Prologue

Welcome to a marvellous intellectual adventure on perspective.

We study perspective in greater detail, broader scope, and more coherence than previously attempted. Ultimately, a comprehensive new theory of perspective is desired that unites all of its different facets under a unified framework, heralding a new subject discipline. 

We begin with introductory remarks on motivations, areas, and scope of analysis, a summary of past work, and future goals on this fascinating topic. Next, we introduce a set of concepts and related terms which enable us to accurately delineate, explore and meticulosity analyse, the field of perspective (as a whole).

Do not worry if at this stage many of these new principles appear highly technical or are a little daunting to commit to memory—because we shall return to these ideas—at a slower pace and in greater detail—many times on this site. This section has been written to explain our motivations in studying perspective, and what we aim to achieve with our activities.

Feel free to skip this section if motivations appear superfluous.


The Fragmentation of Perspective

Perspective lies at the epicentre of progress. Yet people often fail to realise why perspective is pivotal to everything we humans will achieve in the future.

Rhetorically, there was an attack on perspective during the 20th century, to the extent that some have spoken of the death of perspective. But perspective is not a dead subject, far from it. In practice, there have been more publications than ever in the last 100 years, along with a radical increase in alternative methods and innovations in countless modern application areas.

Perspective introduced an objective method for recording or copying the physical world at different levels of abstraction in photographs, cinema, engineering drawings, maps, etc. This is the so-called conquest of realism. Ergo, understood correctly—perspective has been a fundamental driver of artistic, scientific, technological, and cultural progress over the last 500 years. But problems remain.

Unfortunately, perspective is a fragmented field without a clear purpose/direction. It has no established foundations, comprehensive artistic/scientific/technological theory, or standard operational framework. Instead, perspective has been reduced to a set of disparate visual, graphical, imaging, measuring, and modelling techniques. The result is partial and unconnected theories of vision/representation; and localised solutions that apply in only a narrow range of circumstances—leaving many unexplained facts and perplexing mysteries.

Missing is a uniting perspective framework from which to explore spatial reality using a universal frame of reference, complete with generally applicable concepts, principles, theory, methods, etc. Needed are visual explanations that apply universally, and allow students/researchers to leverage much that has been learned over the last 2000 years about perspective.

Subject Without a Home! 

We are concerned with Technical Perspective (or perspective), which refers to any systematic process that produces a detailed visual image, measurement, model or view, of a dimensional object or scene. Perspective is often described as something particularly linked with the Renaissance, which continued until the nineteenth century and then died out. Such is not the case because perspective has continued unabated to the present. 

Can we identify an underlying cause for the apparent demise of perspective?

To begin, perspective never became an independent concept and was therefore subject to the vagaries of classification of four branches of learning: optics, architecture, drawing and geometry. This had two significant consequences. 

First, classification changes, particularly in geometry, have shifted the definition of what constitutes perspective. In the nineteenth century, perspective included one, two, and three-point perspective and also various branches of parallel perspective. In the twentieth century, the scope of the term has frequently been restricted to one, two and three point perspective, whereas all parallel versions are classed as projections. Indeed, some would see perspective merely as an example of dilatation, as one of several mathematical transformations with no special role in spatial organization. 

A second consequence has been no less dramatic. A good deal of literature pertaining to perspective has simply been classed as part of the larger fields. Hence, although work on perspective has continued, it has been classed as work in optics, architecture, drawing or geometry. Our Bibliography and Encyclopaedia of Perspective have ignored the artificial barriers imposed by these fields, collecting hitherto disparate materials relating to perspective.

Distinct Field of Study 

Our ambitious aim is to unite all perspective knowledge under a single subject heading, heralding the birth of perspective as a stand-alone discipline—or primary field of study—with its own foundational theory, and above all, unified laws. 

A key goal is to use all forms of media to gather everything known on perspective. Whereby said field is to be organised in a comprehensive knowledge package, structured in ten levels as detailed below.


