Monday, February 2, 2015

Perspective - Three Point Perspective - Hand & CAD

Everyone sees the world as a 3 (or more) point perspective. Glance over at the table or chair nearest you: you’ll see edges leading to the horizon to the left and right, but the verticals will be converging toward the center of the earth.
Look over at the corner of your room, up where the ceiling meets the walls: again, convergence in 3 directions.
One point perspective is ancient, and is a relatively easy thing to produce by hand. Two point perspective is a product of the Renaissance, and, although harder than one point, is nevertheless a skill that is easily learned. On the other hand, three point perspective has limited uses, and is difficult to lay out by hand. Indeed, 3 point perspective has been a trick used only on special occasions. At least that was the situation before CAD came into general use (but more on that shortly).
So three point perspective is both familiar and, in terms of hand layout, rare. The basics of 3 point are easy to explain. Just pick a spot between 3 equally spaced vanishing points, and draw (we’re not dealing with accuracy here). To approximate a perfect cube, imagine a ball floating inside the cube but touching all edges. The ball will look perfectly round from any angle, so you can draw each of the outside edges touching the circle.
You can use the simple cube to draw more complex shapes, such as a cylinder.

Going from the simple to the complex is hard, and I have no interest in explaining it. This example of a tipped over stool from Die malerische Perspektive by Hauck (1882), gives me a head ache.

That is not to say that I never created a 3 Point perspective by hand. This layout of a highrise in Manhattan may look like a simple 2 point, but on closer inspection you will notice a slight convergence in the vertical lines (the two red lines are parallel to the picture frame). The reason I went to the trouble of drawing the vertical convergence was to limit the natural distortion at the top of a tall building. It was relatively easy to do because I ignored the shortening of the floor heights approaching the top of the building. Luckily you can get away with cheating on such a drawing (there is very little shortening with a distant vanishing point).

When architectural illustrators could do CAD “wireframe” layouts on their desktop computers, 3 point perspective became all too easy. Buildings that weren’t distorted, like the example above, got treated in the same way as very tall towers.

Interiors, like this view of the Whitehall Terminal proposal, perhaps needed the extra vanishing point to be able to describe the shape of the ceiling arch…

…but others did not have a distortion problem. This view of a small theatre space would have worked as well using two point perspective. It’s not that the layout was wrong, it’s just that it was unnecessary.

Of course 3 point perspective can create some eye-catching effects. Lebbeus Woods was a brilliant perspectivist who could work outside the rectilinear world, as well as think/draw in 3 point. The above drawing is from Radical Reconstruction (page 74) by Lebbeus Woods, 1997.

Once CAD modeling became a viable tool for architects and artists, all sorts of fantastic viewpoints became possible. Long ago I painted a street view of the EMC building in Des Moines, Iowa.  Not long after I created this aerial night view. The street view was impressively dignified, but this 3 point aerial caught everyone’s eye.
Computer modeling also allowed for easier photomontage work. The view above of the observation tower at Niagara Falls, is a mixture of a photo and a model rendered in Accurender.

This “bat’s eye view” of a church sanctuary would have been difficult done by hand, but was almost an afterthought of a church design that I accomplished using computer modeling. One of the joys of modern design is the ability to jump from hand sketches to CAD modeling and back (sounds like another subject for posting).
The ability to design and build complex nonlinear spaces has led to exciting spaces seen in exciting ways. This view of the Glass Hall of the Tokyo International Forum is strictly 3 point, but only suggests vanishing points in the floor grids.
Sometimes having the flexibility of CAD modeling is a disadvantage. This layout of the retail area of the Petronas Towers in Kuala Lumpur, Maylasia (Suria KLCC) used a rather extreme convergence to be able to see all 88 floors of the towers. In the final painting the towers were reduced to a background silhouette, but the tilting walls remained.

So what’s my take on 3 point perspective?

It has its uses. You can moderate distortion in tall buildings. You can get a better view of a high interior space. You can exactly match a photo when doing photo montage.

But perhaps the most lasting use of 3 point is its ability to give an unusual viewpoint; to make a so-so building look new and wild. This has its place in architectural illustration, but it also has its drawbacks. Too much of it will deaden the effect: already the movie industry is straining to outdo the last over-the-top computer-generated imagery (CGI). In this area I can’t give reliable advice; you will have to keep watching the graphic horizon and trying out new ideas.

Other posts on Perspective:

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