Perspective System

A Perspective System is an organised arrangement of components and processes operating together as a unit to view, form, capture, project, measure, represent, simulate, display or interpret spatial information.

A Perspective System can be extremely simple or highly complex. It may involve a single perspective process, or combine several Perspective Categories, Types, Principles, Methods and Forms within a longer image chain.

Examples range from the human eye viewing a physical scene, a camera forming an image, or a graphical perspective construction, to cinema, CAD, CGI, Computer Vision, Virtual Reality and large interconnected New Media systems.

Definition of Perspective System

The Dictionary defines a Perspective System as an organised arrangement of components and processes operating as a unit to perform one or more perspective operations.

These operations can include:

viewing;
forming an image;
capturing an image;
projecting;
measuring;
representing;
simulating;
displaying; and
interpreting spatial information.

A system may contain one or more Perspective Categories and functional classes and may itself form only one stage within a longer perspective image chain.

Perspective System as an Operating Unit

The defining characteristic of a Perspective System is that its components operate together as a functional unit.

Volume 1 describes such a system as possessing capabilities for:

image making;
image projection;
image analysis; or
image matching.

Many systems perform more than one of these functions.

Perspective System and Perspective Principle

A Perspective Principle identifies an underlying theoretical mechanism or relationship.

A Perspective System is the larger organised arrangement within which one or more such principles operate.

A central-projection system, for example, can embody principles concerning the relationship between spatial objects, centre of projection, projection rays, picture plane, Vanishing Points and projected image geometry.

The principle explains the relationship; the system provides the complete arrangement in which that relationship operates.

Perspective System and Perspective Method

A Perspective Method is a repeatable procedure applying one or more Perspective Principles.

A Perspective System can contain one method or several methods operating together.

For example, a graphical system may combine Central Projection, measuring-point methods, subdivision methods and a perspective grid. A digital system may combine three-dimensional modelling, virtual-camera projection, Perspective Matching and image processing.

The method is therefore an operating procedure within the larger Perspective System.

Perspective System and Perspective Process

A Perspective Process is the operation through which spatial information is viewed, imaged, projected, measured, transformed, represented, displayed or interpreted.

A Perspective System provides the organised arrangement through which one or more such processes operate.

Several processes may take place simultaneously or sequentially within one complete system.

Perspective System and Perspective Type

Perspective Category Theory distinguishes a Perspective Type as a particular method, system, process or subdivision.

A Perspective System can therefore itself define a Perspective Type in some circumstances, while in other cases a larger system may contain several Perspective Types.

The terms overlap because perspective terminology has historically been used for methods, systems, processes and resulting Forms without consistently distinguishing between them.

Perspective System and Perspective Form

A Perspective System should not be confused with the Perspective Form it produces.

Perspective System: the organised arrangement producing, projecting, analysing or interpreting spatial information.
Perspective Form: the resulting visual, optical, geometrical or spatial appearance.

A system may produce Linear, Parallel, Curvilinear, Spherical or other Forms, while similar Forms can sometimes arise through different perspective systems.

Perspective System and Perspective Instrument

An instrument is not necessarily the complete Perspective System.

A camera, lens, projector, telescope or microscope can form an important component within a Perspective System, but the complete system can additionally contain:

the spatial scene or target;
the imaging or projection process;
image or picture surfaces;
processing stages;
displays;
measurement or matching procedures; and
the final observer or interpreting system.

The Perspective System is therefore the organised functional arrangement rather than simply the apparatus used at one stage.

Perspective System and Perspective Model

A Perspective Model is a particular kind of Perspective System that enables the construction of a comprehensive three-dimensional visual representation of a spatial reality.

A virtual Perspective Model may incorporate:

three-dimensional geometry;
mathematical modelling;
material properties;
optical processes;
linked images;
multiple viewpoints;
multiple scales; and
multiple times.

Examples include CAD and CGI models, GIS environments, Computer-Vision reconstructions and Virtual, Augmented, Mixed and Extended Reality systems.

Perspective Categories within a System

A Perspective System can involve one or more of the principal Perspective Categories:

Natural Perspective;
Visual Perspective Type 1;
Visual Perspective Type 2;
Optical Perspective;
Mathematical Perspective;
Graphical Perspective;
Instrument Perspective;
Simulated Perspective; and
New Media Perspective.

These categories identify the principal source or mode through which particular processes within the system operate.

