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,
Horizon the distance, stimulated the development of projective geometry which posits a point at infinity where parallel lines meet. In her book "Geometry of an Art" (2007), Kirsti Andersen described the evolution of perspective drawing and science up to 1800, noting that vanishing points need not be on the horizon. In a chapter titled "Horizon", John Stillwell recounted how projective geometry has led to incidence geometry, the modern abstract study of line intersection. Stillwell also ventured into foundations of mathematics in a section titled "What are the Laws of Algebra ?" The "algebra of points", originally given by Karl von Staudt