Perspective Representation
The different techniques of perspective representation all have in common the intention to represent the view of objects in three dimensions on a surface , taking into account the effects of distance and position in space relative to the observer. Most of the techniques, but not all, apply to a flat and finite, typically a sheet, under a table or screen. Their complexity is a function of their realism, ie their willingness to create an illusion of three dimensionality. The simplest techniques, such as isometric (see below), have a more realistic summary intention.
Summary |
Parameters
Any prospect should consider:
- Spatial reality (complex, we want to represent)
- An observer-ordinator (the painter was later replaced by the viewer Multiplicity of possible modes of representation
There are various techniques to project a perspective drawing. It has existed since the Middle Ages instruments paths assisting in the perspective representation according to some modes: perspectographs. Despite this, the advent of photography will not change the mode of representation about the prospect because it is not to imitate nature (our eye has a spherical bottom, the canvas is flat, the vanishing parallel join, the infinite is representable). Several systems exist to express graphically like this: perspective line leak , perspective point (s) leak, called monofocal centric perspective curvilinear ... Some representations use the same rules of perspective to show spaces unreal, impossible.
History and evolution
Perspective before the Renaissance
Various civilizations, before the Renaissance in Europe or elsewhere, used a system perspective more or less explicitly formalized. We can mention the prospect of prehistoric paintings, the Romans of Pompeii, that of the Byzantine painting .
The coding system of perspective in the Renaissance
After using the symbolic perspective (where characters adopt the size of their importance in the representation), the codification of the European humanist perspective develops in Umbria , in the middle of the fifteenth century , under the influence of the work of Piero della Francesca : intuition, technical means, the perspective is mathematical theory. However, since 1435 , Alberti , On Painting in his praise "of the painted faces that give the impression to leave the tables as if they were carved. For this, he wants "a painter is instructed, as far as possible in all liberal arts , but (...) especially since it has good geometry "thus defining the beginnings of a theory of perspective.
Examples of perspective works from the Renaissance
Fresco by Masaccio
This painting of Masaccio is one of the first ( 1428 ) featuring a special effort. Only the facade of the building on the left is shown in perspective with a focus monofocal vanishing point , it is a step in the complete discovery of perspective by Renaissance , the full picture is more balanced, it also has a wall right perspective and an awning. Note: The horizontal underside of the eaves, with exposed beams, is a prospect raised approximately. This facade is a vertical plane perpendicular to the plane of the table. In contrast the horizontal plane of the floor is not tiled, it is not in prospect. Note also that the eye of the painter is the same height as the eyes of standing figures. The back wall, regardless of the needs scenic, is very useful to avoid the question of infinity.
Melozzo and the prospect of upward
Melozzo Forl was a famous master of perspective, as his disciple Marco Palmezzano. He was the first who used the prospect of upward The Ideal City (Piero della Francesca?)
The Ideal City in Urbino long ascribed to Piero della Francesca The view above is a picture of 1475. At this phase of "discovery" of perspective, the artist has dealt with many things: the horizontal circles are represented by ellipses , the plans are treated in perspective vertical left and right and the tile floor. The sky itself looks like a horizontal ceiling whose perspective is evoked by parallel rows of clouds with an interval more or less respects the rule of decline. The eye of the painter is at a height compatible with its passage through the door of the baptistery. At that time, one can still notice that the central building, regardless of the needs scenic, was very useful to avoid the question of infinity, although the door ajar gives us hope a beginning meditation on this point.
halos
The choice of perspective will even change the shape of the halos of saints characters do more drawing the perfect circle of Byzantine painting , but an ellipse according to the perspectival space built according to the position of the person wearing it.
Byzantine painting 
St. Dominic
The different forms of spatial perspective
The outlook for the formalized space Renaissance have not always existed and are not final, they are distinguished by their mathematical rigor, they have certain common characteristics:
- monocular;
- the projection of a portion of space on a surface, the "table";
- the painter is still the scene is still, the viewer is stationary (it does not describe the history Storia, but the space);
- the painter's arm is as long as you want;
- the painter's eye has no limitation of viewing angle, although it means "before";
- the viewer's eye is supposed to be located in the same position as the painter's eye.
Depending on whether one adopts a particular variant in the choice of positions in space of the eye and the table, we get different variants of this perspective. The surface is a plane-table or a non-plan, in this case can be unfolded, as the cylinder, or non-fold as the sphere.
The prospect is one of the basic techniques of drawing and we distinguish between the other perspective axonometric and perspective conical called monofocal centered perspective point (s) leak. The use of geometry used to build the resulting images. Several types of instruments drawn, called perspectographs , helped the artist from the Middle Ages to produce these drawings.
