Title:	Polynomial curves with projections to PH curves
Authors:	Lávička, Miroslav Vršek, Jan
Citation:	LÁVIČKA, M. VRŠEK, J. Polynomial curves with projections to PH curves. COMPUTER AIDED GEOMETRIC DESIGN, 2022, roč. 99, č. Nov 2022, s. nestránkováno. ISSN: 0167-8396
Issue Date:	2022
Publisher:	Elsevier
Document type:	preprint preprint
URI:	2-s2.0-85140486935 http://hdl.handle.net/11025/50543
ISSN:	0167-8396
Keywords in different language:	Spatial polynomial curvesPythagorean hodograph curvesParallel projectionOrthogonal projection
Abstract in different language:	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.
Rights:	Plný text je přístupný v rámci univerzity přihlášeným uživatelům. © Elsevier
Appears in Collections:	Preprinty / Preprints (KMA) OBD

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