3-D Displays

In this section, we review principles of 3-D displays as applied to perspective views/images; axioms which apply to certain kinds of: computer monitors/displays/screens typically with stereoscopic/binocular capabilities, or else that generate 3-D models or real-space 3-D images/views such as with holographic, VR, or swept-volume displays etc. For examples of how different displays are applied and used in practice (in relation to perspective), see explanations under the camera perspective section.

In terms of a perspective view/image, whenever we talk of a 3-D display it is important to realise that we are considering how to display a 1-D/2-D/3-D image of a spatial object/scene within a three-dimensional space (real or apparent) or 3-D volume (ostensibly). Ergo we are talking about a so-called 1-D, 2-D or 3-D perspective and related principles as explained in the 2-D display section.

We begin with a general definition of the term three-dimensional or 3-D.

3-D (Natural Space)

The so-called third-dimension or 3-D, or 3-D, refers to the third spacial dimension (depth), but can have subtly different meanings as explained below.

In terms of natural perspective (physical reality), there are two kinds of 3-D:

  • 3-D object space (space itself or the Forms/structures contained therein): A 1-D/2-D/3-D structure in a 3-D object space (spatial scene/object).
  • Viewing a spatial scene using eyes (using monocular or binocular vision): A view of a spatial scene/object using eyes [visual perspective (2nd type)], or looking at physical space with an optical instrument (amplified vision).

While looking at the blue-sky without any clouds in sight, we see a formless extent of colour, without any feeling or judgement of depth whatsoever; apart from the impression of looking into an immensity of open-space. No visible recognisable Forms/structures and no geometrical framework/ structure means no depth is discernible (space itself is not intrinsically visible). Contrast that situation with looking down/along a set of parallel railway-tracks, stretching into the distance and apparently converging to a vanishing point. Here, we get a very real sense of depth, size, and shape for large regions of the depicted space. Such an image is the overt recognition of the railway-track or twin parallel-lines Form, plus standard perspective phenomena including aspect and diminution of size, which result in a central vanishing-point on the horizon line.

However, physical reality is not comprised solely of railway-track type structures! But rather it contains an infinite variety of different Forms. How then is it possible to correctly ‘decode’ images? First, we apply knowledge of common spatial structures, and how these are sized/shaped plus are visually transformed into perspective image facets (and phenomena) by a category such as linear perspective. Second, we must have knowledge of the other perspective facets: optical assembly (scene + method optics/geometry), plus projection and observation mode(s); and further how these affect perspective phenomena.

Linear Perspective and 3-D

A category such as linear perspective embodies standard mathematical relationship(s) for image transformation factors. However, in a real-world situation such as the use of a camera, then apparent distance, size, and shape features may differ significantly from expected results. Such differences increase towards the edges of an eye/lens image, where wide-field perspective distortions can come into play; leading to curvilinear/spherical perspective effects, etc. Patently for cartographic, astronomical, engineering and technical drawing etc., it is desirable to employ accurate image analysis techniques, which explain the use of parallel perspective and/or other counter-distortion perspective types/forms and associated methods.

Linear perspective provides a linear structure for the depiction on a surface of the apparent shape, size, and relative position of the objects constituting a spatial scene in 3-D; that is for the representation of form or what is sometimes called the representation of space. This is a form of perspective image/view that most people are familiar with and learned about, or at least learned to recognise and name in school. In fact, this ‘linear’ shaped image, with converging parallels, is so basic to how humans perceive space that a pre-processing physical image detector for converging parallels has been discovered to exist on the retina of the human eye.

Perspective remains a complex topic because it involves the comparison of fundamentally different categories of space. For example, reconciliation of the 3- D space of the physical world (object space), with the 2-D space of graphical or photographic perspective (perspective space). Often, and despite a strong desire to attempt equality/alignment, this reconciliation is difficult (if not impossible) to achieve with perfect correlation; because one deals with dimensions that must map without any physically- based 1:1 correspondence or identical mapping.

Patently, information may be lost in this process due to the inherent optical limitations of a single point-of- view, plus aspect-of-form shape changes and scale/shape/size relations, etc., resulting in reduced (or concealed/confused) visual information/details that are to be interpreted in a single visual snapshot (very hopefully). Overcoming aspects of this geometric correspondence—or equivalence—problem is a key ‘goal’ of optical/technical perspective.

