LINEAR PERSPECTIVE
It seems obvious that the apparent size of an object decreases the farther you get away from it. It is a surprise that this has not always been understood to be so. There is some indication from looking at mosaics that the ancient Greeks knew how to use perspective but no documents from that time have survived. The first written information about linear perspective appeared about 400 years ago. It was in Europe during the Renaissance that the concept of linear perspective was finally formalized.

Linear perspective is a system for drawing objects that use lines and vanishing points to determine how much an object's apparent size changes with space.

These are true for all types of linear perspective.

The horizon line gets its name because it is (almost) always horizontal.

BASIC CONCEPTS
The horizon line is a theoretical line that represents the eye level of the observer. The horizon line is the same as the horizon (the edge of the land against the sky) only on a large flat plane like the ocean. Most of the time geographic features (hills) and other objects (trees and buildings) make the horizon above the horizon line.

Indoors the horizon is often not visible but there is still a theoretical horizon line representing the point of view of the observer.

Look at the three sketches below. The same telephone pole is in the same position in all of the formats. The horizon (line) is different. Can you tell where you are in relationship to the poles?

The first pole is seen from above, the second from normal eye level and the third appears to be floating over your head. An object's relationship with the horizon line shows whether you are looking up, down or straight at the object.

Vanishing points are points (usually) on the horizon line where receding lines (planes) converge. The vanishing point (v.p.) is on the horizon line when an objects has horizontal planes that are parallel to the ground. When the object's planes are inclined the vanishing points can be above or below the horizon line.

Objects that are placed parallel to one another use the same vanishing points. Objects set at different angles each have their own vanishing points.

There are two basic systems of linear perspective: one-point and two-point named after the number of vanishing points used in each.

All parallel lines follow the same rules. If one goes to a vanishing point then all like lines go to the same vanishing point. In most systems vertical lines are drawn vertical (not in three-point perspective).

The station point represents the eye of the observer. It is the camera in a photograph.

The picture plane is the "window" that is represented by the picture.

The ground line is a line that is parallel to the picture plane at the base of the object being depicted.

ONE-POINT PERSPECTIVE
One-point perspective is what you see when you look straight at the side of an object. It uses only one vanishing point, hence its name.

The line of sight in one-point perspective is perpendicular (at a right angle to) the side of the cube in these examples. That means you see the near side in plane view (actual shape undistorted by perspective).

There are only three kinds of lines used in one-point perspective:

Vertical edges are shown as vertical lines.

Horizontal edges (perpendicular to the line of sight and parallel to the ground) are shown as horizontal lines.

Edges that recede (are parallel to the line of sight) are on lines that converge at the vanishing point on the horizon line.

Note that these same three (and only these three) kinds of lines are used to draw the cubes regardless to where they are in the picture.

Also note that the cube to the left, while technically correct, appears distorted. One-point perspective only depicts objects near the vanishing point with accuracy.

TWO-POINT PERSPECTIVE
Two-point perspective is used when you look at or into the corner of an object. There are two vanishing points since the two sets of sides are receding in two different directions.

In the real world vanishing points are very far apart. Imagine strings streaming out parallel to the edges of a cube going to the horizon. The horizon is miles away so the vanishing points are many miles apart. When you draw them only a few inches apart on a piece of paper there is going to be some distortion in the image produced.

Again there are only three different kinds of lines needed to draw in two-point perspective:

Vertical edges are drawn as vertical lines.

Edges of sides that recede toward the right are on lines converging at the right vanishing point.

Edges of sides that recede toward the left are on lines converging at the left vanishing point.

Both of the cubes in the example use only the same three kinds of lines. You see the top of the cube below the horizon line (your eye level). You see the bottom of the cube above the horizon line and more of its left side because it is to the right of your position in the center of the vanishing points.

USING LINEAR PERSPECTIVE
The use of linear perspective to draw architectural subjects is obvious. All subjects, though, still obey the same rules as geometric shapes. A thorough knowledge of perspective is required to successfully position objects in space.

For a more thorough description of perspective check out: Southern Arkansas University's excellent Art Chalkboard site http://www.saumag.edu/art/studio/chalkboard/draw.html and the Museum of Science in Boston's site about Leonardo de Vinci and perspective http://www.mos.org/sln/Leonardo/LeonardosPerspective.html

ATMOSPHERIC PERSPECTIVE
Atmospheric perspective deals with how the appearance of an object is affected by looking at it through a layer of air. Moisture, dust and pollutants in the atmosphere act to filter the visual information.