The Two Directional Classes within Perspective Systems

Perspective processes operate within two principal directional classes:

Viewing or Imaging Class: light, visual information or spatial data passes from an object, scene or existing image towards an eye, sensor, image plane or imaging system.
Projecting Class: light, images, shadows, lines or spatial information are projected forwards from a source or representational system into physical, graphical, optical or simulated space.

A Perspective System may use one of these directions or both.

Viewing or Imaging Perspective Systems

A Perspective System operating principally within the Viewing or Imaging Class forms or captures information from a spatial target.

Examples include direct human vision, cameras, telescopes, microscopes and other imaging systems.

The process moves from spatial reality towards an image, view, measurement or perceptual result.

Projecting Perspective Systems

A Perspective System operating principally within the Projecting Class sends light, image information, lines, shadows or another representation forwards towards a target space or surface.

Examples include:

cinema projection;
digital projection;
projection mapping;
shadow projection; and
graphical projection from a station point.

The directional logic is therefore the reverse of the image-forming or capturing class.

Single Perspective Systems

Volume 1 distinguishes Single Perspective as a system, image or image chain involving one principal Perspective Category.

The Dictionary similarly defines Single Perspective or Single Category Perspective as an arrangement in which only one category or perspective system is involved in producing the relevant view or image.

Purely single-category systems are comparatively unusual because as soon as an image is captured, processed, displayed or viewed through additional systems, further Perspective Categories may enter the image chain.

Composite Perspective Systems

Composite Perspective occurs when two or more Perspective Categories operate sequentially or in combination within one process, system, image or environment.

A Composite Perspective System can therefore contain several distinct perspective transformations while still functioning as one complete arrangement.

A typical image chain might be:

Natural scene → Optical Perspective → Instrument Perspective → New Media processing → display system → Visual Perspective Type 2.

The complete sequence can be treated as one Composite Perspective System.

Mixed Perspective Systems

Mixed Perspective describes a system in which the two directional classes — Viewing or Imaging and Projecting — both operate.

Mixed Perspective is therefore not a third basic directional class. The two basic classes remain Viewing or Imaging and Projecting.

Examples can include cinema, Virtual Reality, Augmented Reality and certain mirror or display systems in which image formation, viewing, redirection and projection operate together.

Single, Composite and Mixed Describe Different System Relationships

The distinction between these terms is important:

Single Perspective: one principal Perspective Category is involved.
Composite Perspective: two or more Perspective Categories operate in sequence or combination.
Mixed Perspective: both directional classes — Viewing or Imaging and Projecting — operate within the system.

A system can therefore be Composite and Mixed at the same time because the two terms describe different aspects of its organisation.

Category Chaining within a Perspective System

Category Chaining occurs when several Perspective Categories operate sequentially.

An image produced at one stage becomes the input or target of another perspective stage.

A camera image, for example, can become the target of digital processing; the processed image can then become the input to a display; and the displayed image subsequently becomes the target of the human visual system.

The individual stages may be considered separate Perspective Systems while the complete chain can also be analysed as one larger Composite Perspective System.

Object Space and Image Space within a Perspective System

A Perspective System normally relates an object or target space to an image or perspective space.

Object or target space contains the spatial object, scene, image or information upon which the perspective operation acts.

Image or Perspective Space contains the resulting view, image, model, measurement or spatial appearance.

In a chained system, one system’s image space can become the target space of the next system.

The Perspective Image Chain

The concept of the image chain is central to understanding complex Perspective Systems.

Instead of assuming that a final viewed image has been produced through one isolated act, the chain identifies the succession of transformations through which spatial information passes.

A chain may contain:

a physical spatial scene;
optical image formation;
Instrument Perspective;
digital processing;
graphical or mathematical transformation;
projection or screen display; and
human visual perception.

Each stage can preserve, modify, add, remove or transform aspects of the previous perspective information.

Cinema as a Perspective System

Volume 1 uses cinema as a clear example of a complex Perspective System.

The original scene may involve Natural Perspective. A camera forms an image through Optical and Instrument Perspective. Graphical and New Media processes may subsequently modify the image. A projector or display then presents it, after which the resulting image is viewed through Visual Perspective Type 2.

The image therefore passes through several interconnected systems and categories before reaching the final observer.

The Camera as Part of a Perspective System

A camera provides an important example of an image-forming Perspective System.

Its spatial viewpoint, viewing direction, Field of View, lens, aperture, image surface and recording process work together to form and capture an image of spatial reality.

