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
Vanishing point then the vanishing line of is the horizon line . Anderson notes, "Only one particular vanishing line occurs, often referred to as the "horizon". To put it simply, the vanishing line of some plane, say , is obtained by the intersection of the image plane with another plane, say , parallel to the plane of interest (), passing through the camera center. For different sets of lines parallel to this plane , their respective vanishing points will lie on this vanishing line. The horizon line is a theoretical line that represents the eye level of the observer. If the object