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 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 Encyclopedia 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 materials 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 (3000 pages), which unites all of Kim Veltman’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 will be made 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 employed in the past, and also today, in topics such as vision, mathematics and computing.


Figure 1: Perspective window – by Leonardo da Vinci (1480 – 1482)
Figure 2: Image from Codex Huygens (1560-70) – 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.

Today perspective, in one form or another, is key to vision, modelling, and creating appearance(s). Wherein, the disparate applications of perspective theory, within fields like art, mathematics and drawing, are too numerous to list. Indeed, much of modern scientific progress, plus a huge fraction of productive effort(s) within art, culture and technology, is/are built upon perspective method(s).


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 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 with technical perspective; which refers to any systematic process that produces detailed visual image(s) of an object or scene. Noteworthy, is that said processes may be of natural and/or human origin.

According to our new theory of technical perspective, it has five sub-categories:

  • Visual Perspective – direct looking at reality;
  • Mathematical perspective – modelling reality / shaping appearance(s);
  • Graphical perspective – copying reality / creating appearance(s);
  • Instrument perspective – looking at & measuring reality; capturing and projecting view(s);
  • Media perspective – connecting/linking, ordering, constructing (mimesis), matching, mixing, exploring, and cross-matching: multiple perspective view(s).

Let us now analyse each type of perspective in turn.

Visual Perspective 

Firstly, we have natural or visual perspective—sometimes called ‘true’ perspective—that applies when a human views a scene in the real world (unaided eyesight).

It is important to note that visual perspective produces images that are enabled/limited by human vision. Several related visual processes accrue; including: scene projection onto a curved retina, binocular perception, narrow field of distinct vision, shallow and curved plane of distinct vision [horopter], and scene perspective changes due to a moving head/eyeball.

Human vision is inherently complex, and involves many interrelated physiological and psychological mechanism(s), wherein certain key visual processes, such as binocular perception, are not fully understood.

Fig. 10: Visual Perspective by Vitruvius (1521)


Mathematical Perspective 

Secondly, 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 employment 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 13: Mathematical Perspective: Study of the Semi-Regular Solids – Jamnitzer (1568)
Figure 14: Mathematical Perspective: Kepler: Cosmographicum (1597)
Figure 15: Mathematical Perspective: Early map by Seekarte Welt (1660)


Mathematical perspective often contributes to the other kinds of technical perspective. Such mathematical contributions happen, either due to the natural visual effect(s) resulting from the laws of physics, and/or due to the application of human designed algorithm(s) to a visual scene.

Graphical Perspective 

Another 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 effects (SFX, SPFX, FX) etc. Examples of graphical perspective are: linear, parallel, axial.

Linear perspective is a well-known form of graphical perspective, being a technique that developed slowly over a period of several hundred years. Below we see a sampling of images involving the early application of linear perspective, which was employed in order to create various artistic effects (but most importantly depiction of the depth dimension).

Noteworthy, is that in a remarkable painting by Fra Angelico from the year 1435 (see below), he employs several of what we would today call ‘depth cues’, and in order to provide the illusion of a third-dimension; including scale and focus changes, occlusion, light and shading changes, colour intensity and contrast effects.

Nonetheless, the mathematical rules of linear perspective did not emerge until 1450, with the legitimate construction by Alberti.


Figure 16: Graphical Perspective: Example of proto-perspective method(s) by Fra Angelico (1435)
Figure 17: Graphical Perspective: Alberti: legitimate construction [linear perspective] (1450)
Figure 18: Graphical Perspective: Linear perspective image by Paolo Uccello (1467)
Figure 19: Graphical Perspective: 17th Century painting by Pieter Neefs [linear perspective].
Figure 20: 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 else the distorted views of cubism etc.

Debate often crystallises around the number of vanishing points; whereby use of 1, 2, 3, 6 (or 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 21: Graphical Perspective: Painting panorama by Matthew Lopas
Figure 22: Graphical Perspective: Computer Generated Imagery (dinosaur animation) from movie ‘Jurassic Park’ (1992)


Instrument Perspective 

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—and  introduced are image transformation(s) which are unique to the lens itself (or another lens with identical focal length, plus similar optical characteristics).

Figure 23: Instrument Perspective: Photograph by Ansel Adams


Noteworthy is that instrument perspective(s) are often used to capture accurate image(s), and/or to make accurate measurement(s), of reality.

Sometimes a special type of device, named here as a perspective instrument, is employed specifically to make accurate measurements that relate directly to perspective effects in the real world.

Types of perspective instruments used for specific purposes include: for general tasks: the ruler, callipers and compass, for navigation: the quadrant, cosmolabe, the proportional compass and the sextant; for astronomy: astrolabes, sundials and planospheres; and for cartography: the theodolite etc.

Other kinds of instrument perspective(s) are commonly employed, including those provided by movie and television cameras, whereby moving images capture also the dimension of time, and hence moving/roaming perspectives are produced.

Figure 24: Instrument Perspective: Mitchel movie camera used in Hollywood film (1940s)


Movie cameras patently are able to capture multiple perspective views of a scene; and by means of techniques such as: zoom and pan, ‘dolly’ and/or tracking shots, first-person tracking, plus use of multiple lenses on the same camera etc.

It is important to realise, that the instrument perspective(s) of today, provide far more informative views of reality, and because modern views are more detailed, sensitive and all-encompassing.

