Linear Perspective - from Space Illusions to Optical Delusions

CyberEmpathy - Visual and Media Studies Academic Journal ISSUE 9 2014/2015 Cyber Art ISSN 2299-906X

Source of Image: http://aks.rutgers.edu/AksUWW/Psych/305WWW/neuron/Illusion.html

Beata Bigaj - Zwonek

Linear Perspective - from Space Illusions to Optical Delusions


Beata Bigaj-Zwonek

Linear Perspective - from Space Illusions to Optical Delusions

Abstract:

If Agatharchus from Samos, a Greek painter from V century B.C., had looked at the

rendering effect in computer graphics program of 3D type, perhaps he would have exclaimed

– after all it's an image built on the very same principles that I use to build illusion in the

theatrical sets! Do we realize that knowledge of linear perspective exists at least for 26

centuries and actually has not changed since ancient times?

Painter, graphic artist, academic teacher (Andrzej

Frycz Modrzewski Krakow University and Academy

Ignatianum in Cracow) Graduated from the Faculty

of Graphic Arts of the Academy of Fine Arts in

Cracow (diploma in Lithography Workshop in 1997).

In 2005 she got a doctoral degree in fine arts at the

Academy of Fine Arts in Cracow, in 2012 a doctoral

degree in fine arts. Doctor is a member of the artistic

associations "The Kontrapost" and The Focus-Europa

(Germany). A scholar of "The Elizabeth Greenshields

Foundation" (1994), winner of the scholarship "The

Young Poland" of the Minister of Culture and the

National Heritage (2008).


Linear perspective – in other words convergent, geometric, renaissance, decreasing - is

a method of building a three-dimensional image on a two-dimensional surface, based on the

vanishing points to which all lines perpendicular to the eye of the beholder are aiming.

Parallel lines in this perspective stay parallel to each other1. Vanishing points are located on

the horizon line, the position of which changes due to the altitude, from which the viewer

observes a given space. The closer to the horizon line, the less distance between the objects is.

2

Nowadays, it happens that the images based on this kind of perspective are drawn

"almost completely" by a graphics program. Sometimes they are based on photography shot.

However, like centuries ago, students of design and art schools gain knowledge of linear

perspective based mainly on the experience carried over from the direct observation of

reality, without additional technical support. Moreover, to draw an object in this perspective,

and especially a group of objects, is not an easy task.

The issue of drawing without modern "facilitators" seems intriguing at least for two

reasons. Firstly, artists have been creating methods (and even mechanical tools) for imaging

in perspective since the Renaissance. Many times successfully. Secondly, already in the XIX

century the absolute power of perspective was questioned, recognizing that it is only one of

ways to build an image. So maybe the knowledge of perspective is not indispensable in art

and design?

1 Exception is three-point perspective. In this case the third vanishing point is located below or above the horizon line and

the parallel lines are approaching it - as a result they stop being parallel to each other..

2 Giacomo da Vignola, Perspective diagram, 1583, line art , Biblioteca, Bologna, [z:] http://wga.hu


Still I think it is. Even to those who avoid perspective foreshortenings in imaging.

Because there is a difference between conscious avoiding and avoiding out of ignorance.

Therefore, linear perspective still is a chore for future artists and a challenge for mature

artists who are aware that, to reign over the perspective, one must have a practical knowledge

of the principles of its construction and the differences between observation of 3-dimensione

and reflection of it on paper. And - that besides being a tool for creating the illusion - linear

perspective is also an element constructing the form of the artwork, which one can apply in

different ways and to different degrees, thus building thanks to it the very own original

language of artistic expression.

The history of knowledge of perspective - an overview

We know about mentioned Agatharchus, inter alia, from the The ten books on

architecture by Vitruvius. The author mentions in it the artist living centuries ago: "At first,

at the time when Aeschylus presented tragedies, Agatharchus built in Athens a scene and

left the thesis on it"3. In the following part of the text Vitruvius not only highlights the artist's

skills in translating knowledge about the vision to the illusion on the surface, but also briefly

describes the perspective itself, mentioning at the same time its pioneering theorists.

"Encouraged by this, Democritus and Anaxagoras wrote on the same subject, explaining

how to draw the lines corresponding in the natural way to eyes and propagation of rays

from the specified center point, so that images of buildings shown on the stage scenery

captured the nature of a certain thing, and that all paintings on vertical and flat walls

seemed concave or convex"4.

In addition to the text of Vitruvius, we also have other sources of evidence that the

perspective was not alien to the ancient Greeks. Various texts from the era (also later ones,

but relating to Greek art) contain information on the ancient Greek imaging being illusory,

and that it was illusion that brought credit to the creators. Proof of this can be texts of Pliny,

3 Vitruvius, The ten books on architecture. The seventh book, Warsaw 2004, p. 167

4 ibidem


with their admiration for the mastery of Greek artists in expressing nature. It seems that this

illusion had to have support in perspective, as can be evidenced by the passage from The

Natural History about Apelles: "he painted also Alexander the Great with lightning in his

hand [...] the fingers seem to protrude from the picture, and even lightning is as if outside of

the picture" 5.

Philosophy also should be mentioned here - for example, Plato and his criticism of

illusive painting...

The paintings from this period have not survived, however, and we can only presume

on the basis of knowledge about the admiration of the Romans for Greek art, that perhaps

they resembled those found in Pompeii and Herculaneum.