TECHNICAL PERSPECTIVE

LEVELS OF KNOWLEDGE

  1. Classification (ontology): classes, categories, forms etc. **
  2. Definitions (Dictionary / Lexicon of terms): etymology **
  3. Explanations (Encyclopaedia) ***
  4. Titles (Bibliography of literature: primary and secondary) ***
  5. Partial Contents (abstracts, reviews, citation indexes): searching, timeline *
  6. Full Contents (Library, Museum, Gallery): 7-10 below: analysis, products **
  7. Internal Analysis (logic): concepts, principles, theory etc **
  8. External Analysis (relations): practical applications and functions *
  9. Restorations (conservation records) *
  10. New Constructions and Reconstructions (perspective research) **

PRC work: *** task complete, ** task ongoing, and * task started.


Along these lines, PRC has been studying perspective—fervently for over 30 years, and much has been learned/achieved. For example, we have completed our Bibliography of Perspective (up to year 2020), which lists over 15,000 perspective titles; and recently, we published the 8 volume Encyclopedia of Perspective.

Founder Kim Veltman has published a knowledge bank that consists of 350 publications (mostly on perspective or related topics). Plus, as evidenced by the 15,000 titles in our Perspective Bibliography, the world has not been idle concerning ideas and work on perspective; whereby a large number of (sometimes conflicting) concepts, principles and theories on perspective have been identified/formulated.

Evidently, and despite progress, much remains to be done. In particular, we must unify or integrate, the huge number of different concepts, principles, theories, and methods of perspective (where possible). For example, we are building a comprehensive ontology and associated taxonomic tree of perspective types, and formulating a corresponding classification system. Plus, we are producing a Lexicon or Universal Dictionary of all perspective terms. 


Methodology

We wish to establish perspective as a primary subject discipline, and accordingly, it has multiple facets that can be identified, defined and explored. Ergo we have developed a new fundamental Theory of Perspective. 

Classes of Perspective

There are three main classes of perspective: Optical, Mental, and Knowledge.

Optical Perspective seeks to capture, copy or display aspects of the visual world. Optical Perspective can be separated into the Technical and Non-Technical classes of perspective. See later discussion for a definition of the Mental and Knowledge Perspective types.

Technical Perspective (definition)

Technical Perspective refers to any systematic process that produces a detailed visual image, measurement, model or view, of a dimensional object or scene. Technical Perspective is formed using physically, mathematically, geometrically, or logically correct/known/consistent principles.

Technical Perspective can be separated into distinct categories and sub-categories, but importantly, all types of Technical Perspective are recognised by having a direct connection to human vision, environmental optics, and/or related visual processes/methods/instruments/machines.

Technical Perspective includes all naturally occurring optical effects that can be classified under optics of the environment, including for example, optics of the heavens (sun, moon, and stars etc), shadow projection, panoramic views from mountain tops, underwater optics, etc. Also classified under the heading of Technical Perspective is the vision of all animals, including human vision and (for example) birds, frogs, fish and insect eyes etc. 

It is important to realise that most types of representation (including visual illusions) are included under the technical class, and specifically this is so—wherever said effect relates to the ordinary laws of environmental optics or the expected results of human vision (ref. physical and psychological optics).

Non-Technical Perspective (definition)

Non-Technical Perspective is defined as any non-systematic process that produces a detailed visual image, model or view, of a dimensional object or scene. Non-Technical Perspective does not involve the application of a comprehensive visual theory/process/method of image formation or optical projection. Non-Technical Perspective is formed using mathematically, geometrically, or logically incorrect/unknown/inconsistent principles (including nonphysical processes).

Examples of subjects that are normally classified under Non-Technical Perspective include aperspective, axial, inverted, negative, time (images taken at different epochs). Whereby a Non-Technical Perspective category is recognised by evident non-connection to the ordinary laws of optics, or because it fails to match the expected results of human vision.

