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
Parallel (geometry) do not intersect. Equivalently, they are parallel if and only if the distance from a point "P" on line "m" to the nearest point in plane "q" is independent of the location of "P" on line "m". Similar to the fact that parallel lines must be located in the same plane, parallel planes must be situated in the same three-dimensional space and contain no point in common. Two distinct planes "q" and "r" are parallel if and only if the distance from a point "P" in plane "q" to the nearest point in plane "r" is independent of the location