This is most apparent on a foggy day when it may be difficult to see across the street. Even in the clear, dry air of a desert the atmosphere changes the appearance of distant objects.

The changes follow the following general rules:

Contrast is greatest for close objects. Distant objects have less contrast in them and less to their surroundings. Each row of hills receding into the distance has less contract with the next (see photo above).

Remember that value contrast is the strongest contrast when creating spatial illusions.

Colors also change with depth. All of the colors are clear on near objects. Bright colors are only seen on close objects. Warm colors also show up more on near objects. As objects get farther away the colors dull and eventually turn blue gray.

Partially because of this warm colors appear to closer than cool colors (more about this under color). Choose colors in an image accordingly.

Focus in an image also gives depth clues. Close objects are generally more sharply focused than distant objects. It is possible to alter this with a camera but the mind sees softly focused edges as being farther away than sharp edges.

There may be compositional reasons to soften the focus of close objects in an image to call attention on something farther back in space.

Details are much more apparent on near objects because of all of the above. Linear perspective makes more distant details too small to see but it is low contrast that tends to flatten distant objects.

Pay attention to how these concepts play out when you are looking at landscape. The same tree looks not only smaller in the distance (linear perspective) but also less leafy (contrast, detail and focus) and not as bright a green (color). As the trees get farther away they blend into the landscape and eventually all you see are rows of hills, flat as cutouts, receding to the horizon. This is especially true on a hazy day or when looking into the sun.

PROJECT

Student example #1

Student example #2

Student example #3

DEEP SPACE PHOTOMONTAGE
Make a photomontage that uses overlap, linear perspective and atmospheric perspective to give a convincing illusion of deep space (from several feet to several miles). At least three different photo references must be used: one for the foreground, one for the middle ground and one for the background.

PROCEDURE
The foreground and background are the most critical parts. For the foreground look for a large sharply focused picture of an object with bright, warm colors. For the background look for a large photograph that shows deep space and has cool colors in the distance (warm colored sunsets are hard to make look like deep space).

The middle ground must fit somewhere in between the foreground and background in space. There is a lot of flexibility with the middle ground. One strategy is to use the interior of a room for the middle ground with the background seen through a window or door. This allows you to use a smaller photograph for the background.

LINEAR PERSPECTIVE CONSIDERATIONS
Size: Choose the pictures to use for each of the three depths with size in mind. Remember that objects appear to get smaller the farther away they are. Try to judge the depth of the image from the size of the objects in it and choose accordingly.

The foreground object will need to be large (close). The background should include distant mountains (small now in size). A cloudy sky may not be used as a background because the depth is hard to verify. The middle ground should fit in the middle.

Horizon line: Every photograph has a horizon line that represents the level of the camera that took the picture. The horizon lines for all of the picture parts in your photomontage must be on the same line.

Look carefully at each image and try to find where the horizon line is. The only surefire way to tell is if the ocean is in the background. Then the horizon and the horizon line are the same.

Ask yourself if you are looking up, down or straight at the scene or object. This can be difficult with natural objects but lines of perspective will help if there is any architecture in the photo. Your point of view represents the horizon line.

ATMOSPHERIC PERSPECTIVE CONSIDERATIONS
Contrast: Use a highly contrasting image for the foreground. It should have high contrast within it and contrast with its surroundings in your image. As the scene goes farther back, use less and less contrast. Be aware of a highly contrasting background with a softer middle ground.

Color: Keep the foreground bright and warm in color. The background should be the dullest and coolest in color. Be careful of warm colors in the background since they will want to come forward.

Focus: Make the foreground the sharpest in the image, the middle ground the next sharpest and the background the dullest if possible.

Details: Use an object for the foreground that has a lot of details. The background should be chosen because it has little in the way of details. The middle ground, as usual, is in the middle.

Cut out the three layers carefully (you may use more layers) and stack them to see if they give a convincing illusion. You may have to move the parts around some to get the horizon lines to seem right.

The finished product should look like a single photograph that shows a scene that starts close to the observer and goes for miles into the distance.