Natural Perspective (definition)

Natural Perspective is defined as any naturally occurring instrument/process that produces a detailed visual image, view or shadow/outline of a dimensional object or scene. Natural Perspective includes human and animal vision (eyes), shadow projection and environmental optical effects, etc.

Categories of Technical Perspective (primary categories)

According to our new theory of Technical Perspective, it has six sub-categories:

  • Natural Perspective (natural and built worlds) – including Visual Perspective or direct looking at reality (view of a dimensional form / scene);
  • Mathematical Perspective – modelling reality / shaping appearance(s);
  • Graphical Perspective – copying reality / creating appearance(s);
  • Instrument Perspective – looking at, capturing and measuring reality; and projecting appearance(s);
  • Forced Perspective (aka ‘false’ or ‘trick’ perspective) – visual illusion by the construction of a false reality, or by the representation of a false reality (distorted/transposed scene geometry);
  • Media Perspective – connecting/linking, ordering, constructing (mimesis), matching, mixing, exploring, and cross-matching: multiple perspective view(s).

Sub-categories of Perspective (secondary categories)

We can identify various sub-categories of each form of Technical Perspective or Non-Technical Perspective; and these are explored throughout this site.

Goals / Products of Perspective

Three goals of Technical Perspective can be identified (in human terms). 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.

Noteworthy is that the different categories of Technical Perspective reflect varying degrees of abstraction and levels of accuracy, in achieving a close visual correspondence with reality. And usually, the goal is optical veracity—or comprehensive visual truth. Even Forced Perspective and Perspective Illusions are concerned with fooling the eye/brain into believing in a ‘false’ visual reality. Such illusions are produced by using realistic ‘looking’ perspective methods.

The objectives of Non-Technical Perspective are less distinct. They reflect similar goals, but involve arbitrary visual techniques that are less systematic, and not grounded in strict scientific principles. Ergo Non-Technical Perspective is not primarily concerned with achieving a high degree of correspondence with physical reality, but rather with improving the clarity of visual features (for example).

As stated, both the Technical and Non-Technical Perspective types fall under the heading of Optical Perspective, and refer to any process that forms a detailed visual image, measurement, model, or view, of a dimensional object or scene. These outcomes are named the Products of Perspective; noteworthy is that all of these products are related to optical processes, of one kind or another.

In summary, all categories of Optical Perspective seek to capture, copy or display aspects of the visual world; and they only differ in terms of the degree of realism produced (reality correspondence), and the particular visual features that provide said realism.

Distorted, Imaginative and Illusionistic Spaces

Perspective creates an image or view of the one true reality.

Ergo, the goal of perspective is to obtain/form a close visual correspondence with physical reality, or viewing, matching, and making representations of said reality. But this may not always be an adequate definition of perspective as applied to all practical situations.

Thus far, we have been talking about how one perspective movement focussed on realism, leading to topographical views, geometrical and architectural drawings—hence accurate dimensional measurement. However, it is essential to realise that perspective is not always concerned with producing entirely realistic views.

A second perspective movement led to panoramic, distorted, imaginative, and illusionistic spaces. Ergo, perspective enabled 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. 

Henceforth, perspective can also be used to provide views of false ‘realities’ or imaginative/illusionistic spaces. And so, we must adjust our definition of what the aim of perspective is. Perhaps a more accurate definition is to state that the goal perspective is to view, match or represent, in a realistic fashion, dimensional spaces of all kinds, both real and imaginary.

Perspective Forms (components of visual transformation)

It is helpful to consider perspective as a visual process, or a set of visual transformations, that affect changes to the appearance of a dimensional scene.

Perspective happens when a dimensional object located in dimensional object space is transformed into a dimensional image located in dimensional image space. Often this procedure involves a reduction in dimensions, whereby a 3D object is reduced to a 2D image (e.g. a digital camera photographing an object).

