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Scalar-vector algorithm for the roots of quadratic quaternion polynomials, and the characterization of quintic rational rotation-minimizing frame curves

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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


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