Visual perspective produces a structured space that emanates partly from spatial reality, partly from the perspective method/observer, and partly from the visual scale(s)/resolution(s) involved, and such a process happens by the application of perspective principles/methods/theory (whether realised or not).

3-D Perspective (1): Depth Illusion

Depth illusion of spatial forms present in a natural, artificial or synthetic spatial reality. The four classes of perspective ‘depth’ illusion are:

  • Flat/plane picture plane: Spatial illusion by perspective representation on a 2-D surface (monocular depth cues). Includes swept-plane displays / fan-holograms.
  • 3-D modelling perspective: Spatial illusion by physical or computer modelling (monocular/binocular depth cues).
  • Stereoscopic views using mirror images, or virtual reality stereoscopic views/images: Spatial illusion by stereoscopic views of mirror or virtual reality (binocular depth cues).
  • Stereoscopic views of false reality: construction or representation of an artificial 3-D stereoscopic image/view of a spatial reality, formed by an adjusted, illusive, or false reality perspective, which is also called ‘false’ or ‘trick’ perspective (views of natural/built world)—being visual illusion by the construction of a false spatial reality, or by the representation of a false spatial reality (distorted/transposed scene/physical geometry).

3-D Perspective (2): Illusion Types

Perspective techniques are sometimes used to create optical illusions. Typically, a perspective illusion makes false impressions of size, depth, position, place (immersion), or transparency for objects/people. One example is when dimensionality is adjusted within a scene, making an object appear farther away, closer, larger, or smaller than it is.

The four types of optical perspective illusions are:

  • Visual Perspective Illusion: illusion by perceptually adjusted appearance (false direct view of physical reality);
  • Graphical Perspective Illusion (includes perspective drawings/paintings): illusion by graphically constructed appearance (false apparent view of spatial scene);
  • Instrument Perspective Illusion: illusion by secondary visual images (cinema, holograms, etc), and/or projected appearance (false formed view of 3-D scene);
  • Simulated (Forced)/Synthetic Perspective Illusion: illusion by physical construction of a false physical reality (apparent), or by the representation of a false physical reality (distorted/ transposed scene geometry with apparent illusive effects).

3-D Perspective (3): Representation

We can define perspective as the formation of an image/view—or a representational pattern— of a state of affairs present in a spatial reality, whereby this image/view can be formed by a range of natural, artificial, or synthetic processes. Ergo, we can consider perspective to be a representation of a spatial form present in a natural, artificial, or synthetic spatial reality.

The three classes of perspective representation are:

  • Uni-angular image: monocular or fixed-angle binocular: Fixed viewing-angle monocular representation, or notionally fixed central viewing-angle binocular representation; being a 3-D view/image/measurement/calculation (optical/geometric projection) of a spatial form. Includes all types of perspective that exhibit spatial recession on 2- D surface (e.g. linear perspective), and also fixed central viewing-angle stereoscopy and autostereoscopy. Normally, this class of perspective representation has a fixed real, or fixed simulated, viewing position/scale.
  • Multi-angular image: holograms (limited multi-angular binocular images): Multiple viewing-angle stereoscopic image, or a limited multi-angular binocular image, being a view/image/measurement/calculation/representation (holographic projection), of a two or three- dimensional spatial form. Normally, this class of perspective representation has a limited range of viewing position(s)/scale(s).
  • Unlimited-angle image: virtual reality (unlimited binocular), or mirror images: Unlimited viewing-angle(s), plus roaming station point(s), image, of stereoscopic type, being a binocular three-dimensional perspective view/image/measurement/calculation/representation (holographic projection), of two or three-dimensional spatial form. This class of perspective representation has unlimited viewing positions and angles/scales, and is often a New Media system (or mirror system).

3-D Perspective: Stereoscopy

Stereoscopy, stereoscopics or stereo imaging, is a technique for creating the illusion of depth in an image using stereopsis for binocular vision. The word stereoscopy derives from Ancient Greek στερεός (stereós) ‘firm, solid’ and σκοπέω (skopéō) ‘to look, to see’. A stereoscopic image is called a stereogram. 

