Vanishing point of multipoint perspective, and historian Kirsti Andersen compiled these observations. She notes, in terms of projective geometry, the vanishing point is the image of the point at infinity associated with , as the sightline from through the vanishing point is parallel to . As a vanishing point originates in a line, so a vanishing line originates in a plane that is not parallel to the picture . Given the eye point , and the plane parallel to and lying on , then the vanishing line of is . For example, when is the ground plane and is the horizon plane,
Parallel (geometry) same three-dimensional space that do not intersect need not be parallel. Only if they are in a common plane are they called parallel; otherwise they are called skew lines. Two distinct lines "l" and "m" in three-dimensional space are parallel if and only if the distance from a point "P" on line "m" to the nearest point on line "l" is independent of the location of "P" on line "m". This never holds for skew lines. A line "m" and a plane "q" in three-dimensional space, the line not lying in that plane, are parallel if and only if they