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Title:Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Authors:ID Knez, Marjetka (Author)
ID Vitrih, Vito (Author)
Files:URL http://dx.doi.org/10.1016/j.matcom.2012.04.003
 
Language:English
Work type:Not categorized
Typology:1.01 - Original Scientific Article
Organization:UPR - University of Primorska
Abstract:The paper presents an interpolation scheme for G1 Hermite motion data, i.e., interpolation of data points and rotations at the points, with spatial quintic Pythagorean-hodograph curves so that the Euler-Rodrigues frame of the curve coincides with the rotations at the points. The interpolant is expressed in a closed form with three free parameters, which are computed based on minimizing the rotations of the normal plane vectors around the tangent and on controlling the length of the curve. The proposed choice of parameters is supported with the asymptotic analysis. The approximation error is of order four and the Euler-Rodrigues frame differs from the ideal rotation minimizing frame with the order three. The scheme is used for rigid body motions and swept surface construction.
Keywords:Pythagorean-hodograph, Euler-Rodrigues frame, rotation minimizing frame, motion design, quaternion, Hermite interpolation
Year of publishing:2012
Number of pages:str. 1696-1711
Numbering:Vol. 82, iss. 9
PID:20.500.12556/RUP-33 This link opens in a new window
ISSN:0378-4754
UDC:519.65
COBISS.SI-ID:1024447572 This link opens in a new window
Publication date in RUP:15.10.2013
Views:3470
Downloads:102
Metadata:XML DC-XML DC-RDF
:
KNEZ, Marjetka and VITRIH, Vito, 2012, Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves. [online]. 2012. Vol. 82, no. 9, p. 1696–1711. [Accessed 5 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.matcom.2012.04.003
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