Multidimensional Lines

Abstract

There are several point ↔line dualities (such as the very useful Hough transform) in the plane that do not generalize well for higher dimensions. This is because the natural duality is point ↔hyperplane in projective N-space ℙ^N with point ↔line when N = 2. However, in ∥-coords there is a useful and direct generalization, which is the subject of this chapter. At first the basic idea for lines in ℝ^N, rather than ℙ^N, is derived intuitively, paving the way for the general case, which is treated subsequently (as in [106] and [107]).