One-Point Linear Perspectiveas Image Coding Method

Robert A. WolakUniwersytet Jagielloński, Kraków, Poland

After the fall of the Roman Empire the western part of Europe entered a long period of disarray and decline of knowledge. The rule of Charlemagne is perhaps the turning point, the Emperor realized that a well-organized state needed a large group of well-educated clerks. And the recovery of the knowledge of the Ancient started. So deep was the ignorance that in XIth century the contents of Euclid's Elements was unknown, including the Pythagorean theorem. The reconquest in the Iberian Peninsula, the crusades in the Middle East, and the Norman rule in Sicily, in short manifold interactions with much culturally more advanced Islamic countries stimulated interest in scientific research whatever that term meant in those times. These turbulent times also brought another question where one can find the ultimate truth? Is it worth investigating the nature, the universe? Is it a futile occupation as the right answers can only be found in the Scriptures. The three great cultures of the Mediterranean region gave different answers. In the Islamic countries the Koran became the only source of the ultimate truth and slowly the scientific inquiry withered. The Greek guarded the great deposit of their ancestors seemingly adding little. In Latin Europe the great schism of the gnostic movements which considered the created world the domain of the evil was quelled by the end of the XIIIth century. This fight stimulated great minds of the Catholic Church, perhaps the greatest being St. Thomas d'Aquinas. Putting it succinctly he was convinced that as God created the Universe, the Universe, the nature is good. Through the study of Nature, the investigation of the laws of Universe we approach God. If these investigations are well conducted we can arrive at the truth only. There could be no contradiction between religion and science. It opened the way to great scientific revolution in Latin Europe, The centuries XIIIth-XVIth saw the creation and development of European universities. In the same period the Europeans strove to recover as much as possible from the knowledge of their great ancestors the Ancient Greeks and Romans. Ever great number of scientific treatises were translated into the Latin. At the beginning from the Arabic, then more and more directly from the Greek. By the end of the XVth century this process had been completed.

The wise men of the Middle Ages wrote many treatises about the nature, deciphered its laws, and for the convenience of the reader these books were illustrated. But these illustrations even at the beginning of the XVth century were unsatisfactory and unconvincing. The scientist, the illustrator studied the ancient writings on the optics, the vision. Obvious it was based on Euclid's geometry. They studied preserved frescoes but no convincing recipe was provided but nevertheless some hints were provided. The problem

was to represent on the flat surface of a picture a three dimensional object in such a way that the viewer could recreate the object, or at least recover a lot of information about it including the spacial relations and proportions of its dimensions. Therefore the picture was to be a kind of coded pictorial message.

Filippo Brunelleschi (1377-1446) is credited with inventing one-point linear perspective. The years 1402 -1404 Brunelleschi spent in Rome studying ancient monument. Perhaps then he saw some early Roman tromp-l’oeil frescoes with the space illusion created using a version of linear perspective or in Roman basilicas marveled at long lines of marble columns which from the entrance looked like placed along two lines intersecting in a distant imaginary point. According Vasari he created an image of the Florentine Baptistery seen from the entrance to the Cathedral. Perhaps the first painted image wholly subjected to the rules of one-point linear perspective, see http://www.youtube.com/watch?v=bkNMM8uiMww&feature=related or http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-introduction-part-1 .

He noticed that a square section of a floor paved with square slabs is perceived as a trapezoidal section with lines orthogonal to the face converging to a point situated at the eyes' level and the lines parallel to the face remaining parallel. The dimensions of the quadrilaterals obtained in this way are subject to the proportions derived from the Thales theorem. These simple rules based on visual experience supported by the geometrical theory of visual perception permitted to create convincing visual illusion or rather an encoded message about the seen and depicted object. These two rules are that firstly, parallel lines orthogonal to the eyes and the picture plane converge to a point on the viewer's eyes level, and secondly lines parallel to the picture plane are rendered as parallel lines in the image. All the dimensions in the image are calculated and represented proportionally according to the Thales theorem. Therefore the correct perspective image was built on a web of converging and parallel lines. The viewer of such a picture was confronted at the very beginning with the problem of finding the correct point of view, the point from which the image is seen and deciphered properly, the point from which all the dimensional relations encoded in the image can be properly read, that is the so called “viewing point”. There have been many ways to find this point proposed and to prove that it was correct. It was only in the XVIIth century that the convincing proof was proposed and, in fact, it was essentially the so-called Desargues theorem.

The first treatise explaining the basics of one-point linear perspective is Leon Battista Alberti's De Pictura from 1435 which a few years later was also available in Italian as Della pictura.

The coding is so precise that using computer software it has been not so difficult to recreate the spatial information contained in many paintings, some of these can be easily seen on the web:

Masaccio's The Holy Trinity: http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-trinity-masaccio-part-2

Piero della Francesca's Flagellation

https://www.youtube.com/watch?v=7Ggshrp8dHg

Within the space of several decades the one-point linear perspective had become well-known to Italian artists. The appearance of the printed book facilitated the dissemination of this knowledge all over Europe and numerous well-illustrated books on perspective bear witness to the popularity of the topic. By mid-XVIth century perspective images were everywhere in public spaces, church, town hall, facades of private houses, ….. In this way everyone was taught to recognize the image, to read them, to decipher the encoded message.

The images themselves had become more and more complicated, they represented ever more complex objects and spaces. In the second part of the XVIth century appeared first publications depicting various machines like mills, pumps, lifts, etc. which applied the perspective drawing to represent these objects in a very detailed ways. The reader could easily understand the way they operated, could decipher the relations between various parts, the proportions of their dimensions, to put it shortly with some engineering skills could build the machine himself, e.g..

Georg Bauer Agricola De re metallica 1556

Jacques Besson Théatre des instruments mathématiques 1578

Agostino Ramelli Diverse et Artificiose Machine 1588

At the beginning of the XVth century the Chinese were much more advanced technologically but within the space of four centuries Europe managed to close the gap and develop its technology well beyond the Chinese. It was in great extend due to the perfection and dissemination of the technical perspective drawing which facilitated the transfer of technology within the European cultural region.

Images from Perspectiva (1604) by Hans Vredeman de Vries

The rules of perspective drawing also help to represent the microworld; This time small elements were proportionally enlarged, see below the pictures from Robert Hooke's (1635 - 1703) Micrographia published in London in 1665.

Having mastered the perspective representation the artist begun to play with the expectations of the viewer, his/her decoding procedures. Below are the links to podcasts explaining some constructions in Italy in which the artist by geometrical means playing with standard reading of the image created an illusory space.

The Church of Santa Maria presso San Satiro, Milan

http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-church-santa-maria-presso-san-satiro-part-3

Palazzo Spada, Rome

http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-palazzo-spadas-corridor-part-5

Teatro Olimpico, Vicenza

http://www.artbabble.org/video/ngadc/empire-eye-magic-illusion-teatro-olimpico-andrea-palladio-part-7

Further reading:

M. Kemp, The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat . Yale University Press, 1992

K. Andersen, The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge. Springer, 2007.

S. Y. Edgerton, The Heritage of Giotto's Geometry, Art and Science on the Eve of the Scientific Revolution, Cornell Univerisity Press 1991

J. V. Field, The Invention of Infinity, Oxford University Press 1997

J. V. Field, Piero della Francesca. A Mathematician's Art, Yale University Press 2005