In this section we examine the goals, motivations and influences of perspective.

Why study Perspective?

This question can be answered in a myriad of different ways. But implicit is that perspective is a term that encompasses a vast number, and diverse set of visual, modelling, and also representation, methods; and we must consider its multi-variant forms as employed in both Western and Oriental cultures.

Perspective lies at the heart of many vision-related topics, theories, and inventions. It has been directly linked to the development of diverse fields such as optics and vision, astronomy, geography, engineering, cartography, architecture, stonecutting, surveying, and archaeology. 

In conclusion, we study perspective because—in a progressive culture—we cannot help but do so—for it is key to understanding major categories of art, science and technology in the past 500 years.

Perspective lies at the epicentre of human progress, and it will be pivotal to everything that we humans achieve in the future.

Visual Knowledge

What, we may ask, is the ‘goal’ of perspective? Indeed can we even formulate a simple answer to this question for a foundational topic such as perspective?

Well, it so happens that we can answer this question because the central goal of perspective is visual knowledge (from a human mindset). Now and in the future, we humans desire to know what is happening, plus how, why, when, where and in relation to whom/what. And we usually obtain all knowledge, at least at first, visually. Indeed on many occasions, due to problems of distance or scale etc; we can only gather data about the physical universe by visual means.

We obtain this visual knowledge from a vast range of different viewpoints, on multiple scales, and across the full spectrum of universal happenings. That is where perspective, in all of its multi-variant forms, can provide vital impetus. And when used for art, phantasy, illusion, etc., perspective still only provides visual knowledge, of one kind or another (but for entertainment purposes). 

Our discussion assumes that we are leaving behind arguments surrounding whether or not perspective is an objective method. Accordingly, we assume here that perspective is, in fact, at least partially a subjective method, plus being partially an objective method simultaneously. Nevertheless, and regardless of the sources of perspective, the various application(s) of perspective have ‘goals’ that are wholly dependant upon the human mind.

Goals, Products, and Functions

A key ‘goal’ of perspective is visual knowledge, but can we further break down this goal? Doubtless, a modicum of precision with respect to our terminology, can clarify matters. Perspective refers to any systematic process that produces: a detailed visual image, measurement, representation, model or view, of a three-dimensional object or scene. These are the Products of Perspective.

Consequently, three goals of perspective can be identified. They are first viewing reality: observing spatial form; second, matching reality: surveying or modelling spatial form; and finally making representations of reality: copying / constructing images of spatial forms. These are the goals of perspective (in human terms), and it is clear that visual knowledge and images are fundamental to each type.

Note a careful distinction that we are making between a perspective image, defined as a fixed visual representation, copy or picture of any three-dimensional thing, and a perspective view. A perspective view refers to the act of looking directly at the thing itself, being a ‘live aspect’, real-time sight or vision of a three-dimensional thing or apparent three-dimensional thing. Said view is in the form of an optical vista seen directly by the eye, captured in real-time by a camera or perspective instrument, or projected onto a screen or computer display.

Perspective, in general, works to enable viewing, prescribing, matching, modelling, exploringrepresenting, and making images, of the physical world. These are the Functions of Perspective.

Noteworthy is that, for perspective to be helpful in any practical context, it must produce an explicit visual model—that enables new concepts, forms, and conglomerations of objects to be explored. Ergo, perspective is not simply concerned with visual knowledge. That is only the starting point. Instead, the practical goals of perspective are imaging, measuring, modelling, and viewing the spatial world in a detailed, systematic, and analytical manner. QED.

Motivations: The Twin Stories of Perspective

Perspective involves two distinct stories.

Firstly, perspective introduced an objective method for recording or copying the physical world at different levels of abstraction in photographs and maps. This is the  so-called conquest of realism. A key part of this path was that persons began to approach the same objects systematically from different viewpoints and on different scales.

But there is a second story to be told.

The contents of the perspective texts were primarily devoted to something other than realism. The treatises were in fact, repositories for a whole range of new images, including: regular solids, semi-regular solids, lutes, chairs, stairs, complex plays of shadow and reflections, grotesques and caryatids, imaginary gardens, fountains, idealised ruins, panoramas and phantasy architecture.

Hence perspective, in this second sense, is linked to the rendering of singular, distorted, and somewhat ‘unnatural’ appearances for: objects, models and environments. Whereby concern shifts towards idealised, mathematical representations and for illusory and/or highly specific visual affects. The results are playful experiments with appearances, and hence with multiple truths.

