Obálky implicitních ploch

• Thesis title in Czech: Obálky implicitních ploch
• Thesis title in English: Envelopes of implicit surfaces
• Key words: obálka, plocha, Lieova grupa, charakteristická křivka, parametrizace
• English key words: envelope, surface, Lie group, characteristic curve, parametrization
• Academic year of topic announcement: 2020/2021
• Thesis type: diploma thesis
• Thesis language: čeština
• 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: 20.05.2020
• Date of assignment: 20.05.2020
• Confirmed by Study dept. on: 25.05.2020
• Date and time of defence: 11.02.2022 09:00
• Date of electronic submission: 06.01.2022
• Date of submission of printed version: 10.01.2022
• Date of proceeded defence: 11.02.2022
• Opponents: doc. RNDr. Miroslav Lávička, Ph.D.

Guidelines

The system of implicit surfaces will be studied as a homogeneous space of a suitable Lie group. The characteristic curves of the envelope will be described as the intersection of the surface and the suitably embedded element of the corresponding Lie algebra. The possibility of parameterization of the whole envelope and its suitable parts will be investigated.

References

J. Flaquer, G. Garate, M. Pargada, Envelopes of moving quadric surfaces, Comput. Aided Geom. Des., 1992, volume 9, pages 299-312.
M. Peternell, Rational Parametrizations for Envelopes of Quadric Families, Dissertation 2004.
A. Karger, J. Novák, Prostorová kinematika a Lieovy grupy, Praha 1978.
D. Cox, J. Little, D. Oshea, Ideals, Varieties, and Algorithms, Springer 2015.