And after Light came Space

One of the difficulties with visual art is representing the three-dimensional world in two dimensions. The flat surfaces we use to communicate ideas, including print, television, the Web, and motion pictures, all present information in two dimensions.

Phase Two: The Illusion of Depth

To perfect my drawing at the Waverley Station of last Friday I have to find some effective techniques for representing the three-dimensional world using more limited two-dimensional media.

Perspective

There are two simple rules about representing depth. Size decreases with distance, meaning objects that are further away from the viewer appear to be smaller. Objects also overlap when one is in front of the other, hiding part or all of the farther object(s). These two observations are the basis for perspective.

The easiest way to understand how perspective works is to imagine standing in the middle of train tracks (not recommended for safety reasons) and looking along the tracks into the distance. Visually follow the tracks to the horizon (where the earth meets the sky) and the tracks appear to meet at a point in the distance. This converging point is called the vanishing point.

Now imagine that as you look at the train tracks converge into the distance, you are holding a piece of rectangular glass directly in front of you. If you traced what you saw onto the glass with a marker, you would be drawing onto the picture plane. Perspective is a method for representing what is seen through the picture plane on another two-dimensional surface.

The train tracks are an example of one-point perspective, the easiest of the perspective methods. This method is useful when representing landscapes, city streets, and other environments in which things are aligned and converge to one central point.


One-Point Perspective, courtesy of Andrew Kator

One-point perspective images have a tendency to draw the viewer along the lines to the vanishing point. This effect can be used to greater advantage by placing the subject of an image in front of or near the vanishing point. The viewers will more naturally focus their attention because most of the lines in the image converge onto that area. This effective technique has been used for centuries and can easily be seen in Leonardo da Vinci’s Last Supper and works from other artists.


"Last Supper" by Leonardo da Vinci using a one-point perspective

The boxes to the left to the tracks in the one-point perspective example have one face perfectly aligned parallel to the picture plane. This is a limitation of one point perspective. Another problem with this technique is that objects become more distorted the further they are from the vanishing point, as can be seen with the far left box in the example.

Although I was at a Train Station, my scene was definitely not one-point perspective, so I had to learn more...

The real world is rarely so organized as to align objects facing the viewer, nor are we often standing in the correct position to observe objects so directly. Because we view most objects from an angle, and not directly from the front or sides, two-point perspective allows us to represent our world more realistically by orienting two faces of an object obliquely to the picture plane.


Two-Point Perspective, courtesy of Andrew Kator

The book illustration shows an example of two-point perspective. Other than the obvious difference in having two vanishing points, it is also important to note that objects drawn using this method have an edge closest to the picture plane rather than a face as in one-point.

The horizon line in the book image is higher in the two-point example than the horizon in the one-point perspective image. The higher horizon suggests a viewpoint from a higher position, such as looking down upon a book on a table. The position of the horizon line represents the viewer’s eye level and affects how the viewer interprets the image.

A lower horizon suggests that the scene is either from greater distance or that the viewer is lower to the “ground.”

A higher horizon could also be used to suggest the viewer was looking out a window from a tall building. Horizon line placement is similar to using a “bird’s eye view” or a “bug’s eye view” in photography.

These extremes are useful for creating more dramatic visual results. Look for this technique in comic books, where horizon placement and exaggerated perspective are used to suggest action and create more visual interest.

One-point and two-point perspective techniques can be used in the same image if needed to represent different objects. Determine if an object’s face (one-point) or edge (two-point) is closest to the viewer and then use the appropriate method. Each object may also have its own vanishing points, since only aligned objects will share them.
Coming back to our Waverly Station stairs of my drawing assignment, below are the perspective lines drawn on top of the picture.


Waverley Station Stairs with lines in two-point perspective.


Three-Point Perspective, courtesy of Andrew Kator

If the corner of an object is closest to the picture plane, then three-point perspective can be used. The third vanishing point is not on the horizon line. The position where the third vanishing point is placed, either above or below the horizon line, indicates whether the viewer is looking up at the object or looking down.

Notice that in the chair illustration the picture plane does not contain the vanishing points. It is not necessary for the vanishing points to be within the picture plane for perspective to work. When creating smaller images using two or three-point perspective, the results will often appear more natural if no more than one vanishing point is in the picture plane at any given time.