Perspective image of a point (rare term: singular projection of a 1-D point)

One-dimensional (1-D) perspective representation of a point (possibly 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: 1-D, 2-D, 3-D Perspective.

Perspective image of a 2-D form (rare term: e.g., 2-D line projected as 1-D point or 2-D line) 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 a 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, 2-D, 3-D Perspective.

In video games, 2.5-D perspective describes movement or representation largely restricted to a two-dimensional plane within an environment that appears three-dimensional. Early examples often used plan or side-elevation views with sprite-like characters. A common technique is the skybox, in which distant scenery is mapped onto the faces of a cube to create the illusion of a surrounding 3-D world. A skydome uses a sphere or hemisphere instead. Both are forms of fixed 3-D, where real-time foreground objects appear against a relatively static background.

So-called 2.5-D, 3/4 perspective, and pseudo-3-D describe graphical projections and techniques that try to give an impression of spatial depth, typically using parallel projection. Examples of other pseudo-3-D techniques include billboarding (textured objects that face the camera), parallax scrolling, and scaling (approximation of perspective recession).

See: billboarding, parallax scrolling/scaling, pseudo-3-D perspective.

Within artificial perspective, there are at least five kinds of 3-D representation:

Perspective categories, classes, types, forms and 3-D

Three-dimensional space is a mathematical and physical space in which three values or coordinates are normally required to determine the position of a point. In perspective, 3-D may refer to physical object space, to an optical or visual experience of depth, or to a graphical, instrument-generated, simulated or computational representation of spatial reality. Visual Perspective Type 1 is the broad category encompassing the visual presentation or appearance of spatial objects, scenes, views and images. It includes both direct visual appearances and represented images used to depict spatial objects and scenes or create an impression of depth and three-dimensional space. Visual Perspective Type 2 is the human retinal-perceptual subclass within Type 1 and concerns perspective as formed and experienced through the human visual system.

Optical perspective uses light or other electromagnetic radiation to form, transmit, reflect, refract, focus or project views and images of spatial reality. Instrument perspective concerns views and images produced, modified, measured or displayed through cameras, lenses, microscopes, telescopes, mirrors, projectors, surveying devices and related instruments. Technical perspective may be used as a broad descriptive term for systematic methods of viewing, imaging, measuring, constructing, projecting or representing spatial objects and scenes, but it is not treated here as a separate principal category.

Within the Viewing or Imaging Class, perspective commonly operates in the backward or image-forming direction: light, visual information or spatial data passes from an object or scene towards an eye, sensor, image plane or imaging system, where a view or image is formed, captured, measured or perceived. Within the Projecting Class, perspective may operate in the forward direction: light, images, shadows, lines or spatial information are projected from a source, eye point, projector, image plane or representational system into physical, graphical, optical or simulated space. Some perspective systems employ both directions.

Perspective Category Theory distinguishes the principal source or mode of a perspective process from its principal direction. The principal categories are Natural, Visual, Optical, Mathematical, Graphical, Instrument, Simulated and New Media Perspective. The two basic directional classes are Viewing or Imaging, and Projecting. Representing, measuring, modelling, illusion and immersion are treated as functions, goals or outcomes rather than as additional basic classes.

More than one category is often involved in producing, displaying or viewing a perspective image. When categories operate sequentially, the process is called category chaining. The resulting multi-category process, system or image may be described as composite perspective. For example:

Natural scene -> optical and instrument imaging -> New Media processing ->

instrument or New Media display -> Visual Perspective Type 2

This sequence may involve Natural Perspective within the original physical scene, Optical and Instrument Perspective within the camera, New Media Perspective during digital processing, Instrument or New Media Perspective during display, and Visual Perspective Type 2 when the resulting image is viewed and perceived by a human observer. The same perspective term, type or process may also legitimately belong to more than one top-level category. This is called category overloading. A linear-perspective drawing, for example, may be mathematical because it is governed by geometrical relations and graphical because it is constructed in a drawing. A digitally rendered linear-perspective image may also belong to New Media Perspective, while a similar convergence appearing in a camera image may belong to Optical and Instrument Perspective.

