Polynomial curves with projections to PH curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43966146" target="_blank" >RIV/49777513:23520/22:43966146 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0167839622000954" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0167839622000954</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2022.102159" target="_blank" >10.1016/j.cagd.2022.102159</a>

Result language
angličtina
Original language name
Polynomial curves with projections to PH curves
Original language description
Despite the fact that the orthogonal projection of a spatial Pythagorean hodograph (PH) curve into the plane is not a planar PH curve in general, we can find special cases such that the PH property is preserved when the curve is projected. In Farouki et al. (2021) the authors studied how to generate spatial PH curves with planar PH projections. Their approach and presented results motivated us to continue and extend this investigation. We study geometric conditions under which a spatial curve is projected to a PH curve. For this purpose, we introduced a suitable geometric characterization of the curves with PH property via intersection multiplicity of the associated curves described by the hodograph mapping with the absolute conic. As a consequence we will show that a generic polynomial curve of degree higher than five possesses no parallel projection to a PH curve. On contrary, for a spatial cubic there are finitely many ways how to orthogonally project it to a planar PH cubic. And the same holds for oblique parallel projections of spatial quintics. Hence these cases are examined in more detail.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GF21-08009K" target="_blank" >GF21-08009K: Generalized Symmetries and Equivalences of Geometric Data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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