Incidence Algebra Using Conformal Geometric Algebra

Since we detected that the authors have not completed developing the whole extension of the theory of incidence algebra and directed distance in the conformal geometric algebra framework, we decided to derive all the equations to treat the geometric relations and generation of constraints between points, lines, planes, circles, and spheres using incidence algebra, directed distance in conformal geometric algebra \(G_{4,1}\) . For example, we have five geometric entities (points, lines, planes, circles, and spheres), so you can compute 28 combinations of intersections and direct distances. These equations are illustrated graphically, showing how these geometric relations take place. Since we cover all the possible cases, deriving all the necessary equations, the reader can understand the complexity of these geometric relations without missing any detail. Therefore practitioners can use easily these equations to tackle a variety of problems in projective geometry, computer vision, graphics engineering, interpolation, and tracking using EKF techniques as well.