Finding Equal Spacing using Diagonals

In this posting of Understanding Loomis, I will explain the primary method Andrew Loomis outlines in what he calls ‘depth by diagonals’.  This is a rule of drafting which accurately represents depth in a subject matter featuring a repeated pattern, or a repeated spacing of surface feature.  This particular treatment is useful for illustrating a sidewalk receding into the distance, or a tiled floor going off down a hall, or a train track with ties crossing the rails, traveling away to a vanishing point.  It is a very useful mechanic to know.

To emphasize why knowing this mechanic of perspective is important, I will describe a scenario where such knowledge would save the artist painstaking hours of ineffective trial and error, or unconvincing guesswork.  Consider; you as an illustrator have been given the task of drawing a rural road, where small trees and shrubs are growing along the side. Also standing along the road at regular intervals of 30 feet, are a series of 6 telephone poles on the shoulder.  The image is to be drawn with the vanishing point of the road in the centre of the horizon, as if the viewer were standing at the head of the road, looking off to where it fades into the distance.

Drawing the simple one-point perspective of the road is no problem, and the shrubs/trees needn’t be precisely drawn on account of their being organic and irregular in nature, hence their placement is not a problem either.  The telephone poles on the other hand are man-made, and erected with a constant distance of 30 feet between each of the pole bases.  To be able to accurately place each pole as they recede into distance, is a baffling task to those unaware of technical perspective.  Many artists would rely of approximate placement of the poles, by ‘eye-balling’ the spacing.  This may be acceptable in some cases, but where approximation is not acceptable, a technical solution is necessary.

This then is how it is done.

Depth by Diagonal

(For the sake of these perspective lessons, crude sample drawings which were done in Photoshop in a matter of a few seconds, will be used forthwith.  Proper, elegant drawings will be used as examples where actual drawing matters are being considered)
  1. First represent the road and the bushes in one point perspective.  Bushes and trees are organic, and can be represented by eye without difficulty.  The rules of perspective still apply, but the artist can be a little sloppy in representing their relative size, since trees and shrubs are not regular.road1
  2. Next place your first pole.  Use the relative size of the trees around it for its height. road2
  3. Next find the Vanishing point of the road on the horizon line.road3
  4.  Now, draw a diagonal line from the near corner of one of the Lines of Perspective, through the base of the first pole to a secondary point on the horizon line. Let us call this new point on the horizon Point One. road5
  5. Next, draw a horizontal line (i.e. parallel to the horizon line – natch!) from the base of the pole, crossing through both Lines of Perspective.road6
  6. From where this horizontal line meets the opposite Line of Perspective, draw another diagonal line to the secondary point you drew in step 4, which we called Point One.road7
  7. Cast lines to the actual VP from the top and bottom of the telephone pole, and pay attention to where the bottom line crosses the diagonal which you drew in step six.road8
  8. At the crossing point, draw your second telephone pole.  The top line will show you how tall to make it.  road9
  9. Repeat the process, and erase your guidelines.  The end result will show the poles moving off in correct perspective, spaced evenly apart.  road10
  10. Work in reverse  to fill in any posts which should appear before the initial one you drew.road11

The Uses of  Depth by Diagonal

Shown below is a sample of the nuts and bolts of the Depth by Diagonal mechanic.  This example is shown stripped of any context in order to help the student imagine the uses of this rule of perspective.  Some ways I have used this method of representing perspective in drawing comics are as follows:

  • representing regular sized plates of steel, clad on the hull of a ship
  • drawing the separation lines of ceiling panels on a t-bar drop-ceiling in an office
  • sidewalks, with contraction joints showing in the concrete
  • patterned carpet expanses
  • windows, or other architectural features on buildings
  • any regularly spaced series of object, such as telephone poles, the cars of a train, the ties between train track rails, the broken lines on a road which indicate a passing lane etc.

dbydiagonal

Next week, we will examine a variation on this method of finding Depth by Diagonals.  I hope you will join me.

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