A Perspective on Perspective

...and how different types may be generated for illustration

Nick Brooker, Technical Illustrator

Although now primarily a technical illustrator, I've produced perspective illustrations for more than 35 years and since 1987 have specialised in originating all kinds of computer-aided illustration for technical and business documentation. In this article, I would like to briefly discuss the misuse of the expressions ‘parallel perspective’ and ‘true perspective’, describe the basic differences between the more common forms of perspective drawing and also introduce the concept of using curved lines in perspective illustration.

Defining perspective

The Oxford English Dictionary defines perspective as ‘the art of representing three-dimensional objects on a two-dimensional plane’, so one could claim that axonometric (including isometric) projection is a kind of perspective; but is there ‘art’ in projecting parallel lines to give an impression of three dimensions?  This kind of projection is basic geometry and is occasionally referred to as ‘parallel perspective’, particularly when referred to within computer drawing applications.  What is sometimes described as ‘true perspective’ is in fact what artists and illustrators would normally refer to as ‘linear perspective’.

To illustrate in linear perspective, at least one vanishing point is required, although it is possible (and often desirable) to use two, three or even more vanishing points.  The method of obtaining the best representation of an object in perspective will be determined by the object’s size and the required viewpoint.

Types of linear perspective include:

  • One-point
  • Two-point
  • Three-point
  • Curved-line.

There are other types and a single illustration can combine any number of perspective types.  A simplified description of those listed above follows together with some of my drawings to illustrate the differences between and uses for one, two and three-point perspectives.

One-point perspective

This is the simplest way to represent perspective; lines converge to a single point on the horizon line at a selected eye level — the vanishing point. 

Figure 1:  One-point perspective geometry.

This is ideal for focusing the viewer on a single plane and gives an indication of depth, but not size unless a visual reference is included in the illustration.  Figure 1(a) shows five internal but no external planes and is often used to illustrate interiors.

Figure 1(b) shows two external planes and Figure 1(c) shows three external planes. In one-point perspective, all vertical and horizontal lines are parallel.  Any objects within the space not parallel to any of the spatial planes require two-point perspective, with the two points on the same horizon line or eye level as the original point.

Figure 2:  One-point perspective with projection.

The fibreoptic connection unit shown in Figure 2 was originated using one-point perspective.  Faces not on the vertical or horizontal planes were created by simple linear projection, in the same way as orthographic views are projected to create axonometric views; this results in a projection that is in perspective without the need to set up new perspective points.

Two-point perspective

This is probably the most common way to represent perspective in technical illustration.  All the lines on the horizontal planes converge to either of the two points on the horizon line.  All vertical lines are parallel.

Figure 3:  Two-point perspective geometry.

This conveys perspective but does not direct the viewer to any specific point or plane in the drawing.  Careful positioning of these ‘vanishing points’ can give some indication of the object’s size in relation to its height.  Figure 3(a) has the eye level above the object and shows two external and three internal planes; ideal for generating simple visualisation, illustrating objects that can be held in the hand, and floor standing objects not taller than normal eye level.

Figure 4:  Illustrating a small object.

The coin acceptance machine in Figure 4 is approximately 25 x 15cm overall and, to give a better impression of its size, the point on the horizon line to the right of its centre vertical has been moved further into the distance.  This has the effect of making the converging lines appear to be near parallel, suggesting that the object is small.  The wheelchair in Figure 5 is much larger and the point to the right of the centre vertical is, therefore, brought closer to the object, causing the lines to converge more, suggesting its larger size. 

Figure 5:  Illustrating a larger object.

Raising or lowering the ‘eye level’ slightly can also help to give a better indication of the size, as can the inclusion of a reference of known size, such as a hand (Figure 6).

Figure 6: Using objects of known size for reference.

Figure 3(b) (above) has the eye level within the space and is ideal for illustrating interiors and simple floor standing objects that are taller than normal eye level.  However, if an object is more than twice the height of normal eye level, because we expect distant objects to be smaller, the top will appear to be wider than the bottom, unless another point of perspective is introduced.