Most stereoscopic methods present a pair of two-dimensional images to the viewer, or left and right eyes respectively. When viewed, the human brain perceives the images as a single 3-D view, giving the viewer the perception of 3-D depth. However, the 3-D effect lacks proper focal depth, which gives rise to the Vergence-accommodation conflict. Stereoscopy is distinguished from other types of 3-D displays that display an image in three full dimensions, allowing the observer to increase information about the 3-dimensional objects beingdisplayed by head and eye movements.

Binocular Vision

3-D perspective (visual type) is any type of stereoscopic perspective view that gives a human being an impression of depth by using his/her binocular vision or binocular perceptive system. Humans have binocular vision, which means there is an overlap of a portion of the visual world perceived by each eye (each eye sees the same object from a slightly different viewing angle).

This binocularity of human vision or difference in the shape of the separate images from each eye can be used by the brain to provide the impression of 3-D or dimensional relief for nearby objects. Ergo, the physical world appears as a natural 3-D perspective view due (in part) to the binocular capability of human vision. Note that a live mirror image is inherently a stereoscopic image. Note that monocular depth cues (including monocular perspective) also play a (major) part in the human perception of spatial extension or depth. See: binocular vision, mirror.

Binocular Optics

Another way to capture, measure, or produce an artificial 3-D stereoscopic image/view is by using instrumentation. Holograms, stereograms, 3d cinema, Virtual Reality headsets, etc; are all systems that generate binocular images/views that portray binocular depth cues to give a realistic impression of depth.

Autosteroscopy

Form of artificial 3-D stereoscopic view made without using special headgear, glasses or something that affects vision, for example, autostereograms, or lenticular, integral, parallax displays, etc. Volumetric and some LED displays are also (in a sense) autosteroscopic, as they produce a different image for each eye, but only in terms of the apparent screen viewing angle.

3-D: Spherical Panorama

Imaging/projecting (mixed perspective) type of technical perspective that captures/ represents/projects a full 360-degree spherical panorama for a surrounding visual scene.

3-D Film

3-D films are motion pictures made to give an illusion of three-dimensional (3-D) spatial solidity, usually with the help of special glasses worn by viewers. They have existed in some form since the year 1915, but had been largely relegated to a niche in the motion picture industry because of the costly hardware and processes required to produce and display a 3-D film, plus due to the lack of a standardized format for all purposes/applications.

However, 3-D films were prominently featured in the 1950s in American cinema, and later experienced a worldwide resurgence in the 1980s and 1990s driven by IMAX theaters and Disney-themed venues. 3-D films became increasingly successful throughout the 2000s, peaking with the success of 3-D presentations of Avatar in December 2009, after which 3-D films again decreased in popularity.

3-D Modelling

  • Three-dimensional physical model: Three-dimensional physical model of a spatial object/scene (normally single scale image/view, and may be true or actual life-sized scale, or be at a reduced/magnified scale).
  • Three-dimensional computer model: Three-dimensional modelling is the computer graphic process of developing a mathematical coordinate-based representation of the visible surface(s) of a spatial object in three dimensions using specialised software, and by manipulating edges, vertices, and polygons in a 3-D image/model space.

360-Degree Perspective

Formation/generation/viewing of a 360-degree image/view of the entire surrounding spatial scene/ optical vista or panorama. Relates to spherical, total, circular, panoramic, 3-D (type 3) perspective(s), and sphere of vision, looking out/around perspective.

3-D Display – Design

A surface 3-D display device, or other type of optical/volume 3-D display, may be capable of conveying depth to the viewer by application of one or more depth cues, often using film or digital media based images.

There are at least six basic kinds of 3-D surface displays used for binocular vision:

  • Stereoscopic surface display (uni-angular, multi-angular, VR/AR [plus BOOM]): Stereoscopic displays produce a 3-D effect using stereopsis, but can cause eye strain and visual fatigue. Stereoscopic 3-D displays are commonly used in VR / AR. Also a BOOM AR overlays a digital universe onto the physical universe. Holograms are intrinsically stereoscopic (no eye-strain).
  • Light field 3-D surface display (mostly uni-angular type): A light field display produces a realistic 3-D effect by combining uni-angular stereopsis and accurate focussing depth cues for the displayed content.
  • Lenticular auto-stereoscopic 3-D surface display (uni-angular parallel type): A lenticular 3-D display produces a parallax type of 3-D stereoscopic image/view.
  • Holographic 3-D surface display (multi-angular type): A holographic display produces a more realistic 3-D effect using interactive holograms (holographic images of motion type), and by combining multi-angular stereopsis and accurate focussing depth cues, moving station-point, variable resolution effects (zooming), binocular vergence and parallax, plus 3-D shape changes due multiple viewing angles for the displayed content. At the time of writing no widely available holographic displays have been invented or have become available for widespread use (not including mirror images).
  • Swept Plane 3-D Display: a structure from motion technique creating the optical illusion of a volume of light, due to the persistence of vision property of human visual perception. The principle is to have a 2-D lighted surface sweep in a circle, creating a volume. The image on the 2-D surface changes as the surface rotates. The lighted surface needs to be semi-translucent.
  • Virtual 3-D Display (projected field-of-view): generation of 3-D display using VR headset

