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,
Critical point (mathematics) parallel to the y-axis" and the "projection parallel to the x-axis", respectively. A point of is critical for formula_5, if the tangent to exists and is parallel to the "y"-axis. In that case, the images by formula_5 of the critical point and of the tangent are the same point of the "x"-axis, called the critical value. Thus a point is critical for formula_5 if its coordinates are solution of the system of equations This implies that this definition is a special case of the general definition of a critical point, which is given below. The definition of a critical point