A General Construction Scheme for Unit Quaternion Curves with Simple

Hih Order Derivatives (Kim, Kim, and Shin)

Curves and geometric properties break down in even simple
non-Euclidean spaces such as S^3, meaning that we must have new ways
of dealing with curves and geometry in these spaces to be able to
guarentee such differential properties as C2 continuity. The authors
of this paper propose a class of unit quaternion curves that do just
that.

Key ideas/Contributions:

1. A new class of quaternion curves allowing Ck continuity, local
control, and guarentee that the curve remains on S^3.

2. Formulas are provided for constructing Bezier quaternion curves,
Hermite quaternion curves, and B-spline quaternion curves.

Questions:
None