If the table is a plan and if the eye of the painter is at infinity, the prospect is axonometric. With two variants commonly used: if the eye is "at infinity" on the main diagonal of the 3 axes Ox, Oy, Oz perspective is isometric , if the eye is at infinity on the y-axis, the is hidden, it is descriptive geometry.
If the eye of the painter is at finite distance from the table, the prospect is conical. If the picture is more level, we obtain some interesting properties of convergence on the table of parallels in reality.
The cylindrical perspective axonometric or perspective
Main article: axonometric perspective.This type of perspective keeps the relationship between any length taken along a direction in space and the same measured length on the representation that makes the drawing.
It's the same relationship between reality and its representation for surfaces of objects in parallel planes.
However, the report measures the object to its representation is constant only in a direction given right (resp. a plane direction) and varies with the direction of the line or plane as you consider.
We must distinguish first of axonometrics axonometrics straight and oblique.
The axonometrics lines correspond to orthogonal projections on the plane of the drawing. The drawing object is assumed located along an axis perpendicular to the projection table. In these axonometrics, the spheres are represented by circles. These methods of perspective drawing are used fairly, but their details will depend in complicated ways of viewing angles.
In practice, there may be some prospects dimetric (conservation of length in two directions) and above the isometric (preserving lengths in three directions located at 60 to each other.)
The match axonometrics oblique projections of the object to be drawn along an axis not perpendicular to the table. In the standard representations, we use this type of perspective in his version, termed generically "cavalier". Today, the isometric (originally created by the military to study ballistics and fortification to know when we can pull gun on the riders) is sometimes still used in some video games wanting to view a large playing surface The vertical plane (xOz) is in full operation, the angle of escape (Oy) is 30 or 45 for example, the leakage factor is usually 0.5.
The descriptive geometry : theorized by Gaspard Monge 's descriptive geometry uses orthogonal projections on the minimum projection planes needed to solve a problem of intersection between two surfaces eg. It frequently uses only two projection planes (frontal and horizontal), so two axonometric perspective coordinates.
The conical perspective
Main article: Perspective conical.The conical perspective was invented by Filippo Brunelleschi in 1415 before the Baptistery Florence. This invention paved the way for Renaissance art. Since that time, it remained the dominant perspective in the arts.
This is a projection on a beam straight through a single point (the eye, or the viewer) on a surface (table).
From a practical standpoint, we use vanishing points to plot directions, and the representation of distance is shortened gradually as the object moves away from the observer.
The curvilinear perspective
Main article: Perspective curvilinear.
Accelerated perspective of the gallery columns of the Palazzo Spada, built by Francesco Borromini. 
Engraving of William Hogarth , 1753 The curvilinear perspective is a technique of perspective drawing that wants to get closer to the retinal image (projected on the sphere of the eye), more than does the classical perspective with a limit of 40 (-20 to 20 ). It extrapolates the construction of the image to represent a viewing angle of 180 until then go to the club for part of the design.
It solves the problem of linear perspective, which provides only the reduction of objects in depth, ignoring the reduction side. According to Leonardo da Vinci: "curvilinear perspective, which reflects the distortions in width, better reflects the effects of vision" .
It has also been developed by Maurits Cornelis Escher in limited release was a panorama, as in the image of Jean Fouquet cons listed in its research perspective cylindrical and is also used in animation for the backgrounds to represent a rotation of camera.
Use of perspective
The perspective is used in many areas:
- The sham and in particular for the anamorphic ;
- The decor of the theater ;
- the architecture , with a view Accelerated designed to make a room seem longer than it actually is (see article sham ).
- In the industrial design to see the general shape of parts or assemblies of parts.
- We find traces in the construction of certain optical illusions such as the Penrose triangle and the drawings of Escher ,
- Ci-cons, an example of ironic William Hogarth demonstrating the usefulness of the knowledge graph.
Concepts deepen
Representing a three-dimensional space
In fact there is only one cone of space, a half-space (if the maximum opening angle is 180 in curvilinear perspective), because all that is behind the painter is unknown. The only light rays that are considered to come from, we do not allow to superimpose the images that come from the back, except by artifice to include in the decor of mirrors reflecting the background.
The sky became profane
Previously, the background was not a heaven, it was often a solid color vertical gold, we did not need technical perspective for this surface. He represented the sacred space, divine, the characters were mostly saints, God, king by divine right. In the Renaissance the skies turn blue, with or without atmospheric degradation, with or without clouds, like a vertical or horizontal theater background as a high ceiling. This is a real space, human, rediscovered by humans, to say the least profane.
