Methodology

Our journey into the multiple dimensions of perspective begins here.

We start by defining the scope of perspective topics to be examined. Next, we introduce perspective concepts and related terms to accurately delineate, explore and meticulously analyse, the field of perspective (as a whole). Do not worry if said 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.

We wish to establish perspective as a primary subject discipline, and accordingly, a fundamental Perspective Category Theory is developed. 

Nature of Perspective

We begin by asking: what is perspective?

Unfortunately, the task of answering this question is fraught with difficulties. Quite literally, thousands of treatises, theses, books, and scientific papers have been written to tackle the puzzling complications that arise in this respect. Perspective turns out to be one of the most fundamental, theoretically challenging, perplexing, yet elusive topics. In a way, the sole purpose of everything we do at the Perspective Research Centre is to clarify attendant issues.

But why is perspective such a challenging topic? This is partly because many different types of perspective are known. For example, we have visual, mathematical, and graphical kinds of perspective, etc. Secondly, multiple types of perspective tend to operate simultaneously, so it is difficult to identify the root causes of specific visual effects. For example, we cannot easily separate environmental optics (or Environmental Perspective) from the human visual system (Visual Perspective of the second type).

As a result, perspective is an inherently complex topic. Anyone who seeks a deeper understanding of perspective has to engage the old noggin, as my father used to say. But how can we deal with such complexity? Perhaps only by defining all classes of perspective, identifying the salient features of each type, before characterising the particular circumstances that bring each form into play.

We must open our eyes to all of the varied dimensions of perspective!

Primary Classes of Perspective

In the Oxford English Dictionary (2nd Ed.), perspective is variously defined as the science of optics, an optical instrument, the art of representing objects in a three-dimensional (3D) space, a drawing or picture, a visible scene, and the act of looking, etc. Noteworthy is that perspective also refers to a mental view or prospect, etc.

Accordingly, we can define perspective, in general terms, as the formation of an Image—or a representational pattern—of a state of affairs present in a spatial reality (e.g. natural, illusive, imagined space, etc). Perspective may refer to the process or procedure that forms said Image (e.g. Graphical Perspective), or it may refer to the end result, the Image itself (e.g. a perspective drawing).

Said Image may be either of the visual type to reflect visual features of an object/scene, or be of the non-visual type and reflect non-visual characteristics (ostensibly). Accordingly, there are two main classes of perspective: Visual Perspective and Symbolic Perspective (non-visual perspective), which correspond to the two basic kinds of images: Visual and Non-Visual Images.



Figure 1: Primary Classes of Perspective

(Enlarge figure by opening in a separate window)


As the name suggests, Visual Perspective (of the first type, or not overtly related to the human visual system) refers to when a Visual Image is used to view, match or represent the visual appearance of a spatial object/scene.

Alternatively, Symbolic or Non-Visual Perspective deals with Non-Visual Images (e.g., literal, logical, ontological, or algebraic images). Noteworthy is that for the non-visual class of perspective, the ‘images’ formed may relate to spatial/visual features or other non-visual features of the object in question.

Perhaps without realising, we are building a class hierarchy or Taxonomic Tree of Perspective. It is noteworthy that classes are often overloaded on said tree, whereby one class of perspective is the daughter of a higher level class. For example, we have Technical Perspective, a type of Optical Perspective, which is, in turn, a type of Visual Perspective (ref. one branch of the inheritance tree structure).

As our discussion continues, we shall build our knowledge of the lower-level classes, particularly those under the Optical Perspective branch.

Visual and Non-Visual Images

The reader may find the inclusion of the symbolic or non-visual class of images—and associated perspective forms—a little surprising. At least when defined alongside perspective proper (the visual, graphical perspective types etc). Still, Non-visual Images are fundamental throughout literature, science, culture, etc.