For example, we have enormous and high-tech telescopes (on the ground and in space); that can form close-up views of incredibly distant objects (up to 13 billion light years distant—the same objects being unbelievably faint); enabling the universe to be seen on distant scales. Plus we have electron microscopes that can magnify up to 1-50 million times!

Of course instrument perspective(s) are not limited to image analysis/capture; but also relate to image projection and display. Whereby many innovations have occurred, ranging from the earliest such as the Magic Lantern and Kinetoscope, to modern cinema techniques such as wide-screen and 3-dimensional cinema; plus immersive systems such as IMAX, and OMNIMAX theatres.

Figure 25: Instrument Perspective: Magic Lantern (17th century invention)
Figure 26: Instrument Perspective: Cinerama Wide-Screen Cinema (1950s)

Figure 27: Instrument Perspective: Disney Circle Vision 360 (1967)
Figure 28: Instrument Perspective: OMNIMAX Theatre (1991)
Figure 29: Instrument Perspective: OMNIMAX Theatre in Vancouver


Noteworthy is that oftentimes, the visual, mathematical and instrument perspective types, tend to merge, blend and/or combine, on a particular viewing occasion (and often without the observer overtly noticing).  

For example, when looking at a wildlife movie on your television at home; really you are seeing a merging of: instrument perspective from the camera that captured the images; plus instrument perspective from the television that displays the images; and finally you see everything using your own visual perspective whilst looking at the television from a specific point-of-view.

Plus, remember that various different kinds of mathematical perspective, will inherently be involved in, and contribute to, all of these other forms of perspective.

We can conclude, that everyday perspective effects are complex indeed! 

Media Perspective

Finally, we have media perspective, which refers to the particular imaging capabilities, and visual transformations, that are provided by a new media system.

Said media perspective, typically consists of multiple networked instances of other instrument/media perspective(s). Examples of technologies that would fit under the umbrella of media perspective(s) include: Internet and Web based information systems, networked digital television systems, smart phones and networked devices, satellite imaging systems, GPS, plus Virtual Reality (VR), Augmented Reality (AR), Mixed Reality (MR), and Extended Reality (XR) systems etc.

Whereby, in the case of a highly developed media perspective system, views from one or more of the other categories of perspective (listed above), may be connected/linked together and then ordered, constructed, matched, mixed, explored, and cross-matched etc.

The end result is the formation of a new class of multi-perspectival media system. Henceforth, a new era is emerging—termed the multiverse era—or the age of multiple and all-encompassing virtual ‘worlds’! 

Figure 30: Media Perspective: Photosynth application (merging of multiple photographs into a single explorable view)

Figure 31: Media Perspective: Photosynth application – exploration view (merged photograph ‘cloud-points’)


In order to produce a true multi-perspectival system; it is a requirement that all of the contained perspective view(s) must be adequately linked, indexed and hence integrated together, and in such a manner that the resultant digital world is readily explorable. Specific examples of media perspective systems that—are beginning to—work in this way include: Google Maps, Earth, NeRF-W, plus Microsoft Photosynth (latter system is now abandoned, but it is an excellent example of an ‘early-stage’ multi-perspectival media system).

Such systems create full-blown virtual worlds from a combination of thousands of images, often being photographs of the same geographical area, but taken from slightly different viewpoints and/or a variety of locations in space/time.

By means of advanced mathematical techniques, it is then possible to merge all of these images together into a single virtual space. Ergo such a virtual world, enables efficient navigation, and rapid viewing, of a huge number, and great variety, of different perspective views; including also images taken from ‘mathematically’ created and/or normally ‘impossible’ viewpoints!

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.

Future Perspective(s) 

How can we summarise the fascinating topic of perspective?

Well, as we have seen, perspective has exceptionally rich sources, combined with near countless influences/applications.

And it is a topic with multiple interlacing stories, a myriad of relations, and a deep ‘fractal-like’ structure that opens up like a Russian doll into new levels of understanding almost without limit. However, we should not be put off by this complexity. Rather marvel at how the single topic of perspective provides new vistas of knowledge wherever we happen to look!

The modern advances that are enabled by, or which relate to perspective, are numerous and mind-blowing. New technical advances are coming fast, furious and everywhere. A sampling of innovations includes: super high-resolution digital cameras (with 4k – 12k detector pixels in widest aspect); super high-resolution digital monitors/televisions (with 4k, 8k and 10k display pixels in widest aspect); plus high-bandwidth media formats and associated networking capabilities.

Ergo, today images are more detailed, colourful, distinct, wide-field, and realistic etc. Plus images (both still and moving kinds) are patently far more numerous and readily available, and hence informative, than ever before.

Implicit is that perspective is a term that encompasses a diverse set of visual, modelling, and also representation methods; and hence we must consider its multi-variant forms as employed in both Western and Oriental cultures.

Perspective is such a vast, broad and deeply influential topic, that doubtless it should be taught as a distinct subject in schools, colleges, and at universities. In any case, here at the PRC we do intend to fill this evident knowledge gap; providing comprehensive perspective related theories, papers, books, courses, lectures and documentary films—whereby all of these materials shall be free to access/download.

In conclusion, we can state that perspective has profoundly influenced many of the key theories, discoveries, and practical methods, within art, science and technology. Perspective is a keystone to progress; and it is truly a foundation of human civilisation.