Perspective in Perspective

The Perspective Research Centre (PRC) is a research and educational centre focused on the visual dimensions of Art, Science and Technology.

PRC collects materials on the history, theory and applications of perspective, projection methods and spatial concepts. We provide free and open access to perspective resources; for the benefit of all.

Perspective is a relatively new method that is a key to understanding major categories of art/science/technology in the past 500 years. Related topics include: space, time, optics, human eye/vision, colour, structure, drawing and mathematics (geometry), reality, illusion, imagination and representation.

Perspective is central to developments in a variety of subjects; including art, photography, television, cinema, scenography, engineering, architecture, gardens and environment etc. Recent developments also have strong links to perspective; such as hypermedia, geographical information systems (GIS), global positioning systems (GPS), virtual reality (VR), computer graphics (CG), computer generated imagery (CGI), stereography, panoramas, holograms and space imagery.

In sum, perspective lies at the epicentre of progress, and is pivotal to everything that we humans will achieve in the future. QED.

Our Mission

PRC seeks rational insight into the various technical method(s), plus practical application(s), of perspective, and associated visual media.

A basic goal is to gather what is known on perspective in the form of an Encyclopaedia and comprehensive Bibliography of Perspective as developed in Western cultures. Alternative methods in non-Western cultures (aspective, inverted perspective, axial perspective, curvilinear and parallel perspective) are also studied.

By collecting, developing, linking and applying the theories, principles and method(s) of perspective, the PRC is able to support knowledge organisation, education and technology development across a range of scientific, artistic, cultural and environmental disciplines.

Resources

Established over a period of 50 years, is our vast Library On Perspective and related topics (5,500 physical volumes, 4,000 digital items and 12,000 images), plus we own a rare library on Leonardo da Vinci (500 volumes). Today the PRC library is unsurpassed in the private field; and in the future we shall continue collecting new and specialised resources on perspective. 

PRC maintains the standard World Bibliographic Database On Perspective; initially developed by Professor Luigi Vagnetti and later progressed by Professor Kim Veltman—who together spent over 90 years compiling a list of 15,000 perspective titles from throughout time.

In 2020, PRC published the Encyclopedia of Perspective (2,500 pages), being the definitive work on its subject matter that is a wonder to behold. Plus we have plans to publish the Encyclopedia of Leonardo Da Vinci (2000 pages), which unites all of Kim Veltman’s treatise(s)/writing(s) on the great polymath.

We are developing a major lecture series entitled: ‘Dimensions of Perspective’; and producing a related documentary film.

All of these resources are freely available herein.

Perspective Defined 

How can we adequately define Perspective?

One definition in the context of pictorial and scenic art is: “The term ‘perspective’ may refer to any graphic method, geometrical or otherwise, that is concerned with conveying an impression of spatial extension into depth, whether on a flat surface or with form shallower than that represented. Perspective composition results when the artist adopts a visual approach to drawing and consequently portrays perspective phenomena such as diminution of size of objects at a distance and the convergence of parallel lines in recession from the eye.”

However, this simple definition fails to encompass the multiple and diverse ways in which perspective has been, and is today, employed in topics such as vision, mathematics and computing.


Figure 1: Perspective window – by Leonardo da Vinci (1480 – 1482)
Figure 2: Image from Codex Huygens (1560-90) – Renaissance manuscript related to, or copied from, Leonardo da Vinci.
Depicts visual relations between the eye, mind and perspective projection.


The Oxford Dictionary (2nd ed.), defines perspective thusly: 

