Geometric Modelling - NMMB434
Title: Geometrické modelování
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016 to 2023
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Is provided by: NPGR021
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: doc. RNDr. Zbyněk Šír, Ph.D.
Class: M Bc. MMIT
M Bc. MMIT > Povinné
Classification: Informatics > Computer Graphics and Geometry
Mathematics > Geometry
Incompatibility : NPGR021
Interchangeability : NPGR021
Opinion survey results   Examination dates   WS schedule   Noticeboard   
Annotation -
In this course we will concentrate of the subdiscipline of geometric modelling known as computer aided geometric design, which was formed from the mathematical structures and methods used in CAD/CAM systems and subsequently exploited in computer graphics and computer animation. The goal in this course is to examine the basic underlying geometric structures that are used in solving some problems in geometric modelling.
Last update: Voráčová Šárka, Mgr., Ph.D. (06.04.2006)
Course completion requirements - Czech

Zápočet bude udělen za odevzdání tří domácích úkolů, které budou spočívat ve funkční implementaci zadaných problémů geometrickéh modelování.

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (13.10.2017)
Literature -

J. Hoschek, D. Lasser: Fundamentals of Computer Aided Geometric Design ,A K Peters, 1993.

G. Farin, J. Hoschek, M. Kim: Handbook of Computer Aided Geometric Design, Elsevier, 2002.

D. Finn: Geometric Modelling: lecture notes and applets (www).

C.K. Shene, Introduction to Computing with Geometry, lecture notes (web).

I. Linkeová: Základy počítačového modelování křivek a ploch, Vydavatelství ČVUT v Praze, 2008.

I. Linkeová: NURBS křivky, Nakladatelství ČVUT, Praha, 2007.

D. Velichová: Geometrické modelovanie, Bratislava, 2005.

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (29.10.2019)
Requirements to the exam -

Implementation of three homeworks is required during the semester. The exam will have both written and oral parts.

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (29.10.2019)
Syllabus -

1. Representation of surface, curve on surface, first and second fundamental form. Gauss curvature

2. Special surfaces - minimal surfaces, ruled surface

3. Translation surfaces, revolve and screw motion of curve, sweep, extrude, path extrude

4. Joining parametric surface patches, geometric continuity

5. Implicit representation, meta balls, blending function

6. Point data interpolation, Langrange polynomial, cubic spline interpolation

7. Point data approximation, polynomial surface methods

8. Approximation with tensor product patches

9. Coons patches, bicubic Hermite patches

10. Bicubic spline interpolation, knot sequence

11. Rectangular and triangular Bezier patches

12. Rational Bezier surfaces, NURBS

13. Subdivision surfaces - subdivision Doo-Sabin, Catmull-Clark, Loop and Butterfly

14. Polygonal mesh and methods of optimization

Last update: G_I (12.06.2007)
Entry requirements -

Basics of Linear algebra, Calculus and analytical geometry.

Last update: Šír Zbyněk, doc. RNDr., Ph.D. (22.06.2021)