In graphical perspective, a vanishing point is a point in the picture plane π that is determined by a line in space. Given the oculus or eye point O and a line L not parallel to π, let M be the line through O and parallel to L. Then the vanishing point of L is the intersection of M and π. Traditional linear drawings use one to three vanishing points.
The vanishing point theorem is the principle theorem in the science of perspective. It says that the image in a picture plane π of a line L in space, not parallel to the picture, is determined by its intersection with π and its vanishing point. Some authors have used the phrase, "the image of a line includes its vanishing point". Guidobaldo del Monte gave several verifications, and Humphry Ditton called the result the "main and Great Proposition". Brook Taylor stressed its importance, and historian Kirsti Andersen assembled these observations She notes, in terms of projective geometry, the vanishing point is the image of the point at infinity associated with L, as the sightline from O through the vanishing point is parallel to L.
Vanishing line 
As a vanishing point originates in a line, so a vanishing line originates in a plane α that is not parallel to the picture π. Given the eye point O, and β the plane parallel to α and lying on O, then the vanishing line of α is β ∩ π. For example, when α = π = ground plane, then β is the horizon plane with β ∩ π the horizon line.
Use in driving 
Vanishing points can also refer to the point in the distance where the edges of the roadway appear to converge. Movement of the vanishing point can help assess the upcoming curves in the road. If the vanishing point moves towards you or to your sides, the curve radius is reducing, so speed should be reduced. If the vanishing point moves away from you or comes to center, the curve is straightening.
Curvilinear and reverse perspective 
A curvilinear perspective is a drawing with either 4 or 5 vanishing points, in 5-point perspective the vanishing points are mapped into a circle with 4 vanishing points at the cardinal headings N,W,S,E and one at the circle origin.
A reverse perspective is a drawing with vanishing points that are placed outside the painting with the illusion that they are "in front of" the painting.