Perspective Space

Perspective Space is the space associated with the formation, representation, transformation or perception of a perspective image or view.

In its principal modern sense, Perspective Space is synonymous with Image Space: the space in which a resulting image, view, model or representation is formed, located or perceived.

The term can also describe the transformed spatial appearance produced when a Perspective Process relates an original Object or Target Space to a resulting Image or Perspective Space.

The fundamental relationship can therefore be expressed as:

Object or Target Space → Perspective Process → Image or Perspective Space

Perspective Space is consequently not the original spatial object or scene itself. It is the spatial organisation associated with its resulting image, view, model, representation or transformed appearance.

Perspective Space within Perspective Category Theory

Within Perspective Category Theory (PCT), Perspective Space provides a general way of identifying the spatial result associated with a Perspective Process.

A Perspective Category identifies the principal source or mode through which that process operates. One or more categories may transform an Object or Target Space into an Image or Perspective Space.

For example, spatial information may pass through:

  • Natural Perspective;
  • Visual Perspective;
  • Optical Perspective;
  • Mathematical Perspective;
  • Graphical Perspective;
  • Instrument Perspective;
  • Simulated Perspective; or
  • New Media Perspective.

The resulting Perspective Space therefore depends partly upon the original spatial reality and partly upon the Perspective Methods, Processes and Categories through which that reality is viewed, measured, transformed or represented.

Perspective Space and Image Space

In its preferred general sense:

Perspective Space = Image Space

It is the space in which a resulting:

  • image;
  • view;
  • model; or
  • representation

is formed, located or perceived.

This Perspective Space may be optical, visual, graphical, mathematical, instrument-generated or digital.

The term therefore extends beyond the traditional idea of a flat perspective drawing and can describe many different forms of spatial imaging and representation.

The Transformation Sense of Perspective Space

Perspective Space also has a second important meaning: the transformed spatial appearance produced by a Perspective Process.

When Object or Target Space is transformed into Image or Perspective Space, some spatial properties may be preserved while others may be:

  • reduced;
  • concealed;
  • compressed;
  • rescaled;
  • repositioned; or
  • distorted.

Thus:

Object Space → Perspective Transformation → transformed Perspective Space

This transformation is one of the central problems of perspective because the geometry and appearance of the resulting space need not correspond exactly to those of the original spatial reality.

The Historical Pictorial or Fictive Sense

The term Perspective Space has also been used historically in a narrower art-theoretical sense.

In this usage, it refers to the represented or fictive space suggested within a picture or image.

A painting constructed using Linear Perspective, for example, may appear to open onto a three-dimensional spatial world even though the physical picture surface remains flat.

This represented depth may be called pictorial, fictive or perspective space.

The Dictionary treats this as a legitimate but narrower historical meaning and prefers the broader term Image or Perspective Space for general analytical use.

Perspective Space is not Object Space

Perspective Space should be distinguished from Object Space.

Object or Target Space contains the original object, scene or spatial information towards which a Perspective System is directed.

Perspective Space contains, expresses or presents the resulting transformed image, view, model or representation.

The distinction can therefore be expressed as:

Object Space → original spatial relationships
Perspective Space → resulting or transformed spatial relationships

The same Object Space may produce many different Perspective Spaces according to the viewpoint, projection method, imaging system, surface, scale or other Perspective Process involved.

Correspondence between Object Space and Perspective Space

Perspective attempts to establish systematic relationships between Object Space and Perspective Space.

However, the relationship is not necessarily one-to-one.

A three-dimensional spatial object or scene may be represented in a two-dimensional image. Some spatial information can therefore be reduced or lost.

Perspective may also alter:

  • apparent size;
  • apparent shape;
  • position;
  • orientation;
  • depth;
  • line direction;
  • visibility; and
  • scale relationships.

The resulting Perspective Space may therefore correspond systematically to the target while nevertheless differing significantly from it.

Perspective Space and Primary and Secondary Geometry

Volume 1 distinguishes Primary Geometry from Secondary Geometry.

Primary Geometry concerns the three-dimensional arrangement of points, lines, planes and projection relationships in Object or Target Space.

Secondary Geometry concerns the arrangement of corresponding points, lines, shapes and projections within Image or Perspective Space.

Thus:

Primary Geometry → Object Space
Secondary Geometry → Image or Perspective Space

The distinction is important because a perspective representation can sometimes be constructed using Secondary Geometry without reconstructing the complete Primary Geometry of the original spatial reality.

Geometrical Perspective Space

Geometrical Perspective Space concerns the mathematical modelling of the dimensional space of a spatial reality.

The spatial reality being modelled may be:

  • physical;
  • visual;
  • artificial;
  • imaginary;
  • mathematical; or
  • digital.

Geometrical Perspective Space may therefore describe the coordinate, dimensional or projective relationships through which spatial information is represented mathematically.

It provides an analytical framework for relating points, lines, planes, objects and scenes across Object and Image Spaces.

Graphical Perspective Space

Graphical Perspective Space concerns the construction of the appearance of spatial reality through graphical representation.

