| dc.contributor.author |
Farouki, RT |
en |
| dc.contributor.author |
Dospra, P |
en |
| dc.contributor.author |
Sakkalis, T |
en |
| dc.date.accessioned |
2014-06-06T06:52:48Z |
|
| dc.date.available |
2014-06-06T06:52:48Z |
|
| dc.date.issued |
2013 |
en |
| dc.identifier.issn |
07477171 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1016/j.jsc.2013.07.001 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/6182 |
|
| dc.subject |
Pythagorean-hodograph curves |
en |
| dc.subject |
Quadratic equation |
en |
| dc.subject |
Quaternion polynomials |
en |
| dc.subject |
Quaternion roots |
en |
| dc.subject |
Rational rotation-minimizing frames |
en |
| dc.title |
Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1016/j.jsc.2013.07.001 |
en |
| heal.publicationDate |
2013 |
en |
| heal.abstract |
The scalar-vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial. Apart from the familiar vector dot and cross products, this algorithm requires only the determination of the unique positive real root of a cubic equation, and special cases (e.g., double roots) are easily identified through the satisfaction of algebraic constraints on the scalar/vector parts of the coefficients. The algorithm is illustrated by computed examples, and used to analyze the root structure of quadratic quaternion polynomials that generate quintic curves with rational rotation-minimizing frames (RRMF curves). The degenerate (i.e., linear or planar) quintic RRMF curves correspond to the case of a double root. For polynomials with distinct roots, generating non-planar RRMF curves, the cubic always factors into linear and quadratic terms, and a closed-form expression for the quaternion roots in terms of a real variable, a unit vector, a uniform scale factor, and a real parameter τ. ∈. [-. 1, +. 1] is derived. © 2013 Elsevier B.V. |
en |
| heal.journalName |
Journal of Symbolic Computation |
en |
| dc.identifier.volume |
58 |
en |
| dc.identifier.doi |
10.1016/j.jsc.2013.07.001 |
en |
| dc.identifier.spage |
1 |
en |
| dc.identifier.epage |
17 |
en |