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

Appendix H. Quaternion Frame Integration

Classical differential geometry texts present a time-honored method of finding the shape of a curve given a specification for its curvature and torsion throughout the curve along with its initial conditions. For example, an excellent modern treatment that is very compatible with the philosophy of this book, and especially the Mathematica-friendly computational philosophy we often exploit for visualization, is that of Alfred Gray [61].

Table H.1 shows the code for the traditional method of solving the differential equation, as implemented by Gray. Using the quaternion frame methods of Chapter 20, we are led to the much more compact program (shown in Table H.2), which is also slightly more general in that ...