Word Image can build up a picture of an object/scene using purely language-based descriptions, whereby the result is sometimes identical to a Visual Image. This can happen by metaphor, descriptive methods, or mathematical formula (e.g. analytical geometry). For example, the ‘visual image’ of a three-dimensional cube of a specific size and colour can be produced by either image class.

Nevertheless, it is usually the case that Visual and Word Images of the same object/scene, will differ significantly. Fine structural details, contours, spatial relations, optical effects etc, are often more accurately captured with Visual Images. Alternatively, Non-visual Images can convey hidden or difficult-to-see facets missed by visual methods. Said features include chemical, atomic and sub-atomic makeup, invisible forces at play, or other invisible facets, such as micro-processes, etc.

We can make an interesting distinction between permanently and temporarily invisible features. For example, it is sometimes the case that previously invisible features of an object/scene become visible when viewed using the correct perspective or using an appropriate viewpoint, scale, timescale, etc.

Optical Perspective

Given all of the different classes of perspective, how then is it possible to build a single perspective theory to encompass everything? Quite simply, it is not possible (at least right away). We must focus on one area, whereby we study Visual Perspective (chiefly) at the PRC, which deals with visual—or image-related—subject matter (plus related spatial topics).

We are primarily concerned with one particular type of Visual Perspective, named Optical Perspective. We can define Optical Perspective, in general terms, as the process of picturing or representing a spatial reality using optical methods (ref. physical, imagined, illusive reality, etc).

Optical Perspective is concerned with capturing, measuring, or representing realistic views of dimensional space (ref. may involve real, virtual or simulated light rays). Wherein a spatial scene/object is analysed/represented using optical techniques. Optical Perspective encompasses all forms of perspective that use, or purport to use, light, or electromagnetic radiation, to probe a spatial scene; including all wavelength ranges from gamma rays, x-rays, visual spectrum, microwaves, radio, etc.

As we shall learn, there are many different categories of Optical Perspective. Still, all involve projective principles that reflect particular scene geometry aspects with varying degrees of visual realism or accuracy.

Noteworthy is that some forms of Optical Perspective employ artificial/simulated ‘light-rays’ that lie beyond the bounds of ordinary physics. Said techniques can sometimes operate on an impossibly vast or tiny visual scale; or produce images that pass straight through solid objects, etc. However, the use of such techniques does not necessarily make the resultant visual images any less real or accurate (ref. heavenly, sub-atomic and medical optics, Virtual Reality, etc).

Here at the PRC, while mainly dealing with Optical Perspective, we also study other types—namely Mathematical and Contact Perspectives—as explained below.

Mathematical Perspective

We can identify three different kinds of mathematical perspective:

1) Algebraic Perspective [non-visual class] – involves algebraic formulae.

2) Geometrical Perspective [analytical visual class] – graphical calculation. 

3) Projection Perspective [projective visual class] – spatial projection. 


Algebraic Perspective (Type 1) refers to mathematical images composed of letters and symbols. Accordingly, we have categorised this as a form or sub-class of Symbolic Perspective. 

Geometrical Perspective (Type 2) employs Analytic Geometry, also called coordinate geometry, or use of algebraic symbolism and methods to represent and solve spatial problems. Analytic Geometry refers to spatial modelling using graphical points, lines, and multi-dimensional objects and shapes, surfaces, and solids. Ergo, due to the inherent links with Analytical Geometry, we have categorised Geometrical Perspective as a form of Visual Perspective. 

Another form of Visual Perspective is named simply as Projection Perspective (Type 3), which refers to applying projective principles to the creation of an image or view of a spatial scene or object. This latter type of Projection Perspective employs Descriptive and/or Projective Geometry to produce images of a spatial reality.

At the PRC, we study the visual classes of mathematical perspective; namely Geometrical Perspective (images formed by graphical calculation) and Projection Perspective (images formed by visual projection). 

Contact Perspective

Contact Perspective refers to the direct mapping of spatial form, namely a spatial object/scene, and by utilising physical contact using one, two or three dimensional examination procedures (1D/2D/3D space). Contact Perspective is perhaps the purest—or most ‘real’ class of perspective—and because it deals with the physical world in its actuality. 