A perspective type may also name both a method and the visible form produced by that method. Linear perspective, for example, may refer to a mathematical or graphical construction process and also to the resulting geometrical arrangement of lines, apparent sizes, shapes and positions. Perspective must therefore be understood as both a process and an outcome:

Perspective = method or process + resulting image, view or spatial appearance

At least four principal divisions of perspective form can be distinguished:

• Perspective of Form <GEOMETRICAL FACETS>: changes in apparent geometry, outline, size, shape, position or orientation. Linear perspective is one example.
• Gradient of Colour Perspective <OPTICAL FACETS>: changes in colour, hue or saturation associated with distance or optical conditions; aerial perspective is one example.
• Gradient of Acuity Perspective <OPTICAL AND GEOMETRICAL FACETS>: changes in clarity, sharpness, resolution or visible detail.
• Gradient of Chiaroscuro Perspective <OPTICAL FACETS>: changes in light, shade and contrast that contribute to depth or spatial recession.

The graphical type of linear perspective, or perspective of lines and outlines, provides a structured method for depicting on a surface the apparent size, shape and relative position of objects within a three-dimensional scene. It is used to represent physical space through such familiar elements as the horizon line, eye point, perspective window, vanishing point and geometrical or checkerboard grid.

Graphical linear perspective is, however, only one of at least three broad types or applications of linear perspective:

• Graphical or Artificial Linear Perspective: construction of a drawing or image of a spatial object or scene according to one-point, two-point, three-point or related perspective systems.
• Natural, Visual or Optical Linear Perspective: the apparent convergence and geometrical transformation of lines and forms when a spatial object or scene is viewed directly or imaged through an optical instrument. A metric grid or regularly constructed object space may make these effects especially clear.
• Physically Constructed or Simulated Linear Perspective: modification of the physical environment through forced or simulated perspective so that objects and spaces conform to, exaggerate or counteract the apparent rules of one-point, two-point or three-point perspective.

Perspective relates three-dimensional object or target space to visual, optical, graphical or represented image space. Perfect one-to-one correspondence is often impossible because viewpoint, apparent size and aspect, scale, optical aberration and limited resolution may reduce, conceal, compress or distort spatial information. Real-world viewing and camera imaging may therefore differ from ideal geometrical models, especially towards the edges of wide-field eye or lens images, where curvilinear, spherical and other wide-angle effects can arise.

Controlling this correspondence problem is a major goal of visual, optical, graphical and technical perspective. Where accurate dimensions or spatial relations are more important than natural appearance, parallel projection, orthographic systems, calibrated imaging, cartographic methods and other corrective procedures may be used to preserve selected properties and reduce viewpoint-based distortion.

In conclusion, natural, visual and artificial perspective systems produce structured spatial appearances that arise partly from the object or target space, partly from the perspective process or system, and partly from the scale, resolution, viewpoint and medium involved. The resulting 3-D view or image may therefore combine Natural, Visual, Optical, Mathematical, Graphical, Instrument, Simulated and New Media processes. It should be understood by distinguishing its categories, two directional classes, particular types and visible forms.

A surface 3-D display device, or other type of optical/volume 3-D display, can convey depth using binocular cues from film or digital images, and/or by application of one or more other depth cues.

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

Distance from Observer’s Eye

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

Distance of 3-D display:

Display Form

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

Physical screen 3-D display:

Real-space image 3-D display:

Still, other kinds of displays are possible, for example, retinal projection, andotrope displays, etc.

See: 3-D, 3-D perspective (1, 2, 3, 4), volume display, andotrope, fan-hologram, BOOM, visual perspective.

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

See: 3-D display design, hologram, computer display/monitor, andotrope, LED volume screen.

Three-dimensional (3-D) or stereoscopic films create the illusion of spatial depth, using special glasses. Although they originated in 1915, their high production costs and lack of standardisation limited their use. 3-D films gained popularity in the 1950s and saw a resurgence in the 1980s and 1990s, particularly with IMAX and Disney. Their success peaked with Avatar in December 2009, after which interest declined. This may be because stereoscopic/binocular methods are only one class of several ways humans interpret 3-D, including other depth cues and perspective phenomena such as structured changes in image size and shape as seen in ordinary linear perspective.

See: computer/digital perspective, CGI, CAD, geometry, ray-tracing, Hoberman sphere, wire-frame perspective, New Media perspective, 3-D display design, 3-D display views.