3-D: The Third Dimension

3-D, or the Third Dimension, concerns the perception, representation and reconstruction of spatial depth, volume and three-dimensional Form.

We experience the physical world as three-dimensional, yet the optical images formed by the eyes and most conventional photographs, drawings and screens are two-dimensional image structures. The impression of depth therefore depends upon a combination of perspective, visual depth cues, binocular information, movement and interpretation.

3-D should not be equated only with stereoscopic images or 3-D glasses. A painting, photograph, film or ordinary computer screen can produce a powerful impression of three-dimensional space using predominantly monocular depth information, while stereoscopic systems add further binocular information by presenting different but corresponding views to the two eyes.

This page provides an overview of the Third Dimension across physical space, human vision, graphical representation, stereoscopy, moving images, computer-generated environments, virtual reality, holography and volumetric imaging.

What Does 3-D Mean?

In its simplest geometrical sense, three-dimensional space has three independent spatial dimensions:

width;
height;
depth.

A physical object occupies a three-dimensional region of space and possesses volume, spatial position, orientation and Form.

But the expression 3-D is also commonly used for images and technologies that produce an impression of depth. These are not all three-dimensional in the same sense.

It is therefore useful to distinguish between:

physical 3-D space — actual spatial extension;
visual 3-D — the experience or perception of depth;
represented 3-D — depth depicted on a surface or screen;
stereoscopic 3-D — depth generated partly through different left- and right-eye images;
modelled 3-D — mathematical or computational spatial models;
immersive 3-D — environments that surround or respond to the observer;
volumetric or holographic 3-D — systems in which spatial image information is distributed through or apparently located within three-dimensional space.

The Spatial Limitation of a Single Retinal Image

A fundamental problem of vision is that the retinal image does not directly specify the distance of every Object-Space point.

A light ray reaching a particular retinal location principally specifies a direction from the eye. In geometrical terms, many different Object-Space points lying along approximately the same viewing direction could project to the same retinal location.

The visual system therefore cannot recover complete three-dimensional spatial structure from retinal position alone.

Instead, depth is derived from a large collection of visual relationships known as Depth Cues, together with movement, binocular vision, prior knowledge and perceptual interpretation.

Explore Depth Cues →

Explore Depth Perception →

Generators of the Third Dimension

The various sources of depth information can be regarded as Generators of the Third Dimension: visual and spatial relationships that enable an observer to construct an impression of depth, distance, volume and spatial organisation.

They can be grouped broadly into:

monocular or pictorial cues;
motion-based cues;
ocular adjustment cues;
binocular or stereoscopic cues;
environmental and contextual information.

These mechanisms need not all be present simultaneously. A convincing impression of three-dimensional space may arise from only a subset of them.

Monocular Depth Cues

Monocular Depth Cues can operate when the scene is viewed with one eye and are therefore especially important to drawings, photographs, paintings, films and ordinary flat screens.

Important examples include:

Occlusion or overlap — a nearer object hides part of a farther one;
Relative size — comparable Forms occupying smaller visual angles are often interpreted as more distant;
Familiar size — knowledge of an object’s likely physical size assists distance interpretation;
Perspective diminution — apparent size generally reduces with increasing distance;
Foreshortening — Forms change apparent shape as their orientation changes relative to the viewer;
Linear convergence — receding parallel directions can converge towards vanishing structures;
Texture gradient — repeated surface detail becomes progressively smaller and denser with distance;
Height in the visual field — position relative to horizon or ground relationships can suggest distance;
Atmospheric Perspective — contrast, colour and detail commonly diminish through atmospheric distance;
Light and shade — illumination and shadow reveal surface orientation and volume;
Focus and blur — differences in clarity can contribute information about relative depth;
known spatial context — familiar environments and objects constrain possible spatial interpretations.

These cues explain why an ordinary photograph or perspective drawing can appear strongly three-dimensional even though the physical image itself is flat.

Perspective as a Depth Cue

Perspective is one of the most powerful families of depth information.

Changes in apparent:

size;
shape;
scale;
orientation;
spacing;
overlap;
convergence

provide systematic evidence about relationships between the observer and spatial Forms.

This is why graphical systems such as Linear Perspective can produce a convincing impression of deep space without supplying stereoscopic information.

The same principle applies to photography and cinema: a single camera records one projection, yet the resulting image can contain enough monocular information for the viewer to construct a rich three-dimensional interpretation.

Explore Perspective and 3-D Space →

Motion and the Third Dimension

Movement supplies additional depth information that a single stationary image cannot provide.

When an observer or camera changes position, objects at different depths shift relative to one another. This is Motion Parallax.

Nearby objects generally change angular position more rapidly than distant objects.

Movement also reveals:

previously hidden surfaces;
changing overlap;
different Aspects of Form;
relative spatial position;
distance relationships;
spatial continuity.

Optic flow supplies another important source of information as the visual field transforms during movement through an environment.

Moving images, interactive computer graphics and virtual reality can therefore provide depth information unavailable in a single static picture.