In the Middle Ages, the knowledge of linear perspective (or more precisely - of

illusional Roman imaging) lost practical dimension in art, largely due to changes in

philosophy, particularly that associated with religion (it is worth mentioning here the

iconoclast conflict) and as a result of social and economic difficulties. Although, the subject of

perspectiva was taught at school, but as a part of the geometry, where it was associated with

the science of optics (vision, image reflections in different surfaces, propagation of light), and

sometimes with the determination of the distance between objects. However, in the arts the

science of linear perspective, used in the painting practice, became the knowledge of chosen

ones. It was not required from creators, because it did not suit the idea according to which we

should strive to reality perfect in the spirit, not to the miserable earthly one.

The return to linear perspective, or rather its development, because its rules were

created anew, was already in the early Renaissance. Changes in the perception of the world,

nature and human, characteristic of the nascent era resulted in a return to the faithful

recreation of space in the surface. How quickly “arrears” were overtaken can be seen in the

numerous treatises on painting and proportion, and actually perspective. Its significance and

5 Piliny the Older, The natural history [in:] Thinkers, chroniclers and artists about art. From antiquity to, ed. by J. Białostocki,

Warsaw 1988, p. 151


achievements of the Renaissance in the methods of its construction resulted in the later

adoption of the term Renaissance perspective to determine the creation of reality using

vanishing points.

Comparing Giotto from the XIII/XIV century and Masaccio who was creating a

hundred years later, one can see how great was the way passed in imaging-based perspective.

Let's look at the frescoes of the basilica in Assisi, depicting the life of St. Francis by

Giotto Di Bondone. In dozens of icons painted in the church, architecture is a numerous and

significant element. The buildings, in the context of perspective, are constructed here

(nearly?, even) almost good. It was as if a painter sensed its principles, but applied them

inconsistently. Or even as if he did not yet have such knowledge to make the effect of "three-

dimension on the plane" satisfactory. Lines leading into the depths are striving thus almost

towards one vanishing point. Almost, because in reality - analyzing the constructions of

perspective in Giotto’s works – one can point out many places of diverging of the rays that

build the image of objects in perspective. But at the same time, it is clear that the overall

trend of the axle perspective heads towards one, proper vanishing point.

6

6 Giotto di Bondone, Legend of St. Francis 8: the vision of the flaming chariot, fragment, 1297-99, fresco, 270 x 230 cm,

Basillica in Assis, [from:] http://wga.hu


Several creators are deemed the fathers of Renaissance perspective; however, the

precedence in terms of its practical application in the image is given to the artist called

Masaccio, the author of Holy Trinity - the artwork located in the Church of Santa Maria

Novella in Florence. This fresco, in the iconographic type of "throne of grace", shows in the

first place a group of people gathered around the cross, located in the Renaissance

architectural space closed at the top by paneled vaulted ceiling. Both architecture and figures

are located with the use of linear perspective to a common vanishing point – the frontal one.

Vanishing point is quite low; its location is probably close to the height from which the viewer

of the fresco is observing the scene.

7

Vasari provides that Masaccio was constructing perspective in his artworks based on

the knowledge imparted to him by Brunelleschi, whose knowledge of perspective aroused

admiration already among his contemporaries. It is Filippo Brunelleschi who was usually

mentioned as the one who brought perspective to art. Inspired by the mathematical

7 Masaccio, Holy Trinity, 1425-28, fresco, 640 x 317 cm, Santa Maria Novella, Florence, [from:] http://wga.hu


knowledge of his friend Paolo dal Pozzo Toscanelli, the artist led optical experiments that

have contributed to the development of space imaging principles based on geometry. In the

result, they allowed the representation of nature in the surface according to perception. Some

of these experiments concerned the determination of the point of view and in practice meant

an appropriate positioning and reading of images prepared specially by the artist. Biographer

Antonio di Tuccio Manetti represents one of the images along with the «hardware» as

follows: "The first demonstration of the principles of perspective was a plate of about half a

square cubit, where [Brunelleschi] painted a picture of the exterior of the church of Santo

Giovanni in Florence. He painted as much of the temple, as can be caught by a glance,

looking from the outside from the side [...] he made a hole in the picture in the place where

he painted the church of Santo Giovanni, at the point where one’s glance reach, when

looking from the inside of the central portal of Santa Maria del Fiore. [...] This hole from the

side of the image was tiny as a grain of lentil; from the back, however, it expanded in the

form of a pyramid [...]. [Brunelleschi] wished for whoever wanted to view the picture, to

put the image to the eye, bringing it closer with one hand, while holding a flat mirror in

front of him to reflect a painting [...] so that watching it in these conditions [...] one had the

impression that he is observing a reality " 8.

Knowledge of Brunelleschi’s skills in the field of building of an image with proper

perspective can be drawn primarily from biographical descriptions. The principles of

construction of such an image were written down later by, among others, another excellent

creator Alberti in his treatise De pittura, 1435. In addition to comments about the painting,

including the perspective, this text also contains instructions for painters and already in the

introduction mentions the necessity of possession of the considerable knowledge by them.