An example of Contact Perspective is a person feeling/exploring the surface features of a solid object, and by using their hands to gather spatial data and subsequently form an image of said object’s 3D shape. Instruments and machines can perform similar tasks, such as when a robot vacuum cleaner or autonomous Martian Explorer maps an unknown territory by means of physical exploration.

We can identify two different kinds of Contact Perspective:

1) Handling Perspective – scales, rulers, callipers, physical sensors/actuators, etc.

2) Moulding Perspective – casting processes, projection moulding machines, etc.


It would seem difficult to argue with (or contradict) data that arises from direct contact with the object of attention, at least in scientific or materialist terms. However, it is essential to realise that many of the same data-gathering tasks arise with both Contact and Optical Perspective. For example, the problem of determining true object shape versus apparent and/or partial object shape.

Note that we have assigned specific perspective-based handling and calculating methods within our Perspective Category Theory, namely scales, rules, callipers, slide rules, etc., as falling under Instrument Perspective. Measuring/calculating devices are classified under the Technical, Optical Perspective branch. We have done so to simplify the classification scheme. Such devices involve using human vision to take readings or otherwise to apply said methods to physical reality.

In sum, the various kinds of Contact Perspective have strong links to the other types of Visual Perspective; and they have been widely used to develop, validate and certify Mathematical, Graphical, Instrument, and Media types of Perspective. 

Now that we have adequately delimited our primary subject matter, we can explore Perspective Category Theory in detail.

Perspective Category Theory

We adopt a scientific, logical approach to the field of perspective.

Some people may object to applying scientific principles since perspective is evidently both an art and science. However, doing so has many advantages, most notably because we can establish concepts and principles upon which the entire field of perspective is built.

Patently, perspective sometimes deals with unreal, imaginative, and illusionistic three-dimensional spaces. However, these same spaces are often visualised, or represented using realistic ‘looking’ visual images (or perspective proper). Henceforth, visual realism is a key component of all perspective forms.

Desired is a new perspective theory, which hopefully can be used to enable humans to understand, model, and apply complex perspective phenomena in the broadest range of practical circumstances. A first step in building a theory is to identify a group of concepts—or set of matching universal forms—that purports to represent all of the different facets of perspective.

The sections below introduce a set of key principles upon which Perspective Category Theory is built. Wherein most of these concepts can be explicitly/theoretically proven—but if not, then said principles can hopefully be demonstrated empirically.

Perspective Worlds

As stated, there are two main classes of perspective: Visual Perspective and Symbolic Perspective. We are concerned with a specific sub-category of Visual Perspective, namely Optical Perspective.

Optical Perspective seeks to view, match, or represent aspects of the Optical World—or the changing appearance of objects as conveyed to the camera, instrument or the eye by emitted or reflected light (ref. using real, modelled, represented or imaginary light-rays). Ergo, a key goal of perspective is to explore the Physical World by using the Optical World to probe spatial reality accurately or with sufficient realism.

The natural products of human vision are named as the Visual World (unaided eyesight)—or the transformation of the Optical World according to the rules/processes of human vision (ref. physiological and psychological optics). In addition, the Represented World refers to human attempts to depict aspects of the Physical, Optical or Visual World(s).

The Physical, Optical, Visual, and Represented Worlds possess fundamental mapping relations. However (as we shall learn), the precise nature and validity of such correlations are by no means straightforward or guaranteed. Ergo, a secondary goal of Optical Perspective (biggest sense) is to understand how the different facets of each World fit together to produce visual reality.

Optical Perspective can be separated into the Technical and Non-Technical categories of Perspective—as explained below.

Technical Perspective (definition)

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

Technical Perspective can be separated into distinct categories and sub-categories. Still, importantly all types of Technical Perspective are recognised by having a direct connection to human vision, environmental optics, and related visual processes/methods or associated 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 birds, frogs, fish, insect eyes etc. 

