The hierarchical perspective (sometimes called “symbolic” although the whole representation in perspective goes through symbolization) is the representation of the graphic perspective in which the characters have a dimension that varies according to their importance. Hierarchical proportion is a technique used in art, mostly in sculpture and painting, in which the artist uses unnatural proportion or scale to depict the relative importance of the figures in the artwork.

Perspective (from Latin perspicere, “see through”) is in art and architecture a system for depicting three-dimensional objects on a two-dimensional surface. A perspective can be compared to a painted vertical surface interposed between the viewer’s point of view and the subject. If the perspective image is done correctly, the viewer will not be able to see the difference, whether the surface is there or not. Characteristic of perspective images are:
Right angles (in reality) usually turn into oblique angles in perspective.
Parallel lines (in reality) become lines that meet at a meeting point in perspective (e.g. on the horizon line).
Lengths that are equal in size (in reality) are shown with different sizes in perspective due to shortening and different distance.

It is mainly used in the painting of Ancient Egypt, For example, in Egyptian times, people of higher status would sometimes be drawn or sculpted larger than those of lower status. During the Dark Ages, people with more status had larger proportions than serfs. In the Middle Ages and Byzantine, During the Renaissance images of the human body began to change, as proportion was used to depict the reality an artist interpreted. Hierarchical perspective having been gradually abandoned in the Renaissance (since the Italian primitives) where, already under the influence of Humanism, the characters started to adopt a size only related to the depth of the western school on the point of view, said centered monofocal. Several painters were masters of the theory of the new perspective (like Piero della Francesca) and continued to practice it in stylized works as used in medieval times.

The use of figures of a dimension relative to their hierarchical position should not be confused with the absence of technical and artistic knowledge that is observed in naïve art or in children’s art.

History
Already present in Egyptian art and in the plebeian vein of Roman art, they are already found in the reliefs of the Arch of Constantine, where the sovereign is larger than the subjects, and even more evident in the Theodosian era, for example in the Dado di Teodosio. The hierarchical proportions were not only linked to the size of the figures, but also to the individual parts of the body: the head, for example, the seat of reason, could be enlarged compared to the rest.

Having merged into Byzantine art, they adapted particularly well to Christian stylization, with the deference of secondary subjects to the majesty of Jesus and the Virgin. Typical is the undersizing of secondary figures, such as angels, which becomes very strong for earthly figures, such as those of the patrons, when represented.

This convention was maintained for centuries, reaching up to the Late Middle Ages and extending, at various levels, to the Renaissance and beyond. Gradually, with Humanism, the human figure rediscovered naturalism in proportions, visible in the progressive enlargement of the figures of the patrons with respect to the main sacred subjects. Enrico Scrovegni was painted by Giotto in Padua of almost life-size, as well as the two principals in the Pietà of Giottino, but it was only with Masaccio and his Trinity, that hierarchical proportions were set aside firmly.

They lasted longer in peripheral areas, such as Northern Europe: Dürer, in works such as the Paumgartner Altar (c. 1496-1504), still painted tiny figures of the patrons, in accordance with tradition.

Perspective historically
Already in ancient times there was interest in perspective depiction, and examples of this can still be seen in the form of murals in Pompeii, where there are examples of perspective illusion of painted windows with distant views. In the Middle Ages, the interest in correct perspective imagery was rather limited (see picture), but with the scientific approach of the Renaissance to the outside world, development accelerated and the rules of correct perspective imagery were developed and spread as an artistic discipline, initially especially in Renaissance Italy (Filippo Brunelleschi, Leon Battista Alberti). The German Renaissance painter Albrecht Dürer presented at about the same time in a series of teaching woodcuts the basic principles of the linear perspective as well as some practical arrangements for the use of correct perspective depiction.

Spatial image
The aim of spatial imagery is to form a visual three-dimensional notion of the imaged that comes as close to reality as possible. Before the invention of photography, perspective construction was the only way it could be done. The ultimate illusion is achieved when properly constructed linear perspective is combined with skillfully applied air perspective and color perspective. In the 18th century, manual cameras were created, which made it possible to draw very accurately in perspective of nature, and previously the principle of Camera obscura was known. If the depiction is very lifelike, it is Trompe l’oeil, amount of sight. Among other things, this was widely used in the Baroque to create the illusion of vaults high above the physical ceilings of churches and was used already in ancient times to create the illusion of non-existent windows with imaginary views behind (Pompeii). Danish golden age artists such as CW Eckersberg and Christen Købke were driven perspectives.

Perspective drawing was previously a demanding discipline taught in art schools and technical schools worldwide. Today, computers have taken over most of this painstaking work, and they can be used for 3D animations. Realistic shadow effects with shadows, self-shadows and reflectors are also possible to create with the help of “ray-tracing”, which works effortlessly with varying degrees of transparency.

Linear perspective
All perspective representation presupposes the idea of (imaginary) rectilinear se-rays that pass through the visible points of the subject and cut an (imaginary) image plane into points that together form the image. For a true-to-life effect, shadows are applied that reflect an imaginary light source, possibly the sun, which is located at a certain angle to the subject.

