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
Parallel (geometry) parallel lines, one for each direction ideal point of line l. They separate the lines intersecting line l and those that are ultra parallel to line "l". Ultra parallel lines have single common perpendicular (ultraparallel theorem), and diverge on both sides of this common perpendicular. In spherical geometry, all geodesics are great circles. Great circles divide the sphere in two equal hemispheres and all great circles intersect each other. Thus, there are no parallel geodesics to a given geodesic, as all geodesics intersect. Equidistant curves on the sphere are called parallels of latitude analogous to the latitude lines on a