Pythagorean hodograph splines

• Thesis title in Czech: Spline křivky s pythagorejským hodografem
• Thesis title in English: Pythagorean hodograph splines
• Key words: polynomiální křivka, pythagorejský hodograf, preimage, kanálová plocha, spline křivky
• English key words: polynomial curve, Pythagorean hodograph, preimage, canal surface, spline curves
• Academic year of topic announcement: 2017/2018
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Mathematical Institute of Charles University (32-MUUK)
• Supervisor: doc. RNDr. Zbyněk Šír, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 12.12.2017
• Date of assignment: 13.12.2017
• Confirmed by Study dept. on: 19.12.2017
• Date and time of defence: 24.06.2020 09:00
• Date of electronic submission: 22.05.2020
• Date of submission of printed version: 28.05.2020
• Date of proceeded defence: 24.06.2020
• Opponents: doc. RNDr. Miroslav Lávička, Ph.D.

Guidelines

PH křivky jsou zvláštním typem parametrických křivek, které mají polynomiální/racionální závislost rychlosti a délky na parametru. Jsou popsány pomocí křivky v jiném prostoru, která se nazývá preimage. Student bude studovat vztah preimage a výsledné křivky, zejména vliv spline popisu preimage na výslednou křivku a to v dimenzi 2 a 3.

References

Farouki, R. Pythagorean-hodograph curves: algebra and geometry inseparable, Geometry and Computing Vol. 1, Springer, Berlin (728 p. + 204 illus.) ISBN 978-3-540-73397-3 (2008).

Šír, Z., Kosinka, J.: Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves, M. Dæhlen et al. (Eds.): MMCS 2008, LNCS 5862, pp. 394–418, 2010.

K Kadlec, Z. Šír, Smooth cubic Pythagorean Hodograph Splines, Proceedings of the 17th international conference on computational and mathematical methods in science and engineering, J. Vigo-Aguiar ed., p. 1114-1121, CMMSE 2017.

Farouki, R.T., Sakkalis, T.: Pythagorean-hodograph space curves, Advances in Computational Mathematics 2, Issue 1 (January 1994), pp. 41-66.

Farouki R.T., Manni C., Pelosi F., Sampoli M.L.: Design of C2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons. In: Boissonnat JD. et al. (eds) Curves and Surfaces. Curves and Surfaces 2010. Lecture Notes in Computer Science, vol 6920. Springer, Berlin, Heidelberg, 2010.

Albrecht G., Beccari C., Canonne J.Ch., Romani L.: Pythagorean-Hodograph B-Spline Curves, Computer Aided Geometric Design, 2016.