Name
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. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1023/A:1016280811626 | Adv. Comput. Math. |
Keywords | DocType | Volume |
Pythagorean-hodograph curves,Hermite interpolation,quaternions | Journal | 17 |
Issue | ISSN | Citations |
4 | 1572-9044 | 57 |
PageRank | References | Authors |
2.96 | 10 | 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 |