Three-dimensional space

3D, 3 -D or 3D is a common abbreviation for three-dimensional or three dimensions ( in construction " in 3-D" ) and a synonym for the spatial representation of bodies. It is a representation variant that usually, but not necessarily consists of the space dimensions of length, width and height.

Basis

Represent an object in 3 - D is to map each point of the object and its position in space by a vector whose components specify the coordinates in three-dimensional space. The coordinate system is then referred to as follows:

  • (x, y, z) - Cartesian coordinate system for
  • (r θ, φ ) - for spherical coordinates

And especially for two-dimensional coordinate systems with an additional height coordinate:

  • (B, L, H) - where B, L geographic coordinates mean
  • (X, Y, H) - with X, Y as Gauss -Krüger coordinate system

2 ½ -D vs. 3 -D

For the transmission of spatial images and models, various methods are available:

  • Transfer of the entire 3 -D model ( and render the views on the target device )
  • Transferring a 2-D image with the additional depth information ( similar to the color difference signals for color images )
  • Transmission of two or more views of the image.

Each method has advantages and disadvantages and depending on the source material more or less practical.

Transfer of the entire 3 -D model: By far the most expensive method. Technically feasible only when the image is already calculated in the computer. Images are high reality with today's technology can not be calculated in real time. The main advantage is, however, that one can calculate views from all directions. With appropriate tracking mechanisms it is possible to create models to walk around or go inside.

Transferring a 2-D image with the additional depth information: This is often referred to as a 2 ½ -D. It requires very little information for transmission. However, it is not possible to map caused by parallax different overlaps neat. To a limited extent, views for different viewing directions are renderbar.

Transmission of two or more views of the image: Transmission of mostly 2 ( in some processes even up to 8) finished images for the two eyes (or for different direction) are intended. High quality. Direct with suitable cameras produced. Compared to 2 ½ -D but higher data rates and space required.

4D, and the time as another dimension

Often, the time is considered to be another dimension. It is then often spoken of 4- D or 4 dimensions. Although any spatial coordinate represents the time, but is often visualized as a spatial coordinate: This can be done by means of an axis in a graph in which the time combined with an additional information (eg distance ) is applied.

3 -D, 4- D, 2 ½ -D

The term 3 -D is used primarily in the trigonometric calculation and production of spatial volume models.

References made in 3-D coordinates may however also be objects that have fewer than three spatial dimensions and in which the third coordinate describes another property, such as time, color or a color channel:

  • (X, Y, I )

For example, a coordinate of a space axis, the second, the time axis, and the third color, it is possible to describe a distance which varies with time, length and color. Also, one could imagine an area that changes its shape with the time, if it be a two-dimensional surface with a time indication - such as in a time series of images, photomontages, in files, etc.

A three-dimensional model which is additionally defined by a time axis is called 4D model. This term is used in both the physics of the space-time, as well as figuratively for computer models and animations.

Line models are usually described by points with two coordinates that are = on one level with the height coordinate Z 0 are. The additional definition of a Hochzugswertes - an attribute through which the line receives an amount in the Z - axis - you can, however, from a two-dimensional line model very easily generate a spatial model that is called zweieinhalbdimensional, abbreviated as 2 ½ D or 2.5 -D.

The difference between 2 ½ - D and 3- D is in the nature of the height ( attribute instead coordinate) and in certain restrictions. So it may at 2 ½ D models lead to unexpected optical effects, because the intersection of the Hochzugslinien is not mathematical- geometrical clearly defined.

Simulation of three-dimensionality

Many of illustration specific problems and the orientation in space can be solved by spatial perception of the people that is because two different planar images are assembled on the retina to form an image with a spatial depth ( Z) by the distance between the eyes, with their Help us to distinguish the foreground from the background.

  • Perspective is the study of the three-dimensional representation, which is removed by the proportional rejuvenation underlying objects and the enlarged view of the foreground objects is created. This enables it to generate a spatially -looking image in a graphical manner on a two dimensional surface. The 3 -D computer graphics uses this opportunity to create a spatially -looking picture on the flat screen graphics of 3- D- ordinates and levels of brightness using 3D graphics software.
  • A 3 -D image in the three-dimensional photography, stereoscopic image or 3D movie, three-dimensional movie: Subject recording and playback pictures or images that convey a true spatial impression, for example, each eye as in reality is only the corresponding side slightly offset part image is presented, for example by 3D glasses on the basis of anaglyph or polarization or shutter technology, a stereoscopic image into two signal paths separately. Another method of artificially generated three-dimensional image representation is applied in single image stereogram (SIS).
  • Three-dimensional sound: the spatial localizable reproduction of sounds, for example, by several speakers that occupy similar positions as the microphones when recording (stereo, quadraphonic, surround sound, 5 1, 6 1 ) or via headphones at the dummy head stereophonic.
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