February 2006
Intermediate to advanced
600 pages
8h 57m
English
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.