Ergo, perspective is a process that can be broken down into a set of Perspective Forms or components of visual transformation. A particular Category of Perspective reflects a corresponding group of visual changes that occur whilst viewing/surveying/representing a dimensional scene. The Perspective Forms correspond to apparent optical adjustments to: points, lines, plane figures, solid shapes, shades, shadows, reflections, translucency, colour, texture, scale, etc.

Accordingly, standard Perspective Forms (components of visual transformation) delineate the specific visual effects happening whenever a perspective view/image/measurement/model/representation is made. Whereby each Perspective-Form (visual-transformation) can be linked to one of the so-called ‘retinal variables’ or visual variations that are detectable by the human eye (or another image forming process/instrument).

Methods of Perspective

A Perspective Method is any practical or theoretical technique that aids in forming a detailed visual image, measurement, model or view, of a dimensional object or scene. Typically one or more such methods are combined to render a view/image/measurement/model according to a particular instance of a category of Technical Perspective.

Formerly, a Perspective Method is often encapsulated in one or more mathematical formulae/technique(s) that is/are applied systematically to a scene and hence producing a view, image, measurement, model or representation. This methodical procedure can happen naturally as a result of (for example) image formation in a human eye; or else it can be applied using a graphical technique (for example, the method of linear perspective).

The visual results of perspective can appear in various ways; with varying results. Ergo there are many different Categories, Forms, and Methods of Perspective which operate to produce a vast range of different visual effects (image forms). Hence it is by no means clear which particular perspective technique is the most real. This explains the ongoing arguments over whether or not perspective is innate (real/natural) or simply a convention (human invention).

Functions of Perspective

Perspective, in general, works to enable viewingprescribing, matching, modelling, exploring, representing, and mixing images, of the physical world. These are the Functions of Perspective, which are supported by each perspective category, to a greater or lesser degree.

Origins of Perspective

Perspective is central to topics in art (drawing, painting, etc), optics, mathematics, and instrumentation. But stating such tells us little about the nature of perspective. What is perspective? How does it arise (in each case), and what are its origins? 

Well, it may not surprise you to discover that the origins of Technical Perspective lie in the physical, technical, and hence mathematical realm. The Perspective Forms are created by (or reflect) several underlying physical processes that are inherently systematic in Technical Perspective. The ordinary laws of physical and geometrical optics, including the well-known size-distance law, horizon line, vanishing point(s) etc, are known to operate therein.

It is essential to realise that many of the aforementioned visual transformations have roots in optical, geometric or mathematical processes. Whereby Mathematical Perspective, refers to applying algorithmic rules to transform the appearance of scene/object geometry. Mathematical Perspective often contributes to the other kinds of Technical Perspective. Such mathematical contributions happen, either due to the natural visual effects resulting from the laws of physics, inherent instrument perspective, or the application of human-designed algorithms to a visual scene.

The origins of perspective are complex indeed. But luckily we have powerful tools including ontology, logic and relational modelling; which help us to identify, analyse and synthesise the multiple aspects of perspective with a high degree of accuracy.

Perspective Classification

How is it possible to classify a subject that has so many different facets?

Evidently, there are many types of perspective; and we have classified these into distinct cubby-holes as best we can. Nevertheless, certain categories of perspective retain a degree of non-precision—or are highly subjective—and such is the case with the Visual and Graphical Perspective types. As stated, all types of perspective have strong links to Mathematical Perspective, and are also subject to the vagaries of human perception.

Perspective is a foundational topic, having much in common with ‘theoretical’ subjects like algebra, geometry, and number theory, but it also has close links to physical disciplines like art, representation, and scientific imaging/measuring instruments, etc. Perspective is a set of analytical and experimental methods that enable humans to better perceive, measure, model, and create views/images of reality according to our particular needs.