However, a camera can itself form only one component within a larger system containing later processing, display and human viewing stages.

Perspective Imager or Ray Sorter

The Dictionary uses the term Perspective Imager / Ray Sorter for the image-forming component of a Perspective System.

In ordinary physical imaging, light from spatial object points travels in many directions. A sharp imaging system must organise or select the appropriate rays so that light from each object point is related to a corresponding image point.

The eye and camera lens perform such image-forming functions within their respective systems.

The concept helps distinguish the mechanism that forms the image from the larger Perspective System of which it is a component.

The Human Visual System as a Perspective System

Human vision provides a natural Perspective System in which optical and perceptual processes operate together.

Light from spatial reality enters the eye and forms retinal images, while the visual system interprets the resulting information according to viewpoint, apparent size, shape, position, depth cues, acuity and other visual conditions.

This retinal and perceptual process belongs to Visual Perspective Type 2.

Graphical Perspective Systems

A Graphical Perspective System employs drawing, painting, diagramming, drafting or related methods to represent spatial reality.

Linear Perspective can function as such a system, applying geometrical principles through a defined arrangement of viewpoint, object space, picture plane, projection directions and image construction.

Parallel, Axonometric, Oblique, Curvilinear and Spherical Perspective can employ different graphical systems and methods according to their respective projection principles.

Linear Perspective as a System and a Form

Linear Perspective demonstrates an important ambiguity in perspective terminology.

It can describe a system or method for producing an artificial or graphical perspective representation, while the same term can also describe the geometrical Form produced by a natural, optical, photographic or computational process.

The intended meaning — system, method or resulting Form — should therefore be made clear from context.

Computer and Digital Perspective Systems

Computer and Digital Perspective systems can combine mathematical, graphical, imaging and New Media processes within one computational arrangement.

A digital three-dimensional model can contain spatial geometry, a virtual camera, projection rules, image-surface parameters, lighting and display processes.

The same digital spatial model can then generate many different perspective views without reconstructing the underlying model for each viewpoint.

New Media Perspective Systems

New Media Perspective provides some of the most complex contemporary examples of Perspective Systems.

A developed New Media system can connect views derived from Natural, Instrument, Mathematical, Graphical and other perspective categories and then:

link them;
order them;
construct them;
match and cross-match them;
combine or mix them;
overlay them;
index them; and
allow them to be explored interactively.

The resulting system can extend perspective beyond the single fixed image towards a connected spatial-information environment.

Multi-View Perspective Systems

A Multi-View Perspective System combines information obtained from several viewpoints or viewing directions.

Each individual view contains only partial information about the spatial object or scene. Linking and registering several views can therefore provide a more comprehensive representation.

Volume 1 identifies the integration of large numbers of views from different viewpoints, directions, scales and times as an important challenge for advanced New Media Perspective Systems.

Multi-Scale Perspective Systems

A Perspective System can also organise spatial information across several scales.

This is important because the visible and measurable Form of an object can change with projection scale and resolution.

A developed Multi-Scale Perspective System can therefore connect views ranging across different spatial scales rather than treating one fixed scale as a complete representation of reality.

Multi-Time Perspective Systems

Perspective Systems can additionally organise views and images through time.

Volume 1 proposes Multi-Time Perspective as a means of capturing, recording, linking and navigating processes operating at different temporal rates.

A future Multi-Time system could connect differently indexed time flows so that spatial change can be explored across several temporal scales.

Extended Perspective Systems

The Dictionary identifies an Extended Perspective System as a larger unified framework combining existing perspective systems.

Such a system can combine or integrate views from:

Linear Perspective;
Parallel Perspective;
Cylindrical Perspective;
Curvilinear Perspective;
Spherical Perspective; and
other perspective systems.

The goal is not simply to place several images beside one another, but to combine, register, cross-match and integrate them within a larger navigable framework.

Google Maps and Google Earth as New Media Perspective Systems

Volume 1 identifies systems such as Google Maps and Google Earth as examples of contemporary New Media Perspective Systems.

Such systems can combine:

maps;
satellite imagery;
aerial imagery;
panoramic photographs;
terrain information;
three-dimensional models;
multiple viewpoints;
multiple scales; and
images recorded at different dates.

These components are organised within a common navigable spatial framework and may additionally generate views from computationally constructed viewpoints.

