everywhereAcademic Press, INC1998

2

K. J. FalconerFractal Geometry. Mathematical foundations and ApplicationsJohn Wiley and Sons1990

3

D. F. RogersAn introduction to NURBSBirkhäuser2007

Additional Literature

No.

Author

Title

Publisher

Year

1

J. GallierGeometric Methods and Applicationс For Computer Science and EngineeringSpringer2011

2

G.FarinCurves and Surfaces for GACDAcademic press, San Diego, CA2002