Examples include:

  • perspective drawings;
  • paintings;
  • technical representations;
  • Linear Perspective constructions;
  • Parallel Perspective constructions; and
  • other graphical projections.

The resulting represented space may correspond to an existing physical scene, an artificial environment or a completely imagined spatial reality.

Graphical Perspective Space therefore describes the spatial appearance constructed within or through a graphical image.

Natural or Physical Perspective Space

Natural or Physical Perspective Space concerns viewing or imaging the physical space of natural reality.

It includes spatial relationships associated with environmental and visual optics and with the direct observation of physical spatial objects and scenes.

A natural spatial environment may function as Object or Target Space, while its corresponding optical or visual image becomes a resulting Perspective Space.

This distinction is especially important in direct vision, where physical spatial reality, retinal imagery and the resulting Visual Space are related but should not be treated as identical.

Optical Perspective Space

Optical Perspective Space is associated with natural, optical or visual reality.

An Optical Space can operate either as a Target Space or an Image Space depending upon the particular Perspective System being analysed.

For example, a camera may be directed towards a physical optical scene and form a new optical image on a sensor or image surface.

That resulting image can subsequently become the target of another optical or visual process.

The role of an Optical Space therefore depends upon its position within the complete image chain.

Visual Perspective Space

Visual Perspective Space is the image or spatial organisation formed and experienced through the human visual system.

The Dictionary identifies it particularly with Visual Perspective Type 2.

Visual Perspective Space may include experienced relationships of:

  • direction;
  • position;
  • distance;
  • depth;
  • apparent size;
  • apparent shape;
  • orientation; and
  • spatial arrangement.

Visual Perspective Space should not simply be equated with physical space or the retinal surface. It represents a further visual or perceptual stage within the complete perspective process.

Instrument Perspective Space

Instrument Perspective Space concerns spatial reality as viewed, measured, surveyed, imaged or otherwise addressed through an instrument.

An instrument may form its own intermediate Image Space.

Examples can include:

  • camera images;
  • telescopic images;
  • microscopic images;
  • surveying images;
  • scientific imaging systems; and
  • other instrument-generated representations.

An Instrument Perspective Space may form only one stage in a longer image chain before further processing, display or human observation occurs.

New Media Perspective Space

New Media Perspective Space concerns digital and computational representations of spatial reality.

It may participate in processes that:

  • generate images;
  • process images;
  • compare or cross-match images;
  • construct digital models;
  • combine views;
  • display spatial information; or
  • produce interactive environments.

A natural Object Space may therefore pass through optical and instrument processes into a digital Perspective Space before eventually being displayed and visually perceived.

Simulated Perspective Space

Simulated Perspective Space concerns the creation or viewing of a false, altered or deliberately constructed spatial reality.

The spatial appearance may be produced:

  • physically;
  • graphically;
  • optically;
  • instrumentally; or
  • computationally.

Forced Perspective provides a familiar example in which spatial size, scale or recession can be deliberately manipulated to produce a false apparent space.

Simulated Perspective Space therefore demonstrates that Perspective Space need not reproduce an ordinary physical spatial arrangement.

Virtual Perspective Space

Virtual Perspective Space can occur in more than one form.

The Dictionary identifies:

  • optical virtual space, such as mirror space; and
  • digital virtual space, such as Virtual or Augmented Reality space.

In either case, a Virtual Space may serve as a Target Space or as an Image Space within a particular Perspective System.

A mirror, for example, produces an apparent space associated with reflected imagery, while a computer system may generate a navigable or interactive virtual environment.

Perspective Space across the Image Chain

A complete Perspective Image may pass through several different kinds of space.

For example:

Physical Object Space → Optical Space → Instrument Image Space → Digital Perspective Space → Display Space → Visual Perspective Space

These spaces need not be completely separate.

Each may function as an intermediate stage through which spatial information is formed, transformed, recorded, processed or perceived.

The final image or view may therefore be the product of several linked Perspective Spaces rather than a simple direct transfer from Object Space to a single Image Space.

Intermediate Perspective Spaces

Volume 1 emphasises the importance of Intermediate Spaces.

These are transitional spatial representations occurring between the original Target Space and the final Image Space.

A camera may form one Image Space, digital processing another, a display another and the human visual system another.

Thus:

Target Space → Intermediate Perspective Spaces → Final Image / Visual Space

Understanding a final Perspective Image or View may therefore require identifying the sequence of spatial transformations that produced it.

When Perspective Space becomes Target Space

A Perspective Space can change its analytical role within a chained Perspective Process.

An image that is the result of one process may become the target of another.

For example:

physical scene → photograph → scanned image → digital transformation → displayed image

The photograph begins as an Image or Perspective Space but becomes a Target Space when it is subsequently scanned or processed.

Thus:

one system’s Image Space may become another system’s Target Space.

This relationship is especially important in Composite Perspective and Category Chaining.

Transformed Perspective Spaces

Perspective Spaces may be deliberately or naturally transformed to support viewing, matching, representation, illusion, immersion and other visual effects.

