Mapping three dimensional space


John Wattie

Dunedin Railway Station panorama.

Artist's perspective laws are not "perfect". However they have persisted for hundreds of years (since Alberti wrote them down in 1435). They are still the rules accepted by western civilisation as the "correct" way to represent three dimensional scenery on a flat canvas.

It is not the photography which is at fault, just the unfamiliar geometry which we never see with unaided eyes.

Tyranny of windows

In the outside world, our visual field has no edge that we are normally aware of. The edge of our vision is very indistinct and only good for detecting movement, which makes us quickly turn to see what happened. Once we live in houses, things change.

If you look out the window and see other buildings, you will notice the walls of those buildings are all vertical and run parallel to the sides of your window. Now look at the window obliquely so you get "keystone distortion" and the walls outside are still parallel to the window frame. As you move about in your room, the window edge blocks out parts of the outside world, but the world never gets inside your room, in front of the window.

If you go outside, all the buildings are upright. Now line up the corner of a near-by building with the wall of another further away. You get lots of chance to do that in the city and even if you look to the top of a sky-scraper, its wall is always parallel to the reference vertical corner near by. Now look up without a reference wall. Do the sides of the building converge? No of course not - well, not unless you think about it very hard, but life is too short for too much thinking.

A picture on the wall of your castle sits in its frame, much like a window frame, and the picture is your artificial window to another part of the world. So if you were the King of the Castle, before photography, you would expect pictures on the wall to behave like windows and always show vertical lines parallel to the picture frame. You would get upset if the picture was hanging crooked, because a decent window should be parallel to the walls and corners of your room. So some serf brings you photographs which show walls that converge and fail to stay parallel to the frame, "Get with the real world you ignorant varlet! That is not how things are! Remove your picture from here forthwith!"

Early photographers took great care to make pictures which showed vertical lines as vertical, or they were just laughed at.

Converging verticals

Santa Maria Della Salute
with converging verticals. The church is "falling over backwards".
John Wattie Photography

In ordinary photography, when the camera is pointed up to show a tall building, the sides of the structure converge. Professional photographers overcome that by using a shift lens, which allows the film plane to remain vertical while the lens moves up.

John Wattie Photography

The sides of the building then stay straight up and down, which is how buildings are still drawn by artists and architects. 

Puhinui Homestead, Howic Historical Village

Modern photograph in the old style. 1850's costume, 1870's house 1920's car and 21st century photograph, but without converging verticals, using the old (or professional) convention.
John Wattie Photography

Artists show horizontal lines with perspective, converging to infinity, because on a flat canvas that is the best way to show depth. Architects in the middle ages did not draw with perspective, because it makes the pictures rather useless when the artisan comes along and tries to build from the drawings. The back wall has to be the same height as the front wall, not shorter as it looks in a perspective drawing or photograph. Many architects were in fact great artists first and knew all about perspective. Canaletto in his writings said he purposely did not draw buildings with perspective, except in paintings for framing, because he found out early in his career that any measurements taken from them were hopeless. His drawings have the perspective of a super- long telephoto lens, photographing from far away: in another word - zilch.

 Although the sides of buildings do converge when we look up, it seems the brain allows for that and tells us the walls are actually vertical. The artist's perspective laws insist that vertical lines are vertical on pictures too. Walls must be parallel to the vertical sides of the picture frame.  People who have not spent much time with photographs still find it disturbing when pictures of buildings have converging verticals, despite amateur photographs showing this most of the time. The "buildings falling backwards" syndrome is decried by photo-club judges, despite them knowing an amateur camera can do no better. 

Dunedin railway Station. Click for big version Click for bigger version


In real life, walls do converge as we look up. With the help of stereoscopy and other clues, the brain interprets converging verticals as really being parallel lines. The brain is so accurate at this, we can tell when an unstable building is leaning over, despite the perspective convergence. As pointed out in the Physiology section, stereoscopic vision is a learned response requiring brain computation, and this applies to all our perceptions of the third dimension. 

Click for Salute in stereo Click for stereo version

For example, a person blind from birth who suddenly gained sight after an operation reported that space was strange. His eyes "saw everything at the same time". His spatial concept had been that things were separated by time. With only tactile sense, he would feel one thing and a bit later feel another, so the concept of simultaneous was strange to him. (I guess he was one of the few people who could understand Einstein's space/time).

  1. Converging verticals in stereoscopic photography tells us the camera was looking up or down. It is easier to accept tilting buildings when stereo clues are provided, although many people still prefer even stereo cameras to be kept horizontal. 

    This is especially true for projection stereo. When using a hand viewer, the stereoscopic impression is improved while viewing scenes where the camera was pointed down, if the viewer is also pointed down. Or up if the camera pointed up. This option of proprioceptive reinforcement is not available during slide projection, where the audience has to steadfastly look straight ahead.

  2.  Similarly the "law" that perspective enhancement ("distortion") from wide angle lenses is unacceptable in portrait photography does not apply to stereoscopic portraits, as long as the stereo shift is no more than the inter-ocular distance. This gives realistic stereo and we are prepared to accept a big nose on a face when the 3d impression tells us we are very close to that face.