Perspective and Illusion

Perspective and Illusion are closely connected because perspective determines how spatial reality appears, while illusion occurs when that appearance produces a false, altered, ambiguous or misleading impression of the underlying reality.

A Perspective Illusion can make an object or scene appear larger or smaller, nearer or farther away, deeper or flatter, differently positioned, differently shaped, transparent, invisible, floating, extended into space, or located within an apparently different spatial environment.

Perspective has consequently been used for thousands of years not only to view, image, measure and represent spatial reality, but also to create convincing illusions of it — from painted architecture and theatrical scenery to mirrors, photography, cinema, holography, projection mapping, Virtual Reality and contemporary digital environments.

The crucial distinction is that perspective itself is not necessarily an illusion. Perspective describes real relationships between spatial objects, viewpoints, optical processes, projections and resulting images. An illusion arises when those relationships or their resulting visual information are interpreted as indicating a spatial reality that differs from the actual physical, geometrical or represented arrangement.

What Is a Perspective Illusion?

A Perspective Illusion occurs when the resulting view or image produces a false or misleading impression of spatial reality.

Volume 1 defines Perspective Illusion in relation to optical, geometrical, physiological and psychological factors. The resulting illusion commonly affects the apparent:

  • size of an object;
  • depth of a scene;
  • position of an object;
  • place or apparent location of the observer or object;
  • shape or dimensionality of a Form;
  • distance between objects;
  • transparency or opacity of Forms; or
  • more generally, the apparent geometry or optical character of a spatial scene.

The apparent spatial reality may therefore differ substantially from the physical or geometrical reality that produced it.

Perspective Phenomenon and Perspective Illusion Are Not the Same

A fundamental distinction must be made between a Perspective Phenomenon and a Perspective Illusion.

Perspective Phenomena are changes of visual appearance that arise through defined spatial, optical, geometrical or perceptual conditions. Examples include:

  • Diminution of Size;
  • Foreshortening;
  • line convergence;
  • Vanishing Points;
  • Diminution of Form;
  • Gradient of Acuity;
  • Gradient of Colour;
  • Gradient of Chiaroscuro;
  • texture gradients;
  • occlusion; and
  • changes in apparent shape or position.

These effects can be entirely normal consequences of viewing or imaging spatial reality. They become components of an illusion when their spatial meaning is misinterpreted, deliberately manipulated or presented in an arrangement that produces a false apparent reality.

Converging railway tracks, for example, are a normal perspective phenomenon. The physical rails remain parallel. An illusion would arise if the projected convergence were interpreted or manipulated so that the apparent spatial structure differed from the actual arrangement.

Illusion Is a Function or Goal of Perspective

Perspective Category Theory does not treat illusion as an additional basic directional Class.

The two basic directional Classes remain:

  • Viewing or Imaging; and
  • Projecting.

Creating illusion is instead one of the important functions or goals of perspective, alongside viewing, imaging, projecting, measuring, matching, representing and producing immersion.

The Dictionary defines the related Illusion or Immersion Function as creating an impression of spatial depth, altered geometry, presence or immersion within an artificial, simulated or represented environment.

The Four Principal Types of Perspective Illusion

The Dictionary and Volume 1 distinguish four principal types of optical Perspective Illusion:

  1. Visual Perspective Illusion — a false or perceptually adjusted direct view of physical reality.
  2. Graphical Perspective Illusion — a false apparent spatial view constructed through drawing, painting or another graphical representation.
  3. Instrument Perspective Illusion — a false or transformed secondary view produced or projected through an optical, photographic, cinematic, mirror, holographic or related instrument system.
  4. Forced Perspective Illusion — an illusion created through the physical construction or representation of a deliberately altered spatial reality.

These types can operate separately, but complex illusions frequently combine several of them.

Visual Perspective Illusion

A Visual Perspective Illusion occurs when the direct appearance of spatial reality is interpreted in a way that differs from its actual physical or geometrical arrangement.

The cause may involve a combination of:

  • environmental optics;
  • viewpoint;
  • geometrical arrangement;
  • retinal imaging;
  • physiological processes;
  • perceptual assumptions; and
  • psychological interpretation.

A familiar example is a partly submerged straight stick that appears bent because refraction changes the apparent position of the underwater portion.

