Prospect (representation)

Different the technical from representation in prospect in common intends to represent the sight of objects with Three dimensions on a Surface, by taking account of the effects of the distance and of their position in space compared to the observer. The majority of the techniques, but not all , apply to a plane surface and finished, typically a sheet, the framework of a table or a screen. Their complexity is function of their realism, i.e of their will to cause an illusion of three-dimensionality. The simplest techniques, like the riding Prospect (see below), do not have any realistic intention.

Any prospect must take into account:

the space reality (complex, that one wants to represent)
a observer-director (the painter replaced then by the regardor )
plane surface (on which the representation will be)
a mode of transformation (of which the choice will depend on the selected matter; symbolic system, naturalist, expressive, cubist, etc).

Multiplicity of the possible modes of representation

There exist various techniques to represent a prospect in drawing. There exists since the Moyen-âge instruments of layouts helping with the perspective representation according to certain modes: the Perspectographe S. In spite of that, the arrival of the Photographie will not change of anything the matter mode of representation by the prospect because it is not a question to imitate the Nature (our eye has a spherical bottom, the fabric is punt, the reducing parallels meet, the infinite one is representable). Several systems coexist to be expressed graphically by this kind: Prospect with creepage distance, prospect at point (S) for escape, known as monofocale centered, curvilinear Perspective… Certaines representations use even the rules of the prospect to show not only imaginary worlds but unreal, impossible spaces.

History and evolution

The coding of the system of the prospect

The coding of the prospect develops in Ombrie, in the middle of the 14th century, under the influence of the work of Piero della Francesca: of intuition, of average technique, the prospect is made mathematical theory. However, as of 1435, Alberti, in its Of Painting speaks in praise “of the painted faces which give the impression to leave the tables as if they were carved. ” For that, it wishes “that a painter either educated, as much as possible in all the Liberal arts, but (…) especially that it has the geometry well” thus defining the first steps of a theorization of the prospect.

Two examples of prospect for works of the Rebirth

This painting of Masaccio is one of the first (1428) putting in scene a very particular effort. Only the frontage of the building of left is represented in perspective monofocale centered with a Break point , it acts of a stage in the complete discovery of the prospect by the Renaissance; the complete table is more symmetrical, it has also a wall of right-hand side in prospect and a hood. Note: the horizontal plane of the lower part of the hood, with its beams, is of a prospect hardly evoked roughly. This frontage is a vertical plan perpendicular to the plan of the table. On the other hand the horizontal plane of the ground is not tiled, it is not in prospect. It is also noticed that the eye of the painter is with the same height as the eyes of the characters upright. The wall of the bottom, independently of the scenographic needs, was quite useful to avoid putting the question of the infinite one.

The sight above is a table of 1475. With this phase of “discovered” of the prospect, the painter treated many things: the horizontal circles are represented by ellipse S, the plans treated in prospect are the vertical ones of left and right-hand side as well as the tiled ground. The sky itself resembles a horizontal ceiling for which the prospect is evoked by rows for parallel clouds whose interval complies with the rule of decrease more or less. The eye of the painter is with a height compatible with its passage by the door of the baptistry. At that time, one can still notice that the central building, independently of the scenographic needs, was quite useful to avoid putting the question of the infinite one, although the half-opened door lets to us hope for a beginning of meditation on this point.

Various forms of space prospect

The space prospects formalized since the Renaissance did not always exist and are not the ultimate ones, they are characterized by their mathematical rigor, they have certain common characteristics:

a monocular vision;
the projection of part of space on a surface, the “table”;
the painter is motionless, the scene is motionless, the spectator is motionless (one does not describe the history Storia , but space);
the painter has the arm as long as one wants;
the eye of the painter does not have any limitation of angle of vision, although he sees " devant" ;
the eye of the spectator is supposed being located at the same position as the eye of the painter.

According to whether one adopts such or such alternative in the choice of the positions in the space of the eye and the table, one obtains various alternatives of this prospect. The surface-table is a plan or a not-plan, in this case can be dépliable, as the cylinder, or non-dépliable like the sphere.

If the table is a plan and if the eye of the painter is ad infinitum, the prospect is axonometric . With two usual alternatives: if the eye is “ad infinitum” on the principal diagonal of 3 axes OX, OY, OZ the prospect is isometric , if the eye is ad infinitum on axis OY, this one is hidden, one is in descriptive Géométrie .

If the eye of the painter is remotely finished table, the prospect is conical . So moreover the table is plane, one obtains interesting properties of convergences on the table of parallel straight lines in reality.

Drawing in prospect

The prospect belongs to the basic techniques of the Dessin and one distinguishes inter alia the axonometric Perspective and the conical Perspective known as prospect monofocale centered with not (S) for escape. The use of the geometry makes it possible to build the resulting images. Several types of instruments of layouts, called Perspectographe S, helped the draftsman since the Moyen-âge to carry out these drawings.

The axonometric prospect or cylindrical prospect

This type of prospect preserves the relationship between any length taken according to a direction space and this same length measured on the representation as makes the drawing of it. The same applies to relationship between the reality and its representation for surfaces of objects located in parallel plans.

However, the report/ratio of measurements of the object to its representation is constant only according to one line direction given (resp a direction of plan) and varies with the direction of the right-hand side or the plan which one considers.

It is necessary to distinguish first of all from the right axonométries and the oblique axonométries.

The right axonométries correspond to orthogonal projections on the Plan of the drawing. The drawn object is supposed to be located according to an axis perpendicular to the table of projection. In these axonométries, the spheres are represented by circles. These methods of drawing in prospect are used enough, but their detail depends in a complicated way of the angles on observation.

In practice, one uses sometimes dimetric prospects (conservation lengths according to two directions) and especially the isometric Perspective (conservation lengths according to three directions located at 60° ones compared to the others.)

The oblique axonométries correspond to projections of the object to draw according to an axis nonperpendicular to the table. In the standard representations, one uses this type of prospect only in his particular version known as in a generic way " cavalière". Today, the riding Perspective is mainly used in design (Technical design, CAD, Architecture) like for the video games (created in an original manner by the soldiers to study the Balistique and the Fortification S to know at which time one can draw with the gun on the riding ). The vertical plan (xOz) is full-scale, the angle of escape of (OY) is 30° or 45° for example, the coefficient of escape is often 0,5.

The descriptive Geometry : theorized by Gaspard Monge the descriptive geometry uses orthogonal projections on the minimum of plans of projection necessary to the resolution of a problem of intersection between two surfaces for example. It is frequent that it uses only of two plans of projection (frontal and horizontal), therefore of two axonometric prospects coordinates.

The conical prospect

The curvilinear prospect

Uses of the prospect

The prospect is used in many fields:

the Trompe-l'oeil and in particular for the Anamorphosis;
the Decoration of Theater;
the Architecture, with the accelerated prospect which aims at making appear longer one part than it is not actually (see the article trompe-l'oeil).
In the draftsmanship to visualize the general form of the parts, or the whole of parts.
One finds of them traces in the construction of some optical illusions like the Triangle of Penrose and the drawings of Escher,
to note an ironic example of William Hogarth showing the utility of this graphic knowledge (see Hogarth)

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