Introduction: CAGD, CAD and CAM, Bernstein basis polynomials, Bezier curves, de Casteljau algorithm, properties of Bezier curves (derivative, blossom, subdivision, extrapolation, degree elevation, degree reduction).
Bezier spline curves: continuity conditions, construction of C^1 and C^2 spline curves, geometric continuity.
Rational Bezier curves: definition and properties, weight points, rational de Casteljau algorithm.
Tensorproduct Bezier surfaces: bilinear interpolant, de Casteljau algorithm, continuity conditions, tensorproduct Bezier splines.
Triangular Bezier patches: barycentric coordinates, Bernstein basis polynomials, triangular meshes, triangular de Casteljau algorithm, blossom, properties of triangular Bezier patches, continuity conditions.
Splines over triangulations: Argyris element.
Introduction to subdivision schemes
Introduction to motion design construction
Computer aided (geometric) design
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
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.
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.
Lectures, exercises, homeworks, consultations
Type (examination, oral, coursework, project):
project
oral exam
Grading: 15 (fail), 610 (pass) (according to the Statute of UL)
Jan Grošelj:
 GROŠELJ, Jan, SPELEERS, Hendrik. Three recipes for quasiinterpolation with cubic PowellSabin splines. Computer Aided Geometric Design. Dec. 2018, vol. 67, str. 4770 [COBISSSIID 18516313]
 GROŠELJ, Jan, KNEZ, Marjetka. A Bspline basis for C1 quadratic splines on triangulations with a 10split. Journal of Computational and Applied Mathematics. [Print ed.]. Dec. 2018, vol. 343, str. 413427 [COBISSSIID 18379609],

GROŠELJ, Jan. A normalized representation of super splines of arbitrary degree on PowellSabin triangulations. BIT Numerical Mathematics. Dec. 2016, vol. 56, iss. 4, str. 12571280 [COBISSSIID 17901657]
Marjetka Knez: 
KNEZ, Marjetka. G1 motion interpolation using cubic PH biarcs with prescribed length. Computer Aided Geometric Design. Dec 2018, vol. 67, str. 2133 [COBISSSIID 18537561]
 KNEZ, Marjetka. Interpolation with spatial rational Pythagoreanhodograph curves of class 4. Computer Aided Geometric Design. Aug. 2017, vol. 56, str. 1634 [COBISSSIID 18144345]
 GROŠELJ, Jan, KNEZ, Marjetka. Interpolation with C2 quartic macroelements based on 10splits. Journal of Computational and Applied Mathematics. [Print ed.]. Dec. 2019, vol. 362, str. 143160 [COBISSSIID 18846809]
Emil Žagar:
VAVPETIČ, Aleš, ŽAGAR, Emil. A general framework for the optimal approximation of circular arcs by parametric polynomial curves. Journal of Computational and Applied Mathematics. [Print ed.]. 2019, vol. 345, str. 146158 [COBISSSIID 18388057]
KNEZ, Marjetka, ŽAGAR, Emil. Interpolation of circular arcs by parametric polynomials of maximal geometric smoothness. Computer Aided Geometric Design. July 2018, vol. 63, str. 6677 [COBISSSIID 18372953]
 ŽAGAR, Emil. Circular sector area preserving approximation of circular arcs by geometrically smooth parametric polynomials. Journal of Computational and Applied Mathematics. [Print ed.]. July 2018, vol. 336, str. 6371 [COBISSSIID 18218329]