Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10052006" target="_blank" >RIV/00216208:11320/10:10052006 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves
Original language description
In our contribution we study cubic and quintic Pythagorean Hodograph (PH) curves in the Euclidean and Minkowski planes. We analyze their control polygons and give necessary and sufficient conditions for cubic and quintic curves to be PH. In the case of Euclidean cubics the conditions are known and we provide a new proof. For the case of Minkowski cubics we formulate and prove a new simple geometrical condition. We also give conditions for the control polygons of quintics in both types of planes. Moreover, we introduce the new notion of the preimage of a transformation, which is closely connected to the so-called preimage of a PH curve. We determine which transformations of the preimage curves produce similarities of PH curves in both Euclidean and Minkowski plane.
Czech name
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Czech description
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Project
<a href="/en/project/GA201%2F08%2F0486" target="_blank" >GA201/08/0486: Statistical analysis of functional random variable and its applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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