2-D Displays

In this section, we review principles of 2-D displays as applied to perspective views/images; axioms which apply to all kinds of: computer monitors/displays/screens, televisions, smartphone and tablet displays, LCD/LED panels, and also projection systems such as data projectors, cinema screens, etc. For examples of how different displays are applied and used in practice (in relation to perspective), see the explanations given under the camera perspective section.

In terms of a perspective view/image, whenever we talk of a 2-D display, we usually consider how to display a 1-D/2-D/3-D image of a spatial object/scene on a two-dimensional or 2-D surface (ostensibly). Ergo, as explained below, we are dealing with a so-called 1-D, 2-D or 3-D perspective image and related representation principles.

We begin with general definitions for 1-D, 2-D, and 3-D perspective.

1-D Perspective

Refers to a perspective image of a point (rare term: singular projection of a 1-D point). Defined as a one-dimensional (1-D) perspective representation of a point (aberration free projection), being a 1-D perspective view/image/measurement/calculation, or 1-D plan/elevation projection, etc., of one-dimensional (1-D) object point, present in a 2-D or 3-D object space, and represented in a 2-D or 3-D image space. See: 2-D, 3-D Perspective.

2-D Perspective

Refers to a perspective image of a 2-D form (rare term: e.g. 2-D line projected as 1-D point or 2-D line). Defined as a one or two-dimensional (1-D/2-D) perspective representation of a 2-D form (line or planar shape), being a 1-D/2-D perspective view/image/measurement/calculation, or 1-D/2-D plan/elevation projection, etc., of two-dimensional (2-D) object form, present in a 2-D or 3-D object space, and represented in a 2-D or 3-D image space. See: 1-D, 3-D Perspective.

3-D Perspective

Refers to a perspective image of a 1-D / 2-D / 3-D form (ordinary definition of perspective). Defined as a one, two or three-dimensional (1-D/2-D/3-D) perspective representation of 1-D/2-D/3-D form, being a 1-D/2-D/3-D view/image/measurement/calculation, or 1-D/2-D/3-D plan/elevation projection, etc., of 1-D/2-D/3-D spatial form, present in a 3-D object space, and represented in a 2-D or 3-D image space. See: 1-D, 2-D Perspective.

Now that we have these basic definitions for the different kinds of perspective, we can consider what an artificial representation of a spatial object/scene is.

3-D: Artificial Representation

An artificial representation of a spatial object/scene can be defined and/or considered in several ways.

To begin, we can consider the ordinary definition; where any non-natural perspective view/image is considered ‘artificial’ whereas all graphical, mathematical, instrument perspectives and basically all human-made images/views are considered to be of the artificial class. In this sense, natural perspective images like environmental and visual perspective are considered entirely separate from the artificial class.

However, because natural and visual images are often created by, or used in combination with, instrument perspective and/or new media perspective, etc, we realise that the distinction between natural and artificial perspective is not so well-defined and that artificial perspective and related images in a sense encompass the natural kind.

In artificial perspective (imaging class), there are at least five kinds of 3-D representation:

Uni-angular, monocular representation of spatial scene/object: A 1-D/2-D/3-D image/view/measurement/calculation of a spatial scene/object captured/depicted from a single viewpoint or viewing angle. A 2-D linear perspective image of a spatial scene/object projected onto a 2-D surface or picture plane, is one example, captured from a fixed viewing angle.
Uni-angular, binocular representation of spatial scene/object: A 1-D/2-D/3-D image/view/measurement/calculation of a spatial scene/object captured from a fixed central viewing angle, using a binocular method (twin apertures looking at very slightly different viewing angles). Viewing a stereoscopic image of spatial scene/object is one example, employing monocular perspective depth cues, and certain binocular depth cues.
Multi-angular, monocular, or binocular representation of spatial scene/object: A 1-D/2-D/3-D image/view/measurement/calculation of a spatial scene/object captured from multiple viewing angles, using either a monocular or binocular method. Viewing a hologram image is an example of multi-angular binocular 3-D, employing depth cues such as monocular perspective, focussing plus (partial) natural scaling and variable resolution effects, binocular vergence and parallax, plus 3-D shape changes due to (a narrow range of) multiple viewing angles, etc.
Unlimited-angle representation of spatial scene (monocular or binocular, includes mirrors): A 1-D/2-D/3-D image/view/measurement/calculation/model of a spatial scene/object captured/ modelled from (ostensibly) every viewing angle, using either a monocular or binocular method. Viewing/exploring a digital model (CAD computer modelling), or a Virtual Reality world, is an example of either unlimited viewing-angle monocular or binocular 3-D. With binocular 3-D, employed can be depth cues such as monocular perspective (looking out/around plus looking in/at), possibly focussing, and (fully) natural scaling, and variable resolution effects (zooming perspective), binocular vergence and parallax, plus 3-D shape changes due multiple viewing angles, etc.
Omnidirectional representation of 2-D scene/object (monocular) or 3-D scene/object (binocular): For example, 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.

The above list is by no means exhaustive. Any of the monocular/binocular depth-cues are available to aid in the representation of 3-D, or can be seen in a (2-D display projected) natural/visual view of spatial reality, depending upon the limitations of the perspective method/system (or category) and also media employed.

2-D Display – Varied Definition(s)

We can now consider what a 2-D display is, in and of itself.

Unfortunately, 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 2-D display; because there are many different kinds of representation and associated display methods (as listed above), and hence a variety of 2-D display types are in common use.

Perhaps for the term 2-D display, we can settle on uni-angular, monocular perspective representations, whereby the image or view is displayed on a 2-D surface, or a planar surface, being the ordinary flat-panel television, computer monitor or smartphone screen, etc. Alternatively, we could include under the term 2-D display, also a uni-angular, binocular representation of spatial scene/object, or the typically ‘flat’ but perceived as stereoscopic duel red-blue images, etc.

Overall, we can state that a 2-D display is normally considered to be a flat or planar LCD/LED panel (in form / physical shape) upon which ‘flat’ or ‘planar’ perspective images can be displayed, such images being similar to those captured on a camera with a planar/flat shaped image detector, equivalent to a planar perspective window or planar picture plane. In other words, such a 2-D display is being used to display central perspective images similar to those captured/created by a 1-2-3 point linear perspective category/form or graphical method, etc.

However, patently in the modern world 2-D display screens can also be of the curved/spherical type (ref. one or more 2-D screens arranged or shaped/warped to provide a curved/spherical shape for the overall display), plus also be external displays (curved screens looked at from the outside), or internal displays (curved screens looked at from the inside). Such displays can be used for displaying either ‘flat’; or central perspective images, or alternatively spherical perspective images and/or multi-directional images. However, whether or not curved/spherical displays are included as existing under the 2-D display moniker is debatable (some people place such displays under the 3-D display class, including, for example, volume displays, etc).

In sum, the classification of a display into either the 2-D/3-D display class, may depend upon application, usage scenario, and even the types of images commonly displayed on said device.