We aim to bring a rigorous understanding to the central topic of perspective. Accordingly, we have developed a new categorical theory of perspective that elucidates links between the different types of perspective, outlines the big picture, and encompasses all aspects of perspective in a single model. Our primary objective is to identify all of the Goals, Classes, Categories, Forms, Products, and Functions of Perspective; without worrying so much about the underlying mathematical explanations or the Methods of Perspective.

It is important to recognise that on many occasions, one kind of perspective will involve multiple types of space; for example when looking at painting of a mountain-scape scene, the viewer of the painting creates a Visual Space from a painting consisting of elements of Graphical and Mathematical Space(s) (for example). Ergo understanding the nature of dimensional space is of central importance if we wish to understand perspective.

Categories of Space

Optical Perspective seeks to capture, copy or display aspects of the visual world.

 As stated, Optical Perspective can be separated into the Technical and Non-Technical classes of perspective. But a question remains as to the precise nature of the ‘dimensional space’ that these types of perspective involve. Normally, when we speak of Visual Reality or the Visual World, we are referring to the optical appearance of physical reality—composed of three spatial dimensions and one time dimension.

But remember, that we had identified a more accurate definition that the primary goal perspective is to view, match or represent, in a realistic fashion, dimensional spaces of all kinds, both real and imaginary. Ergo, we need to define the precise form(s) of perspective of which we speak.

We can analyse Optical Perspective in terms of the type of visual space involved:

  • Visual Perspective = Visual Space (physiological and psychological optics)
  • Mathematical Perspective = Geometric Space (theory of projection)
  • Graphical perspective = Graphical Space (theory of representation)
  • Instrument Perspective = Optical Space (physical/wave optics of light)
  • Media Perspective = Virtual Space (digital hypermedia and multiverse)

Note that we have not defined the kind of space involved in Forced Perspective, and this is due to the fact that this type of perspective does not have a preferable type of space within which it tends to operate; but rather multiple, layered and juxtaposed spaces are commonly employed.

It is worth noting also that we are employing the word ‘visual” in two different senses. First we have the concept of a visual ‘space’ category that relates (generally) to any one of several types of space that can exists in the visual dimension. Examples include the Visual, Mathematical, Graphical, Instrument and Media forms of visual spaces. Secondly we have the particular form of Visual Space (capitalised here) which refers to a human being looking at spatial reality.

Perspective remains a complex topic because it involves the comparison of fundamentally different categories of space. For example, reconciliation of the 3D physical space of reality, with the 2D space of Graphical Perspective. Often, and despite a strong desire to attempt equality, this reconciliation is impossible; because one deals with dimensions that must be mapped without 1:1 correspondence (e.g. transform 3D space to a 2D space).

The upshot is that anyone who wishes to apply perspective to a visual problem, has to decide firstly which types of visual space are involved; before identifying which Perspective Class, Category, Form(s), Visual Features, and Methods to select, and so to obtain the desired Perspective Product.

Perspective Instruments / Machines

An Instrument Perspective; is generated whenever an instrument, of one type or another, is used to view, capture, measure, or project an image of a scene. 

For image viewing and capture we have instruments such as cameras, telescopes, microscopes etc. Other instruments have been developed for image projection and display. In this respect, many innovations have occurred, ranging from the earliest such as the Magic Lantern and Kinetoscope, to modern cinema techniques, such as wide-screen and 3D cinema, plus immersive systems, including IMAX theatres. 

Today we have new types of media and networked computing devices, including smartphones and tablets; which can display and manipulate a whole variety of perspective views. However it is important to realise, that perspective instruments and machines are conceptualised, built, and operated, according to mathematically, geometrically, and logically correct/known principles. In other words, all such devices are enabled by valid perspective theory/methods.

Desired is a single theory, and unified logical reality, to entirely encompass the new subject discipline of perspective—without contradiction(s). But specific problems remain that work against any grand unification of perspective theory/methods.

Ergo, it is helpful to identify specific pivotal issues right away.