The object itself has not changed shape. The altered optical path creates an apparent spatial relationship that differs from the physical geometry of the stick.

Perspective Illusion and Visual Perspective Type 2

Most Perspective Illusions ultimately involve Visual Perspective Type 2 because the resulting view must normally be perceived and interpreted through the human visual system.

However, perspective-based optical or geometrical transformations can also exist independently of whether a human observer happens to interpret them at that moment.

The distinction is important. The Perspective Research Centre uses Perspective Illusion principally for illusions involving projected geometry, optical structure, outlines, colour, intensity or spatial relationships — rather than attempting to include every visual illusion caused solely by psychological or neurological processing.

Graphical Perspective Illusion

A Graphical Perspective Illusion is produced when a drawing, painting or other graphical image creates the appearance of a spatial reality that does not physically exist in the image surface itself.

A flat picture can create a compelling impression of depth even though the physical surface possesses virtually no corresponding spatial depth.

The image can employ:

  • Linear Perspective;
  • Foreshortening;
  • Diminution of Size;
  • overlap and occlusion;
  • Aerial Perspective;
  • colour gradients;
  • acuity gradients;
  • texture gradients;
  • light and shade;
  • Chiaroscuro;
  • cast shadows; and
  • other Perspective Phenomena.

Together these provide information that the visual system can interpret as three-dimensional spatial structure.

The Illusion of 3-D Space on a 2-D Surface

One of the central achievements of graphical perspective is the creation of an apparent three-dimensional space on a physically two-dimensional surface.

The painted or drawn surface remains flat, but its represented Forms can appear to occupy different distances, depths and orientations.

This apparent transformation from 2-D surface to 3-D Image Space is not dependent upon Linear Perspective alone. Colour, clarity, texture, light, shade, occlusion and other Perspective Phenomena can contribute strongly to the impression of depth.

The spatial illusion is therefore normally a compound visual result produced by several interacting depth and perspective relationships.

Perspective Gradients and Depth Illusion

The Dictionary emphasises that perspective depth is not produced solely by lines and Vanishing Points.

Important depth-illusion methods include:

  • Gradient of Colour Perspective — systematic changes in hue, saturation or colour relationships;
  • Gradient of Acuity Perspective — systematic changes in sharpness, clarity, resolution and visible detail;
  • Gradient of Chiaroscuro Perspective — systematic changes in light, shade and contrast;
  • Texture Gradients — progressive compression or alteration of repeated surface information; and
  • Perspective of Form — changes in apparent size, shape, position and orientation.

These processes can operate in natural vision as well as in deliberately constructed images.

Illusionism and Trompe-l’œil

Illusionism in art deliberately creates a convincing false appearance of reality. The most familiar example is trompe-l’œil — literally a visual strategy intended to “trick the eye”.

Perspective illusionism can make represented Forms appear to extend beyond the physical limits of the picture surface and apparently enter the viewer’s space.

Applications include:

  • trompe-l’œil wall paintings;
  • illusionistic ceiling painting;
  • painted architectural extensions;
  • quadratura;
  • di sotto in sù;
  • false windows, doors and openings;
  • painted niches and sculpture;
  • theatrical scenery; and
  • imaginary extensions of real architectural space.

The aim may be complete visual deception, an extension of represented space into physical space, or a deliberate interaction between the two.

Baroque Perspective and Architectural Illusion

Baroque perspective developed some of the most spectacular examples of graphical and spatial illusion.

Painted architecture, extreme Foreshortening, deep spatial recession and carefully controlled viewpoint geometry could make a physical ceiling appear to open into a much larger architectural or heavenly space.

Such images often combine several Perspective Types at once:

  • Graphical Perspective;
  • Linear Perspective;
  • Anamorphic Perspective;
  • Forced Perspective;
  • Visual Perspective Illusion;
  • Chiaroscuro Perspective;
  • Aerial Perspective; and
  • Foreshortening.

The resulting represented architecture may appear to continue seamlessly from the actual architecture when viewed from the intended station point.

Andrea Pozzo and The Glory of St Ignatius

Volume 1 uses Andrea Pozzo’s The Glory of St Ignatius as an important example of a complex Perspective Illusion.

The fresco employs Anamorphic Perspective and distorted painted geometry so that false columns, architecture and strongly foreshortened figures appear correctly formed when seen from the designated viewing position.