"But I'd like the painter to be, above all, a good and educated man, so that he could

maintain his fame with dignity - wrote Alberti - I wish the painter had as far as possible

training in all the liberal arts, but primarily in geometry. I agree with Pamfilus, an

excellent painter of antiquity - who educated many young noble men in the art of painting –

8 Antonio di Tuccio Manetti, The life of Brunelleschi [in:] Thinkers, chroniclers and artists about art. From antiquity to 1500,

ed. by J. Białostocki, Warsaw 1988, p. 527


in his opinion, one who does not know geometry, cannot become a good painter in the

future"9.

Art historians emphasize in the context of Alberti treaties that perspective - almost

mathematically described by him - not only facilitated creation of a realistic picture, but also

was proof that art has the characteristics of science, and as such, it could be a match for

always-appreciated geometry or arithmetic.

Interestingly, Alberti's treatise was not illustrated, but in later centuries, in successive

editions, paintings were added to explain perspective. Alberti's treatise was followed by other

texts of famous artists, often, however, already illustrated, also by outstanding artists (eg.

Piero della Francesca wrote - and illustrated - De Prospectiva Pingendi between 1474 and

1480 years. And between 1496 and 1498 the publication of Luca Pacioli - De divina

proportione – was supported in drawings by figures in perspective by Leonardo da Vinci

himself).

10

11

9 Leon Battista Alberti, On painting [in:] ibidem, p. 388

10 Piero della Francesca, De Prospectiva Pingendi, print from 1576, Biblioteca Palatina, Parma

http://www.atlantedellarteitaliana.it/artwork-13334.html

11 De divina proportione ,iluminated manuscript from 1498,

http://www.codicesillustres.com/catalogue/de_divina_proportione/


The interest in perspective was growing, and so was tendency of artists to fascinate

audience with possibilities of its application. Significant in this context is the statement of

Uccello (written down by Vasari), addressed to the wife who was encouraging the artist to

postpone the creative work and go to bed: "oh, what a sweet thing is this perspective"12.

Perspective is visible in virtually all of Ucello’s pictures. They are populated by figures of

people and animals drawn precisely with respect to the vanishing point. Uccello is also the

author of extraordinary drawings showing the mesh of objects, such as the following picture.

13

As time passed, however, knowledge of perspective has become so obvious that it has

ceased to be the main subject of imaging, and became only (even?) one of the building blocks

of three-dimensional space. The obviousness of combining linear perspective with other

discoveries - even in the field of color - can be seen in the expression of Leonardo, who, in

addition to linear perspective, mentions two more ones that are important for imaging:

"There are three kinds of perspective. The first is related to the causes of [apparent]

decrease of the opaque bodies depending on their distance from the eye, and is known as the

linear perspective. The second concerns the way in which colors change depending on the

distance from the eye. The third and final one addresses the matter of how the contours of

12

Cit. from: J. Białostocki, Sztuka cenniejsza niż złoto (Art. Is more precious than gold), Warsaw 1991, p.289

13 Paolo Uccello, ink, 1430, 290 x 241 mm, Uffizi Gallery, Florence, [from:] Galleria degli Uffizi, Florence,

http://commons.wikimedia.org


objects [in the picture] should be less clear, in proportion to the distance between them [in

the picture]"14.

Methods and tools assisting the creation of the illusion of space

The fact that proper application of the principles of perspective in the image has

become a condition for its correctness does not mean that building the world in perspective

has become easier. No surprise then that already in the beginning of the Renaissance helping

methods in its drawing were sought.

Alberti in Treatise on painting mentioned a supporting method related to velum:

"there is no more suitable method than applying velum, which I call the intersection among

friends [...]

It is as follows: loosely woven curtain made of thinnest possible thread, of any color,

divided by thicker threads to parallel parts and divided into squares, I stretch on frames

and place between the subject that I am going to present, and eyes, so that pyramid of view

was penetrating loose fabric. This intersection, thanks to velum, gives considerable

advantages: first, it always provides the same surfaces motionless; having the boundaries

marked, you always find the original top of the pyramid, which is a very difficult thing with

no intersection.15”

14

Leonardo da Vinci, Sketches and notes, ed. H. Anna Suh, UK 2006, p. 92

15 Leon Battista Alberti, About painting [in:] Thinkers, chroniclers and artists about art. From antiquity to, ed. by J.

Białostocki, Warsaw 1988, p. 375


The device described by Alberti could have presented itself as below:

16

Similarly - a few decades later, Leonardo da Vinci provides descriptions of the methods

/ equipment similar to that described above. There he highlights that the whole scene is

observed from a fixed point (in the first following description this is served by the wax ball, in

the second – by a "stabilizer" of the head). Furthermore, he recommends observing a view

with one eye:

"If you want to learn how to properly and correctly adjust your figures, place

between your eye and the drawn nude a rectangle, that is the frame divided by threads into

squares, and draw lightly the same squares on the paper where you intend to draw the

mentioned nude. Then place a wax ball in the place of grid that serves you for a fixed point,

looking though which at the nude you always find fossa supraclavicularis [...]. And those

threads will define to you all the parts of the body in every position, located

[perpendicularly] under fossa supraclavicularis [...]

But always keep the mesh in the perpendicular line and act so that all the nude parties

seen by you matched to the grid squares were reproduced in the appropriate boxes in a

painted mesh"17.