  • The science of sight; optics.
  • An optical instrument for looking through or viewing objects with; a spy-glass, magnifying-glass, telescope, etc.
  • The art of delineating solid objects upon a plane surface so that the drawing produces the same impression of apparent relative positions and magnitudes, or of distance, as do the actual objects when viewed from a particular point.
  • The appearance presented by visible objects, in regard to relative position, apparent distance, etc.
  • The relation or proportion in which the parts of a subject are viewed by the mind; the aspect of a matter or object of thought, as perceived from a particular mental ‘point of view’. Hence the point of view itself; a way of regarding (something).
  • A drawing or picture in perspective; a ‘view’; spec. a picture so contrived as seemingly to enlarge or extend the actual space, as in a stage scene, or to give the effect of distance.
  • A picture or figure constructed so as to produce some fantastic effect; e.g. appearing distorted or confused except from one particular point of view, or presenting totally different aspects from different points.
  • A visible scene; a (real) view or prospect; esp. one extending in length away from the spectator and thus showing distance, a vista.
  • A mental view, outlook, or prospect, esp. through an imagined extent of time, past or (usually) future; hence sometimes = expectation, ‘look-out’.
  • Drawn or viewed in accordance with the rules or principles of perspective.
  • The action of looking into something, close inspection; the faculty of seeing into a thing, insight, penetrativeness.

Patently, according to these various facets, perspective is a term that can portray multiple meanings! How then is it possible to better grasp the concept of perspective—and to develop a complete understanding of the different ways that it can be applied to practical situations? 

Well to begin, we ask what is the etymological root of the term ‘perspective’?

Etymology 

‘Perspectiva’, says Durer, ‘is a Latin word and means ‘Durcheshung’: a view through something. But the word perspectiva also sometimes refers to perspicere in the sense of  looking directly at something or ‘seeing a form clearly‘ with your eyes.

Durer’s definition, gives an excellent and brief description of ‘perspective’; as understood in post-medieval usage including our own time—forming ‘accurate’ representations of ‘reality’ as opposed to direct ‘looking’. 

Although perspectiva is a direct translation of the greek optiki (optics)—it is not a literal one; there is nothing in optiki corresponding to the per of perspectiva, a prefix originally meaning ‘through’. Hence the pre-fifteenth century perspectiva, referred originally to perspicere in the sense of ‘seeing through’.


Figure 3: Perspective study by Leonardo da Vinci (1481)
Figure 4: Perspective window (technique) by Albert Durer, Der Zeichmer des liegendem Weibes, 1525


Along this same track, vision theorists from throughout history, such as Aristotle and Alhazen, entailed the idea of a transparent corporeal medium between the object seen and the viewer, a medium generally called either diaphanum, a translation of Aristotle’s word for ‘transparency’; or perspicuum, a Latin equivalent, unmistakingly derived from perspicere—the sense of ‘seeing through’.

Whatever the steps involved in the establishment of its modern meaning(s), by the 1480’s Brunelleschi had developed  what painters today call ‘perspective’—a series of method(s) of graphic representation of a dimensional scene (typically 2D view of a 3D scene) as opposed to the overlaid processes of purely ‘visual perspective‘ employed when looking directly at a scene.

Figure 5: Idealised view of Urbino City (after 1470)
Figure 6: Chateau de Versailles – Linear perspective applied to the whole environment (1608)
Figure 7: Linear perspective painting by Dirck van Delen (1633)


In sum, our discussion further teaches that perspective has not been in the past, and is not today, a single topic. We have multiple meanings for the term. Ergo, it is vital to establish basic definitions.

Categories of Perspective 

We have three basic classes of perspective, namely: technicalliterary, and mental outlook. On this site we are concerned primarily with technical perspective. Whereby technical perspective, refers to any systematic method that produces detailed visual image(s) of an object (or scene).

According to our new theory of technical perspective, it has five sub-categories named as visualmathematical, graphical, instrument, and media perspective(s). Let us now analyse each type in turn.

Firstly, we have natural or visual perspective—sometimes called ‘true’ perspective—that applies when a human observer views a scene in the real world (unaided eyesight). It is important to note that visual perspective produces images that are enabled/limited by the human visual system (e.g. scene projection onto a curved retina, narrow field of distinct vision, and moving head/eyeball etc).

Fig. 10: Visual Perspective by Vitruvius (1521)
Figure 11: Visual Perspective: visual proportions, from: ‘Drawing Manual’, Bosse (1667)


Next, we have mathematical perspective, which refers to the application of algorithmic rule(s) to transform the appearance of scene/object geometry.