Ocular Adjustment Cues

The visual system also receives information from adjustments made by the eyes.

Accommodation

The crystalline lens changes optical power when focusing upon objects at different distances. Information associated with this adjustment can contribute to depth estimation, particularly at relatively close range.

Vergence

The two eyes rotate so that their visual axes correspond with an object of attention. The amount of convergence required varies with viewing distance and can provide information about the distance of nearby objects.

Binocular Vision

Human beings possess two laterally separated eyes. Because the eyes occupy different positions, each receives a slightly different view of nearby spatial reality.

The differences between corresponding left- and right-eye images are known as binocular disparity.

The visual system can use this disparity to produce stereopsis: a powerful impression of depth and dimensional relief.

Binocular depth information is particularly useful at relatively close viewing distances. At greater distances, the angular differences between the two eye positions become progressively smaller and monocular, contextual and movement-based information becomes increasingly important.

Explore Binocular Vision →

3-D Does Not Mean Only Stereoscopic 3-D

A common misconception is that an image is only meaningfully three-dimensional if separate views are supplied to the two eyes.

This confuses three-dimensional appearance with one particular depth mechanism.

When one eye is closed, physical space does not suddenly appear completely flat. Most of the major monocular and movement-based cues remain available.

Similarly, an ordinary:

drawing;
painting;
photograph;
television image;
film;
computer image

can provide a convincing representation of a three-dimensional scene without stereoscopic disparity.

Stereoscopic information therefore adds to the perception of depth; it does not create the entire phenomenon of three-dimensional vision by itself.

Stereoscopic 3-D

Stereoscopic 3-D deliberately presents two corresponding images from slightly different viewpoints, one to each eye.

The system reproduces some of the disparity relationships encountered in ordinary binocular viewing.

Examples include:

stereographs;
stereoscopes;
anaglyph images;
polarised 3-D cinema;
active-shutter displays;
head-mounted virtual-reality displays;
stereoscopic computer graphics.

A stereoscopic system therefore involves at least:

two viewpoints → two corresponding images → controlled delivery to the two eyes → binocular integration

Explore Stereography / Stereoscopy →

Stereographs and the Stereoscope

The stereograph was one of the earliest practical methods for reproducing binocular spatial information.

Two photographs of the same scene are taken from slightly separated positions corresponding approximately to the lateral separation of the eyes.

A stereoscope presents:

the left image to the left eye;
the right image to the right eye.

The resulting disparity can produce a vivid impression of depth and spatial relief.

Stereoscopy provided an important historical bridge between photography, three-dimensional imaging and contemporary virtual-reality systems.

Autostereoscopic 3-D

Autostereoscopic systems attempt to provide different views to the two eyes without requiring conventional stereoscopic glasses or a head-mounted viewer.

Methods include:

lenticular displays;
parallax-barrier displays;
integral imaging;
multi-view displays;
some light-field display systems.

The observer receives different images according to viewing position, allowing binocular disparity and sometimes viewpoint-dependent image changes to be reproduced.

Represented 3-D on a Flat Surface

A flat image can depict three-dimensional space while remaining physically two-dimensional.

This distinction is fundamental:

Physical surface: 2-D
represented or perceived space: potentially 3-D

Graphical Perspective systems produce this effect by transforming relationships from Object Space into Image Space.

Linear Perspective is especially familiar, but it is not the only method. Other systems include:

Curvilinear Perspective;
Spherical Perspective;
Cylindrical Perspective;
Axonometric Perspective;
Oblique Perspective;
Panoramic Perspective;
multi-perspective and compound systems.

Different systems preserve and transform different spatial relationships. There is therefore no single graphical method that should simply be equated with three-dimensional vision itself.

Linear and Curvilinear Representation

Linear Perspective maps spatial directions onto a flat rectilinear Picture Plane. Over moderate Fields of View it can provide a powerful and geometrically systematic representation of spatial depth.

At very wide Fields of View, however, a single rectilinear projection produces increasing marginal scale and lateral deformation.

Curvilinear and spherical systems distribute a wider angular field differently and can reduce some forms of marginal stretching, although straight spatial lines may then appear curved.

These are different mappings of three-dimensional spatial relationships rather than simply correct and incorrect versions of the same image.

Explore Linear Perspective →

Explore Curvilinear Perspective →

Moving-Image 3-D

Cinema and animation add the dimension of time to represented space.

A moving camera can continuously reveal:

motion parallax;
changing overlap;
changing apparent size;
successive Aspects of Form;
newly visible surfaces;
spatial pathways;
relationships between objects at different depths.

A moving monocular image can consequently generate an extremely powerful impression of three-dimensional space even without stereoscopy.

Stereoscopic cinema combines these temporal cues with binocular disparity.

Computer-Modelled 3-D

Computer graphics allows three-dimensional Forms and environments to be represented as mathematical structures rather than merely as finished flat images.

A digital 3-D model may contain information about:

position;
scale;
orientation;
surface geometry;
materials;
lighting;
camera location;
movement;
spatial relationships.

New perspective images can then be calculated from different virtual viewpoints.

