# User Contributed Dictionary

### Verb

foreshortening- present participle of foreshorten

# Extensive Definition

Perspective (from Latin
perspicere, to see through) in the graphic
arts, such as drawing, is an approximate
representation, on a flat surface (such as paper), of an image as it is perceived by the
eye. The two most
characteristic features of perspective are that objects are drawn:

- Smaller as their distance from the observer increases
- Foreshortened: the size of an object's dimensions along the line of sight are relatively shorter than dimensions across the line of sight (see later).

## Basic concept

Perspective works by representing the light that passes from a scene through an imaginary rectangle (the painting or photograph), to the viewer's eye. It is similar to a viewer looking through a window and painting what is seen directly onto the windowpane. If viewed from the same spot as the windowpane was painted, the painted image would be identical to what was seen through the unpainted window. Each painted object in the scene is a flat, scaled down version of the object on the other side of the window. Because each portion of the painted object lies on the straight line from the viewer's eye to the equivalent portion of the real object it represents, the viewer cannot perceive (sans depth perception) any difference between the painted scene on the windowpane and the view of the real scene.### Related concepts

Some concepts that are commonly associated with perspective include:- foreshortening (see later)
- horizon line
- vanishing points

All perspective drawings assume a viewer is a
certain distance away from the drawing. Objects are scaled relative
to that viewer. Additionally, an object is often not scaled evenly:
a circle often appears as an ellipse and a square can appear as a
trapezoid. This distortion is referred to as foreshortening.

Perspective drawings typically have an—often
implied—horizon line. 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. A master in this thing was Johannes
Vermeer

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. Such a perspective would thus have no
vanishing points.

## History

### Early history

commons Evolution
of Perspective

Before perspective, paintings and drawings
typically sized objects and characters according to their spiritual
or thematic importance, not with distance. Especially in Medieval
art, art was meant to be read as a group of symbols, rather
than seen as a coherent picture. The only method to show distance
was by overlapping characters. Overlapping alone made poor drawings
of architecture; medieval paintings of cities are a hodgepodge of
lines in every direction. With the exception of dice, heraldry typically ignores
perspective in the treatment of charges,
though sometimes in later centuries charges are specified as in
perspective.

Perspective perhaps first entered mainstream
artistic use around the 5th century B.C. in ancient Greece in the
subject of skenographia: using a flat
panel on a stage to give the illusion of depth. The philosophers
Anaxagoras and
Democritus
worked out geometric theories of perspective for use with
skenographia. Alcibiades had
paintings in his house designed based on skenographia, thus this
art was not confined merely to the stage. Euclid's Optics
introduced a mathematical theory of perspective; however, there is
some debate over the extent to which Euclid's perspective coincides
with a modern mathematical definition of perspective.

Some of the paintings found in the ruins
of Pompeii show a remarkable realism and perspective for their
time.

A clearly modern optical basis of perspective was
given in 1021, when Alhazen,
an Iraqi
physicist and mathematician,
in his Book of
Optics, explained that light projects conically into the
eye. This was, theoretically, enough to translate objects
convincingly onto a painting, but Alhalzen was concerned only with
optics, not with
painting. Conical translations are mathematically difficult, so a
drawing constructed using them would be incredibly time
consuming.

The artist Giotto di
Bondone attempted drawings in perspective using an algebraic
method to determine the placement of distant lines. The problem
with using a linear ratio in this manner is that the apparent
distance between a series of evenly spaced lines actually falls off
with a sine dependence. To
determine the ratio for each succeeding line, a recursive ratio must be used.
This was not discovered until the 20th
Century, in part by Erwin
Panofsky.

One of Giotto's first uses of his algebraic
method of perspective was
Jesus Before the Caïf. Although the picture does not conform to
the modern, geometrical method of perspective, it does give a
decent illusion of depth, and was a large step forward in Western
art.

### Mathematical basis

One hundred years later, in about 1415, Filippo Brunelleschi demonstrated the geometrical method of perspective, used today by artists, by painting the outlines of various Florentine buildings onto a mirror. When the building's outline was continued, he noticed that all of the lines converged on the horizon line. According to Vasari, he then set up a demonstration of his painting of the Baptistry in the incomplete doorway of the Duomo. He had the viewer look through a small hole on the back of the painting, facing the Baptistry. He would then set up a mirror, facing the viewer, which reflected his painting. To the viewer, the painting of the Baptistry and the Baptistry itself were nearly indistinguishable.Soon after, nearly every artist in Florence used
geometrical perspective in their paintings, notably Donatello, who
started sculpting elaborate checkerboard floors into the simple
manger portrayed in the
birth of Christ. Although
hardly historically accurate, these checkerboard floors obeyed the
primary laws of geometrical perspective: all lines converged to a
vanishing point, and the rate at which the horizontal lines receded
into the distance was graphically determined. This became an
integral part of Quattrocento
art. Not only was perspective a way of showing depth, it was also a
new method of composing
a painting. Paintings began to show a single, unified scene, rather
than a combination of several.