Ergo perspective, which at first seems to be about copying and reflecting the one true reality, becomes concerned with imagination and illusion, or the creation of fantastic, new, and partially/entirely human-made realities.

The twin stories of perspective have profound influences on a range of fields, as explained below.


Medical imaging is a field that would not exist without modern perspective imaging/viewing techniques.

New kinds of ‘transparent’, multi-layer, multi-view, and multi-scale perspective views, and associated visualisation technologies, have received prominence in recent medical work; and ever since the development of the first x-ray and various types of microscopes. Later technologies such as computed tomography, magnetic resonance imaging, and sonography further expanded the range of medical imaging techniques. One example, is that these technologies allow for the visual exploration and representation of the human body using new perspective views and images that vastly extend the capacities of human sight.

With the aid of computers, all the information now available through the study of anatomy can be coordinated to create three-dimensional (3D) perspective models exterior and interior, macroscopic and microscopic, of  human bodies. With the help of x-rays and the latest visual tracing devices, the problem area can be accurately probed in 3D.

Ergo, with the aid of far clearer and measurable perspectives, the physician can be in a much better position to make an accurate judgment of how to restore balance in the organism. 

Life Sciences 

To those in the life sciences, generally, such total simulation techniques extend far beyond restoring balance in unbalanced conditions: they introduce new dimensions to the study of organic development. The growth of an organism from its beginnings as sperm or seed to its final stages of maturity can be seen as a slow transformation process. 

If one takes enough stills of each stage of this process and then combines them, the process of growth can be simulated with one crucial variation: the process that would normally take years or even centuries can be recapitulated as quickly as one chooses, so that the growth of a plant or a man, or even an oak tree can (or could), potentially be recapitulated in a matter of minutes. 

The upshot is that new kinds of spatial/temporal visual and cross-matched media perspectives are envisaged; enabling reality to be probed on a vast range of visual scales (variable scale perspectives), and across spans of variable time that can be ‘throttled’ just like a computer game (variable time perspectives).

At the macroscopic level, this might well seem little more than a visual gag: but if our knowledge at the microscopic level is integrated into this picture, we stand to learn enormously from a method that systematically recapitulates the growth sequence and can, with the aid of focus and lens techniques, systematically eliminate the gap between macro- and micro-scopic techniques by introducing a simple continuum between far (macro) and near (micro) views.

In short, we shall in the future have motion pictures of entire processes rather than stills of set stages in both animal and plant development. We already see early examples of such variable time perspectives, within time-lapse photography in wild-life films and also ‘speeded-up’ environmental space imagery etc.

Similar applications of perspective can be seen in the natural sciences. Although we now still tend to separate clearly between the organic and natural sciences, in a sense, they both belong to the same continuum. And because we know that the mineral world also develops: it too is an organic process, only in slow motion. So the same techniques could theoretically be used in recapitulating in minutes the evolution of millions of years. 


In terms of science, it is known that the development of perspective was integrally connected with the rise of instrumentation and that this focussed attention on proportion, scale, and finally, quantification in science. 

It is claimed that the nature of perspectival representation, which permitted a systematic treatment of both views and scales of an object, led away from questions of essence to those of distinct functions which could be isolated and catalogued. This approach was applied to machines, extended to living organisms, as if they were mechanical objects, and eventually used in cataloguing what had hitherto been abstract powers of nature.

In the process, perspective introduced a visual standard for scientific truth, which led to observation, experiment, measurement, and the other familiar characteristics of early modern science. 

Hence, in theory, perspective introduced a method of passively recording the physical world as a practical demonstration of the philosophical distinction between subject and object. In practice, its implications were far more wide-ranging. It introduced a new ideal of matching, making copies of the physical world. This changed the meaning of metaphor and the whole relation of verbal texts to visual expressions.

Ergo, it is no exaggeration to state that the development of Technical Perspective made possible and supported the development of the scientific culture of today.

Figure 1: Perspective machine drawings by Leonardo da Vinci (approx.1500)

Figure 2: Anatomical multi-views and motion perspectives by Leonardo da Vinci (approx. 1500)

A remarkable example of perspective being applied to scientific studies, exists in the notebooks of Leonardo da Vinci, who produced over 100,000 drawings spread across 6,500 pages. Many of Leonardo’s sketches employ perspective; to accurately capture appearances, improve the clarity of depicted features, illustrate viewpoint changes, or depict a vast range of natural processes and mechanical inventions/principles.