16 A picture from Johann II of Bavaria and Hieronymus Rodler, Ein schön nützlich büchlein und unterweisung der Kunst des

Messens (1531), [from:] William C. Wees, Light Moving in Time: Studies in the Visual Aesthetics of Avant-Garde Film, University of California Press, Berkeley · Los Angeles · Oxford 1992, {after:] http://publishing.cdlib.org/ucpressebooks/view?docId=ft438nb2fr;chunk.id=d0e997;doc.view=print


18

“The way to take the proper position.

Take a glass pane of the royal semi-folio’ size and strengthen it well in front of your

eyes, i.e. between the eye and the thing, which image you want to get. Then move away

with the eye from mentioned pane for two-thirds of the arm and fix the head in the

appropriate tool so that it could not move. After that shut or cover one eye and mark on the

glass with brush or hematite stone what is on the other side, trace it on the good card, and

then paint it, if you want, making a good use of air perspective”19.

It is worth noting that the second method described by Leonardo gave another benefit -

thanks to it, the artist obtained the traced image at the card, which did not have any

supporting lines, like mesh, so it looked as if the artist sketched the difficult views by a steady

hand with no support.

These methods don’t seem to be difficult to use, but probably did not give the precise

results, hence perhaps another idea appeared - by Durer - related to threads leading from the

observer's eye to the points of the drawn objects. The device looked like this:

17

Leonardo da Vinci, Traktat o malarstwie [w:] Myśliciele, kronikarze i artyści o sztuce. Od starożytności do 1500, red. J. Białostocki, Warszawa 1988, str. 563

18 The picture by Leonardo (fragment) – of a suport device for perspective, [from:]

http://www.classicalart.org/6/post/2013/04/a-brief-history-of-perspective.html

19 Leonardo da Vinci, Modo de ritrare un sieve Loretto [in:] Mieczyslaw Porębski, Iconosphere, ch. Picture as a

window painting, Warsaw, 1972, p. 174


20

As you can see, two people operated it.21 The apparatus consisted of a wooden frame, in

which two threads were attached - in the middle of the upper part and in the middle of one of

the vertical sides (threads had to have at least a length corresponding to the height / width of

the frame, and hang freely). The door was attached to the frame. The next element of the

device was a thread passing through the hook a’la the eye of a needle, nailed to the wall (in

such a way that the thread could move freely in the catch. To fix the thread in the hole, it was

laden with the additional weight). The thread was pulled through the frame and ended with

the pin to facilitate its grip. The artist assistant had to move the end of the thread with the

bolt and place it at different points of the observed object (according to Durer’s illustration -

the lute). After tensioning, the thread stopped on different levels inside the frame. At this

moment, the artist had to grip the threads respectively, this time the ones attached to the

frame, so that they mark the position of the thread running from the wall. Then he connected

both threads of the frame with wax and ordered the assistant to loosen tensioning of the main

thread, shut the door and mark on it the point of intersection of the threads from the frame.

In this way, putting the main thread to the relevant fragments of the observed object, one

could get its outline. It should also be mentioned, that the point of settlement of the thread

on the wall corresponds to the place from which the object was “observed”. As you can see

from the description and the fact of necessity to work at least for two persons, the idea of

20

Albrecht Durer, Drawn lutes, 1525, woodcut, Metropolitan Museum of Art, New York, [with:] http://www.usc.edu/schools/annenberg/asc/projects/comm544/library/images/626.html 21

Description by text Albrecht Durer: The Letter of measuring with calipers and the line, in 1525 [in] theorists, writers and artists on art from 1500 to 1600, ed. J. Białystok, Warsaw 1985, p. 64-65


Durer may have been good, but it is associated with arduous work and is rather inadvisable

when drawing the large quantities or complex objects.

Therefore, there is no wonder that, when someone apparently unexpectedly observed the

phenomenon of the focused sunlight passing through the hole in the wall of a darkened room

in such a way, that the image of view stretching in front of him appeared on the opposite wall

of the room, only reversed, he picked it up making the device called the camera obscura. Who

was the first? Probably the ancients have already used a camera obscura. In contrast, perhaps

the most famous early description of the phenomenon (and in some sense the device) was left

by Leonardo in the Codex Atlanticus. He wrote in it: "If the facade of a building, or a

landscape is illuminated by the sun, and there is a hole in the darkened wall located

opposite the building, then the illuminated objects will send through the hole their image

and the image will be reversed."22

In time, someone began to adapt the camera method to the work of artist - in the boxes

with a hole it was mounted the mirror inverting the image and transferring it to the paper

used for sketching landscapes.

23

22

Leonardo da Vinci's Codex Atlanticus, [after:] Zbigniew Tomaszczuk, The Hunter of Images; sketches about the history of photography, Warsaw, 1998

23 Illustration from: A. Ganot, Traité élémentaire de physique (Paris, 1855), [from:]

http://innman.blogspot.com/2009/05/camera-obscura.html


In 1807, William Hyde Wollaston (the British chemist) has invented a drawing tool

called the camera lucida. The artist looked in the sight glass and, not taking his eyes off, he

drew the object on a piece of paper.

