Course: Numerical and Geometric Modelling

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Course title Numerical and Geometric Modelling
Course code KMA/NGM
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Bastl Bohumír, Doc. Ing. Ph.D.
  • Ježek František, Doc. RNDr. CSc.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
1. Solving the equation f (x) = 0 - separation of roots, secant method and tangent method, iteration. 2. Solving systems of linear algebraic equations - finite methods, iteration. 3. Interpolation - Lagrange polynomial, spline functions. 4. Approximation - method of least squares. 5. Numerical integration and solving differential equations - initial task. 6. Difference method and finite elements. 7. Solving partial differential equations - method of networking (nets). 8. Ferguson cubic and spline curves. 9. Bezier curves and surfaces. 10. B-spline and NURBS curves and surfaces. 11. Coons patches. 12. Geometric model in CAD - edge, surface and volume model. Overview of CA in terms of methods of geometric modeling. Basic trends in geometric modeling. 13. Presentation of student projects.

Learning activities and teaching methods
Students' portfolio, Laboratory work, Lecture, Practicum
  • Contact hours - 39 hours per semester
  • Presentation preparation (report) (1-10) - 9 hours per semester
  • Preparation for comprehensive test (10-40) - 10 hours per semester
  • Individual project (40) - 10 hours per semester
  • Preparation for an examination (30-60) - 40 hours per semester
prerequisite
professional knowledge
Students should be familiar with a high school algebra, calculus and analytical geometry.
learning outcomes
Student is informed on the numerical methods in linear algebra and mathematical analyses. She/he has a overview of principles, which are used in CAD/CAM systems and has good orientation in modelling technics. She/he is able to use mathematic software (Matlab) for basic geometric modeling.
teaching methods
Lecture
Practicum
Laboratory work
Students' portfolio
assessment methods
Combined exam
Recommended literature
  • Černá, Růžena; Machalický, Miroslav; Šánová, Ladislava. Základy numerické matematiky a programování II. dot. 1. vyd. Praha : ČVUT, 1982.
  • Žára, Jiří; Beneš, Bedřich; Felkel, Petr. Moderní počítačová grafika. Praha : Computer Press, 1998. ISBN 80-7226-049-9.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Land-use Planning (2013) Special and interdisciplinary fields 3 Winter
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Land-use Planning (2014) Special and interdisciplinary fields 3 Winter