Horizon science of graphical perspective. Assuming the picture plane stands vertical to ground, and "P" is the perpendicular projection of the eye point "O" on the picture plane, the horizon is defined as the horizontal line through "P". The point "P" is the vanishing point of lines perpendicular to the picture. If "S" is another point on the horizon, then it is the vanishing point for all lines parallel to "OS". But Brook Taylor (1719) indicated that the horizon plane determined by "O" and the horizon was like any other plane: The peculiar geometry of perspective where parallel lines converge in
Point at infinity Point at infinity In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line. In the case of an affine plane (including the Euclidean plane), there is one ideal point for each pencil of parallel lines of the plane. Adjoining these points produces a projective plane, in which no point can be distinguished, if we "forget" which points were added. This holds for a geometry over any field, and more generally over any division ring. In the real case, a point at infinity completes a line into a topologically closed curve.