The Morgan Kaufmann Series in Interactive 3D Technology: Visualizing Quaternions

Chapter 22. Optimal Quaternion Frames

In this chapter we continue to study the nature of orientation frames on curves and surfaces and their corresponding quaternion structures. Our visualizations again exploit the fact that quaternions are points on the three-sphere or hypersphere S³ embedded in 4D. The methods in this section follow closely techniques introduced in Hanson and Ma [78,80] and Hanson [70,71] for analyzing families of coordinate frames on curves and surfaces using quaternion maps.

Background

General questions involving the specification of curve framings have been investigated in many contexts. For a representative selection of approaches see, for example, Bloomenthal [21], Klock [114], Max [121], and Shani and Ballard [147]. The ...