Pythagorean hodograph spline spirals that match G3 Hermite data from circles

Handle URI:
http://hdl.handle.net/10754/564114
Title:
Pythagorean hodograph spline spirals that match G3 Hermite data from circles
Authors:
Li, Zhong; Ait-Haddou, Rachid; Biard, Luc
Abstract:
A construction is given for a G3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Elsevier BV
Journal:
Journal of Computational and Applied Mathematics
Issue Date:
Apr-2015
DOI:
10.1016/j.cam.2014.10.005
Type:
Article
ISSN:
03770427
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorLi, Zhongen
dc.contributor.authorAit-Haddou, Rachiden
dc.contributor.authorBiard, Lucen
dc.date.accessioned2015-08-03T12:32:45Zen
dc.date.available2015-08-03T12:32:45Zen
dc.date.issued2015-04en
dc.identifier.issn03770427en
dc.identifier.doi10.1016/j.cam.2014.10.005en
dc.identifier.urihttp://hdl.handle.net/10754/564114en
dc.description.abstractA construction is given for a G3 piecewise rational Pythagorean hodograph convex spiral which interpolates two G3 Hermite data associated with two non-concentric circles, one being inside the other. The spiral solution is of degree 7 and is the involute of a G2 convex curve, referred to as the evolute solution, with prescribed length, and composed of two PH quartic curves. Conditions for G3 continuous contact with circles are then studied and it turns out that an ordinary cusp at each end of the evolute solution is required. Thus, geometric properties of a family of PH polynomial quartics, allowing to generate such an ordinary cusp at one end, are studied. Finally, a constructive algorithm is described with illustrative examples.en
dc.publisherElsevier BVen
dc.subjectG3 Hermite interpolationen
dc.subjectHighway designingen
dc.subjectPath planningen
dc.subjectPH curvesen
dc.subjectRational spiralen
dc.titlePythagorean hodograph spline spirals that match G3 Hermite data from circlesen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalJournal of Computational and Applied Mathematicsen
dc.contributor.institutionDepartment of Mathematics and Science, Zhejiang Sci-Tech UniversityHangzhou, Zhejiang, Chinaen
dc.contributor.institutionLaboratoire Jean Kuntzmann, Université Joseph FourierGrenoble, Franceen
kaust.authorAit-Haddou, Rachiden
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