Course: Geometric Modelling 1

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Course title Geometric Modelling 1
Course code KMA/GM1
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 3
Semester Winter and summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
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.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Spline function, cubic spline curve, splines of higher degrese, spline under tension, nonlinear spline. Bézier curve - Bernstein polynomials, de Casteljau algorithm. B-spline bases, de Boor algorithm, features of B-spline curves. Rational Bézier curves and NURBS (non-uniform rational B-spline) curves. Tensor product surfaces - spline surfaces, Bézier surfaces, B-spline and NURBS surfaces. Coons interpolation - bilinear, bicubic and Ferguson patch, patching. Barycentric coordinates, interpolation on a triangle. Applications of geometric modelling.

Learning activities and teaching methods
Project-based instruction, Students' portfolio, Lecture, Practicum
  • Contact hours - 52 hours per semester
  • Preparation for an examination (30-60) - 45 hours per semester
  • Presentation preparation (report in a foreign language) (10-15) - 15 hours per semester
  • Team project (50/number of students) - 20 hours per semester
prerequisite
professional knowledge
Basic orientation in terms of matrix calculus, techniques of planar/spatial analytic geometry and methods of differential calculus. Mastering the basic curves/surfaces methods of differential geometry is also welcomed. In case of insufficient background knowledge, the teachers will suggest reading material to make up for it.
learning outcomes
Upon completion of the course a student will be able to establish a geometric model for fundamental problems reflecting the requirements of modern CAGD (Computer Aided Geometric Design). He/she understands algorithms operating on the geometric kernel of the CAx systems, GIS and other graphics-oriented systems. In addition, He/she can use math software for creating geometric models and based on this can derive their other properties. Finally, using scientific literature students are able to prepare a presentation on the topics from the field of geometric modelling.
teaching methods
Lecture
Practicum
Project-based instruction
Students' portfolio
assessment methods
Combined exam
Individual presentation at a seminar
Recommended literature
  • Farin, Gerald; Kim, Myung-Soo; Hoschek, Josef. Handbook of computer aided geometric design. 1st ed. Amsterdam : Elsevier, 2002. ISBN 0-444-51104-0.
  • Ježek, František. Geometrické a počítačové modelování. ZČU, 2009.
  • Marsh, Duncan. Applied Geometry for Computer Graphics and CAD. London: Springer, 2005. ISBN 1-85233-801-6.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Computer Graphics (2017) Informatics courses 1 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 2 Winter
Faculty of Mechanical Engineering Manufacturing Processes - Technology of Metal Cutting (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Winter
Ladislav Sutnar Faculty of Design and Art Design, specialization Industrial Design (4) Art and applied art 2 Winter
Faculty of Mechanical Engineering - (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Land-use Planning (2017) Special and interdisciplinary fields 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Winter
Faculty of Mechanical Engineering Medical Technique Design (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 3 Winter
Faculty of Mechanical Engineering Materials Engineering and Engineering Metallurgy (1) Special and interdisciplinary fields 1 Winter
Faculty of Mechanical Engineering - (1) Special and interdisciplinary fields 1 Winter
Faculty of Mechanical Engineering Design of Power Machines and Equipment (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Mechanical Engineering Design of Manufacturing Machines and Equipment (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Mechanical Engineering Design of Manufacturing Machines and Equipment (2005) Mechanical engineering and mechanical production 1 Winter
Faculty of Mechanical Engineering - (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2015) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2017) Pedagogy, teacher training and social care 2 Winter
Faculty of Mechanical Engineering - (1) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 3 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 1 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Winter
Faculty of Applied Sciences Computer Graphics (2015) Informatics courses 1 Winter
Faculty of Mechanical Engineering Materials Engineering and Engineering Metallurgy (2004) Special and interdisciplinary fields 1 Winter
Faculty of Mechanical Engineering Manufacturing Processes - Technology of Metal Cutting (2004) Mechanical engineering and mechanical production 1 Winter
Faculty of Applied Sciences Land-use Planning (2016) Special and interdisciplinary fields 3 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 3 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2016) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 3 Winter
Faculty of Mechanical Engineering - (1) Mechanical engineering and mechanical production 1 Winter