Horizon science of graphical perspective. Assuming the picture plane stands vertical to ground, and "P" is the perpendicular projection of the eye point "O" on the picture plane, the horizon is defined as the horizontal line through "P". The point "P" is the vanishing point of lines perpendicular to the picture. If "S" is another point on the horizon, then it is the vanishing point for all lines parallel to "OS". But Brook Taylor (1719) indicated that the horizon plane determined by "O" and the horizon was like any other plane: The peculiar geometry of perspective where parallel lines converge in
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