The physical ceiling remains bounded, yet the represented image can appear to open into an immense three-dimensional space populated by architecture and figures.

The effect combines Visual Perspective Illusion, Forced Perspective Illusion and Graphical Perspective Illusion.

Anamorphic Perspective Illusion

Anamorphic Perspective deliberately distorts an image so that it becomes visually coherent only from a particular viewpoint, direction or optical arrangement.

From an ordinary viewing position the image can appear highly stretched, compressed or otherwise distorted. From the intended station point, the distortion is corrected by the viewing geometry.

An anamorphic image painted onto a flat wall or floor can even appear to project outwards into three-dimensional space, creating the impression of a solid Form where only a two-dimensional image exists.

This reveals one of the most important principles of Perspective Illusion: an apparently distorted image can produce a convincing spatial reality when the distortion is precisely matched to a particular viewpoint.

Viewpoint Is Fundamental to Perspective Illusion

Many Perspective Illusions depend critically upon the location of the observer.

The apparent spatial effect may exist only from a particular:

  • station point;
  • height;
  • viewing direction;
  • Field of View;
  • viewing distance; or
  • range of viewing positions.

If the observer moves away from the intended position, the geometrical construction may become visible and the illusion can weaken or disappear.

The distinction between true physical geometry and apparent viewpoint-dependent geometry lies at the heart of many forced, anamorphic and blended perspective effects.

Forced Perspective Illusion

Forced Perspective deliberately modifies physical or represented spatial arrangements to produce a desired false appearance.

The technique can alter:

  • object scale;
  • spacing;
  • distance;
  • scene geometry;
  • horizon position;
  • Vanishing Point relationships;
  • background geometry; or
  • the relationship between two differently scaled spatial systems.

An object may consequently appear much larger, smaller, nearer or farther away than it really is.

Forced Perspective is a particularly important example of Simulated Perspective, in which physical space, Forms or images are deliberately arranged or constructed to create a particular spatial appearance or illusion.

Physical Reality Can Be Altered to Produce a False Appearance

Forced Perspective differs from a purely graphical illusion because the physical scene itself may be altered.

Objects that are supposed to appear equally sized can actually possess different physical scales. Walls may not be parallel. Floors can slope. Distances can be compressed. Architectural details can systematically reduce in size.

From the intended viewpoint these irregularities can combine into a convincing apparent spatial reality.

The illusion therefore arises not because the representation inaccurately depicts the physical scene, but because the physical scene has itself been designed to produce a misleading perspective appearance.

Accelerated Perspective

Accelerated Perspective increases apparent spatial recession.

This can be achieved by deliberately increasing convergence, changing object scale or spacing, or otherwise modifying the expected perspective geometry so that a space appears deeper or longer than its actual physical dimensions.

The result may employ false or adjusted Vanishing Points and deliberately altered scene geometry.

Accelerated Perspective is therefore a form of Simulated and potentially Synthetic Perspective and is closely related to Forced Perspective.

Decelerated Perspective

Decelerated Perspective performs the opposite operation.

Instead of increasing apparent recession, it reduces the expected degree of perspective diminution or convergence so that a spatial region appears shallower or less extended than it physically is.

Accelerated and Decelerated Perspective demonstrate that apparent spatial depth can be deliberately manipulated by modifying the geometrical structure that normally communicates recession.

Blended and Double Perspective Illusions

A Blended Perspective can combine two or more differently structured spatial geometries within one apparent scene.

If the geometries are carefully aligned relative to the intended viewpoint, the observer may perceive them as one continuous homogeneous space even though they possess different scales, dimensions or structural relationships.

Double Perspective can similarly conjoin separate perspective spaces or metric systems so that they appear to form one direct or simulated reality.

Such arrangements can produce:

  • apparent changes of human scale;
  • apparently enlarged or diminished Forms;
  • false distances;
  • multi-scale spaces;
  • hidden spatial regions; and
  • objects apparently disappearing within otherwise visible space.

Instrument Perspective Illusion

An Instrument Perspective Illusion is produced when an optical, photographic, projection or related instrument forms or presents an apparent view that differs in some important respect from the underlying physical scene.

