Rational space curves are not ""unit speed""

dc.contributor.author	Farouki, RT	en
dc.contributor.author	Sakkalis, T	en
dc.date.accessioned	2014-06-06T06:47:55Z
dc.date.available	2014-06-06T06:47:55Z
dc.date.issued	2007	en
dc.identifier.issn	01678396	en
dc.identifier.uri	http://dx.doi.org/10.1016/j.cagd.2007.01.004	en
dc.identifier.uri	http://62.217.125.90/xmlui/handle/123456789/3864
dc.subject.other	Curve fitting	en
dc.subject.other	Graph theory	en
dc.subject.other	Integral equations	en
dc.subject.other	Polynomials	en
dc.subject.other	Problem solving	en
dc.subject.other	Pythagorean quartuples	en
dc.subject.other	Rational functions	en
dc.subject.other	Rational space curves	en
dc.subject.other	Computer aided design	en
dc.title	Rational space curves are not ""unit speed""	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.cagd.2007.01.004	en
heal.publicationDate	2007	en
heal.abstract	A method is developed to solve the problem of spatial curves (n = 3) by invoking a sufficient-and-necessary characterization for Pythagorean quartuples of polynomials. The method shows that the curve degenerates to a straight line parallel to the x-axis if the hodograph components ý and ź of the polynomials vanish identically. It is necessary to first identify a sufficient-and-necessary form for Pythagorean (n+1)-tuples of polynomials to extend the argument to &ℝn, with n > 3. The method shows that the existence of curves in &Rdbl;3, which is parameterized by rational functions of the arc length, is transformed into a problem of identifying four polynomials u(t), v(t), p(t), and q(t) so that the three indefinite integrals will yield rational functions.	en
heal.journalName	Computer Aided Geometric Design	en
dc.identifier.issue	4	en
dc.identifier.volume	24	en
dc.identifier.doi	10.1016/j.cagd.2007.01.004	en
dc.identifier.spage	238	en
dc.identifier.epage	240	en