Virtual and Augmented Reality Systems

Virtual and Augmented Reality provide further examples of complex Perspective Systems.

A Virtual Reality system can combine a digital spatial model, moving viewpoint, virtual camera, stereoscopic display and human Visual Perspective Type 2.

An Augmented Reality system can first image physical spatial reality and then introduce graphical or digital information into the resulting view.

Such systems frequently combine several Perspective Categories and both principal directional classes.

Perspective Systems and Field of View

Field of View is a fundamental variable in many Perspective Methods, instruments and systems.

It determines the angular extent of spatial reality included within a particular outward-looking perspective image or view.

Perspective systems have repeatedly been developed to expand beyond the limited field represented by a conventional narrow view, leading to panoramic, cylindrical, spherical, multi-view and immersive systems.

Perspective Systems and Viewpoint

The viewpoint is another fundamental system variable.

A view of a spatial object can change substantially as the observer or camera changes position or Direction of Vision.

A single-view system records or represents one selected viewpoint, while Multi-View and moving-viewpoint systems can connect or generate a succession of different spatial aspects.

Perspective Systems and Scale

A Perspective System also operates at a particular projection scale and resolution.

The size, Form and amount of structural information visible within a perspective image therefore depend partly upon the scale and resolving capability of the system.

Volume 1’s Scale-Shape-Size Problem demonstrates why perspective cannot be interpreted solely through the Size–Distance Law. Viewpoint, orientation, projection geometry, scale, resolution, shape sufficiency and measurement method all contribute to the resulting image.

Functions and Goals of Perspective Systems

Perspective Systems can serve several broad functions or goals:

View — observe or capture spatial reality;
Match — measure, compare, survey, classify or cross-match spatial information;
Represent — copy, model, index, link, mix or explore spatial reality;
Illusion — create an alternative or false spatial appearance; and
Immersion — create the apparent experience of being located within a represented spatial environment.

These are functions, goals or outcomes of Perspective Systems rather than additional Perspective Classes.

Products of a Perspective System

A Perspective System can produce many different kinds of outcome.

Volume 1 identifies products including:

visual images;
views;
measurements;
representations; and
models.

The information extracted from such products may concern whole-part structure, figure, size, scale, position, state or activity within the original spatial reality.

Perspective Systems Can Overlap

Perspective Systems should not be treated as rigidly isolated structures.

The Dictionary emphasises that Perspective Categories and systems frequently:

overlap;
combine;
operate sequentially;
exchange images or information; and
change category as an image passes between physical, optical, graphical, computational and perceptual processes.

Perspective Category Theory provides a framework for identifying these different stages and relationships.

A System Can Be a Component of a Larger System

The boundaries of a Perspective System depend partly upon the level at which the situation is being analysed.

A camera can be analysed as a Perspective System in its own right. The same camera can also be one component of a larger cinematic system containing editing, digital effects, display and human viewing.

That cinematic system can in turn become one component of an even larger networked or interactive media environment.

A Perspective System can therefore be nested within another Perspective System.

System Boundaries Depend on the Question Being Asked

The practical boundary of a Perspective System should be chosen according to the problem being analysed.

If the question concerns optical image formation, the relevant system might consist primarily of scene, lens and image plane. If the question concerns how a photograph is finally perceived, the analysis may need to include capture, processing, display, viewing conditions and the human visual system.

Perspective Category Theory allows these different levels to be separated without losing their relationship to the complete process.

Natural and Artificial Perspective Systems

Perspective Systems may arise through natural processes or through deliberately constructed artificial arrangements.

Natural systems include physical and optical relationships within spatial reality and the human visual system.

Artificial Perspective Systems can include Mathematical, Graphical, Instrument, Simulated and New Media processes.

Complex systems can combine natural and artificial processes within one complete image chain.

Perspective Systems Can Produce Similar Forms by Different Means

The visible Perspective Form does not uniquely identify the system that produced it.

A Linear Perspective Form, for example, can occur in direct optical vision, photography, graphical construction or computer-generated imagery.

The resulting line geometry may be related while the underlying Perspective Categories, methods and system components are very different.

This is one reason why perspective theory must distinguish the process or system from the resulting image Form.

The Same System Can Produce Different Perspective Forms

The converse is also possible: one Perspective System can generate several different Perspective Forms.

A computer model, for example, can potentially generate:

Linear Perspective;
Parallel Perspective;
Orthographic views;
Axonometric views;
Curvilinear Perspective;
Spherical Perspective; and
multiple changing viewpoints.