We can also classify surface displays in terms of distance from the observer’s eye:

  • Distance of 3-D display: A: Near-eye, B: Distant as in TV or theatre screen: 3-D displays can be: near-eye displays as in VR headsets, or they can be further away from the eyes like a 3-D-enabled mobile device or 3-D TV, or a 3-D movie theatre.

We can also classify the displays in terms of display/image form:

  • Physical screen 3-D display: C: Flat, D: Volumetric (curved / spherical): Notably the term “3-D display” can also be used to refer to a volumetric display which may generate content that can be viewed from multiple angles (volume screens etc).
  • Real-space image 3-D display
  • Hologram
  • Reflection hologram
  • Other

Still other kinds of displays are possible, for example, projection onto retina, and andotrope, etc. See: 3-D, 3-D perspective (1, 2, 3, 4), volume display, andotrope, fan-hologram, BOOM, visual perspective.

3-D Display – Views

For an artificial perspective image display system, there are four kinds of 3-D view:

  • Uni-angular view of uni-angular image of spatial scene/object: Ordinary 2-D perspective image displayed on a surface display or computer monitor.
  • Multi-angular view of uni-angular image of spatial scene/object: The term “3-D” is also used for a volumetric display which displays uni-angular images observed from multiple angles (onlooker changes to direction of gaze), whereupon the images are notionally viewed in 3-D, but without experiencing image-based angular perspective changes. Only (uni-angular) perspective cues are available. Example: flat or 2-D images viewed/present in a 3-D space.
  • Multi-angular view of multi-angular image of spatial scene/object: The term “3-D” is also used for a volumetric display which generates content that can be viewed from multiple angles, the same being multi-angular images captured/generated by/for viewing from multiple viewing angles, whereupon the onlooker (may) experience multi-angular perspective depth cues (on directional screen canvas). Example: spatial or 3-D images/views that are viewed/present in a 3-D space and that are presented/viewed from multiple or changing viewpoints (or viewing angles).
  • Omnidirectional representation of 2-D scene/object (monocular): A type of 3-D perspective that enables a flat 2-D image to project the same aspect or geometry from omnidirectional viewpoints. See Andotrope, Zoetrope, and 3-D/2-D Perspective.

3-D Display – Basic Definition

We can now consider what a 3-D display is, in and of itself.

Unfortunately, as with our definition for 2-D displays, and given the definitions established above, and other related definitions given in our Dictionary of Perspective, it becomes difficult to provide a single all-encompassing definition for the term 3-D display; because there are many different kinds of representation and associated display methods (as explained above), and hence a variety of both 2-D and 3-D  display types are in common use; to say nothing of many hybrid types such as volume displays, etc.

Perhaps for the term 3-D display, we can settle on uni-angular or multi-angular, stereoscopic perspective representations, whereby the image or view is displayed either on a 2-D or 3-D surface/volume, but is of the binocular type (red/blue or lenticular display, etc). Whereby the term refers to both uni-angular and multi-angular images; and therefore encompasses standard 3-D television and 3-D cinema techniques, holograms, plus Virtual Reality (VR/AR/XR) and CAD/CAM perspective models, etc, plus includes the new kinds of volume and volumetric displays as well.

In sum, the classification of a display into either the 2-D/3-D display type, may be dependent upon application, usage scenario, and probably depends upon the types of images commonly displayed on said device; whereby the term 3-D normally refers to stereoscopic images; but may include multi-view systems such as VR or CAD/CAM models, and also multi-viewpoint or multi-angular images, etc.