Problem of Scale 

A fundamental tenet of Renaissance perspective was the inverse size-distance law which stated that if one doubled the distance, the represented size was one-half. If one trebled the distance, the size was one-third and so on. Indeed this law is still basic and applied to many problems in science and engineering.

In 1967 Benoit Mandelbrot (1924-2010) wrote an interesting article on Fractals that questioned the universal applicability of the size-distance law. Mandelbrot’s article concerned the size of the coast of Britain, and implicitly introduced a spanner into this assumption by showing that size was a function of both scale and distance.

The measured coastline length depends upon scale or the apparent ‘jaggedness’ of coastal outline. Accordingly, walking or taking a boat around the coastline will involve travelling vastly different distances in each case! Modern mapping systems like GoogleMaps do (or should) implicitly consider related ‘scaling’ effects when calculating different route distances/arrival-times for walking, driving, etc.

In a sense, we have been vaguely aware of this ever since the seventeenth century. The shape of an ordinary image is transformed entirely when we change its scale in a telescope or a microscope. What is needed is a new approach to perspective—Multi-scale Perspective—that takes into account scale as well as distance, whereby any given shape only applies within a given range of scales.

This multi-scale capability is vitally important in a world where we travel between scales with greater frequency. True multi-scale views/images/measurements would open the way for better understanding of, and links between, nanoscopic, microscopic structures and macroscopic happenings.

Problem of Viewpoint 

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.

But there is a problem that is fundamental to all perspective methods and applications. Images taken from separate viewpoints are wholly different in shape, one from another. This is due to the singular optics and geometry associated with a particular vantage point. Each view contains unique (but partial) information about the scene or object under inspection.

To visually probe—or model/understand—an object/scene sufficiently, often, we need to consider multiple views. A Multi-view Perspective, is when we combine views taken from different locations or viewing directions. Usually, this can be achieved using a new media system (networked digital media). Accordingly, views taken from two or more vantage points, may be connected/linked together and then ordered, constructed, matched, mixed, explored, and cross-matched, etc.

The problem of viewpoint integration is a common, but largely unsolved, requirement for media systems in general.

Problem of Time 

Time is the dimension of spatial permanence (or change). Like space, time has three dimensions: past, present, and future. But humans live in the present, and we must observe reality using a narrow time window—at least using unaided eyesight.

Desired are ways to explore time on multiple scales; viewing images using natural-speed, slow-motion, or fast-forward time-flows, much like a typical video player. However, we are not speaking of standard Motion Perspective available from ordinary moving images; but directly manipulating time. We wish to make time more space-like; in terms of the generic connection of time-flows across multiple images, zooming/panning time-flows, plus unrestricted navigation (temporally).

We need to—capture, record, and manipulate systemised time-flows—in our perspective views—using Multi-time Perspective. With the aid of ‘temporal’ focus and lens techniques, a continuum eliminates the gap between macro- and micro-time-flows. Ergo, the viewer can jump straight to any point in space/time, and choose the correct time-flow rate to observe a particular process—for example, spanning from nano-seconds to millions of years (modelled). 

Typically today, we see a narrow range of time-flows provided by a single image stream, limited at one end by the camera frame rate—and the other by the overall length of recording time. Needed are ways to overcome this deficiency—and develop ‘conjoined’ image space(s) with hyperlinked time-flows that can be—indexed, classified, linked, searched and explored.

To those in the physical and life sciences, such total simulation techniques extend far beyond visualisation of previously invisible processes: they introduce new dimensions of study and hence ways to attain comprehensive modelling of development processes. 


Perspective Research 

Perspective has a rich history and has been diligently studied for more than 2000 years. For example, our Bibliography of Perspective lists 15,000 publications on the subject, suggesting a vast undercurrent of complexity.

One might suppose that the sources, theory and methods of perspective are well-understood today and that further research into perspective would not be necessary. However, such is not the case because the field of Technical Perspective contains many unexplained facts, perplexing mysteries, and exciting possibilities.

