| dc.contributor.author |
Farouki, RT |
en |
| dc.contributor.author |
Al-Kandari, M |
en |
| dc.contributor.author |
Sakkalis, T |
en |
| dc.date.accessioned |
2014-06-06T06:45:04Z |
|
| dc.date.available |
2014-06-06T06:45:04Z |
|
| dc.date.issued |
2002 |
en |
| dc.identifier.issn |
10197168 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1023/A:1016280811626 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/2232 |
|
| dc.subject |
Hermite interpolation |
en |
| dc.subject |
Pythagorean-hodograph curves |
en |
| dc.subject |
Quaternions |
en |
| dc.title |
Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1023/A:1016280811626 |
en |
| heal.publicationDate |
2002 |
en |
| heal.abstract |
The interpolation of first-order Hermite data by spatial Pythagorean-hodograph curves that exhibit closure under arbitrary 3-dimensional rotations is addressed. The hodographs of such curves correspond to certain combinations of four polynomials, given by Dietz et al. [4], that admit compact descriptions in terms of quaternions - an instance of the ""PH representation map"" proposed by Choi et al. [2]. The lowest-order PH curves that interpolate arbitrary first-order spatial Hermite data are quintics. It is shown that, with PH quintics, the quaternion representation yields a reduction of the Hermite interpolation problem to three ""simple"" quadratic equations in three quaternion unknowns. This system admits a closed-form solution, expressing all PH quintic interpolants to given spatial Hermite data as a two-parameter family. An integral shape measure is invoked to fix these two free parameters. |
en |
| heal.journalName |
Advances in Computational Mathematics |
en |
| dc.identifier.issue |
4 |
en |
| dc.identifier.volume |
17 |
en |
| dc.identifier.doi |
10.1023/A:1016280811626 |
en |
| dc.identifier.spage |
369 |
en |
| dc.identifier.epage |
383 |
en |