## Bézier curves and C2 interpolation in Riemannian manifolds

- Tomasz Popiel, Lyle Noakes
- Journal of Approximation Theory
- 2007

1 Excerpt

- Published 1996 in Journal of Visualization and Computer Animation

Construction methods are presented that generate hermite interpolation quaternion curves on SO(3). Two circular curves C 1 (t) and C 2 (t), 0 t 1, are generated that interpolate two orientations q 1 and q 2 , and have boundary angular velocities: C 0 1 (0) = ! 1 and C 0 2 (1) = ! 2 , respectively. They are smoothly blended together on SO(3) to generate a hermite quaternion curve Q(t) 2 SO(3), 0 t 1, which satisses the boundary conditions: Q(0) = q 1 ; Q(1) = q 2 ; Q 0 (0) = ! 1 , and Q 0 (1) = ! 2 .

@article{Kim1996HermiteIO,
title={Hermite Interpolation of Solid Orientations with Circular Blending Quaternion Curves},
author={Myung-Soo Kim and Kee-Won Nam},
journal={Journal of Visualization and Computer Animation},
year={1996},
volume={7},
pages={95-110}
}