Possible instruments and systems include:

  • mirrors;
  • lenses;
  • cameras;
  • projectors;
  • cinema systems;
  • holograms;
  • stereoscopes;
  • lenticular displays;
  • volume displays;
  • Virtual Reality headsets;
  • Augmented Reality systems; and
  • New Media display systems.

The instrument itself may transform the optical image, or it may become one stage within a larger Composite or Mixed Perspective System.

Mirror Perspective and Illusion

Mirrors provide some of the oldest and most diverse examples of Instrument Perspective Illusion.

A plane mirror creates a virtual image that appears behind the mirror surface. The apparent mirror world occupies spatial positions where no corresponding physical objects exist.

Curved mirrors can magnify, diminish, distort, reverse or transform apparent spatial Form. Multiple mirrors can create repeating, fragmented, splintered or apparently infinite spaces.

Mirror Perspective demonstrates an important distinction:

  • Forced Perspective can physically manipulate Object Space;
  • Mirror Perspective can transform apparent or Image Space without requiring equivalent changes to the original physical scene.

The resulting mirror image can nevertheless appear completely integrated with the observer’s visible environment.

Types of Mirror and Reflection Illusion

Volume 1 identifies a wide range of mirror-related perspective effects, including:

  • plane-mirror virtual worlds;
  • depth reversal using mirror arrangements;
  • anamorphic mirror distortion;
  • convex mirror and mirror-ball views;
  • multi-faceted mirror images;
  • Pepper’s Ghost;
  • Reflection Holograms;
  • Infinity Mirrors;
  • fragmented and splintered reflections;
  • semi-transparent mirror effects;
  • Magic Cabinet illusions;
  • anti-gravity mirror illusions;
  • mirror-based invisibility effects; and
  • multiple or Double Perspective reflections.

The diversity of these effects illustrates how strongly apparent space can be transformed by controlling the paths of light reaching the observer.

Pepper’s Ghost and Combined Reality

Pepper’s Ghost provides a particularly clear example of several perspective processes operating together.

A partially reflective transparent surface introduces a reflected image into the observer’s view of a real physical scene. If the glass or mirror itself is concealed, the reflected figure can appear to occupy the real space beyond it.

The observer therefore sees both:

  • a direct view of physical reality; and
  • a reflected or projected secondary image.

The two spaces can be optically aligned so convincingly that they appear to constitute one environment.

Volume 1 consequently treats sophisticated Pepper’s Ghost effects as combinations involving Visual Perspective Illusion, Forced Perspective Illusion and Instrument Perspective Illusion.

Transparent Perspective Illusion

Transparent Perspective Illusion creates views in which objects, images or spatial layers appear transparent, semi-transparent or visually superimposed.

The apparent result can reveal spatial structures that would normally be hidden behind opaque surfaces.

Such systems can include:

  • transparent graphical images;
  • semi-transparent mirror overlays;
  • medical-image overlays;
  • multilayer displays;
  • Augmented Reality;
  • Extended Reality;
  • head-mounted displays; and
  • computer-generated transparent models.

Perspective can therefore create not only false depth but also apparently impossible visual access through otherwise opaque Forms.

Projection Mapping and Spatial Illusion

Projection Mapping uses physical objects and architectural surfaces as projection screens.

Projected imagery can be geometrically aligned with the actual surface so that the physical object appears to:

  • change shape;
  • move;
  • open;
  • collapse;
  • expand;
  • become transparent;
  • acquire new depth; or
  • transform into an entirely different spatial structure.

The physical geometry may remain unchanged while projected optical information transforms its apparent Form.

Projection Mapping therefore provides a contemporary example of the longstanding relationship between Perspective, projection, spatial transformation and illusion.

Perspective and Invisibility

Some of the most striking Perspective Illusions make an object or region of space appear invisible.

The basic principle is not necessarily to make the physical object disappear, but to prevent the visual information revealing that object from reaching the observer in the expected way — while replacing it with visual information corresponding to the scene apparently located behind it.

The observer consequently sees what appears to be an unobstructed region of space.

Perspective Invisibility methods can broadly include:

  • optically produced invisibility;
  • mirror or prism arrangements;
  • lenticular systems;
  • filmic or digital invisibility;
  • New Media image replacement; and
  • combined optical and digital systems.

