Vanishing point is below the horizon line, its vanishing lines angle up to the horizon line. If the object is above, they slope down. All vanishing lines end at the horizon line. 1. Projections of two sets of parallel lines lying in some plane appear to converge, i.e. the vanishing point associated with that pair, on a horizon line, or vanishing line formed by the intersection of the image plane with the plane parallel to and passing through the pinhole. Proof: Consider the ground plane , as which is, for the sake of simplicity, orthogonal to the image plane. Also, consider a
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