24

There were also invented other devices allowing support to the work of an artist, as

presented below:

25

How often, actually, were these devices used? According to the great English artist

David Hockney, the author of Secret Knowledge: Rediscovering the Lost Techniques of the

24

Illustration from Scientific America Supplement, January 11, 1879 [from:], http: // en.wikipedia.org

25 Carl Augustus Schmalcalder Profile Machine, 1806 {from:] Pablo Garcia, Machine Drawing Drawing Machines,

[from:] http://pablogarcia.org/projects/machinedrawing-drawingmachines


Old Masters, even the artists that were never "suspected” of that, could draw / paint

projecting the models through the "projectors" of those times. And that was a universal

"practice". However, as Hockney stated in his book, such practice does not reduce the artists’

talent, but indicates their wisdom. Why should not one use the supporting techniques (ac. to

Hockney- quite hard in practice), if the optics was undergoing boom in the science of that

times? Moreover, the use of these methods and devices at times could be based on the need

to support the drawing from the point of view of similarity or perspective, but from the need

to achieve the effect of a specific expression, which is difficult to obtain some other way (eg.

use of the "strength" of the precise detail). Hockney, based on his own practical experience

and the knowledge acquired from the reputable researchers, says that since the 30's of the XV

century the artists used the technical support, especially the (concave) mirrors and lenses.26

The Hockney’s researches, combined with a practical demonstration of making of the

images, based on the projective methods, seem to convince about the rightness, at least of the

part of his theses. However, we do not have the direct evidences (in the sense of confirmation

by the artists of the times). In the texts of the masters and their biographies, there is lack of

the information about the support of the creative work by the optical discoveries...

From the linear perspective to the bizarre perspective

As it was already mentioned, the knowledge of perspective increased with time. The

successive artists made the increasingly difficult perspective systems. Yet the "first in terms

of the perspective" picture –Masaccio's St. Trinity – does not only point to the skills of

building the space in the image by the constructor and painter, but it also impresses with the

concern for the viewer to be able to see this space as if it actually appeared in front of his eyes

- in this aim locating the vanishing point sufficiently low, respectively to the level of the

recipient. These types of treatments have been also used by others; Mantegna was one of the

most "zealous" ones in using this method. In the frescoes attributed to him, which remained

in the Church of the Eremitani in Padua (largely destroyed by bombing in 1944) the junction

26

[cf:] David Hockney, Secret Knowledge: Rediscovering the Lost Techniques of the Old Masters, Krakow 2006


points are almost always close to the bottom edge of the plane. Mantegna is also the author of

one of the best solutions of the "false", fantastically constructed in perspective sky. From the

ceiling of the Camera degli Sposi (Camera picta) in the Palazzo Ducale in Mantua, the

characters look at the audience located underneath - so beautifully portrayed in perspective

that they seem to be real.

For me personally, an unusual display of skill of the space construction on the surface is

the fresco by mentioned earlier Uccello, showing a scene from the flood of Chiostro Verde at

Santa Maria Novella in Florence. Such an artistry perspective can be already compared to the

skills of mannerist, much later Tintoretto, known for bold solutions in the space making.

27 28

In both the Southern and Northern Renaissance, it began also to use a method, which

encrypts the image through the mesh transformation - Anamorphosis. It also demanded a

deep knowledge of optics. Leonardo tried the anamorphic drawing (the sketch of eyes), but

perhaps the most famous image of the transformation of this type is The Ambassadors by

Hans Holbein the younger, with the anamorphic skull in the foreground. In Germany, after

Durer, there was the woodcutter artist Erhard Schon, who used the anamorphoses to hide the

political messages in his works. His most famous artwork of this type is The Three Kings and

27

Paolo Uccello, Flood And Waters Subsiding (detail), 1447-1448, fresco, Chiostro Verde, Santa Maria Novella, Florence, [with:] http://wga.hu

28 Jacopo Tintoretto, Gathering of Manna, c. 1593, oil on canvas, 377 x 576 cm, San Giorgio Maggiore, Venice

[from:] http://wga.hu


the Pope, 1535, where under the guise of landscape the rulers of those times are concealed.

However, above all, anamorphosis was played with - hence the numerous remains of

anamorphosis in portraits and idyllic landscapes. A great example of this is the portrait of

Charles III, Duke of Lorraine, and his daughter Christina, by Ludovico Buti, 1593, where one

can see alternatively (daughter or father) thanks to the flat mirror set at an angle. This

anamorphosis exists thanks to the corresponding bending of the picture.29

30 31

The term anamorphosis arose with the XVII century’s publication by Jean-François

Niceron “La perspective curieuse“ (Bizarre perspective). Not only the author showed in it

how the anamorphic drawing mechanism has looked like, but also he included a number of

other complex images of the perspective – of different, often very difficult objects. Likewise,

the authorship of the difficult paintings belong to the architect Jan Vredeman De Vries. He

used, among others, the method of three point perspective, already described in the text De

Artificiali perspectiva, 1505 by the canon of the cathedral in Toul, Jean Pelerin of Le Viator

(The Traveller), the secretary of King Louis XI. In Pelerin’s theory it has been pointed out for

29

James L. Hunt, John Sharp, The Mathematics of the Channel Anamorphosis

30 Lodovico Buti, Optical Illusion with Portraits of Charles II and His Daughter Christine of Lorraine 1593, Oil on

prismatic panels, glass, 82 x 112 cm, the Istituto e Museo di Storia della Scienza, Florence, [from:] http://www.wga.hu

31 The Anamorphosis by Jean-François Niceron'a [from:] James L. Hunt, John Sharp, The Mathematics of the

Channel Anamorphosis, http://www.physics.uoguelph.ca/phyjlh/Channel.pdf


the first time the importance of the perspective of the horizon line, as well as description of

the perspective with centrally located point of confluence and two vanishing points from the

two point perspective. Pelerin applied them as a solution to the problem of the perspective of

the building, in which none of the walls were parallel to the horizon or did not coincide at a

central point. "This idea - writes M. Josse Parramon – of “three points” in general was not

known to artists, until the invention by the Italian theater directors of the scene per angolo

two centuries later "32.

