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
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