Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
type: Item
instance of: scholarly article
title: Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
zbMATH Open document ID: 1263.65018
author: Marjeta Krajnc
author: Vito Vitrih
published in: Mathematics and Computers in Simulation
publication date: 2012-11-15T00:00:00Z
review text: A method for computing rational motions of a rigid body is presented. The method is based on the construction of spatial quintic Pythagorean-hodograph (PH) spline curves interpolating \(G^1\) Hermite motion data, i.e. initial/final points and rotations at the given points. The orientation of the rigid body coincides with the Euler-Rodrigues frame. The Euler-Rodriques frame is rational by construction and always non-singular at inflection points. The resulted PH curve is expressed with three free parameters used to control the length of the curve (or to provide a \(C^1\) interpolant) and to guarantee that the Euler-Rodrigues frame is as close as possible to the corresponding rotation minimizing frame. The presented method can be applied in computer animation, robot manipulation, construction of a smooth camera motion, spatial path planning in manufacturing and in many other areas where the motion of a rigid body along curved paths is considered.
reviewed by: Ivana Linkeová
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 6107058
zbMATH Keywords: Euler-Rodrigues frame
zbMATH Keywords: rotation minimizing frame
zbMATH Keywords: spline interpolation
zbMATH Keywords: Hermite interpolation
zbMATH Keywords: motion design
zbMATH Keywords: quaternions
zbMATH Keywords: rational motions of a rigid body
zbMATH Keywords: spatial quintic Pythagorean-hodograph spline curves
zbMATH Keywords: computer animation
zbMATH Keywords: robot manipulation
zbMATH Keywords: camera motion
zbMATH Keywords: path planning
MaRDI profile type: Publication
full work available at URL: j.matcom.2012.04.003
OpenAlex ID: W2080955464
Wikidata QID: Q114149983
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DOI: 10.1016/J.MATCOM.2012.04.003
description: scientific article; zbMATH DE number 6107058