| dc.contributor.author |
Farouki, RT |
en |
| dc.contributor.author |
Al-Kandari, M |
en |
| dc.contributor.author |
Sakkalis, T |
en |
| dc.date.accessioned |
2014-06-06T06:45:09Z |
|
| dc.date.available |
2014-06-06T06:45:09Z |
|
| dc.date.issued |
2002 |
en |
| dc.identifier.issn |
01678396 |
en |
| dc.identifier.uri |
http://dx.doi.org/10.1016/S0167-8396(02)00123-1 |
en |
| dc.identifier.uri |
http://62.217.125.90/xmlui/handle/123456789/2270 |
|
| dc.subject |
Pythagorean-hodograph curves |
en |
| dc.subject |
Quaternions |
en |
| dc.subject |
Spatial rotations |
en |
| dc.subject.other |
Computational methods |
en |
| dc.subject.other |
Computer aided manufacturing |
en |
| dc.subject.other |
Eigenvalues and eigenfunctions |
en |
| dc.subject.other |
Interpolation |
en |
| dc.subject.other |
Matrix algebra |
en |
| dc.subject.other |
Polynomials |
en |
| dc.subject.other |
Pythagorean hodographs (PH) |
en |
| dc.subject.other |
Computer aided design |
en |
| dc.title |
Structural invariance of spatial Pythagorean hodographs |
en |
| heal.type |
journalArticle |
en |
| heal.identifier.primary |
10.1016/S0167-8396(02)00123-1 |
en |
| heal.publicationDate |
2002 |
en |
| heal.abstract |
The structural invariance of the four-polynomial characterization for three-dimensional Pythagorean hodographs introduced by Dietz et al. (1993), under arbitrary spatial rotations, is demonstrated. The proof relies on a factored-quaternion representation for Pythagorean hodographs in three-dimensional Euclidean space - a particular instance of the ""PH representation map"" proposed by Choi et al. (2002) - and the unit quaternion description of spatial rotations. This approach furnishes a remarkably simple derivation for the polynomials ũ(t), ṽ(t), p̃(t), q̃(t) that specify the canonical form of a rotated Pythagorean hodograph, in terms of the original polynomials u(t), v(t), p(t), q(t) and the angle θ and axis n of the spatial rotation. The preservation of the canonical form of PH space curves under arbitrary spatial rotations is essential to their incorporation into computer-aided design and manufacturing applications, such as the contour machining of free-form surfaces using a ball-end mill and real-time PH curve CNC interpolators. © 2002 Elsevier Science B.V. All rights reserved. |
en |
| heal.journalName |
Computer Aided Geometric Design |
en |
| dc.identifier.issue |
6 |
en |
| dc.identifier.volume |
19 |
en |
| dc.identifier.doi |
10.1016/S0167-8396(02)00123-1 |
en |
| dc.identifier.spage |
395 |
en |
| dc.identifier.epage |
407 |
en |