Local coordinates


Local coordinates

Local coordinates are measurement indices into a "local coordinate system" or a "local coordinate space". A simple example is using house numbers to locate a house on a street; the street is a local coordinate system within a larger system composed of city townships, states, countries, etc.

Local systems exist for convenience. Continuing the geographic example, one could use latitude and longitude for all terrestrial locations, but unless one has a highly precise GPS device, this is impractical.

Local coordinate spaces are also useful for their ability to model independently transformable aspects of geometrical scenegraphs. 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. The disadvantage is 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 millimetres 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 centimetres, and the terrain that the car travels on could be specified in meters.

In differential topology, local coordinates on a manifold 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.


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Local search (Internet) — Local search is the use of specialized Internet search engines that allow users to submit geographically constrained searches against a structured database of local business listings. Typical local search queries include not only information… …   Wikipedia

  • Local post — A local post is a mail service that operates only within a limited geographical area, typically a city or a single transportation route. Historically, some local posts have been operated by governments, while others, known as private local posts… …   Wikipedia

  • Local Land and Property Gazetteer — A Local Land and Property Gazetteer (LLPG) is an address database maintained by local authorities in the United Kingdom. In the UK local authorities have responsibility for creating all addresses, however, until recently those same local… …   Wikipedia

  • Normal coordinates — In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space… …   Wikipedia

  • Fermi coordinates — In the mathematical theory of Riemannian geometry, Fermi coordinates are local coordinates that are adapted to a geodesic. More formally, suppose M is an n dimensional Riemannian manifold, gamma is a geodesic on M, and p is a point on gamma. Then …   Wikipedia

  • Isothermal coordinates — In mathematics, specifically in differential geometry, isothermal coordinates on a Riemannian manifold are local coordinates where the metric is conformal to the Euclidean metric. This means that in isothermalcoordinates, the Riemannian metric… …   Wikipedia

  • Canonical coordinates — In mathematics and classical mechanics, canonical coordinates are particular sets of coordinates on the phase space, or equivalently, on the cotangent manifold of a manifold. Canonical coordinates arise naturally in physics in the study of… …   Wikipedia

  • Museum of Local History (Milton, Florida) — Coordinates: 30°37′23″N 87°02′12″W / 30.6231°N 87.0366°W / 30.6231; 87.0366 …   Wikipedia

  • Meddon Green Local Nature Reserve — Coordinates: 50°55′59″N 4°27′07″W / 50.933°N 4.452°W / 50.933; 4.452 …   Wikipedia

  • Curvilinear coordinates — Curvilinear, affine, and Cartesian coordinates in two dimensional space Curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian… …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.