TENSORIAL CALCULUS OF LINE AND PLANE IN HOMOGENEOUS COORDINATES

In (Mace, 1996) we have shown how Cayley's Algebra can be used to obta in expressions of generation and intersection of lines and planes. Thi s tool is of great interest in homogeneous coordinates. This paper sho ws how the introduction of line and plane as kernels of linear mapping s leads to tensorial formulation easier to manipulate than traditional Plucker-Grassmann coordinates. After extensors and duality for antisy mmetric tensors are defined, we show that line and plane generation in projective space is always an orthogonality problem solved by an exte nsor. The use of duality gives us analogous formulas for intersections . The results are simple and have a wide area of applications. (C) 199 7 Elsevier Science B.V.