One example, is the transformation of an object’s form/scale and/or outline/shadow (visual appearance) according to a particular mathematical law/rule. Ergo, mathematical perspective is comprised of geometric transformations; such as projection, translation, reflection, and rotation etc; plus related image distortion effects.

Mathematical perspective often involves the application of a valid theory of spatial geometry as applied to a real-world problem (sometimes on a grand scale). Examples include: modelling of sun position relative to an earth-bound observer, Global Positioning Satellite (GPS) calculations, calculation of latitude/longitude position, mapping of spherical earth coordinates onto 2D maps, and astronomical calculations such as prediction of planetary orbits.

Fig 14: Mathematical Perspective: Study of the Semi-Regular Solids – Jamnitzer (1568)
Figure 15: Mathematical Perspective: Kepler: Cosmographicum (1597)
Figure 16: Mathematical Perspective: Early Map by Seekarte Welt (1660)


Mathematical perspective often contributes to the other kinds of technical perspective (ref. laws of physics and/or the application of a human designed algorithm to a visual scene).

A second form of technical perspective is—graphical perspective—which attempts to create accurate representation(s) of reality. For example, graphical perspective may simulate an illusory three-dimensional (3D) view—produced by notional and ‘natural looking’ vanishing points etc.

Often graphical perspective is employed for transcription purposes in technical drawing, or else for artistic purposes. Graphical perspective is also extensively employed for computer generated imagery, including applications such as Computer Aided Design (CAD), animation, and movie special affects (SFX, SPFX, FX) etc. Examples of graphical perspective are: linear, parallel, axial etc.

Figure 17: Graphical Perspective: Alberti: legitimate construction [linear perspective] (1450)

Figure 18: Graphical Perspective: 17th Century painting by Pieter Neefs [linear perspective].
Figure 19: Graphical Perspective: Painting on a 3D Sphere by Dick Termes [6-point] (1990s?)


Noteworthy, is that a debate, and long-running disagreement, exists between various artists, art-movement theorists, scientists and visual designers; as to which kind of graphical perspective is the most natural and/or ‘real’.

Some experts claim that linear perspective is the most realistic, whilst others opt for curvilinear perspective, or the distorted views of cubism etc. Debate often crystallises around the number of vanishing points; whereby use of 1, 2, 3, 6 (or even more) vanishing points are employed within a single representation. The upshot is that a variety of different—forms of graphical perspective—are applied, producing a huge number of diverse (and sometimes surpising) visual effects.

Figure 20: Graphical Perspective: Painting Panorama by Matthew Lopas


Next we have instrument perspective; which is generated whenever an instrument, of one type or another, forms an image of a scene, being an image that has undergone a particular set of transformation(s) relative to scene geometry. One example is when a camera lens, creates a two-dimensional (2D) image of a 3D scene—whereby  introduced are image transformation(s) which are unique to the lens itself (or a lens with the same focal length).

Figure 21: Instrument Perspective: Photograph by Ansel Adams


Noteworthy is that perspective instruments are often used to capture accurate images, and/or accurate measurements, of reality.

Types of perspective instruments used for particular purposes include: for general tasks: the ruler, callipers and compass, for navigation: the quadrant, cosmolabe, the proportional compass and the sextant; for astronomy: astrolabes and sundials, plus telescopes; for cartography: the theodolite etc. Other kinds of instrument perspective(s) include those captured by movie cameras, whereby films also capture the dimension of time, and hence moving/roaming perspectives.

Finally we have media perspective, which refers to the particular imaging capabilities, and visual transformations, that are provided by typical media such as photographic, film, GPS, Virtual Reality (VR) and remote sensing systems etc.

Whereby, for a particular media perspective, any of the other kinds of perspective may sometimes be employed together at one and the same time (and possibly combined using networking capability). Ergo, a new type of visual mixing, exploring and cross-matching environment is enabled—heralding the multiverse era—or the age of multiple virtual ‘worlds’!

