Local coordinates are the ones used in a ''local
coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
'' or a ''local
coordinate space''. Simple examples:
* Houses. In order to work in a house construction, the measurements are referred to a control arbitrary point that will allow to check it: stick/sticks on the ground, steel bar, nails...
* Addresses. Using house numbers to locate a
house on a
street
A street is a public thoroughfare in a built environment. It is a public parcel of land adjoining buildings in an urban context, on which people may freely assemble, interact, and move about. A street can be as simple as a level patch of di ...
; the street is a local coordinate system within a larger system composed of city townships, states, countries, postal codes, etc.
Local systems exist for convenience. On ancient times, every work was made on relative bases as there was no conception of global systems. Practically, it is better to use local systems for small works as houses, buildings... For most of the applications, it is desired the position of one element relative to one building or location, and in a more local way, relative to one furniture or person. In a regular way, you will not give your position by geographical coordinates rather than "I am 15 meters away of the entry to the building". So it is a pretty common way to locate things.
It is possible to bring
latitude and longitude for all terrestrial locations, but unless one has a highly precise
GPS device or you make astronomical observations, this is impractical. It is much simple to use a tape, a rope, a chain... The position information (global) should be transformed into a location. Position refers to a numeric or symbolic description within a spatial reference system, where as location refers to information about surrounding objects and their interrelationships. (
Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called poin ...
)
Use
In
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
and
computer animation, local coordinate spaces are also useful for their ability to model independently transformable aspects of geometrical
scene graphs. When modeling a car, for example, it is desirable to describe the center of each wheel with respect to the car's coordinate system, but then specify the shape of each wheel in separate local spaces centered about these points. This way, the information describing each wheel can be simply duplicated four times, and independent transformations (e.g., steering rotation) can be similarly effected. Bounding volumes of objects may be described more accurately using extents in the local coordinates, (i.e. an
object oriented bounding box, contrasted with the simpler
axis aligned bounding box). The trade-off for this flexibility is additional computational cost: the rendering system must access the higher-level coordinate system of the car and combine it with the space of each wheel in order to draw everything in its proper place.
Local coordinates also afford digital designers a means around the finite limits of numerical representation. The tread marks on a tire, for example, can be described using millimeters by allowing the whole tire to occupy the entire range of numeric precision available. The larger aspects of the car, such as its frame, might be described in centimeters, and the terrain that the car travels on could be specified in meters.
In
differential topology, local coordinates on a
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
are defined by means of an
atlas of charts. The basic idea behind coordinate charts is that each small patch of a manifold can be endowed with a set of local coordinates. These are collected together into an atlas, and stitched together in such a way that they are self-consistent on the manifold.
In
Cartography
Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an i ...
and
Maps, the traditional way of works are
local datum. With a local datum
the land can be mapped on relative small areas as a country. With the need of global systems, the transformations on between datum became a problem, so geodetic datum have been created. More than 150 local datum have been used in the world.
See also
*
Bounding volume hierarchy
*
Coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sig ...
*
Geographic coordinate system
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...
*
Laboratory frame of reference
*
Local reference frame
In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime.
The term is most often used in t ...
*
Local tangent plane coordinates
Local tangent plane coordinates (LTP), also known as local ellipsoidal system, local geodetic coordinate system, or local vertical, local horizontal coordinates (LVLH), are a spatial reference system based on the tangent plane defined by the local ...
*
Skeletal animation
References
{{DEFAULTSORT:Local Coordinates
Cartography
Computer graphics
Geometry
Coordinate systems