It is essential to realise that most types of representation (including visual illusions) are included under the technical class. 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).

The Systemisation of Space (and Time)

Perspective fosters the systematic analysis of space (and time). 

By accurately prescribingindexing, and modelling reality; perspective enables accurate systemised worlds to be developed on media. Through perspective views, new kinds of visual solutions can be created in the human mind or model and subsequently be recorded on media. 

The explicit three-dimensional worlds made possible using perspective machines/methods enable new ideas, concepts, forms, and conglomerations of objects to be explored. Some objects/processes are really existent ones, and some only imaginary (at a particular time). 

Perspective gifted humans with a god-like power to create the world in our image; because it ensures that objects/processes of all kinds are accurately conceived, perceived, manufactured, and employed! 

Non-Technical Perspective (definition)

Non-Technical Perspective is defined as any non-systematic process that produces a detailed visual image, representation, model or view, of a three-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 optically, 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 (random 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.

Non-Technical Perspective includes graphical methods that today are classified as Ancient Perspective (e.g. Aspective or Egyptian Perspective) or Byzantine Perspective (Reverse/Inverse/Inverted Perspective).

The first systematic or Technical Perspective ever developed is usually agreed to be Renaissance Perspective (i.e. central or linear perspective). Whereas today other forms of Technical Perspective are known; including Parallel, Oblique, 6-point, and many different kinds of optical projection including mapping projections of the earth and heavens, etc.

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 three-dimensional object or scene. Natural Perspective includes Visual Perspective (second type) or human and animal vision (eyes).

Environmental Perspective is a type of Natural Perspective that refers to naturally occurring optical effects such as projection of shadows/outlines, line-of-sight problems, translucency/reflection/colour effects, etc., that happen in the natural environment (and without human interference). For example, astronomical, atmospheric, underwater optics,  optics of crystals, rainbows, etc. Noteworthy is that all forms of Architectural buildings are herein classed as a form of Environmental Perspective.

Categories of Technical Perspective (primary categories)

The primary categories of Technical Perspective are listed below and encompass the vast majority of perspective methods employed in modern times.

Technical Perspective has six primary categories:

  • Natural Perspective (views of natural and built worlds) – including Visual Perspective (second type) or direct looking at reality using human or animal vision (view of a three-dimensional form / scene). Includes also Environmental Perspective or naturally occurring optical effects such as projection of shadows/outlines, line-of-sight problems, translucency/reflection/colour effects, astronomical, atmospheric, underwater optics, etc; Environmental Perspective Includes human designed optical vistas (e.g. architecture).
  • Mathematical Perspective (views of natural and built worlds) – modelling reality / shaping appearance(s); includes the second mathematical type or Geometrical Perspective, and also the third type dealing with optical projections;
  • Graphical Perspective (views of natural and built worlds) – copying reality / creating appearance(s);
  • Instrument Perspective (views of natural and built worlds) – looking at, capturing and measuring reality; and projecting appearance(s);
  • Forced Perspective – aka ‘false’ or ‘trick’ perspective (views of built world) – visual illusion by the construction of a false reality, or by the representation of a false reality (distorted/transposed scene geometry);
  • Media Perspective (views of natural and built worlds) – connecting/linking, ordering, constructing (mimesis), matching, mixing, exploring, and cross-matching: multiple perspective view(s).

We shall go on to explore the six-categories of Technical Perspective in great detail throughout this site (beginning under the Definitions section). Literally hundreds of perspective sub-categories (and forms) fall under these six headings.

Note that the form of Visual Perspective listed under the Natural Perspective category is identified as the second type of Visual Perspective; which relates directly to human vision. This form is contrasted with the first form of Visual Perspective, existing at the top of the Perspective Taxonomic Tree, under which all classes/categories of Optical Perspective are contained.