The methods of “three points” should not be confused with worm's-eye view or a three-

point bird's-eye view, in which the parallel lines are no longer parallel. In the method

according to Pelerin, two types of perspective are juxtaposed in a single image. Based on this

method, Jan Vredeman De Vries’ paintings in turn inspired Rembrandt, who in 1632 painted

a picture in which one of the most important elements are the spiral stairs...

33 34

32

Jose M. Parramon, How to draw in perspective, ch. Two - vanishing points and the line of the horizon, Lodz 2003, p. 26

33 Jan de Vries Vredeman – The illustration of 'Perspective', 1604-1605, [from:]

http://perspectiveresources.blogspot.com/p/history.html

34 Rembrandt Harmenszoon van Rijn, The philosopher during meditation, 1631, oil on canvas, 29 x 33 cm,

Louvre, Paris, [from:] http://www.wga.hu

http://www.wga.hu/


In subsequent eras, the artists amazed the audiences by skills. The challenge was to

paint in such a way that the recipient had the impression that the character or object "was

coming out" of the picture. They painted the "hard objects", such as balls breaking the image,

or reflections in the mirrors. And so in 1524 the mannerist painter Parmigianino painted

himself, as he was seen in the barbeshop mirror. Here's how Vasari describes the history of

the picture: "He decided one day to paint a self-portrait, looking at himself in the barber’s

mirror. And when he saw, what the uniqueness brings the roundness of the mirror, how the

beam piquantly bends, and the doors and walls of the building make the strange grimace,

he got the desire - just like on a whim – to paint it all.

Thus, he ordered to prepare the wooden bowl on the mobile prop. He split the bowl

into two halfs of the mirror’ size and reproduced on them what he saw in the mirror, and

above all his own likeness, so correct that it was admirably hard to believe.

Because all the objects seen closer in the mirror increased and the remote ones decreased,

he portrayed his hand slightly enlarged, as showed in the mirror; he did it perfectly, so it

looked like a real hand"35.

36

35

Giorgio Vasari, Lives of the most famous painters, sculptors and architects, Warsaw-Krakow 1986, p. 152-153

36 Parmigianino, Self-portrait in a convex mirror, approx. 1524, oil on panel, 24.4 cm, Kunsthistorisches

Museum, Vienna, [from:] http://www.wga.hu

http://www.wga.hu/


In the Baroque, illusion of space affected the churches. Their walls groan under the

weight of the unreal images; the angels fly in the unreal heaven; the columns support the

unreal ceiling. What else in the proficiency of actual imaging could be demonstrated?

Can we believe our eyes? "Debunking" of the perspective – two dimension,

three dimension, or maybe a fourth dimension?

The Renaissance and post-Renaissance artists were aware of the opportunities offered

by the linear perspective. The possibilities of deception of the human eye. The anamorphic

presentation makes an evidence of knowledge of optics, but also confirms the interest in the

optical illusions. With the knowledge of the "imperfections" of the human eye, a skillful artist

could hide a lot of (unintentional) or conscious mistakes in a drawing based on the principles

of perspective. On the other hand, also a recipient’ skillful approach, through image referring

to the perspective rules, could disguise (consciously or not) the mistakes of the construction

of plans and space. In 1754, William Hogarth created a picture of Satire on the false

perspective placed on the cover of the booklet Dr. Brook Taylor's Method of Perspective

Made Easy both in Theory and Practice. The brochure of a Hogarth’s friend, John Joshua

Kirby, was a pamphlet on the linear perspective. The picture by Hogarth, very valid at first

sight, has therefore a number of purposely-made mistakes. Such a treatment had to prove

that the artist must be aware of the easiness of confusion in the field of drafting the

perspective. The caption of the picture has the slogan: Who makes THE PROJECT without

the knowledge of PERSPECTIVE will make such absurdities as those contained in the image

on the cover.


37

After years of the unappealing undeniable reign, in the XIX century they began,

however, “to point out” the vanity of this illusion. Here Cezanne paints the pictures in which

the edges of the table do not inosculate with each other. They do not inosculate, because the

artist undermines the validity of the presentation of a set of the objects (nature mort in this

case) from one point of view.

Has the image making with taking into account the fact, that painting (ie, at the same

time observing reality) we change the points of view - that is disagreement with the reality

observed by one eye and, therefore, marking the one-sidedness of this perspective – become

the discovery of not noticed? No - after all, from the beginning of describing perspective in

the Renaissance it has been noted that the reality in it is created from the point of view of a

stationary eye. In the already cited here device descriptions –methods - facilitators the idea

scrolls that the Renaissance perspective involves vision of the nature from a single point. This

purpose was served by the device for holding Leonardo’s head steady and his order to look

37

William Hogarth, Satire on false perspective, in 1754, [from:] en.wikipedia.org/wiki/Satire_on_False_Perspective


with one eye ("after that shut or cover one eye"); or the anchored by Durer threads on the

wall ("Do therefore in such a way: if you are in the room stab into the wall a large pin with

a large ear and accept that it is the eye"38). It was, however, considered that this is the

convention, which is used to write and receipt the space on the surface, because it is

compatible with the natural human vision.