The basic principles and techniques of Graphical Perspective have been established (for example); but there are many other classes of perspective that remain largely unexplored. Perspective is a fast-developing field with modern application areas that are predicated on perspective-related research and development activity.

In truth, much is unknown, and many questions remain unaddressed.

Fundamental areas of inquiry:

  • Space/time: nature of, underlying geometry, number of dimensions, etc.
  • Mechanisms of human vision: perceptive processes, binocular vision, etc.
  • Categories of perspective: debate as to objective/subjective methods, etc.
  • Nature of spatial form: understand and systematically model, the apparent transformations of shape with viewing position and scale!
  • Levels of Abstraction: systematically model how perspective involves more than copying the physical world, because it applies equally to different levels of abstraction and serves as a bridge between the concreteness of nature and abstractions of mathematics.
  • Multi-scale, Multi-view, Multi-time perspective(s): how to attain and explore multi-scale/view/time perspectives, using global synthesis and indexed lookup.
  • Mapping of visual, represented and geometrical space: find ways to foster certification of sight, measurement, and representation (universally).

Theoretical needs (substance or definition problems):

  • Nature of perspective (convention or not)
  • Taxonomic tree of all perspective types (ref. a new ontological theory).
  • Lexicon of integrating definitions, explanations, principles and methods.
  • History of perspective, timeline, links to history of vision/representation.
  • Identify key visual building-blocks, shape grammars (ludo geometrico).
  • Explain origins of perspective (ref: world view, workshop practice, architecture, ground/plan method, surveying, cartography, astronomy)

Theoretical needs (function or relational problems):

  • Universal theory/method: combine all perspective types into a single model.
  • Applications of perspective, foundational mapping for other subjects.
  • Relations between analytic, descriptive, and projective geometry.
  • Account for apparent failure of distance/size laws (Multi-scale Perspective).
  • All views embody transformations of form, reconcile (Multi-view Perspective).
  • Static views ignore dimension of time, reconcile (Multi-time Perspective).

Theoretical needs (quantitative problems):

  • Reconciliation of physical and visual space – mapping (not 1:1)
  • Reconciliation of physical and geometric space – mapping (not 1:1)
  • Reconciliation of physical and modelled space – mapping (not 1:1)
  • Correspondence of perspective and reality – mapping (not 1:1)
  • Correspondence of perspective and vision – mapping (not 1:1)
  • Correspondence of perspective and measured world – mapping (not 1:1)
  • Correspondence of perspective and modelled world – mapping (not 1:1)

Practical needs (sample):

  • Vision: vastly expand the field/range/depth of human vision.
  • Scale: Mapping, linkage and indexing of macroscopic, microscopic and nanoscopic worlds, leading to mastery of the environment on all scales.
  • Time: Capture/link/explore views of reality using systemised time-flows. 
  • Visual Encyclopaedia: a Universal Knowledge Machine with contextualising instruments and continuous transitions between locations/scales/times, plus easy way-finding to any item/relation/pattern on the macrocosm/microcosm.
  • Multi-scale/view/time perspective(s): to enable pattern recognition (synthesis) and exploration (analysis) from all viewpoints, scales and times.
  • Integrated perspective(s): universal media format (+ metadata) to index, link, and explore all the world’s images (stationary and moving images, 2D, 3D, etc).
  • Mapped/decoded perspective(s): universal image format enables a systematic mapping between physical, graphic, and semantic space(s). Each image frame (2D/3D) contains a scaleometer that allows the user to select a scene voxel (3D spatial region), and quantify its true position, shape, and size (ref. scale in 2 senses: spatial extent, resolution). Automatic decoding of 2D view to 3D geometry by modelling using shape grammars plus multi-view perspective [ludo geometrico to identify key building blocks of reality].
  • Hypergrams: data-rich media that may be explored freely or queried in stylised ways; and that can be arranged and linked in multiple ways.
  • Virtual Reality: VR, AR, MR, XR: dynamism of egocentric/exocentric, inner/outer, ways to navigate the different levels of abstraction, scale, etc.