As shown by the quick proliferation of accurate
perspective paintings in Florence, Brunelleschi likely understood
(with help from his friend the mathematician
Toscanelli), but did not publish, the mathematics behind
perspective. Decades later, his friend Leon
Battista Alberti wrote Della
Pittura, a treatise on proper methods of showing distance in
painting. Alberti's primary breakthrough was not to show the
mathematics in terms of conical projections, as it actually appears
to the eye. Instead, he formulated the theory based on planar
projections, or how the rays of light, passing from the viewer's
eye to the landscape, would strike the picture plane (the
painting). He was then able to calculate the apparent height of a
distant object using two similar triangles. The mathematics behind
similar triangles is relatively simple, having been long ago
formulated by Euclid. In viewing a
wall, for instance, the first triangle has a vertex
at the user's eye, and vertices at the top and bottom of the wall.
The bottom of this triangle is the distance from the viewer to the
wall. The second, similar triangle, has a point at the viewer's
eye, and has a length equal to the viewer's eye from the painting.
The height of the second triangle can then be determined through a
simple ratio, as proven by Euclid.

Piero
della Francesca elaborated on Della Pittura in his De
Prospectiva Pingendi in 1474. Alberti had
limited himself to figures on the ground plane and giving an
overall basis for perspective. Della Francesca fleshed it out,
explicitly covering solids in any area of the picture plane. Della
Francesca also started the now common practice of using illustrated
figures to explain the mathematical concepts, making his treatise
easier to understand than Alberti's. Della Francesca was also the
first to accurately draw the Platonic
solids as they would appear in perspective.

Perspective remained, for a while, the domain of
Florence. Jan van
Eyck, among others, was unable to create a consistent structure
for the converging lines in paintings, as in London's The
Arnolfini Portrait, because he was unaware of the theoretical
breakthrough just then occurring in Italy.

### Leonardo da Vinci

Leonardo
da Vinci distrusted Brunelleschi's formulation of perspective
because it failed to take into account the appearance of objects
held very close to the eye. He built his understanding of
perspective not only upon the rigid formulations of rays of light, but what he directly
observed. His understanding of perspective thus took in not only
the light, but the air it traveled through. He believed that the
way an object's color seemed to change with distance, and the way
an object's borders become indistinct with distance, are primary parts of
perspective.

Leonardo believed that understanding perspective
was crucial to painting and drawing, as illustrated in the
following statement; "Practice must always be built upon strong
theory, of which
perspective is the signpost and the gateway, and without
perspective nothing can be done well in the matter of painting".
The technique of painting objects in the distance with soft, cool
colors is called aerial
perspective.

### Computer graphics

3-D computer
games and ray-tracers
often use a modified version of perspective. Like the painter, the
computer program is generally not concerned with every ray of light
that is in a scene. Instead, the program simulates rays of light
traveling backwards from the monitor (one for every pixel), and
checks to see what it hits. In this way, the program does not have
to compute the trajectories of millions of rays of light that pass
from a light source, hit an object, and miss the viewer.

CAD software, and some
computer games (especially games using 3-D polygons) use linear
algebra, and in particular matrix multiplication, to create a sense
of perspective. The scene is a set of points, and these points are
projected to a plane (computer screen) in front of the view point
(the viewer's eye). The problem of perspective is simply finding
the corresponding coordinates on the plane corresponding to the
points in the scene. By the theories of linear algebra, a matrix
multiplication directly computes the desired coordinates, thus
bypassing any descriptive
geometry theorems used in perspective drawing.

## Varieties

Of the many types of perspective drawings, the most common categorizations of artificial perspective are one-, two- and three-point. The names of these categories refer to the number of vanishing points in the perspective drawing.### One-point perspective

One vanishing point is typically used for roads, railroad tracks, 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.One-point perspective exists when the painting
plate (also known as the picture
plane) is parallel to two axes of a rectilinear (or Cartesian)
scene — a scene which is composed entirely of linear elements that
intersect only at right angles. If one axis is parallel with the
picture plane, then all elements are either parallel to the
painting plate (either horizontally or vertically) or perpendicular
to it. All elements that are parallel to the painting plate are
drawn as parallel lines. All elements that are perpendicular to the
painting plate converge at a single point (a vanishing point) on
the horizon.

#### Examples

### Two-point perspective

Two-point perspective can be used to draw the
same objects as one-point perspective, rotated: looking at the
corner of a house, or looking at two forked roads shrink into the
distance, for example. One point represents one set of parallel
lines, the other point represents the other. Looking at a house
from the corner, one wall would recede towards one vanishing point,
the other wall would recede towards the opposite vanishing
point.

