Quaternions

Joan Lasenby introduces geometric algebra, tracing its roots to Grassmann and Clifford and describing how David Hestenes developed it as a practical mathematical language. She explains how it represents geometric objects such as lines, planes, and rotations, and why this can make problems in computer vision, graphics, physics, and engineering easier to express and solve. Examples include reconstructing scenes from moving cameras, working with rotations, and modeling circles and spheres in conformal geometric algebra. She also discusses the approach’s learning curve, its growing tools and community, and where it may prove useful.