Invisible Perspective

Invisible Perspective can create an apparently empty or unobstructed region of space that actually contains hidden objects or altered spatial geometry.

Mirrors can divert the observer’s sight around an object while presenting light from another part of the environment. Digital systems can perform a related operation by recording background imagery and displaying or projecting it over the hidden object.

The illusion succeeds because the observer receives visual information compatible with the assumption that light has travelled directly through an apparently empty region.

The object has not ceased to exist; the visual evidence of its presence has been replaced or redirected.

Floating and Levitating Perspective Illusions

Perspective methods can also make Forms appear to float or levitate.

Mirror arrangements can conceal physical supports or replace their appearance with reflected background information. Holographic and projection systems can form images apparently suspended within or in front of a physical scene.

Volume 1 discusses the Star Wars land-speeder effect as an example in which angled mirrors concealed the vehicle’s wheels by reflecting the surrounding ground, making the vehicle appear to hover.

The apparent antigravity is therefore achieved not by changing gravity but by changing the perspective information available to the observer.

Natural Perspective Illusions

Not all Perspective Illusions are intentionally produced.

Natural Perspective Illusions can arise from environmental optical conditions, spatial alignments or the relationship between physical reality and the observer.

Volume 1 includes examples such as:

  • mirages;
  • rainbows;
  • reflections in water;
  • structured shadows;
  • apparent astronomical movement; and
  • other naturally occurring optical and geometrical appearances.

An important qualification follows: once the physical or optical mechanism is understood, an appearance may cease to seem mysterious and instead be recognised as a normal optical or geometrical phenomenon.

The boundary between phenomenon and illusion can therefore partly depend upon how the appearance is interpreted.

Natural, Artificial and Synthetic Illusions

Perspective Illusions can also be considered according to their origin.

  • Natural Perspective Illusion — arises without deliberate human construction, through physical, optical or environmental conditions.
  • Artificial Perspective Illusion — deliberately created through drawing, painting, architecture, physical construction, instruments, cinema, computers or related techniques.
  • Synthetic Perspective Illusion — results when two or more natural and/or artificial Perspective Categories or processes combine into a perceptually unified appearance.

This classification is separate from the four principal illusion types and describes the broader source and organisation of the illusion.

Simulated Perspective

Simulated Perspective is produced by deliberately modifying, arranging or constructing physical space, objects or images to create a particular appearance, illusion or spatial effect.

Forced Perspective is one important example.

Simulated Perspective can therefore create a spatial reality whose apparent geometry is intentionally different from its ordinary or expected arrangement.

The resulting illusion may be physical, graphical, optical, instrument-based, computational or a combination of several processes.

Synthetic Perspective

Synthetic Perspective occurs when two or more Perspective Categories or processes combine to produce a perceptually unified view, image or spatial appearance.

Perspective Illusions frequently become synthetic because a final effect may combine:

  • physical scene geometry;
  • Natural Perspective;
  • Optical Perspective;
  • Graphical Perspective;
  • Instrument Perspective;
  • Simulated Perspective;
  • New Media Perspective; and
  • Visual Perspective Type 2.

The observer experiences one apparent spatial reality even though several different processes have contributed to its formation.

Composite Perspective and Illusion

Composite Perspective describes a process, image, environment or system involving several Perspective Categories operating in sequence or combination.

A film illusion might combine:

  • physical scenery;
  • Forced Perspective;
  • camera imaging;
  • mirrors;
  • miniatures;
  • painted mattes;
  • front or rear projection;
  • CGI;
  • digital compositing; and
  • final display and human perception.

The apparent simplicity of the final image can therefore conceal a long and complex Perspective Image Chain.

Combined Perspective

Combined Perspective can place real and represented views together within the same visual field.

A direct view of physical reality may be seen simultaneously with a graphical, optical or digital overlay.

Examples include sighting devices and Augmented Reality systems.

In Combined Perspective the component spaces can remain visibly distinct, even though they are spatially coordinated.

Mixed Perspective and Illusion

Mixed Perspective describes a system in which both principal directional Classes — Viewing or Imaging and Projecting — operate.

A camera/projector system may capture spatial reality in one direction and subsequently project an image into another spatial environment.

Mirror, cinema, projection and Virtual Reality systems can similarly combine image formation, viewing and projection.

