CRN 148 MECH 576 Computer Graphics & Geometric Modeling

An attempt is made to present, with some semblance of unity, various representations and notions of rigid body displacement. Topics touched on include • equivalence between Euler parameters and real quaternions; homogeneity and norm, inversion and populating a homogeneous rotation matrix by rote, • dual quaternions, the Study condition and multipli-cation, • point, plane, octonian and subgroup transformation, • comparing planar mapping conventions and • an appendix containing a Grassmannian demonstration of transformative dual-adjoint equivalence and some simple examples using the general 8 × 8 transformation, its adjoint to compute “reciprocals ” and its inverse. It is believed that these are revealed for the first time