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
Skew lines value of the real number formula_4 determining where the point is on the line, and similarly for arbitrary point on the line through particular point in direction . The cross product of b and d is perpendicular to the lines, as is the unit vector The distance between the lines is then (if |b × d| is zero the lines are parallel and this method cannot be used). Expressing the two lines as vectors: Line 1: formula_7 Line 2: formula_8 The cross product of formula_9 and formula_10 is perpendicular to the lines. formula_11 The plane formed by the translations of