Linear perspective

Linear perspective is the art of representing three-dimensional constructions on a two-dimensional surface. It presupposes a fixed viewpoint and a desire to create an "objective" recording of one's visual experience - two conditions which have been the most dominant in the Western art of the past half-millennium.

Once the observer assumes a single point of view, several conclusions follow logically. The first and most important is this: objects appear to get smaller as their distance from the observer increases. That this is not self-evident in art is apparent from even a casual perusal of the art of other cultures and eras - most frequently objects are drawn or painted a certain size for reasons that have nothing to do with their position in space. In medieval Last Judgement paintings, for example, the relative scale of the various figures is determined only by their sacred significance; the most important are the largest.

Once the diminishment of scale with distance is noted, it is an easy step to understanding why the space between parallel lines must also appear to diminish. A wall retreating from the observer will appear to get progressively shorter, and the top and bottom edges of the wall will thus appear to move closer together.

It was an enormous conceptual leap when artists concluded that these lines, if extended indefinitely, would appear to meet at a single point on the horizon. This idea, long since verified, was likely made from a theoretical analysis of the process of seeing rather than direct observation. Van Eyck, for example, was unable to create a consistent structure for the converging lines in paintings like London's The Arnolfini Portrait because he was not aware of the theoretical breakthrough just then occurring in Italy.

Below are descriptions of the three main varieties of perspective technique.

Contents

1 1-point perspective 2 2nd kind of vanishing points 3 3rd kind of vanishing points 4 See also 5 External links

1-point perspective

If the viewpoint is pointing directly into a linear object like a building or a road, one would use one vanishing point, that is the principal focus. All lines perpendicular to the painting plate would vanish in the vanishing point.

2nd kind of vanishing points

If the lines have angles to the painting plate, they would vanish in the other vanishing points. There are lot of vanishing points homologous to different angles. But all vanishing points should be located in the same horizontal line with the focus.

In other words, two-point perspective is derived from one-point perspective by yawing the line of vision so that the line of vision will be at an acute angle away from the focus. Then the lines which used to be horizontal and parallel will now be concurrent, intersecting at the horizon. Interpreted according to projective geometry, the horizontal parallel lines of one-point perspective are actually concurrent, intersecting at the point at infinity [1:0:1]. When the head is turned by a slight angle, these lines no longer intersect at an ideal point, but at an affine point on the horizon, so they are no longer parallel.

3rd kind of vanishing points

If the lines have angles from the painting plate up or down, one would use the other kind vanishing points. Those vanishing points must located in the same vertical line with the focus. Looking at the object from above or below, the horizontal line with the focus and all other 2nd VPs would left the horizon up or down.

See also

• Curvilinear perspective
• Perspective
• Atmospheric perspective

External links

• Mathematics of Perspective Drawing
• Drawing Comics - Perspective
• 1-point perspective:
  • Another World by M. C. Escher
• 2-point perspective:
  • Belvedere by M. C. Escher
  • Dream by M. C. Escher
• 3-point perspective:
  • Depth by M. C. Escher
  • Cubic Space Division by M. C. Escher
  • Tower of Babel by M. C. Escher