Sub-categories of Optical 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 correspondence with spatial 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’ Physical World. Such illusions are produced by using natural 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, representation, model, or view, of a three-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 Optical 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 (the Physical World).

Ergo, the goal of perspective is to obtain/form a close visual correspondence with spatial 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 spatial 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 (generally) is to view, match or represent, in a realistic fashion, three-dimensional spaces of all kinds, real, imaginary and illusionistic.

Perspective 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 three-dimensional scene (particular scenario).

Ergo, perspective is a process that can be broken down into a set of Perspective Components of visual transformation (for a specific imaging scenario). A particular Category of Perspective reflects a corresponding group of visual changes that occur while viewing/surveying/representing a spatial scene. The Perspective Components correspond to all of the optical adjustments happening to a scene’s Visual Features; including the appearance of points, lines, plane figures, solid shapes, shades, shadows, reflections, translucency, colour, texture, etc.

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

The individual Perspective Components (of visual transformation) are numerous and varied in degree of effect – and may include (for example) – varying shape changes to objects according to position within a perspective image. It may be very difficult (if not impossible for a specific scenario) to quantify/measure all of the existing Perspective Components.

A better approach, therefore is to identify and map general Perspective Phenomena that lie behind changes to Visual Features (for a particular category of perspective), and hence to comprehensively analyse how any particular perspective image comes to be.

Perspective Phenomena (or visual facets)

An individual category of perspective demonstrates, and is recognised by, certain Perspective Phenomena. The Perspective Phenomena (or visual facets) refer to all of the intrinsic, or general, changes to Visual Features that occur according to a particular Category of Perspective and its inherent processes. 

The Perspective Phenomena comprise, in each case, all of the defining features of a particular Category of Perspective; including types such as Visual, Mathematical, Graphical, Instrument Perspective, etc. An example might be a specific form of Graphical Perspective, for example Linear Perspective, whereby some of the (generalised) Perspective Phenomena include:

  • The apparent diminution of remote objects;
  • The apparent foreshortening of dimensions not perpendicular to the direction of vision;
  • The apparent convergence of parallel lines;
  • ++ several other Perspective Phenomena that affect Visual Features.

Patently each class of perspective will exhibit a unique set of Perspective Phenomena, whereby certain phenomena are shared (or embodied) by a number of different categories of perspective. Embodiment of the Perspective Phenomena may happen by certain naturally occurring visual processes, or else by human design, but irrespective of cause we refer to the instantiation of said phenomena as the Methods of Perspective.

Methods of Perspective

A Perspective Method is any practical or theoretical technique that aids in forming a detailed visual image, measurement, representation, model or view, of a three-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 (for example).

Formerly, a Perspective Method is often encapsulated in one or more mathematical formulae/technique(s) that is/are applied systematically to a scene—to produce a view, image, model or representaion. This methodical procedure can happen naturally due to (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).

Typically one or more Perspective Methods are combined to render an image according to a particular Category of Technical Perspective. Practical examples include Perspective Instruments such as a lens, camera, the perspective window, planisphere, projector, computer, etc. Perspective Methods include all instrument design features plus operating methods. Examples of theoretical methods include a particular projection algorithm, vanishing point(s), field-of-view, projected scale, etc.

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

Perspective Forms (of visual instantiation)

Each type of Optical Perspective can be realised in a specific Perspective Form; whereby there may be a whole variety of different kinds of Perspective Forms possible for each Perspective Category or Sub-Category.

For example, Linear Perspective is a Sub-Category of Graphical Perspective. Still, it can manifest itself in a whole variety of different Perspective Forms, including in forms such as in a drawing, painting, computer-generated image, virtual reality, etc. Each instantiated Perspective Form may be significantly, or subtly, different from the other Forms; even for a notionally identical image/view of the same three-dimensional scene/object.