Mixed Perspective is therefore particularly important for understanding many sophisticated Instrument Perspective Illusions.

Perspective Illusion in Photography and Cinema

Photography and cinema enormously expanded the possibilities of Perspective Illusion.

The apparent spatial relationships recorded by a camera can be manipulated through:

  • camera viewpoint;
  • camera distance;
  • Field of View;
  • lens and optical effects;
  • miniatures;
  • Forced Perspective;
  • painted backgrounds;
  • glass shots;
  • mirror shots;
  • front projection;
  • rear projection;
  • multiple exposure;
  • matte compositing;
  • anamorphic methods;
  • CGI; and
  • digital post-production.

Several independently created spatial elements can thereby be made to appear as though they occupy one coherent photographic reality.

Special Effects Are Often Perspective Systems

Many visual and special effects can be understood as carefully constructed Perspective Systems.

The illusion succeeds when separate image or spatial elements possess sufficiently compatible:

  • viewpoints;
  • Vanishing Points;
  • horizon relationships;
  • projection scales;
  • lighting;
  • shadows;
  • colour;
  • clarity;
  • movement; and
  • spatial orientation.

The final image can then appear to depict one natural scene even though it has been assembled from several unrelated physical, graphical, optical or computational sources.

New Media Perspective and Illusion

New Media systems extend earlier perspective-illusion methods rather than replacing their underlying principles.

Computer graphics and digital imaging can now calculate, transform and combine perspective spaces with extraordinary precision.

Digital systems can:

  • construct imaginary 3-D environments;
  • alter viewpoint;
  • change object scale;
  • replace backgrounds;
  • blend real and artificial Forms;
  • match virtual and physical camera geometry;
  • simulate optical effects;
  • create transparent Forms;
  • remove or conceal objects;
  • project virtual Forms into physical views; and
  • create interactive immersive environments.

The fundamental Perspective Problem remains the same: making independently generated visual information appear to belong to one coherent spatial reality.

Virtual Reality and the Illusion of Place

Virtual Reality extends Perspective Illusion from the appearance of individual Forms towards the apparent experience of occupying an alternative spatial environment.

A VR system can coordinate:

  • stereoscopic views;
  • head position;
  • changing viewpoint;
  • Field of View;
  • perspective transformation;
  • movement;
  • scale;
  • spatial sound; and
  • interactive 3-D models.

The result can produce a compelling impression that the observer is physically located within the represented environment.

The illusion therefore concerns not merely the apparent depth of an object but the observer’s apparent place within space.

Illusion and Immersion Are Related but Different

Illusion and immersion are closely related Perspective Functions, but they are not identical.

  • Illusion concerns a false, altered or convincingly simulated spatial appearance.
  • Immersion concerns the apparent experience of being located within, surrounded by or perceptually engaged with a spatial environment.

A small trompe-l’œil painting may create a powerful illusion without producing substantial immersion. A large panoramic theatre or Virtual Reality environment may create strong immersion by occupying much of the viewer’s Field of View and responding to viewpoint changes.

The two functions can also operate together.

Stereoscopy and the Illusion of Depth

Stereoscopic systems create depth by presenting slightly different images to the two eyes.

The binocular differences can produce an impression of spatial relief even though the images may originate on flat physical surfaces.

However, stereoscopy is only one way of creating apparent 3-D space. Monocular Perspective Phenomena such as size diminution, occlusion, Foreshortening, texture, motion, colour, clarity and Chiaroscuro can also produce powerful depth information.

A convincing spatial illusion can consequently occur with or without binocular stereopsis.

The Ponzo Illusion

The Ponzo Illusion demonstrates how perspective context can affect apparent size.

Two physically equal lines placed between converging lines can appear different in length. The converging framework is interpreted as indicating recession into depth, and the line apparently positioned farther away can consequently appear larger.

The illusion demonstrates how strongly apparent size can depend upon the spatial context within which an image element is interpreted.

Perspective Can Create Impossible Space

Graphical Perspective can also construct spatial arrangements that appear locally plausible but cannot exist as a coherent physical three-dimensional object or scene.

Individual lines, corners and surfaces can each appear perspectivally meaningful while their combined geometrical structure becomes impossible.