If the life and natural sciences can profit directly from this ability to simulate the three-dimensional coordinates of ordinary space, plus the extra dimension of time; then the mathematicians will find a method of visualising various types of Euclidean and non–Euclidean forms of space.

For didactic purposes, it will be useful to demonstrate what transformations are introduced when a set of objects arranged in Euclidean space is suddenly re-arranged in accordance with Riemannian, Lobachevskian, or other alternative forms of space. 

However these methods should be interesting to those at the frontiers of research in mathematics as they are to teachers of the subject. For the mathematical thinker who has traditionally gone to the blackboard to convey to a colleague a rough sketch of the spatial display of which he is thinking, suddenly finds himself with a dramatic alternative: because he can now freely project unto the six surfaces of the room outside himself the structures he ”sees” inside his mind, whereby the projection room can theoretically simulate the space of his mind. 

In short digital screens, and projectors, have become a display of the thinker’s mind and hence the colleague will now have the privilege of an experience equivalent to being inside the mind of the thinker. The old question: do you see what I mean, has now become: do you see what I see? Needless to say, this has revolutionised the possibilities, accessibility, power and applications of thought.

Art and Design

Patently, perspective, being concerned with appearance and representation, has had a strong influence on all aspects of the visual and graphic arts (drawing, painting, sculpture), the plastic arts (sculpture, modelling), the decorative arts (furniture design, mosaics), the performing arts (theatre, dance, music), and architecture (environmental design). 

In this section, we shall focus on drawing (and, by extension, painting). It is necessary to make a distinction between pleasurable and useful drawings.

For reasons of brevity, we shall exclude pleasurable drawings here; other than to say that one of the key movements in this respect was focussed on making increasingly realistic representations of reality. Whereby perspective obviously played an important role in the realistic depiction of spatial affects, and especially the illusion of depth.

In terms of useful drawings, the indispensability of engineering and construction drawing, obviously included applications to professions such as architecture and construction engineering and the various trades such as bricklayers, carpenters, decorators, locksmiths, masons, etc.

Overall, during the 19th century, ever more specific branches of drawing were introduced, including: architectural, engineering, industrial, map, plan, technical, etc. These methods were extended to so-called machine drawing, geometrical drawing  and/or mechanical drawing, whereby such technical methods were undoubtably key tools that enabled Industrial Revolution, and also by extension, the computer, telecommunication and space ages.

It is not possible to detail here all of the different ways perspective has influenced artistic output and enabled a variety of different drawing methods and associated art movements. Suffice to say that perspective is one of the fundamental techniques involved in the generation, and viewing, of artistic creations.

Engineering and Technology

Perspective has influenced technological developments in three primary ways.

Firstly we have Perspective Instruments, which have been manufactured according to specific theories of perspective for the purposes of making accurate dimensional measurements in relation to the real world. In particular, perspective instruments enabled systematic mapping of distance, scale, shape, etc.; and so fostered knowledge of physical environments and associated object forms. 

Types of perspective instruments used for particular purposes include: for navigation: the quadrant, cosmolabe, the proportional compass, and the sextant; for astronomy: astrolabes and sundials, plus telescopes; for cartography: the compass, calliper and theodolite etc.

Secondly, we have the application of perspective theory in science, explicitly employed to aid in the development of entirely new scientific theories. In terms of the theoretical influences of perspective, we find innumerable examples going back through history, including perspective methods behind the ideas of Euclid, Copernicus, Darwin, Newton and Einstein, etc. 

Thirdly, we have application of perspective to practical disciplines. In terms of subjects influenced by perspective methods, for example, we have: optics, statics, hydrostatics, nautical science, architecture, military machines, geography, astronomy, nuclear physics, chemistry, biology, and chronology, etc. 

Perspective introduced a systematic approach to three-dimensional spaces and objects contained therein. Ergo perspective techniques were used to produce accurate engineering drawings. Whereby accurately scaled and correctly proportioned drawings could be produced with views such as plan, elevation and sectional elevation. Such drawings could then be used as blue-prints for manufacture.

This approach led to new instruments, mechanisms, and machines in all areas, combined with novel associated working methods/systems. Manufacturing capability exploded as a result. Vastly improved working efficiency was the result, which magnified human physical powers, and enabled all kinds of automation technologies, leading to steam engines, automobiles, aeroplane, etc.

Overall, it is difficult to imagine that the explosion in science, engineering and technology that took place during the last 500 years, could have happened without intimate knowledge of perspective and its various mathematical forms and associated practical methods.

