Construction of G[sup]3 rational motion of degree eight

Ferjančič, Karla; Knez, Marjetka; Vitrih, Vito

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Title:	Construction of G[sup]3 rational motion of degree eight
Authors:	ID Ferjančič, Karla (Author) ID Knez, Marjetka (Author) ID Vitrih, Vito (Author)
Files:	http://www.sciencedirect.com/science/article/pii/S0096300315011297
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	IAM - Andrej Marušič Institute
Abstract:	The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with $G^3$ smoothness. The motion is determined through interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity in the spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. Sufficient conditions on the regions for the curvature data are derived, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is proposed too. The theoretical results are substantiated with numerical examples.
Keywords:	motion design, geometric interpolation, rational spline motion, geometric continuity
Year of publishing:	2015
Number of pages:	str. 1-12
Numbering:	Vol.
PID:	20.500.12556/RUP-7157
ISSN:	0096-3003
UDC:	519.651
DOI:	10.1016/j.amc.2015.08.073
COBISS.SI-ID:	1537829572
Publication date in RUP:	15.10.2015
Views:	3779
Downloads:	127
Metadata:
:	FERJANČIČ, Karla, KNEZ, Marjetka and VITRIH, Vito, 2015, Construction of G[sup]3 rational motion of degree eight. [online]. 2015. P. 1–12. [Accessed 6 April 2025]. DOI 10.1016/j.amc.2015.08.073. Retrieved from: http://www.sciencedirect.com/science/article/pii/S0096300315011297 Copy citation