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# Computer aided (geometric) design

2019/2020
Programme:
Financial Mathematics, Second cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M4
ECTS:
6
Language:
slovenian, english
Course director:

Prof. Dr. Gašper Jaklič, Prof. Dr. Emil Žagar

Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

Introduction: de Casteljau algorithm, Bernstein form of Bezier curve, Bezier curves (general), Bezier splines, rational Bezier curves
Geometric continuity: geometric continuity of curves and surfaces, geometrically continuous splines
Bezier surfaces: tensor products, triangular patches, rational Bezier surfaces
Conics: rational quadratic Bezier curves, exact representation of conics
B-spline curves: properties, algorithms for manipulating B-spline curves

Readings

G. Farin: Curves and Surfaces for Computer Aided Geometric Design : A Practical Guide, 4th edition, Academic Press, San Diego, 1997.
C. de Boor: A Practical Guide to Splines, Springer, New York, 2001.
R. H. Bartels, J. C. Beatty, B. A. Barsky: An Introduction to Splines for Use in Computer Graphics and Geometric Modeling: Morgan Kaufmann, Palo Alto, 1996.
M.-J. Lai, L. L. Schumaker, Spline functions on triangulations, Cambridge University Press, 2007

Objectives and competences

An introduction to computer aided geometric design, use of Bezier curves and surfaces, rational Bezier curves and geometrically smooth splines.
With individual presentations and team work interactions within seminar/project activities students acquire communication and social competences for successful team work and knowledge transfer.

Intended learning outcomes

Knowledge and understanding:
Knowledge of basic facts on curves and surfaces. Basic programming skill in Matlab or Mathematica. Skill to implement algorithms in programming language.
Application:
Application of interpolation and approximation with polynomials and splines in CAGD.
Reflection:
Understanding theory based on application.
Transferable skills:
Skill of using theory in practical use. Skill of interconnecting knowledge from numerical mathematics, analysis and computer science. Critical judgement of differences between theory and practical applications.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

Project
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

JAKLIČ, Gašper, KOZAK, Jernej, KRAJNC, Marjetka, VITRIH, Vito, ŽAGAR, Emil. High order parametric polynomial approximation of conic sections. Constructive approximation, ISSN 0176-4276, 2013, vol. 38, iss. 1, str. 1-18. [COBISS-SI-ID 16716121]
JAKLIČ, Gašper, KOZAK, Jernej, KRAJNC, Marjetka, VITRIH, Vito, ŽAGAR, Emil. Hermite geometric interpolation by rational Bézier spatial curves. SIAM journal on numerical analysis, ISSN 0036-1429, 2012, vol. 50, no. 5, str. 2695-2715. [COBISS-SI-ID 16449369]
JAKLIČ, Gašper, ŽAGAR, Emil. Planar cubic G [sup] 1 interpolatory splines with small strain energy. Journal of Computational and Applied Mathematics, ISSN 0377-0427. [Print ed.], 2011, vol. 235, iss. 8, str. 2758-2765. [COBISS-SI-ID 15770969]