But the researchers of Cezanne in the XX century drew (among others) a lesson from

his experience, that the perspective of the Renaissance cannot transmit the nature fully. Or

otherwise - that three-dimension, according to this record, does not give the complete

information about the world. And if not it, then maybe the “fourth dimension” should

appear? The futurist Gino Severini in his article "Measuring space and the fourth dimension"

wrote about the need for a deeper recording of the knowledge about the object: "The

ordinary space, with which the geometrician deals, is based, generally speaking, on the

inviolable convention of three dimensions. The painters, whose ambitions are endless,

always felt the narrowness of this convention. This means that to the usual three

dimensions they try to add the fourth, which summarizes them and which is expressed

differently, but - so to speak - was the goal of the art of all ages"39.

The "opposition" to the illusion of reality were the currents that were undermining

imaging of the external reality in order to reach the reality of ideas. The creator of

Suprematism, Kazimir Malevich, wrote: [The Art] is "able, creating a new reality beyond

reason (...), to overcome the apparent contradictions of the world of three-dimensional logic

and to combine the opposites in a higher unity"40.

38

Albrecht Durer, The Letter of measuring calipers and lines, 1525 [in:] The theorists, writers and artists on art from 1500 to 1600, ed. J. Białystok, Warsaw 1985, p. 64-65

39 Cit.: Artists on Art. From Van Gogh to Picasso, ed.: E. Grabska, H. Morawska, Warsaw, 1969, p. 166

40 Casimir Malevich [cit:] Andrzej Turowski, United utopian avant-garde. Artistic and social utopias in Russian

art 1910-1930, Warsaw 1990, [after:] Przemyslaw Chodań, Suprematism Kazimir Malevich as an example of avant-garde utopia. [From:] http://teksty.bunkier.art.pl


The voices of the discouraged from illusive presenting were so significant that the

theorists and art historians began to accentuate its contractual imaging data formula. Thus,

one of the well-known thinkers Herbert Read spoke: "the prospect theory developed in the

XV century is a scientific convention, it is just one of the ways of describing the space and,

therefore, it does not have the absolute value"41.

Skepticism to illusion in the art has teamed up with the interest and discoveries in the

field of optics and the optical illusion. In the 40th of the XX century the American

ophthalmologist Adelbert Ames Jr. designed a space called today the Ames room; if one will

look at it from a certain assumed in advance point, the size of figures will seem completely

unbelievable.

42

The Ames room is based on a non-standard shape (the plan from above is below) and

the necessity of looking at the image from one position:

41

Herbert Read [after:] Ernst Gombrich, Art and illusion. The psychology of pictorial presentation, Warsaw 1981, p.242

42 http://aks.rutgers.edu/AksUWW/Psych/305WWW/neuron/Illusion.html


43

Ames is also the author of the experiment with chairs – non-chairs ("through three

visors, we look with one eye at the three items, located within a certain distance. All three

look like chairs made of the steel pipes. When we look at them from another angle, we see

that only one of the objects has a normal shape"44).

And the experiment with a window (to those interested in it, as well as in other, similar

ones, I recommend the film posted on the page of Professor Richard Gregory:

http://www.richardgregory.org/)

How did these experiments hurt the "good name" of Renaissance perspective? As

Gombrich writes: "Ames and his colleagues decided to [...] prove that "the perceptions do

not reveal the reality”45.

43

http://en.wikipedia.org/wiki/File:Ames_room.svg

44 Ernst Gombrich, Art and illusion. The psychology of pictorial presentation, Warsaw 1981, p. 243

45 ibidem, p. 244

http://www.richardgregory.org/


46

Thus, the XX-century artistic theories, cut-off from the perspective and the

experiments indicating the easiness of deceiving the human eye, caused – it could be

considered the same way as in the Middle Ages – the disturbance of faith in the infallibility of

the linear principles of the space creating. Although, this time the process does not concern

all the authors and recipients. And it proceeds with the consciousness of the freedom of

choice. The fact that in the publication quoted above Gombrich defends the perspective ("The

necessity of cooperation of the viewer for the correct interpretation of the perspective

images [...] is not in any contradiction with the statement, that the perspective is a method

useful in transmitting the images according to the nature and induction of illusion"47) does

not mean that today the linear perspective is at stake. Firstly – as for Gombrich - when he

wrote Art and illusion (first publication - 1960 year) the abstraction dominated in the

contemporary imagery, and the figurative art was torpedoed by the allegations of illusion,

falsehood, hypocrisy. Hence, perhaps, in the Gombrich works there is a feeling of the

necessity to defend the perspective. However - secondly - today there is a lot of realism in art

and even photorealism. And, probably, none of those who reach out for this form will

undermine the validity of the linear perspective. Of course - we have to agree here with

Gombrich, as for the rightness, where the images should be consistent with nature also

[when] inducting illusion.

46

Ames experiment with chairs, [scan from:] Ibid, p. 243

47 Ibid, p. 245


…………………………..

