| dc.contributor.author |
Sakkalis, T |
en |
| dc.contributor.author |
Farouki, RT |
en |
| dc.date.accessioned |
2014-06-06T06:52:00Z |
|
| dc.date.available |
2014-06-06T06:52:00Z |
|
| dc.date.issued |
2012 |
en |
| dc.identifier.issn |
03770427 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1016/j.cam.2012.04.002 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/5810 |
|
| dc.subject |
Complex numbers |
en |
| dc.subject |
Hopf map |
en |
| dc.subject |
Octonions |
en |
| dc.subject |
Parameterization of n-tuples |
en |
| dc.subject |
Pythagorean-hodograph curves |
en |
| dc.subject |
Quaternions |
en |
| dc.subject.other |
Complex number |
en |
| dc.subject.other |
N-tuples |
en |
| dc.subject.other |
Octonions |
en |
| dc.subject.other |
Pythagorean-hodograph curves |
en |
| dc.subject.other |
Quaternions |
en |
| dc.subject.other |
Number theory |
en |
| dc.subject.other |
Polynomials |
en |
| dc.subject.other |
Kinematics |
en |
| dc.title |
Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3 |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1016/j.cam.2012.04.002 |
en |
| heal.publicationDate |
2012 |
en |
| heal.abstract |
A polynomial Pythagorean-hodograph (PH) curve r(t)=( x1(t),..., xn(t)) in Rn is characterized by the property that its derivative components satisfy the Pythagorean condition x1′2(t) +⋯+xn′2(t)= σ2(t) for some polynomial σ(t), ensuring that the arc length s(t)=∫σ(t)dt is simply a polynomial in the curve parameter t. PH curves have thus far been extensively studied in R2 and R3, by means of the complex-number and the quaternion or Hopf map representations, and the basic theory and algorithms for their practical construction and analysis are currently well-developed. However, the case of PH curves in Rn for n>3 remains largely unexplored, due to difficulties with the characterization of Pythagorean (n+1)-tuples when n>3. Invoking recent results from number theory, we characterize the structure of PH curves in dimensions n=5 and n=9, and investigate some of their properties. © 2012 Elsevier B.V. All rights reserved. |
en |
| heal.journalName |
Journal of Computational and Applied Mathematics |
en |
| dc.identifier.issue |
17 |
en |
| dc.identifier.volume |
236 |
en |
| dc.identifier.doi |
10.1016/j.cam.2012.04.002 |
en |
| dc.identifier.spage |
4375 |
en |
| dc.identifier.epage |
4382 |
en |