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
Distance from a point to a line length of this projection is given by: Now, thus Since "Q" is a point on the line, formula_27, and so, It is possible to produce another expression to find the shortest distance of a point to a line. This derivation also requires that the line is not vertical or horizontal. The point P is given with coordinates (formula_29). The equation of a line is given by formula_30. The equation of the normal of that line which passes through the point P is given formula_31. The point at which these two lines intersect is the closest point on the original line