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

Chapter 24. Quaternion Maps of Streamlines

We now apply quaternion frame methods to the study of data containing a large number of related curves. We assume that we are given a family of analytic or experimentally sampled curves, with sufficient information to extract smooth first derivatives (and perhaps higher derivatives) from the data. A representative application domain is a flow field that has been processed to generate streamlines by integrating the paths of test particles. Standard methods are typically limited to visual representations showing the 3D spatial positions of the test particle traces. The methods we shall study indicate that the data contain a wealth of additional information we can exploit using intrinsic geometric features ...