The Dictionary identifies many forms of transformed Perspective Space, including:

  • Accelerated or Forced Space;
  • Anamorphic Space;
  • Blended Space;
  • Combined Space;
  • Composite Space;
  • Convergent Space;
  • Divergent Space;
  • Fragmented or Split Space;
  • Invisible Space;
  • Manifold Space;
  • Mirror or Virtual Space;
  • Multi-Plane Space;
  • Multi-Scene Space;
  • Multi-View Space;
  • Parallel or Paraline Space;
  • Simulated Space;
  • Spherical Space;
  • Synthetic Space;
  • Virtual-Reality Space;
  • Augmented-Reality Space; and
  • Volume-Display Space.

These demonstrate the very wide range of spatial organisations that may result from Perspective Processes.

Blended, Combined and Composite Space

Several transformed Perspective Spaces correspond closely to relational concepts within Perspective Category Theory.

Blended Space combines two or more spatial scenes, views or Image Spaces so that their boundaries become partly or wholly indistinct.

Combined Space presents two or more distinct views, scenes or forms of space together within one image or environment.

Composite Space results when several Perspective Categories, Processes or image-forming stages operate together or sequentially.

These terms identify different ways in which multiple spatial structures can contribute to a final Perspective Space.

Manifold and Multi-View Space

Manifold Space occurs when two or more spatial views occupy the same visual field, as when reflection and transmission are simultaneously visible through glass.

Multi-View Space occurs when one object or scene is represented from several viewpoints, directions or viewing positions within a single image, model or interactive system.

These examples show that Perspective Space need not correspond to a single viewpoint or a single continuous spatial representation.

Parallel and Convergent Perspective Space

The geometry of a Perspective Space may also differ according to the projection system employed.

In Parallel or Paraline Space, principal sets of parallel lines remain parallel in the represented image.

In a Convergent Perspective Space, lines, forms or apparent sizes may converge or diminish with represented distance.

Different Perspective Systems can therefore map the same Object Space into markedly different Perspective Spaces while each remains internally systematic according to its own rules.

Spherical Perspective Space

Spherical Perspective Space is organised, viewed or represented in relation to a spherical field, surface or system.

It differs from ordinary planar Perspective Space because spatial directions and image relationships are organised over or within a spherical geometry rather than a single flat picture plane.

Spherical Perspective is therefore especially relevant to wide-field, panoramic and surrounding visual systems in which the geometry of a conventional planar image is insufficient to describe the complete represented field.

Perspective Space and Perspective Form

Perspective Space and Perspective Form are closely related but should be distinguished.

Perspective Space concerns the spatial domain or transformed spatial organisation in which the image, view or representation exists.

Perspective Form concerns the particular visual, optical, geometrical or spatial appearance produced within that space.

Thus:

Perspective Space → where or within what spatial organisation the result exists
Perspective Form → how the resulting spatial relationships appear

One Perspective Space can therefore contain many different Perspective Forms.

Perspective Space and Perspective Image / View

A Perspective Image / View is a visual outcome produced through a Perspective Process.

Perspective Space is the space in which that image or view is formed, located, represented or perceived.

The distinction can therefore be expressed as:

Perspective Image / View → visual product
Perspective Space → spatial organisation containing or defining that product

A Perspective Image can consequently be understood only in relation to the Image or Perspective Space in which its points, lines, surfaces, forms and depth relationships are organised.

Perspective Space and Spatial Knowledge

Perspective Space provides a means through which spatial reality can be viewed, represented, measured, compared and interpreted.

However, a Perspective Space is normally a transformed representation or model of a target rather than a perfect duplication of it.

Volume 1 emphasises that perspective commonly attempts to reconcile different kinds of space, particularly the three-dimensional physical world with two-dimensional visual or represented spaces.

Perfect correspondence may be difficult because information can be lost or transformed through viewpoint, projection, scale, shape, size and other Perspective Phenomena.

Understanding Perspective Space therefore requires asking not only what appears in the image, but also how the spatial relationships of the original target were transformed to produce that appearance.

Why Perspective Space matters

Perspective Space provides a common concept for understanding the many spatial results produced through natural, optical, graphical, mathematical, instrument, simulated and digital Perspective Processes.

It helps distinguish:

  • Object Space from Image Space;
  • the spatial target from its representation;
  • original geometry from transformed geometry;
  • physical space from graphical or visual space;
  • primary geometry from secondary geometry;
  • a single Perspective Space from chained Intermediate Spaces;
  • ordinary spatial representation from transformed or simulated spaces; and
  • the Perspective Image itself from the spatial organisation in which it is formed or perceived.

Perspective Space is therefore the space in which a Perspective Image, View, Model or Representation is formed, located or perceived, and in its transformation sense the spatial appearance produced when Object or Target Space is transformed through a Perspective Process.

Related Perspective Topics

Object Space →
Image Space →
Perspective Object / Scene →
Perspective Image / View →
Perspective Process →
Perspective Form →