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,
Clifford parallel Clifford parallel In elliptic geometry, two lines are Clifford parallel or paratactic lines if the perpendicular distance between them is constant from point to point. The concept was first studied by William Kingdon Clifford in elliptic space. Since parallel lines have the property of equidistance, the term "parallel" was appropriated from Euclidean geometry, but in fact the "lines" of elliptic geometry are curves, and they have finite length, unlike the lines of Euclidean geometry. The algebra of quaternions provides a descriptive geometry of elliptic space in which Clifford parallelism is made explicit. The lines on 1 in elliptic space are