Central projection
The kind of perspective most reminiscent of modern photographic reproduction is based on the geometric discipline of central projection. Here the theoretical premise is that the se-rays of the subject all meet in an imaginary moment, it has a completely fixed position in relation to. If the exact position of the subject’s points is known in height, depth and laterally, the correct position of the individual pixels on the image plane can be constructed using well-defined methods. When the finished image is viewed with an eye placed in the location of the pixel in front of the image plane, a naturalistic depth effect is obtained, completely as when viewing a larger photograph at the right distance from the focus of the photograph.

X-perspective
The technique in X-perspective is based on the fact that many motifs such as buildings and utensils are described in projections that are perpendicular to each other and partly have axes of symmetry that follow the three main directions: a horizontal direction, a vertical direction and a depth direction.

In X perspective, the vertical direction is parallel to the image plane, while the horizontal direction and the depth direction are more or less skewed relative to the horizontal direction of the image plane. In the image, it will then be the case that all the horizontal lines of the subject will meet in a vanishing point on the horizon, just as all lines in the subject going in depth in the image will meet in another vanishing point on the horizon some distance from the first vanishing point.

Front perspective
Front perspective differs from X perspective in that there is only one vanishing point that is identical to the focus point of the image. Both the horizontal and vertical lines of the subject thus remain horizontal and vertical in the image, respectively. Only those of the subject’s lines that go in depth are depicted so that their extensions all meet at one vanishing point. It is from ancient times this perspective form of depiction that has been most used, among others by the masters of the Renaissance and has been dominant in architectural contexts.

Bird’s eye view
The bird’s eye view has a high horizon line, namely at the viewer’s eye level, which gives the impression of hovering high above the subject.

Seed perspective
Frog perspective also called fish perspective is the opposite of the bird’s eye view and have a low angle. As a result, the horizon line and any vanishing points will be low in the image.

Parallel projection
Parallel projection is characterized by no disappearance. The imaged objects are thus imaged in equal sizes, whether they are close or far away. This form of depiction is less photographically realistic, but suitable for many decorative and practical purposes. For example, with this method you can make illustrative upright cards. The method has been used on old French and Persian miniatures, among other things, and has been used extensively in computer games in the past.

Isometry
In isometry, the three spatial directions are measured along three axes with a mutual angle of 120 o between each other, of which the vertical is drawn vertically on the image plane. The scale along each of the three directions is the same, and all in all, this form of depiction is very easy to construct when the actual dimensions of the subject are known. The method is particularly useful in connection with technical illustrations, assembly instructions in connection with knock-down furniture, as well as, for example, for the production of exploded views, X-ray representations, sectioned images of various machines and apparatus, etc..

Axonometry
Axonometry differs from isometry in that the angles between the three main directions are optional. The same applies to the scale ratios along the three axes. It is this form of depiction that is used for upright cards. Here, the two horizontal main directions are perpendicular to each other, while the vertical direction continues to be drawn vertically in the image. By using different horizontal main directions, the same image can be used to image different rectangular buildings that are placed at an angle to each other.

Air perspective
Air perspective is based on the fact that removing objects due to the haze of the air seems weaker drawn than objects seen up close. By simulating this in an image, a certain depth effect can be achieved, which has nothing to do with the line course of the subject, and thus depict the distance of mountains, forests and similar landscape elements in a convincing way. Removing objects will also tend to appear more cool and tinted in color than objects seen close by. Remote mountains near the sea surface can even be difficult to distinguish from cloud formations and stand out only slightly from the blue-gray background of the sky. In other words, air perspective consists of mimicking this effect to create depth in the image. It is also the only option available to create depth effects where there are no perspective lines,

The term aerial perspective was invented in the Renaissance by Leonardo da Vinci, but the perspective was also used by ancient Roman painters. In Leonardo da Vinci’s time, the effect was often exaggerated with an unnatural blue background, and in general the aerial perspective has in recent times been used in a much more discreet and thus lifelike way (see, for example, Købke’s picture of Freriksborg Castle)..

Meaning perspective
Meaning perspective is a form of perspective mainly used in medieval painting and also known in Egyptian representations, where superiors and greater gods were portrayed as greater than subordinates.

Meaning perspective is about acquiring people in an image varying in size depending on the meaning in a given hierarchy. For example. it is often seen that Jesus is made very large, whereas figures next to him are reproduced on a much smaller scale.

The front perspective, which was already used to a certain extent in antiquity, was again forgotten in the Middle Ages and instead made room for the meaning perspective. The idea of spaciousness was lost, and did not return until the Renaissance. Instead, figures and persons were depicted in relation to their significance, so that saints, for example, were drawn large and in the middle of the image, while the benefactors of the work were made smaller by their side, without taking into account spatial proportions.

Depictions in meaning perspective can often be seen in naivety and in children’s drawings.