Philosophy: Illusion, Phantasy, Imagination

These new perspectival images led to an emphasis on illusionism and trompe-l’oeil involving a new interplay between real scenes; realistic scenes as if theatrical; theatrical scenes as if realistic; an interplay between reconstructions of past structures and interpretations of existing, possible and ideal ones.

Ergo it is precisely this blurring of boundaries between the natural and the fictive, which inspired that extraordinary proliferation of visual images which is unique to the West and that herein lies the true significance of linear perspective: not simply as a tool for realism, but as a catalyst to our imagination, playfulness, creativity, and freedom. Perspective amplified visual powers and boosted mental outlooks.

Knowledge of perspective led to all kinds of new developments, including: panoramas, cycloramas, stereographic devices, magic lanterns, camera obscura, camera lucidia, etc; and it even played a key role in the development of photographic cameras and early cinema.

Different forms of perspective drew attention to the plasticity of images, hence to the role of illusion and multiple truths that may be possible not only in the imagination, but also in perceiving objects in the real-world.

Perspective drew attention to the perspectival nature of reality; and the various processes—optical, perceptual, and mental—that are ongoing between viewer and object, and further to relations between objective truth and illusion.

Figure 3: Rotunda building for panoramic viewing (1801)
Figure 4: Rotunda panorama (1806)

Goals of Representation

How does progress happen?

One of the keys to progress is accurate representation, whereby information from the real world is first perceived, recorded, gathered together, and processed; before being represented and indexed for rapid access. Patently, perspective introduced new techniques of vision and representation that have enabled humans to map, model and shape reality accurately. This is the conquest of the real.

However today we have a new universe of the internet and digital media, whereby inert objects all around us are suddenly waking up and becoming ‘smart’.

Digital intelligence is invading everything that we do. Regardless of whether we see the digital universe as being inside the real universe—or vice-versa— it remains the case that the various methods of perspective can help us to more accurately, rapidly and efficiently, meet the six stages of representation: connecting, ordering, mimesis, matching, mixing, and exploring.

In the past decades, there has been a new goal, namely, cross-matching, which entails giving the simulated world of the digital multiverse precedence over the physical world of the universe. Along these same lines, doubtless, in the future, new hybrid forms of Technical Perspective will be invented to progress the cross-matching goal. Whereby humans and intelligent machines will together generate ever more complex and helpful versions of reality.

Ergo, the future of perspective is bright. Get your Virtual Reality (VR) headset ready!


How can we summarise the influences of perspective on human culture?

Everything considered, it is difficult to imagine that we humans could have evolved much past stone/bronze age times without the tremendous amplification in perceptual and cognitive powers enabled by perspective, and further the attendant practical abilities provided in so many areas.

Perspective has fundamental influences within art, science, mathematics, engineering, and technology. And other fields such as astronomy, architecture, navigation, and map-making could not have developed without the systematised space introduced by perspective techniques.

We can conclude that the various perspective categories, phenomena, methods, products, and applications; have been indispensable to the development of human civilisation as it exists today. But perhaps the story of perspective has only just begun, whereby perspective will shape our human future in such profound and varied ways that we can barely imagine the possibilities.



Kim Henry Veltman (1980 - 2017).
Alan Stuart Radley (2023).


Radley, A.S. (2023) 'Perspective Category Theory'. Published on the Perspective Research Centre (PRC) website 2020 - 2023.

Veltman, K.H. (1994) 'The Sources of Perspective' - published as an online book (no images). Later published with images as 'The Encyclopaedia of Perspective' - Volumes 1, 2 - (2020) by Alan Stuart Radley at the Perspective Research Centre.

Veltman, K.H. (1994) 'The Literature of Perspective' - published as an online book (no images). Later published with images as 'The Encyclopaedia of Perspective' - Volumes 3, 4 - (2020) by Alan Stuart Radley at the Perspective Research Centre.

Veltman, K.H. (1980s-2020) 'The Bibliography of Perspective' - began as a card index system in the 1980s; before being transferred to a dBASE-3 database system on an IBM PC (1990s). Later the bibliography was made available on the web on the SUMS system (2002-2020). In 2020 the Bibliography of Perspective was published as part of'The Encyclopaedia of Perspective' - Volumes 6, 7, 8 - by Alan Stuart Radley at the Perspective Research Centre.

Copyright © 2020-23 Alan Stuart Radley.
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