Fig 22

At the PRC, we are concerned with all types of technical perspective (hereafter referred to simply as perspective). Note that many additional perspective sub-categories exist including: the atmospheric and colour perspective types, plus the geometric projective kinds: linear, axial, parallel, aspective, reverse, inverse, curvilinear types etc.

We do not limit our interests—and all forms of technical perspective are welcome!

Significance of Perspective

Perspective has been described (Edgerton 1975) as the most important discovery of the West. In the fifteenth and sixteenth centuries it involved many of the key individuals in Renaissance art and architecture, notably Brunelleschi, Alberti, and Piero della Francesca.

The projection methods of perspective were linked with astronomy (astrolabes and sundials), cartography, stonecutting, and surveying. Leonardo da Vinci linked perspective with physics and made it one of the cornerstones in his new approach to science through his pyramidal law, a principle that inspired the first universal analogue reckoning instruments: the sector and proportional compass.

Since the seventeenth century, the development of perspective has entailed some of the leading mathematicians: Desargues, Pascal, Euler, Monge and Poncelet. In its metaphorical sense, perspective has been explored by philosophers such as Leibniz and Nietzsche; played a fundamental role in the work of Schutz, one of the founding fathers of modern sociology, and has affected profoundly most major disciplines, including anthropology, ethnography, psychology and even theology.

The significance of perspective has to be assessed in terms of science, art, the environment and the imagination, in order to draw attention to a paradox: How was it that a method of representation that imposed scientific rules became a new key to artistic freedom and creativity? 

There are reasons why has perspective become increasingly linked with psychology. One concerns the status of perspective: whether it is merely a convention or an objective method. Experiences with deliberately distorted perspectival views such as the Ames Room have led some to claim that perspective is purely conventional.  On the other hand the work of psychologists points: a) to basic proportions within which the principles apply and: b) to innate dimensions of perspective present even in blind persons.

In any case perceptions change in different media—and since our spatial perception is altered by every new medium we introduce—we need to manage, measure and understand such affects.

Kim Veltman

Much of what we do at the PRC flows from the work of Professor Kim Veltman (1948-2020). Kim was a polymath who authored 4 published books, 3 major treatises; 12 electronic books; 82 articles in books; 24 articles in refereed journals; 5 articles; 79 electronic articles, 16 reviews and 10 vision statements. His important and monumental contribution(s) cut right across traditional subject disciplines in the arts and sciences.

Kim H. Veltman was Scientific Director of VMMI (Virtual Maastricht McLuhan Institute); author and consultant on implications of new media for scholarship, culture and society. He taught at the universities of Gottingen, Rome, Carleton; was Director of the Perspective Unit, McLuhan Program, Toronto (1990-1996), and Director of the Maastricht McLuhan Institute (1998-2004). He worked as a consultant in new media for the CEO of Bell Media Linx (1996-1998), and for the director of advanced technologies at Nortel Networks (1995-1998). 

Kim Veltman was a ‘historian of the future’; a world-renowned scholar who fervently studied the past—so that we might all learn how to shape the future conscientiously for the benefit of humanity. He did so whilst being cognisant of the fact that there are —in reality—no isolated topics and/or unbreachable boundaries between things/processes or people/organisations; because everything is connected to everything else (in one sense or another).

Kim sought holistic viewpoints and uniting world-views—and he emphasised the myriad of links between different cultures, religions, subjects, alphabets and languages. Kim was a universalist who endeavoured to identify, analyse and synthesise fundamental truths. Indeed, he amassed a vast collection of axiomatic facts and explanatory theories through exhaustive study of the occidental/oriental libraries held in major institutions such as the Vatican, the Warburg and Welcome Institutes, the Getty Center for the History of Art, and the Universities of London, Gottingen, York and Toronto.

Kim’s life-long quest—as an impassioned cartographer of knowledge—was to study general and particular Things in their broadest, deepest and most essential patterned relations; whilst disclosing the same in erudite publications to enable their auspicious application in a wide-range of circumstances. 

Kim’s work stands as a testament to the comprehensive approach of the generalist—someone who studies all subjects meticulously and expansively—and who follows penetrating causal chains wherever they may lead.