Vanishing point line that lies in the plane , which is defined by the equation . Using perspective pinhole projections, a point on projected on the image plane will have coordinates defined as, This is the parametric representation of the image of the line with as the parameter. When it stops at the point on the axis of the image plane. This is the vanishing point corresponding to all parallel lines with slope in the plane . All vanishing points associated with different lines with different slopes belonging to plane will lie on the axis, which in this case is the horizon
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