Vanishing point is below the horizon line, its vanishing lines angle up to the horizon line. If the object is above, they slope down. All vanishing lines end at the horizon line. 1. Projections of two sets of parallel lines lying in some plane appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line formed by the intersection of the image plane with the plane parallel to and passing through the pinhole. Proof: Consider the ground plane , as which is, for the sake of simplicity, orthogonal to the image plane. Also, consider a
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