Two-point perspective exists when the painting
plate is parallel to a Cartesian scene in one axis (usually the
z-axis) but not to the other two axes. If the scene being viewed
consists solely of a cylinder sitting on a horizontal plane, no
difference exists in the image of the cylinder between a one-point
and two-point perspective.

### Three-point perspective

Three-point perspective is usually 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 those walls recede into the ground. This third vanishing
point will be below the ground. Looking up at a tall building is
another common example of the third vanishing point. This time 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.
Image constructed using multiple vanishing points.

One-point, two-point, and three-point
perspectives appear to embody different forms of calculated
perspective. The methods required to generate these perspectives by
hand are different. Mathematically, however, all three are
identical: The difference is simply in the relative orientation of
the rectilinear scene to the viewer.

### Zero-point perspective

Due to the fact that vanishing points exist only when parallel lines are present in the scene, a perspective without any vanishing points ("zero-point" perspective) occurs if the viewer is observing a nonlinear scene. The most common example of a nonlinear scene is a natural scene (e.g., a mountain range) which frequently does not contain any parallel lines. A perspective without vanishing points can still create a sense of "depth," as is clearly apparent in a photograph of a mountain range (more distant mountains have smaller scale features).### Other varieties of linear 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.## Methods of construction

Several methods of constructing perspectives exist, including:- Freehand sketching (common in art)
- Graphically constructing (once common in architecture)
- Using a perspective grid
- Computing a perspective transform (common in 3D computer applications)
- Mimicry using tools such as a proportional divider (sometimes called a variscaler)

### Example

One of the most common, and earliest, uses of geometrical perspective is a checkerboard floor. It is a simple but striking application of one-point perspective. Many of the properties of perspective drawing are used while drawing a checkerboard. The checkerboard floor is, essentially, just a combination of a series of squares. Once a single square is drawn, it can be widened or subdivided into a checkerboard. Where necessary, lines and points will be referred to by their colors in the diagram.To draw a square in perspective, the artist
starts by drawing a horizon line (black) and determining where the
vanishing point (green) should be. The higher up the horizon line,
the lower the viewer will appear to be looking, and vice versa. The
more off-center the vanishing point, the more tilted the square
will be. Because the square is made up of right angles, the
vanishing point should be directly in the middle of the horizon
line. A rotated square is drawn using two-point perspective, with
each set of parallel lines leading to a different vanishing
point.

The foremost edge of the (orange) square is drawn
near the bottom of the painting. Because the viewer's picture plane
is parallel to the bottom of the square, this line is horizontal.
Lines connecting each side of the foremost edge to the vanishing
point are drawn (in grey). These lines give the basic, one point
"railroad tracks" perspective. The closer it is the horizon line,
the farther away it is from the viewer, and the smaller it will
appear. The farther away from the viewer it is, the closer it is to
being perpendicular to the picture plane.

A new point (the eye) is now chosen, on the
horizon line, either to the left or right of the vanishing point.
The distance from this point to the vanishing point represents the
distance of the viewer from the drawing. If this point is very far
from the vanishing point, the square will appear squashed, and far
away. If it is close, it will appear stretched out, as if it is
very close to the viewer.

A line connecting this point to the opposite
corner of the square is drawn. Where this (blue) line hits the side
of the square, a horizontal line is drawn, representing the
farthest edge of the square. The line just drawn represents the ray
of light travelling from the viewer's eye to the farthest edge of
the square. This step is key to understanding perspective drawing.
The light that passes through the picture plane obviously can not
be traced. Instead, lines that represent those rays of light are
drawn on the picture plane. In the case of the square, the side of
the square also represents the picture plane (at an angle), so
there is a small shortcut: when the line hits the side of the
square, it has also hit the appropriate spot in the picture plane.
The (blue) line is drawn to the opposite edge of the foremost edge
because of another shortcut: since all sides are the same length,
the foremost edge can stand in for the side edge.

Original formulations used, instead of the side
of the square, a vertical line to one side, representing the
picture plane. Each line drawn through this plane was identical to
the line of sight from the viewer's eye to the drawing, only
rotated around the y-axis ninety degrees. It is, conceptually, an
easier way of thinking of perspective. It can be easily shown that
both methods are mathematically identical, and result in the same
placement of the farthest side (see Panofsky).

## Foreshortening

Foreshortening refers to the visual effect or optical illusion that an object or distance is shorter than it actually is because it is angled toward the viewer.In art, the term "foreshortening" is often used
synonymously with perspective, even though foreshortening can occur
in other types of non-perspective drawing representations (such as
oblique
parallel projection).

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.

Figure F1 shows two different projections of a
stack of two cubes, illustrating oblique parallel projection
foreshortening ("A") and perspective foreshortening ("B").

## Other topics

The following topics are not critical to
understanding perspective, but provide some additional information
related to perspectives.