The people at the center of the universe
During the Renaissance man (not God) is placed at the center of the universe, what is translated in first reading by the painter (his eye) is at the center of the table. It is a shortcut. For what is at the center of the table is the projection of the eye. At the center of the painting there is often a monument, a secular character, a religious figure (it is in Jesus Marriage at Cana of Veronese ?). Sometimes the central character looks away, sometimes he looks at the painter or the viewer straight in the eye. But it is true that this is not God who is mostly in the center of the table. Hence a new riddle of perspective, if there was no God or no character building, what would there? The focus at infinity, a concept being elucidation.
The question of the infinite
The boat in the central vanishing point
Ulysses Returning to his father Chryseis Gelle Claude (~ 1644), Muse du Louvre, ParisThe huge question remains suspended in the long hesitation. It is certain that the Renaissance has understood the rules of representation of paved ground, regularly tiled with the rule of decreasing intervals. The construction of Alberti gives the edge of the table, the chart drawing shortcut tiles gradually with distance from the painter.
But in general it is careful not to extend the ground to infinity, to the point where all vanishing perpendicular to the table converge, which incidentally is the projection of the painter's eye. It might fall on two contradictions, first the eye of the painter is at finite distance from the table even point would be infinitely far away from the other side, where glaring asymmetry, on the other hand, it eliminates the Divine from the center of the universe and replace it with a new transcendence, the infinite. Moreover, in the Renaissance as well as today no scientist would dare to say that the universe is infinite in size, the painter is entitled to be reluctant to replace God with a concept may be physically false.
Very appropriate in most cases the line of sight of the infinite tiling is stopped en route by a character, a wall, a mountain, a building. If the door of the building opens, the line of sight ahead a little but bang against the back wall of the building. Later we can replace the building with a triumphal arch, a road will continue after the arc, we can even place two successive arcs, the latter being represented in the vacuum of the first, the road will continue unperturbed, two sides could reach the center of the table, what to do? But have we seen a road go to infinity? In a pinch you arrive at the seaside, the entity that is as far as one wants to be the plan of the sea, if the Earth is flat or spherical will lead the "horizon line" on the table we sidestep the mystery of the figuration of the central point at infinity representing a central horizontal border that delimits two areas of color painted, the area of water and the sky.
Long after the Renaissance, there is the trick of placing a ship on the providential central point, like Claude Gelle that uses them in Chryseis Ulysses Returning to his father (c. 1644), or to place a sun in a dazzling halo or, where a haze sky and water mingle, see Pilgrimage to Cythera.
Anamorphosis
The mathematical perspective is correct in a real universe, but will often be "aberrant" visually: eg, the sphere which is mathematically a construction based on the logical intersection of ellipses, which visually appear absurd, while a simple circle appears much more accurate ... artists like Scott Robertson or Feng Su are masters in the visual perspective applied to the game or film.
The anamorphosis is widely used as a palliative to the restriction to simulate a two-dimensional motion (perspective cylindrical, spherical or anamorphic).
References
- "It's the viewers who make the tables" words of Marcel Duchamp
- Panofsky
- Fast presentation on his difference with the linear perspective.
- curvilinear perspective of Andre Barre and Albert Flake published by Flammarion in 1968
See also
- Optical illusion
- Anamorphosis
- Mural
- Vanishing Point
- Trompe l'oeil
- 3D Graphics
- Conical perspective
- Perspectograph
- View folded
- Color perspective
on Bibliography
- 1435 : Leone Battista Alberti , De Pictura (1436) translated into the vernacular with the title Della pittura, treatise published in French in 1869 under the title of the statue and painting, the first scientific study of perspective (new titles published in French in 1992 and 2004).
- 1505 : Jean Pelerin Viator , of Artificial Perspectiva, Toul
- 1545 : Sebastiano Serlio
- 1576 : Jacques Androuet Hoop Lessons positive outlook
- 1583 : Giacomo Barozzi da Vignola , the two rules of practical perspective, trans. French, Paris, CNRS ed. , 2003.
- 1604 : Hans de Vries Vredeman
- 1932 : Erwin Panofsky , Perspective as Symbolic Form, trans. French, Paris, ed. Midnight, and reissued in 1976.
- 1998 : D. Raynaud hypothesis Oxford essay on the origins of the perspective, Paris, PUF, 1998.
- 1999 : Daniel Arasse , Italian Annunciation. A history of perspective, Paris, Hazan, 1999.
External Links
- Mathematical analysis of perspective - Sciences.ch
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