Polynomial curves with projections to PH curves

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial curves with projections to PH curves

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Polynomial curves with projections to PH curves

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF21-08009K" target="_blank" >GF21-08009K: Zobecněné symetrie a ekvivalence geometrických dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

COMPUTER AIDED GEOMETRIC DESIGN

ISSN

0167-8396

e-ISSN

1879-2332

Svazek periodika

99

Číslo periodika v rámci svazku

Nov 2022

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

nestrankovano

Kód UT WoS článku

000878094700001

EID výsledku v databázi Scopus

2-s2.0-85140486935