### Limitations

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?"

The essence of perspective is to show things as
they appear, not as they are. Because of this, a number of problems
can arise. As comics theorist Scott
McCloud put it, "Western perspective works fine most of the
time, but all you need to do to see its limitations is to stand on
a set of train tracks. The lines appear to converge on the horizon
like they're supposed to, but if you look down you see the tracks
curve around your feet and meet up again on the other side!"

Perspective images are calculated assuming a
particular vanishing point. In order for the resulting image to
appear identical to the original scene, a viewer of the perspective
must view the image from the exact vantage point used in the
calculations relative to the image. This cancels out what would
appear to be distortions in the image when viewed from a different
point. These apparent distortions are more pronounced away from the
center of the image as the angle between a projected ray (from the
scene to the eye) becomes more acute relative to the picture plane.
In practice, unless the viewer chooses an extreme angle, like
looking at it from the bottom corner of the window, the perspective
normally looks more or less correct. This is referred to as
"Zeeman's Paradox." It has been suggested that a drawing in
perspective still seems to be in perspective at other spots because
we still perceive it as a drawing, because it lacks depth of field
cues.

For a typical perspective, however, the field of
view is narrow enough (often only 60 degrees) that the distortions
are similarly minimal enough that the image can be viewed from a
point other than the actual calculated vantage point without
appearing significantly distorted. When a larger angle of view is
required, the standard method of projecting rays onto a flat
picture plane becomes impractical. As a theoretical maximum, the
field of view of a flat picture plane must be less than 180 degrees
(as the field of view increases towards 180 degrees, the required
breadth of the picture plane approaches infinity).

In order to create a projected ray image with a
large field of view, one can project the image onto a curved
surface. In order to have a large field of view horizontally in the
image, a surface that is a vertical cylinder (i.e., the axis of the
cylinder is parallel to the z-axis) will suffice (similarly, if the
desired large field of view is only in the vertical direction of
the image, a horizontal cylinder will suffice). A cylindrical
picture surface will allow for a projected ray image up to a full
360 degrees in either the horizontal or vertical dimension of the
perspective image (depending on the orientation of the cylinder).
In the same way, by using a spherical picture surface, the field of
view can be a full 360 degrees in any direction (note that for a
spherical surface, all projected rays from the scene to the eye
intersect the surface at a right angle).

Just as a standard perspective image must be
viewed from the calculated vantage point for the image to appear
identical to the true scene, a projected image onto a cylinder or
sphere must likewise be viewed from the calculated vantage point
for it to be precisely identical to the original scene. If an image
projected onto a cylindrical surface is "unrolled" into a flat
image, different types of distortions occur: For example, many of
the scenes straight lines will be drawn as curves. An image
projected onto a spherical surface can be flattened in various
ways, including:

- an image equivalent to an unrolled cylinder
- a portion of the sphere can be flattened into an image equivalent to a standard perspective
- an image similar to a fisheye photograph

## See also

## Notes

## References

- The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat
- Architectural Representation and the Perspective Hinge
- The Origin of Perspective, Translated by John Goodman
- Brunelleschi in Perspective
- Renaissance and Renascences in Western Art
- The Lives of the Artists ">http://easyweb.easynet.co.uk/giorgio.vasari/}}

## External links

- Teaching Perspective in Art and Mathematics through Leonardo da Vinci's Work at Convergence
- Mathematics of Perspective Drawing
- Drawing Comics - Perspective
- Quadrilateral Perspective by Yvonne Tessuto Tavares
- The Perspective Page A short interactive introduction to the geometry of perspective drawing

foreshortening in Persian: ژرفانمایی
(گرافیک)

foreshortening in Arabic: منظور

foreshortening in Bulgarian: Перспектива

foreshortening in German: Perspektive

foreshortening in Spanish: Perspectiva

foreshortening in French: Perspective
(représentation)

foreshortening in Korean: 원근법

foreshortening in Italian: Proiezioni centrali o
prospettiva

foreshortening in Hebrew: פרספקטיבה

foreshortening in Lithuanian: Perspektyva

foreshortening in Macedonian: Перспектива

foreshortening in Dutch: Lijnperspectief

foreshortening in Japanese: 遠近法

foreshortening in Norwegian: Perspektiv
(kunst)

foreshortening in Polish: Perspektywa

foreshortening in Portuguese: Perspectiva
(gráfica)

foreshortening in Russian: Перспектива

foreshortening in Finnish: Perspektiivi

foreshortening in Swedish: Perspektiv

foreshortening in Tamil: இயலுறு தோற்றப்
படம்

foreshortening in Thai:
การเขียนแบบทัศนียภาพ

foreshortening in Turkish: Perspektif

foreshortening in Ukrainian: Аксонометрія

foreshortening in Chinese: 透视