Patently our list of perspective-related problems is incomplete. In addition, the task of finding solutions to some of the grander questions is monumental, and lies far beyond the capabilities of any one organisation, university, or scientific institution. Indeed, we might have to wait for the emergence of a new era before work even begins (on certain problems). Cross your fingers.


Classification of Perspective

If perspective is to be recognised as a distinct field, then to which subject class does it belong? Should we ascribe it as an art, science, or else a practical discipline?

Professor KIm Veltman makes a salient comment in this respect:

From the outset, the classification of perspective posed problems. Etymologically it was linked with optics, which could not be classed simply. Historically it was linked with architecture, which equally eluded simple classification. By the nineteenth century the nature of the problem began to come into focus. Systems of classification had forged clear distinctions between (subjective) art and (objective) science, as well as between (theoretical) science and (practical) technology. Perspective had the embarrassing characteristic of belonging clearly to all of these. It belonged to art, because it created spatial effects in paintings and it was accordingly classed under drawing. At the same time its theoretical principles were so clearly connected with the mathematical projections underlying scientific demonstrations, that it came to be listed under descriptive geometry. Finally, it also involved instruments, such that it was also classed under technology. 

The Encyclopedia of Perspective: Volume 1 [Chapter 4, p. 193] by Kim Veltman.

Perspective is a science. But it is a science that often involves other scientific disciplines such as physics (space/time), optics, geometry, human vision, engineering drawing, mathematics, and computing. Each area consists of both theory and practice, and our new perspective science must take everything in its stride without missing a beat (unambiguously). Desired is to possess all of the logic, and hence predictive power, of true science.

Perspective is also an art. 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).

Perspective is also a technology. Whereby optical, matching and surveying instruments enable humans to probe dimensional reality and to obtain accurate views, images, models, and measurements. Perspective technology has been central to the development of many other technologies, including photography, cinema, geographical information systems (GIS), global positioning systems (GPS), virtual reality (VR), computer graphics (CG), computer-generated imagery (CGI), computer vision, robotics, etc.

On this site, we shall explore all of the different classes, facets, and applications of perspective; while following our primary goal of unifying all perspective knowledge into a single framework.


Perspective and the Two Cultures

We have argued for the need to establish perspective as a new subject discipline, hopefully to enable focussed development of subject matter, and hence to foster rapid and fundamental progress in this key area. But there is another compelling reason why perspective knowledge must be gathered together, and then integrated into a single subject framework, and this relates to a well-known cultural dilemma.

Patently, establishing perspective as new subject discipline is a highly ambitious goal that involves many difficulties—including problems emanating from artistic, scientific and technical domains. But perhaps one of the biggest blockages to progress in perspective knowledge is cultural, as explained by Sir C.P. Snow in his 1959 book ‘The Two Cultures and Scientific Revolution’. Whereby the science and humanities have become split into ‘two cultures’; and that division has been a major handicap to both in solving the world’s problems. 

If Dr Snow is correct—and much evidence says that he is—then our call to establish a separate subject discipline for perspective is also correct, especially given the tremendous number of relationships, and interrelations of perspective across art, science, technology, and culture. Perspective seems to be a special case in this respect; because it is deeply embedded in all of the various sub-disciplines of each subject; and it is difficult to find any visual/imaging/representation topic that is not ‘perspectival’ in one way or another.

Perspective is such a vast, broad, and profoundly influential topic that it should be taught as a distinct subject in schools, colleges, and universities. Whereby perspective is the very definition of an interdisciplinary subject, with countless sources, links, and fundamental relations penetrating to the core of key phenomena in the arts, sciences, culture, and technology.

Hopefully perspective can, at last, take its rightful place as a leading subject discipline, being classed as a legitimate field in its own right. QED.