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Course, academic year 2017/2018
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Geometric Modelling - NPGR021
Czech title: Geometrické modelování
Guaranteed by: Department of Software and Computer Science Education (32-KSVI)
Faculty: Faculty of Mathematics and Physics
Actual: from 2016
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Additional information:
Note: předmět je možno zapsat mimo plán
povolen pro zápis po webu
Guarantor: doc. RNDr. Zbyněk Šír, Ph.D.
Class: DS, softwarové systémy
DS, obecné otázky matematiky a informatiky
Informatika Mgr. - volitelný
Classification: Informatics > Computer Graphics and Geometry
Is incompatible with: NMMB434
Is interchangeable with: NMMB434
Annotation -
Last update: Mgr. Šárka Voráčová, Ph.D. (06.04.2006)

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.
Literature - Czech
Last update: doc. RNDr. Zbyněk Šír, Ph.D. (15.02.2016)

  • 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.

Syllabus -
Last update: G_I (12.06.2007)

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

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