Normally, we recognise a particular Form of Perspective through the unique changes imbued (Perspective Phenomena) to a specific set of Visual Features linked to a three-dimensional scene or object. For example, a perspective drawing will have an evident physical embodiment, possessing a unique set of Perspective Components (of visual instantiation), and be created in a specific way (e.g. pen and ink drawing on paper).

A Perspective Form will be instantiated by means of a specific set of Perspective Methods as explained above.

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.

Perspective Classification

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

We have classified these facets into distinct cubby-holes as best we can. Nevertheless, specific categories of perspective retain a degree of non-precision—or are highly subjective—and such is the case with Visual and Graphical Perspective(s).

As stated, all types of perspective have strong links to Mathematical Perspective, and most are subject to the vagaries of human perception. Indeed perspective raises fundamental questions about the nature and limits of human perception/understanding of reality, whereby related problems have been puzzled over for 2000 years—and are still debated today.

Perspective is a foundational topic, having much in common with ‘theoretical’ subjects like algebra, geometry, and number theory. Still, it also has close links to physical disciplines like art, representation, scientific imaging/measuring instruments, etc. Perspective is a set of natural, 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 in a single model. Our primary objective is to identify all of the Goals, Classes, Categories, Components, Phenomena, Products, Methods, Forms, and Functions of Perspective; without worrying so much about the underlying philosophical questions (at least initially).

Visual Perspective is concerned with forming views of three-dimensional reality. Ergo understanding the different categories of space is of central importance if we wish to understand perspective.

Categories of Space (Mapping Relations)

Perspective seeks to reflect visual aspects of the Physical World (typically).

Perspective is concerned with obtaining views of space (of one category or another), and it deals with transformation of one kind of space to another kind of space. Whereby perspective happens when a three-dimensional Object located in three-dimensional Object Space (real, virtual, or imaginary) is transformed into a two or three-dimensional Image located in dimensional Image Space (real or virtual).

Perspective remains a complex topic because it involves the comparison of fundamentally different Categories of Space. For example, reconciliation of the 3D space of the Physical World (Physical Space), with the 2D space of Graphical Perspective (Graphical Space). Often, and despite a strong desire to attempt equality, this reconciliation is impossible to achieve completely; because one deals with dimensions that must map without any physically-based 1:1 correspondence (e.g. transform 3D space to a 2D space).

It is essential to realise that one kind of perspective will typically involve multiple types of space. Let us take the example of a person looking at a painting of distant mountains. The viewer creates a Visual Space using pictorial elements perceived from a Graphical Space (the painting), including an inherent Mathematical Space expressed by the artist as a Linear Perspective projection. The overall effect is an apparent (or illusionistic) perspective view of a Natural or Physical Space (ref. Environmental Perspective).

The upshot is that anyone who wishes to apply perspective to a visual problem has to decide first which Categories of Space are involved; before identifying which Perspective Categories, Components, Phenomena, Methods, and Forms are operating, and so to understand the generated Perspective Product(s). Ergo understanding the different Categories of Space, and operating processes of perspective, is of central importance if we wish to explain how and why the Optical, Visual and Represented Worlds appear as they do.

The Manifold Nature of Perspective

Technical Perspective is key to vision, spatial modelling, and creating appearances.

We have defined Technical Perspective as any systematic process that produces a detailed visual image, measurement, representation, model or view, of a three-dimensional object or scene. Whereby said Perspective Products are comprised of a specific set (or pattern) of Visual Features including points, lines, plane figures, solid shapes, shades, shadows, reflections, translucency, colour, texture, scale, etc.

Perspective prescribes how an object’s Visual Features appear from a particular location and angle-of-view, distance, etc; and according to a specific observation scenario. But it is often challenging to discover the root causes of even a simple perspective effect. This is because it is usually the case that we have several optical, visual, modelling, or representation-based Perspective Methods happening simultaneously. Our only hope is to identify and classify perspective changes to Visual Features (Perspective Components), and then analyse how each piece of the perspective ‘puzzle’ fits together to produce the visual world as we know it.