This demonstrates an important limitation of image interpretation: the visual system can infer plausible local spatial relationships even when the complete represented geometry is internally contradictory.

Perspective, Appearance and Reality

Perspective Illusion exposes a fundamental distinction between what exists and how it appears.

A physical object possesses one spatial arrangement at a particular moment, but it can generate many different appearances according to:

  • viewpoint;
  • viewing direction;
  • distance;
  • orientation;
  • Field of View;
  • optical conditions;
  • image-surface geometry;
  • scale;
  • resolution;
  • lighting; and
  • the visual or imaging system involved.

A strange appearance is therefore not automatically evidence that physical reality itself has changed.

Perspective theory must continually distinguish Object Space from Image Space, physical geometry from apparent geometry, and the source scene from its visual interpretation.

True Image, False Image and Partial Truth

A Perspective Illusion does not necessarily mean that every aspect of the resulting image is false.

An instrument or representation may accurately preserve some properties while transforming others.

A mirror can accurately preserve many colour and shape relationships while relocating the apparent image into virtual space. A forced-perspective set can produce a photograph that accurately records the constructed scenery while giving a misleading impression of the true dimensions of that scenery.

Perspective images can therefore contain combinations of accurate correspondence, transformation and illusion.

The Plasticity of Perspective Space

Perspective Illusions reveal what Volume 1 describes as the plasticity of image perception and space.

Physical Object Space can be altered through Forced, Accelerated or Blended Perspective. Apparent Image Space can be transformed through mirrors, lenses, cameras, projections and computational processes.

Several spaces can also be:

  • combined;
  • blended;
  • overlaid;
  • reflected;
  • projected;
  • scaled;
  • distorted;
  • made transparent;
  • fragmented; or
  • synthetically unified.

The resulting appearance can seem completely coherent even when the underlying physical or image structures are radically different.

Perspective Illusion and the Correspondence Problem

Perspective Illusion is closely related to the Correspondence or Equivalence Problem of Perspective.

A single two-dimensional image does not normally contain enough information to determine one unique three-dimensional source scene.

Different physical arrangements can therefore be designed to generate the same or very similar projected image from a particular viewpoint.

Forced Perspective exploits precisely this ambiguity. The observer interprets one possible three-dimensional reality from an image that could in fact have been generated by a very different spatial arrangement.

The capacity of perspective images to support more than one possible spatial interpretation is therefore one of the fundamental reasons Perspective Illusions are possible.

Perspective Illusion Is Not Necessarily an Error

An illusion should not automatically be understood as a failure of perspective.

Many Perspective Illusions are deliberately and accurately engineered.

The physical, graphical, optical or computational system can be constructed with great geometrical precision specifically so that its resulting appearance differs from the ordinary interpretation of the underlying reality.

An anamorphic painting, Forced Perspective film set or Pepper’s Ghost installation may therefore be technically correct precisely because it produces the intended false appearance from the prescribed viewpoint.

Perspective Illusion Depends upon Assumptions

Visual interpretation depends upon assumptions about how spatial reality normally behaves.

We commonly assume that:

  • parallel walls remain parallel;
  • people of similar type possess broadly comparable size;
  • objects do not change physical scale simply because they move farther away;
  • light generally reaches us along predictable optical paths;
  • surfaces continue behind occluding objects;
  • shadows correspond to Forms and light sources; and
  • familiar architectural structures possess regular geometry.

A Perspective Illusion can exploit these assumptions by constructing visual evidence that is compatible with one interpretation while being produced by another spatial arrangement.

When an Illusion Stops Being an Illusion

Volume 1 raises an important question: once the cause of an apparent anomaly is understood, should it still be called an illusion?

A mirage, reflection, refraction or unusual projected shadow may initially appear mysterious. Once the relevant optical geometry is understood, the same appearance can be recognised as the normal result of a physical process.

The visual appearance has not changed — our interpretation of it has.

This is one reason why Perspective Illusion is important scientifically as well as artistically: studying an illusion can expose the hidden optical, geometrical and perceptual assumptions underlying ordinary vision.

Perspective Illusion across Art, Science and Technology

Perspective Illusion occurs across an unusually wide range of fields.

