ABSTRACT
In this paper, we are using projective two-or three-space with points a = [x,y, z]T or a = [x, y, 2, tu]T. Points whose coordinates differ by a constant factor denote the same location.
Once four points, no three of them collinear, have been determined, and coordinates have been assigned to them, the coordinates of every point in the projective plane are determined: we say that the four points constitute a projective reference frame for the projective plane. Without loss of generality, we may assign coordinates e l = [1,0,0]T,e2 = [0, l,0]T,e3 = [0,0,1]T, and [1,1,1]T to these four points. Fig. 1 shows how they generate a coordinate system: the lines of constant parameter values are shown. Notice that these lines form three pencils, each pencil containing one edge of the triangle. (A pencil is a set of straight lines through one common point, the center of the pencil.) The centers of these pencils are collinear, corresponding to the coordinates [—oo, oo, 0]T, [—oo, 0, oo]T, and [0, — oo,oo]T. We shall call the line that contains them the fundamental line F of our coordinate system. For more details, see [2,3,6].