In any practical situation, we may have several different Categories of Perspective working together to produce the Products of Perspective. Accordingly, many different types of space are involved simultaneously. In a perspective process, we see a flow of Visual Features translated between different spaces that accordingly experience a series of visual transformations.

Hopefully, the reader begins to see how the different facets of perspective work together to produce perspective’s (frequently) manifold nature.

Perspective Instruments / Machines

Our discussions thus far have side-stepped an essential aspect of perspective: the use of instruments and machines to view, image, measure, model and represent visual aspects of the Physical World. 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 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 variety of perspective views. However, it is essential to realise that perspective instruments and machines are conceptualised, built, and operated, according to mathematically, geometrically, and logically correct principles. In other words, all such devices are enabled by valid perspective theory/methods.

Patently, perspective instruments and machines have the potential to add further complexity to the already complex perspective topic. But we should not be worried because often perspective instruments can simplify, expedite and clarify matters. This happens because perspective devices give us new choices regarding what we see, how, when and where. In the process, we are magnifying our natural visual capacities and boosting the efficiency, number, and usefulness of perspective images and techniques, measurements, models, etc.

Perspective Terminology

It is helpful to summarise Perspective Category Theory, in the form of the basic terminology that we shall employ to identify perspective categories, and to characterise perspective processes and outcomes.

We are proud to present the salient features—or fundamental principles—of our new Perspective Category Theory in the table below. In the pages of this site, it shall be our task to build out said theory and significantly—to develop a full Taxonomic Tree for all of the different categories of Optical Perspective.


Perspective ConceptDefinitionProcess / Outcomes
PerspectiveFormation of an Image—or a representational pattern—of a state of affairs present in a spatial reality.Image is formed by a range of natural and/or artificial processes.
ClassTwo main classes: Visual Perspective and Symbolic Perspective.Visual or Symbolic Image.
Visual Perspective (first type or not related to human vision)When a Visual Image is used to view, match or represent the visual appearance of a three-dimensional object/scene.Visual Image formed by a projection (optical perspective), analytical geometry (mathematical perspective), or a contact process (contact perspective).
Goal  (Ref. Visual Perspective)Viewing, matching, and making representations of a spatial reality.Perspective Products.
Optical PespectiveVisual Image of a three-dimensional reality created primarily using light (may involve real, virtual, or simulated light rays).Visual Image formed by optical method.
Technical Perspective (Ref. Optical Perspective)Systematic process that produces a detailed visual image, measurement, representation, model or view, of a three-dimensional object or scene.Visual Image is formed using optically, mathematically, geometrically, or logically correct, known, and consistent principles.
CategoryTechnical Perspective has six primary categories.Natural (includes Visual Perspective of second type or human vision), Mathematical, Graphical, Instrument, Forced, and Media Perspective(s).
World (types)Primary domains of operation for perspective (generally).Natural (Physical), Optical, Visual (2nd type), Represented World(s).
Spatial MappingPerspective can be defined in spatial terms as follows: A three-dimensional Object located in a three-dimensional Object Space (real, virtual, or imaginary) is transformed into a two or three-dimensional Image located in two or three-dimensional Image Space (real or virtual).Typically perspective is a staged mapping transformation, which may include different types of space, including one or more of the following: Natural (Physical), Visual (2nd type), Mathematical, Graphical, Optical, Instrument, Illusory (real or virtual), and Media space(s), etc.
Visual FeaturePerspective prescribes how an object’s Visual Features appear from a particular location and angle-of-view, distance, etc; and according to a specific observation scenario.Visual Features include points, lines, plane figures, solid shapes, shades, shadows, reflections, translucency, colour, texture, size, etc.
Components of Visual TransformationA particular instantiation of a Category of Perspective reflects a corresponding group of visual changes that occur while viewing/surveying/representing a three-dimensional scene (particular case).Apparent optical adjustments to Visual Features for an individual imaging scenario.
FormA number of different Perspective Forms are possible for each Perspective Category.Example: Graphical Perspective (e.g. Linear Perspective) can manifest itself in a variety of Forms, including in a drawing, painting, computer-generated image, virtual reality, etc.