The model itself is not identical to the displayed image. Rather:

3-D model → virtual camera / projection → 2-D or stereoscopic image → viewer

3-D Reconstruction

Three-dimensional structure can also be reconstructed from photographs, measurements or other image data.

Methods include:

stereo matching;
photogrammetry;
Structure from Motion;
laser scanning;
LiDAR;
depth cameras;
computer vision;
medical tomography;
multi-view reconstruction.

These methods attempt to infer Object-Space position and Form from measurements or multiple representations.

The task is related directly to the Correspondence or Equivalence Problem: determining which three-dimensional spatial arrangement corresponds to the available image information.

Explore 3D Reconstruction →

Virtual Reality

Virtual Reality combines several of the principal Generators of the Third Dimension within one responsive system.

A typical VR system can provide:

stereoscopic left- and right-eye images;
a wide Field of View;
head tracking;
motion parallax;
changing perspective;
interactive movement;
occlusion;
scale and texture cues;
spatial sound and other non-visual information.

As the observer turns or moves, the displayed perspective is recalculated so that the virtual environment responds approximately as a surrounding physical space would.

VR is therefore not merely a stereoscopic picture. It is a dynamic perspective system linked to observer movement.

Explore Virtual Reality →

Augmented and Mixed Reality

Augmented Reality places represented or simulated objects within a view of physical spatial reality.

To appear correctly located, the inserted content may need to correspond with:

observer or camera position;
Viewing Direction;
physical scale;
surface position;
occlusion;
illumination;
changing movement.

Mixed Reality extends this relationship by allowing physical and virtual elements to appear to share and interact within one spatial environment.

Holographic 3-D

Holography records and reconstructs aspects of the optical wavefront associated with a scene.

Unlike an ordinary photograph, a holographic image can provide different views as the observer changes position, supplying:

binocular disparity;
motion parallax;
changing occlusion;
viewpoint-dependent image information.

A holographic image can therefore provide more of the optical information associated with a three-dimensional object than a conventional flat photograph.

Nevertheless, a holographic image is still a particular optical representation and should not automatically be treated as identical to the physical object or scene it represents.

Explore Holograms →

Volumetric and Light-Field Displays

Other 3-D display systems attempt to distribute visual information through physical space or across many viewing directions.

Volumetric displays generate visible image information at different spatial positions within a physical volume.

Light-field displays attempt to reproduce different directional rays so that the image changes according to the observer’s viewpoint.

Such systems can provide richer viewpoint-dependent information than a conventional flat screen, although each has practical limitations involving resolution, viewing region, brightness, field size and complexity.

Physical 3-D and Apparent 3-D Are Different

A central distinction is between the physical dimensionality of a display or object and the dimensionality experienced or represented by the viewer.

For example:

a painting is physically flat but may depict deep space;
a stereoscopic screen is physically flat but can produce binocular depth;
a virtual environment may appear extensive although generated by displays close to the eyes;
a sculpture is physically three-dimensional whether or not it is interpreted pictorially;
a holographic image may appear located in front of or behind its physical recording surface.

Thus the phrase 3-D should always be qualified by asking: three-dimensional in what sense?

The Third Dimension and Perspective Category Theory

Three-dimensional appearance can emerge through many Perspective Categories rather than belonging exclusively to one.

Examples include:

Natural Perspective — spatial appearance arising through ordinary viewing;
Visual Perspective Type 2 — the retinal and perceptual view experienced by an observer;
Graphical Perspective — three-dimensional space represented through drawing or another graphical method;
Instrument Perspective — cameras, stereoscopes and other instruments capturing or presenting spatial views;
Simulated Perspective — deliberately constructed or altered spatial appearances;
New Media Perspective — computer graphics, virtual environments, AR, VR and other digital spatial systems.

A single 3-D experience can therefore involve several Perspective Categories acting together through an image or optical chain.

There Is No Single “True 3-D” Representation

Different 3-D systems preserve different parts of spatial information.

A perspective drawing may reproduce powerful monocular depth relationships but no binocular disparity.

A stereoscopic photograph adds binocular disparity but remains limited to the recorded viewpoints and image boundaries.

A hologram can provide viewpoint-dependent optical information but may have a restricted viewing region.

Virtual Reality can reproduce many visual cues dynamically but remains constrained by display resolution, tracking, latency, Field of View and the difference between physical and simulated environments.

The useful question is therefore not simply:

“Is this true 3-D?”

but rather:

“Which three-dimensional relationships and depth cues does this system reproduce, and which does it omit or transform?”

Why the Third Dimension Matters to Perspective

The Third Dimension lies at the centre of perspective because perspective continually relates:

spatial reality;
Viewpoint;
distance;
direction;
Form;
projection;
Image Space;
visual perception.

Perspective explains how three-dimensional spatial relationships become visible appearances and how those appearances can subsequently be represented, reconstructed, simulated and interpreted.

3-D is therefore not a single technology or optical effect. It is a broad family of relationships connecting physical space, vision, representation and spatial experience.

Explore Theory

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