The Perspective System and resulting Perspective Form are therefore related but analytically distinct.

Perspective Systems and Visual Elements

Within particular Linear Perspective arrangements, the Dictionary also identifies the Visual Element of a System of Parallel Lines.

This is the line belonging to a directional system of parallels along which, or parallel to which, the observer sights. It can coincide with the observer’s Line of Sight in a particular arrangement but may also be positioned off-centre within the view.

The concept demonstrates that even within one larger Perspective System, separate directional sub-systems can possess their own geometrical organisation.

Perspective Systems and Perspective Category Theory

Perspective Category Theory provides the framework for analysing Perspective Systems.

It distinguishes:

Perspective Categories;
the two directional Classes;
Perspective Types;
Perspective Forms;
Perspective Principles;
Perspective Methods;
Perspective Processes;
functions and goals; and
outcomes or products.

These distinctions make it possible to analyse a complex Perspective System without treating every component, operation and visible result as though they were the same kind of thing.

Why Perspective Systems Become Complex

Modern perspective images commonly pass through many separate transformations.

A physical scene may be:

viewed;
optically imaged;
captured by an instrument;
digitised;
mathematically transformed;
combined with graphical imagery;
displayed or projected;
viewed from another physical position; and
finally interpreted perceptually.

A system-level analysis is therefore necessary whenever the final visible image cannot be explained adequately by reference to only one isolated Perspective Method or Category.

Common Misconceptions about Perspective Systems

A Perspective System is not simply a Perspective Method. A method is a repeatable procedure; a system is the larger organised arrangement in which one or more methods operate.
A Perspective System is not the same as a Perspective Principle. A principle identifies an underlying mechanism; a system embodies and applies principles.
A Perspective System is not necessarily one instrument. An instrument may be only one component within a larger image chain.
A Perspective System is not the same as its resulting Perspective Form. Similar Forms can arise from different systems, and one system can produce several Forms.
A Perspective System does not necessarily belong to only one Perspective Category. Complex systems commonly contain several categories.
A Perspective System can use either or both directional Classes. Viewing or Imaging and Projecting remain the two fundamental directions.
Mixed Perspective is not a third basic Class. It describes a system in which both directional Classes operate.
Composite Perspective and Mixed Perspective are not identical. Composite concerns multiple Perspective Categories; Mixed concerns the operation of both directional Classes.
A Perspective System does not have to produce a drawing. It can form images, measurements, models, projections, matches or interpretations.
Perspective Systems can be natural as well as artificial. The human visual system and direct optical processes are as relevant to perspective theory as graphical and computer systems.
A system boundary is not always fixed. One Perspective System may form a component or stage within a larger system.
Modern digital systems do not eliminate older Perspective Principles. They can calculate, combine and extend principles previously implemented optically, mathematically or graphically.
A final perspective image may contain a long history of transformations. Understanding the image may therefore require analysis of the entire image chain.

Why Perspective System Matters

The concept of a Perspective System matters because perspective rarely consists of one isolated geometrical rule or drawing procedure.

A complete perspective situation can involve spatial reality, viewpoint, optical processes, mathematical relationships, graphical transformations, instruments, computers, image surfaces, displays and human visual perception, all operating together or sequentially.

Thinking in terms of systems makes it possible to identify where each transformation occurs and which Perspective Category, Class, Principle, Method, Process and Form belongs to each stage.

This is particularly important for contemporary perspective technologies such as cinema, digital photography, CAD, CGI, Computer Vision, GIS, Virtual Reality, Augmented Reality, Mixed Reality and interconnected New Media environments, where the final view can be the outcome of many interdependent perspective processes.

Understanding Perspective System therefore provides a foundation for understanding Perspective Principle, Perspective Method, Perspective Process, Perspective Type, Perspective Form, Perspective Category, Perspective Class, Perspective Model, Perspective Image Chain, Perspective Imager, Viewing or Imaging Perspective, Projecting Perspective, Single Perspective, Composite Perspective, Mixed Perspective, Category Chaining, Category Overloading, Multi-View Perspective, Multi-Scale Perspective, Multi-Time Perspective, Extended Perspective Systems, Computer Perspective, Digital Perspective and New Media Perspective.

Explore Theory

Explore the principal theories, classifications, types, forms, geometries, spatial concepts and visual phenomena of perspective.