Perspective Phenomena
(Visual Facets)











A general category of perspective demonstrates, and is recognised by, certain Perspective Phenomena or Visual Facets. The Perspective Phenomena refers to all of the intrinsic changes to Visual Features that occur according to a particular Category of Perspective and its inherent processes.
The Perspective Phenomena comprise, in each case, all of the generalised defining features of a particular Category of Perspective; including types such as Visual, Mathematical, Graphical, Instrument Perspective, etc. 
Patently each class of perspective will exhibit a unique set of Perspective Phenomena, whereby certain phenomena are shared (or embodied) by a number of different categories of perspective. Embodiment of the Perspective Phenomena may happen by certain naturally occurring visual processes, or else by human design, but irrespective of cause we refer to the instantiation of said phenomena as the Methods of Perspective.
MethodA Perspective Method is any practical or theoretical technique that aids in forming a detailed visual image, measurement, representation, model or view, of a three-dimensional object or scene.Typically one or more Perspective Methods are combined to render an image according to a particular Category of Technical Perspective. Practical examples include Perspective Instruments such as a lens, camera, the perspective window, planisphere, projector, computer, etc. Perspective Methods include all instrument design features plus operating methods. Examples of theoretical methods include a particular projection method/algorithm, vanishing point(s), field-of-view, projected scale etc.
ProductA detailed visual image, measurement, representation, model, or view, of a three-dimensional object or scene.Visual Image or related aspect.
FunctionViewing, prescribing, matching, modelling, exploring, representing, and mixing images, of a three-dimensional reality.Applied to multiple application areas.
Table A : Perspective Concepts



Figure 2: Perspective Category Theory

(Enlarge figure by opening in a separate window)


A theory is a systematic statement of the general principles—or laws—of a branch of knowledge. It is a scheme of ideas to explain a group of facts or phenomena. A theory is comprised of Things and Principles (causal Things), which must be adequately defined as Concepts and in terms of Type, Properties, and including also Context of usage/application

How does our burgeoning theory of perspective hold up according to these prescriptions? To answer this question, let us now summarise what has been achieved (thus far).

We have defined a comprehensive set of Claims—concerning what we believe are the fundamental Perspective Concepts lying behind all perspective phenomena. In other words, we have identified the universal principles or basic laws of perspective. But these are not yet proven, especially in light of a consensus of scientific opinion, which can only come with time and through a wide readership.

Armed with these strict logical definitions, we can develop and test a new theory for the entire subject matter of perspective. Cross your fingers! 

Conclusion

We have concluded our brief introduction to perspective methodology; previewing perspective concepts employed throughout this site. Further, we have developed the founding principles of Perspective Category Theory.

What have we learned? Only that perspective is by no means an old, abandoned, or dead subject. On the contrary, today, we see more types and applications of perspective than ever before. Perspective instruments such as telescopes, microscopes, cameras, televisions, computers, etc., take perspective methods to a new level of usefulness. The primary functions of perspective are significantly improved in scope, accuracy, and the sheer number of eminently practical application areas.

The primary perspective goals are certification of sightmeasurement, and representation, whereby we make accurate views, maps, and models. In this manner, we can develop and test real-world theories. Concordant with such developments has been using perspective to aid in the accurate mapping of environments, and creating new environments.

Overall, perspective is the preeminent way for humans to view, match, and represent a whole universe of visual complexity. Perspective has a fascinating past, exciting present, and promising future. By utilising advanced perspective methods/instruments, we vastly expand the field/range/depth of human vision. And given the amazing triumphs provided by the remarkable history of perspective, who can say what incredible heights perspective can take humanity to?

Prepare yourself for an invigorating ride as we embark on a fascinating journey into the marvellous and varied world(s) of perspective!