# 3D

Three-dimensional Cartesian coordinate system with the X, Y and Z coordinates
3D effect of a sphere

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

The term is u. a. also used to delimit objects with spatial expansion from two-dimensional ( 2-D ) objects, where the essential elements are in one plane .

## basis

To represent an object in 3-D means to map every point of this object and its position in space by a vector , the components of which determine the coordinates in three- dimensional space. The coordinate system is then designated as follows:

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

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

## 2½-D vs. 3-D

Various methods are available for transferring spatial images and models:

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

Each method has advantages and disadvantages and is more or less practical, depending on the starting material.

Transfer of the entire 3-D model : by far the most complex process. Technically only feasible if the image is calculated in the computer anyway. Images of high reality cannot be calculated in real time with today's technology. The main advantage, however, is that you can calculate views from all directions. With suitable tracking mechanisms it is possible to walk around or inside models.

Transmission of a 2-D image with additional depth information : This process is often referred to as 2½-D. Little information is required for transmission. However, it is not possible to properly map different overlaps caused by parallax. To a limited extent, views for different viewing directions can also be rendered.

Transfer of 2 or more views of the image : Transfer of mostly 2 (with some methods up to 8) finished images for which both eyes (or for different directions) are intended. High quality. Can be generated directly with suitable cameras. Compared to 2½-D, however, higher data rates and storage space are required.

## 4-D and time as a further dimension

Often time is seen as an additional dimension. We often speak of 4-D or 4 dimensions. Although time does not represent a spatial coordinate, it is often visualized like a spatial coordinate. This can be done, for example, by means of an axis in a diagram in which the time is plotted combined with further information (e.g. distance).

## 3-D, 4-D, 2½-D

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

Information in 3-D coordinates can, however, also concern objects that have less than three spatial dimensions and for which the third coordinate describes another property, such as time, color or a color channel :

• ${\ displaystyle (X, Y, i)}$

For example, if one coordinate is a spatial axis, the second is the time axis and the third is a color, you can describe a route that changes length and color over time. One could also imagine a surface that changes its shape over time if it is a two-dimensional surface with a time specification - such as a time series of images, photo montages , in files , etc.

A three-dimensional model that is also defined by a time axis is called a 4D model. This term is used both in physics for space-time and, in a figurative sense, for computer models and animations .

Line models are usually described by points with two coordinates each, which are located on a plane with the height coordinate Z = 0. With the additional definition of a pull-up value - an attribute that gives the line a height in the direction of the Z-axis - it is very easy to create a three-dimensional model from a two-dimensional line model, which is called two-and- a- half -dimensional , abbreviated 2½D or 2.5 -D .

The difference between 2½-D and 3-D lies in the type of height (attribute instead of coordinate) and in certain restrictions. With 2½D models, for example, unexpected optical effects can occur because the intersection of the elevation lines is not clearly defined mathematically and geometrically.

## Simulation of three-dimensionality

Lilac blossom in 3-D (anaglyph, red filter on the right)

.

Many imaging-specific problems and the orientation in space can be solved by the spatial perception of humans, which is based on the fact that two different flat images on the retina are combined into one image with a spatial depth (Z) through the distance between the eyes Help us to distinguish the foreground from the background.

• Perspective is the theory of three-dimensional representation that is created by the proportional tapering of distant objects and the enlarged representation of foreground objects. This enables a three-dimensional image to be created on a two-dimensional surface using graphic means. The 3D computer graphics uses this opportunity by means of 3D computer graphics software to generate a spatially looking image on the flat screen of graphics 3D-ordinates and brightness gradations.
• A 3-D image in three-dimensional photography , stereoscopic image or 3D film , three-dimensional film: if it concerns the recording and playback of images or films that convey a real spatial impression, for example, each eye will only see the corresponding side, as in reality Slightly offset partial image is presented, for example using 3D glasses based on anaglyphs or polarization or a stereoscopic image separated into two signal paths using shutter technology . Another, artificially created method of three-dimensional image representation is used in the single image stereogram (SIS).
• Three-dimensional sound : the spatial, localizable reproduction of sounds, for example through several loudspeakers that take up positions similar to those of the microphones during recording ( stereo , quadrophonic , surround sound 5 + 1, 6 + 1) or through headphones for artificial head stereophony .
• 3-D modeling is a method of creating 3D models that are used for virtual reality. These can be used in the context of the digital factory as virtual means of production (robots, load carriers, conveyor technology, etc.) as well as for private use, as 3D printing is becoming more and more affordable. 3D models can also be derived from photos.
• 3-D printing or prototyping is a method of generating real 3-D models from 3-D data using material printers.