At the end

In the case of the realistic imaging the perspective of the Renaissance is a fantastic

support. It is also a chore to those, who learn it. It evokes the need to take into account the

principles and methods that one should know in the theory and practice. It is also ruthless to

the realistic image - if one commits a mistake somewhere in perspective (and does not know

how to hide it by the tricks of "almost perspectives") – it will be blazing more than anything

else. In painting, you can agree or not agree on the colors used, discuss the tools or

techniques, but an error in the perspective in the realistic convention cannot be defended.

Over the years, the technologies, paints, tools and media changed. We stopped creating

frescoes in mass, we rarely paint on wood, more rarely on linen canvas. The traditional

graphic techniques have been replaced by the digital prints. The eye of the painter sometimes

is almost "replaced" by the camera...

And yet ... the old perspective is still ongoing...

And even using the most modern techniques to support the creation of the three-

dimension in the image, one has to know the rules of perspective. Indeed, as in the XVII

century the French architect and art theorist Roland Fréart Chambray stated: "the painter

tries to imitate things as he sees them; it is certain that if he sees them wrongly, he’ll present

them according to his bad imagination and make a bad picture; so before he takes a pencil

and brushes, he should improve his eye by reasoning, based on the principles of art, which

teaches one how to not only see things just as they are, but also the way they should be

presented. It would be sometimes a bad mistake to handle them as the eye can see -

although it seems a paradox"48.

48 Roland Fréart de Chambray, Idea of perfection of painting, 1662, [in:] The history of artistic doctrines, Volume

III, selected and edited by J. Bialystocki, scientific editing and additions by Poprzęcka M., A. Ziemba, Warsaw

1994, p. 497


Bibliography:

1. Artyści o sztuce. Od van Gogha do Picassa, edit. by: E. Grabska, H. Morawska,

PWN, Warsaw 1969

2. Jan Białostocki, Sztuka cenniejsza niż złoto, PWN, Warsaw 1991

3. Elena Capretti, Brunelleschi, from the series Klasycy sztuki, transl. by H.

Borkowska, Rzeczypospolita, HPS, Warsaw 2006

4. Przemysław Chodań, Suprematyzm Kazimierza Malewicza jako przykład

awangardowej utopii. [in:] http://teksty.bunkier.art.pl

5. Pablo Garcia, Machine Drawing Drawing Machines, [in:]

http://pablogarcia.org/projects/machinedrawing-drawingmachines/

6. Ernst Gombrich, Sztuka i złudzenie. O psychologii przedstawiania

obrazowego, transl. by Jan Zarański, PIW, Warsaw 1981

7. Historia doktryn artystycznych, volume III, selected and edited by J.

Białostocki, scientific editing an completing by M. Poprzęcka, A. Ziemba, PWN,

Warsaw 1994

8. James L. Hunt, John Sharp, The Mathematics of the Channel Anamorphosis,

http://www.physics.uoguelph.ca/phyjlh/Channel.pdf

9. David Hockney, Wiedza tajemna. Sekrety technik malarskich Dawnych

Mistrzów, transl. by J. Holzman, Universitas, Krakow 2006

10. Myśliciele, kronikarze i artyści o sztuce. Od starożytności do 1500, ed. by J.

Białostocki, PWN, Warzaw, 1988

11. Leonardo da Vinci, Szkice i zapiski, ed. by H. Anna Suh, Parragon, transl. by B.

Brózda, Books Ltd, UK 2006

12. Mieczysław Porębski, Ikonosfera, PIW, Warsaw, 1972

13. Jose M. Parramon, Jak rysować w perspektywie, Galaktyka, Lodz 2003

14. Teoretycy, pisarze i artyści o sztuce 1500 - 1600, ed. By J. Białostocki, PWN,

Warsaw, 1985


15. Zbigniew Tomaszczuk, Łowcy Obrazów; szkice z historii fotografii, Centre for

Culture Animation, Warsaw 1998, [in:]

http://biblioteka.teatrnn.pl/dlibra/Content/9620/Lowcy_obrazow.pdf

16. Vitruvius, O architekturze ksiąg dziesięć, transl. by K. Kumaniecki, Prószyński i

S-ka SA, Warsaw 2004

17. William C. Wees, Light Moving in Time: Studies in the Visual Aesthetics of

Avant-Garde Film, University of California Press, Berkeley · Los Angeles ·

Oxford 1992, {aftrer:]

http://publishing.cdlib.org/ucpressebooks/view?docId=ft438nb2fr;chunk

.id=d0e997;doc.view=print

18. Giorgio Vasari, Żywoty najsławniejszych malarzy, rzeźbiarzy i architektów,

edit. by K. Estreicher, PWN, Warsaw-Krakow 1986

19. http://www.richardgregory.org

Linear Perspective – from Space Illusions to Optical Delusions / B. Bigaj-Zwonek

CyberEmpathy: Visual Communication and New Media in Art, Science, Humanities, Design

and Technology. ISSUE 9 2014/2015. Cyber Art.

ISSN 2299-906X. Kokazone Marika Wato.

Mode of access: Internet via World Wide Web: www.CyberEmpathy.com

http://www.richardgregory.org/

http://www.cyberempathy.com/

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Linear Perspective - from Space Illusions to Optical Delusions