  • Painting — trompe-l’œil, quadratura, anamorphosis and illusionistic depth.
  • Architecture — Forced Perspective, false scale, accelerated and decelerated spatial layouts.
  • Gardens — controlled vistas, manipulated scale and apparent distance.
  • Theatre — painted scenery, mirrors, Pepper’s Ghost and false architecture.
  • Photography — viewpoint-controlled scale, lens effects and spatial alignment.
  • Cinema — miniatures, matte paintings, mirrors, projections, compositing and CGI.
  • Optics — mirrors, lenses, refraction, reflection and virtual images.
  • Display technology — stereoscopy, holography, lenticular and volumetric systems.
  • New Media — CGI, projection mapping, Virtual Reality, Augmented Reality and Mixed Reality.

The same underlying perspective principles therefore connect apparently different traditions of artistic illusion, optical science and advanced imaging technology.

Common Misconceptions about Perspective and Illusion

  • Perspective is not itself an illusion. Perspective describes real spatial, optical, geometrical and representational relationships; illusion is one possible function or outcome.
  • Not every Perspective Phenomenon is an illusion. Diminution, Foreshortening and line convergence can be normal consequences of viewing spatial reality.
  • Illusion is not a third Perspective Class. The two directional Classes remain Viewing or Imaging and Projecting.
  • Perspective Illusion is not limited to psychology. It may involve physical, optical, geometrical, graphical, instrument and perceptual processes.
  • Graphical illusion is not limited to Linear Perspective. Colour, acuity, Chiaroscuro, texture, occlusion and other Perspective Phenomena can contribute strongly to depth.
  • A flat image does not physically become three-dimensional. It can nevertheless produce a convincing visual impression of three-dimensional space.
  • Forced Perspective is not merely a camera trick. The physical or represented scene itself may be deliberately constructed or altered.
  • Anamorphic Perspective is not simply incorrect perspective. Its distortion can be precisely calculated to produce a coherent image from a particular viewpoint.
  • A mirror image does not occupy the apparent virtual space behind a plane mirror. The mirror creates an optical virtual image.
  • Invisibility does not necessarily require an object to cease reflecting light. Perspective systems can redirect or replace the visual information that would reveal the object.
  • Illusion and immersion are not identical. Illusion concerns altered apparent reality; immersion concerns the observer’s apparent presence within a spatial environment.
  • Stereoscopy is not the only source of apparent 3-D. Monocular Perspective Phenomena provide extensive spatial information.
  • A Perspective Illusion can be geometrically accurate. It may be precisely constructed to produce a deliberately false apparent reality.
  • A final illusion may have several causes. Visual, Graphical, Instrument, Forced, Simulated, Synthetic, Composite, Combined, Mixed and Blended Perspective can operate together.

Why Perspective and Illusion Matter

Perspective Illusion matters because it exposes the difference between spatial reality and visual appearance.

What we see is not simply the physical world transferred unchanged into the eye. Spatial reality is transformed through viewpoint, light, optics, projection, image surfaces, instruments and perceptual interpretation.

Most of the time these processes provide highly useful information about the world. But the same mechanisms can also be manipulated, combined or misinterpreted to produce convincing appearances of realities that are physically different from what they seem.

Perspective Illusions therefore reveal the extraordinary plasticity of apparent space. A wall can appear to open into an infinite painted world. A small stage can appear enormous. A person can appear gigantic or miniature. A mirror can create a virtual room. An object can seem invisible or suspended in air. A flat screen can appear to contain deep space. A headset can apparently transport an observer into another world.

The same field extends from ancient reflections, painted scenery and Renaissance perspective through Baroque illusionism, mirrors and theatrical stagecraft to photography, cinema, holography, CGI, projection mapping and Virtual, Augmented and Mixed Reality.

Understanding Perspective and Illusion therefore provides a foundation for understanding Visual Perspective Illusion, Graphical Perspective Illusion, Instrument Perspective Illusion, Forced Perspective Illusion, Simulated Perspective, Synthetic Perspective, Composite Perspective, Combined Perspective, Mixed Perspective, Blended Perspective, Double Perspective, Anamorphic Perspective, Trompe-l’œil, Accelerated Perspective, Decelerated Perspective, Mirror Perspective, Transparent Perspective, Invisible Perspective, Perspective of Form, Perspective Gradients, Depth Illusion, 3-D Perspective, Virtual Reality, Augmented Reality and Immersion.