Putting things into perspective.

Perspective in the graphic arts is an approximate representation, generally on a flat surface (such as paper), of an image as it is seen by the eye. The two most characteristic features of perspective are that objects are smaller as their distance from the observer increases; and that they are subject to foreshortening, meaning that an object’s dimensions along the line of sight are shorter than its dimensions across the line of sight.

Staircase in two-point perspective

Perspective drawings have a horizon line, which is often implied. This line, directly opposite the viewer’s eye, represents objects infinitely far away. They have shrunk, in the distance, to the infinitesimal thickness of a line. It is analogous to (and named after) the Earth’s horizon.

Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing. A one-point perspective drawing means that the drawing has a single vanishing point, usually (though not necessarily) directly opposite the viewer’s eye and usually (though not necessarily) on the horizon line. All lines parallel with the viewer’s line of sight recede to the horizon towards this vanishing point. This is the standard “receding railroad tracks” phenomenon. A two-point drawing would have lines parallel to two different angles. Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing.

Perspectives consisting of many parallel lines are observed most often when drawing architecture (architecture frequently uses lines parallel to the x, y, and z axes). Because it is rare to have a scene consisting solely of lines parallel to the three Cartesian axes (x, y, and z), it is rare to see perspectives in practice with only one, two, or three vanishing points; even a simple house frequently has a peaked roof which results in a minimum of six sets of parallel lines, in turn corresponding to up to six vanishing points.

In contrast, natural scenes often do not have any sets of parallel lines and thus no vanishing points.

 

One-point perspective

A drawing has one-point perspective when it contains only one vanishing point on the horizon line. This type of perspective is typically used for images of roads, railway tracks, hallways, or buildings viewed so that the front is directly facing the viewer. Any objects that are made up of lines either directly parallel with the viewer’s line of sight or directly perpendicular (the railroad slats) can be represented with one-point perspective. These parallel lines converge at the vanishing point.

One-point perspective in action.

Two-point perspective

A drawing has two-point perspective when it contains two vanishing points on the horizon line. In an illustration, these vanishing points can be placed arbitrarily along the horizon. Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or at two forked roads shrinking into the distance, for example. One point represents one set of parallel lines, the other point represents the other. Seen from the corner, one wall of a house would recede towards one vanishing point while the other wall recedes towards the opposite vanishing point.

Three-point perspective

Three-point perspective is often used for buildings seen from above (or below). In addition to the two vanishing points from before, one for each wall, there is now one for how the vertical lines of the walls recede. For an object seen from above, this third vanishing point is below the ground. For an object seen from below, as when the viewer looks up at a tall building, the third vanishing point is high in space.

Three-point perspective exists when the perspective is a view of a Cartesian scene where the picture plane is not parallel to any of the scene’s three axes. Each of the three vanishing points corresponds with one of the three axes of the scene. One, two and three-point perspectives appear to embody different forms of calculated perspective, and are generated by different methods. Mathematically, however, all three are identical; the difference is merely in the relative orientation of the rectilinear scene to the viewer.

Three-point perspective

 

Four-point perspective

Four-point perspective, also called infinite-point perspective, is the curvilinear  variant of two-point perspective. A four-point perspective image can represent a 360° panorama, and even beyond 360° to depict impossible scenes. This perspective can be used with either a horizontal or a vertical horizon line: in the latter configuration it can depict both a worm’s-eye and bird’s-eye view of a scene at the same time.

City scene in five-point perspective.

Like all other foreshortened variants of perspective (one-point to six-point perspectives), it starts off with a horizon line, followed by four equally spaced vanishing points to delineate four vertical lines. The vanishing points made to create the curvilinear orthogonal are thus made ad hoc on the four vertical lines placed on the opposite side of the horizon line. The only dimension not foreshortened in this type of perspective is that of the rectilinear and parallel lines perpendicular to the horizon line – similar to the vertical lines used in two-point perspective.

One-point, two-point, and three-point perspective are dependent on the structure of the scene being viewed. These only exist for strict Cartesian (rectilinear) scenes. By inserting into a Cartesian scene a set of parallel lines that are not parallel to any of the three axes of the scene, a new distinct vanishing point is created. Therefore, it is possible to have an infinite-point perspective if the scene being viewed is not a Cartesian scene but instead consists of infinite pairs of parallel lines, where each pair is not parallel to any other pair.

Zero-point perspective

In its usual sense, zero-point perspective is not truly “zero-point”. Rather, because vanishing points exist only when parallel lines are present in the scene, a perspective with no vanishing points (“zero-point” perspective) occurs if the viewer is observing a non-linear scene containing no parallel lines. The most common example of such a nonlinear scene is a natural scene (e.g., a mountain range) which frequently does not contain any parallel lines. This is not to be confused with elevation, since a view without explicit vanishing points may still have been drawn such that, there would have been vanishing points had there been parallel lines, and thus enjoy the sense of depth as a perspective projection.

Foreshortening

Foreshortening is the visual effect or optical illusion that causes an object or distance to appear shorter than it actually is because it is angled toward the viewer. Additionally, an object is often not scaled evenly: a circle often appears as an ellipse and a square can appear as a trapezoid.

Although foreshortening is an important element in art where visual perspective is being depicted, foreshortening occurs in other types of two-dimensional representations of three-dimensional scenes. Some other types where foreshortening can occur include oblique parallel projection drawings.

In painting, foreshortening in the depiction of the human figure was perfected in the Italian Renaissance, and the Lamentation over the Dead Christ by Andrea Mantegna (1480s) is one of the most famous of a number of works that show off the new technique, which thereafter became a standard part of the training of artists.

Foreshortening

Plato was one of the first to discuss the problems of perspective.

“Thus (through perspective) every sort of confusion is revealed within us; and this is that weakness of the human mind on which the art of conjuring and of deceiving by light and shadow and other ingenious devices imposes, having an effect upon us like magic… And the arts of measuring and numbering and weighing come to the rescue of the human understanding – there is the beauty of them – and the apparent greater or less, or more or heavier, no longer have the mastery over us, but give way before calculation and measure and weight?”

 

Leave a Reply

Your email address will not be published.

This site uses Akismet to reduce spam. Learn how your comment data is processed.