In Figure 7 below, the room and kitchen cabinets were sketched in one-point perspective and the table and chairs were sketched in two-point perspective.

Figure 7: Combining one and two-point perspectives.

Three-point perspective

Drawing starts to get a bit complicated but we are now able to introduce more depth into the illustration. 

Figure 8:  Three-point perspective geometry.

Looking down on the object as shown in Figure 8(a), lines along the sides converge to a point beneath the object.  Looking up at an object as shown in Figure 8(b), lines along the sides converge to a point above the object.

Three-point perspective requires two points on the horizon line and one on the vertical.  Note that both of these sketches exaggerate the perspective because the point on the vertical is too close to the object.  A lot more space would be required to position this point in order to make the object appear ‘true’.  As shown in Figure 8(a), the horizon line may be slightly rotated to improve the viewpoint.

As with two-point perspective, careful positioning of these points can help to indicate size, but how the object is positioned relative to the centre vertical can also give some indication of distance.

Figure 9:  Part of a multi-layerered assembly drawing.

In technical illustration, three-point perspective is ideal for drawing exploded assemblies and large objects.  The refrigeration box in Figure 9 is just one of the main layers of a complete assembly drawing for a commercial coffee making machine.  All layers share the same three-point perspective but each of the main layers may be extracted for annotating separately in the illustrated parts catalogue.  By sharing the perspective on all drawings in the parts catalogue, the user has no difficulty understanding the orientation of the different assemblies illustrated. 

If however, the object being illustrated is a skyscraper and it is not being viewed from above (or below), then a fourth point of perspective needs to be considered.  Any object requiring four points to illustrate in perspective from the same viewpoint requires the use of curved lines to either the vertical, or one or both of the horizontal planes.

Curved-line perspective

This is when there are four or more vanishing points required and, although it maybe a little difficult to comprehend at first, it follows on from what has already been described above.

Figure 10:  Curved-line perspective geometry.

Consider viewing a 130-storey skyscraper building from the sixty-fifth floor of an adjacent, but not too close, skyscraper.  The horizon line is your eye level and as illustrated in Figure 10, when you look towards the top of the building, the vertical lines converge to a point somewhere in the sky.  From the same point, when you look down to the base of the building, the vertical lines converge to somewhere in the earth.  There is no position on the vertical sides where the lines actually change direction, so the only way to represent this illustratively is to curve these vertical lines.

When we look up and down the outside edges of tall or wide buildings, we actually see a series of straight lines that form a curve, but our brain interprets it as a single straight line simply because we know that it must be straight.  The Ancient Greeks used this principle to enhance the size of their temple structures by curving column sides, entablature and stylobate so that when they were viewed close up, they would be seen as straight, giving an exaggerated perspective and even greater size.  As far as I am aware, the only commercial use for using curved-line perspective is when illustrating extremely tall or wide buildings and the size of the building needs to be accentuated.

In summary

If technical illustration is to fulfil its objective of visually describing or clarifying text, I believe that constructing perspective using a computer requires more than a drawing application that can produce axonometric views.  The position of the vanishing point or points needs to be carefully selected to establish the best viewpoint and indicate the object’s relative size, position and distance.  Perspective illustration does not have to be geometrically perfect, but some artistic ability is required when copying and re-using existing drawing elements, which may have to be foreshortened by scaling and shearing.

Linear perspective is not difficult for a trained illustrator.  Using three points enables the illustrator to adjust the angle of perspective and depth of field to enhance the object’s size and shape.  Whether produced manually or with the aid of a computer, linear perspective used for technical illustration also provides an opportunity to add realistic visual references (such as hands), artistic styling (such as line thickening to represent the shadow side) and, of course, that all-important human touch, which in my opinion can help to generate more attractive technical documents.

For more information about constructing perspective:

Go to: www.handprint.com/HP/WCL/tech10.html

For another view of curved-line perspective:

Go to: www.termespheres.com/mh-page2.html

© Copyright Nick Brooker, the MicroArt studio

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