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Cubic Spiral Transition Matching G2 Hermite End Conditions

Published online by Cambridge University Press:  28 May 2015

Zulfiqar Habib  and
Manabu Sakai
Zulfiqar Habib*
Affiliation:
COMSATS Institute of Information Technology, Department of Computer Science, Defense Road, Off Raiwind Road, Lahore, Pakistan
Manabu Sakai*
Affiliation:
Department of Mathematics & Computer Science, Koorimoto 1-21-35, Kagoshima 890-0065, Japan
*
Corresponding author.Email address:drzhabib@ciitlahore.edu.pk
Corresponding author.Email address:msakai@sci.kagoshima-u.ac.jp
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Abstract

This paper explores the possibilities of very simple analysis on derivation of spiral regions for a single segment of cubic function matching positional, tangential, and curvature end conditions. Spirals are curves of monotone curvature with constant sign and have the potential advantage that the minimum and maximum curvature exists at their end points. Therefore, spirals are free from singularities, inflection points, and local curvature extrema. These properties make the study of spiral segments an interesting problem both in practical and aesthetic applications, like highway or railway designing or the path planning of non-holonomic mobile robots. Our main contribution is to simplify the procedure of existence methods while keeping it stable and providing flexile constraints for easy applications of spiral segments.

Keywords

65D0565D0765D1065D1765D18Path planningspiralcubic BézierG2 HermiteComputer-Aided Design (CAD)computational geometry
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 4 , Issue 4 , November 2011 , pp. 525 - 536
Copyright
Copyright © Global Science Press Limited 2011

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