Name
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 u'(t), v'(t), p'(t), q'(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. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1016/S0167-8396(02)00123-1 | Computer Aided Geometric Design |
Keywords | Field | DocType |
pythagorean hodographs,real-time ph curve,arbitrary spatial rotation,ph representation map,three-dimensional pythagorean,pythagorean-hodograph curves,structural invariance,spatial pythagorean hodographs,factored-quaternion representation,spatial rotations,spatial rotation,pythagorean hodograph,quaternions,canonical form,ph space curve,euclidean space,three dimensional,computer aided design,real time | Topology,Pythagorean field,Polynomial,Invariant (physics),Quaternion,Canonical form,Hodograph,Euclidean geometry,Pythagorean theorem,Mathematics | Journal |
Volume | Issue | ISSN |
19 | 6 | Computer Aided Geometric Design |
Citations | PageRank | References |
34 | 1.98 | 22 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rida T. Farouki | 1 | 1396 | 137.40 |
| Mohammad al-Kandari | 2 | 105 | 6.09 |
| Takis Sakkalis | 3 | 347 | 34.52 |