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Local coordinates
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<h2 id="use">Use</h2> <p>In <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a> and <a href="/facts/Computer_animation/rPW63nm0">computer animation</a>, local coordinate spaces are also useful for their ability to model independently transformable aspects of geometrical <a href="/facts/Scene_graph/faNe9vSu">scene graphs</a>. 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 <a href="/facts/Object_oriented_bounding_box/oFHL8bxI">object oriented bounding box</a>, contrasted with the simpler <a href="/facts/Axis_aligned_bounding_box/oFHL8bxI">axis aligned bounding box</a>). 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. </p><p>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. </p><p>In <a href="/facts/Differential_topology/Y21eGQe0">differential topology</a>, local coordinates on a <a href="/facts/Manifold/rXPERJtu">manifold</a> are defined by means of an <a href="/facts/Atlas_(topology)/pjoya29t">atlas of charts</a>. 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. </p><p>In <a href="/facts/Cartography/8YdDAAeX">Cartography</a> and <a href="/facts/Map/KxQX4B2U">Maps</a>, the traditional way of works are <a href="/facts/Datum_reference/pwGglGnJ">local datum</a>. With a local datum<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> 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. </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Bounding_volume_hierarchy/1FBFkwNe">Bounding volume hierarchy</a></li> <li><a href="/facts/Coordinate_system/Mtd0q4SP">Coordinate system</a></li> <li><a href="/facts/Geographic_coordinate_system/RkjfcY6k">Geographic coordinate system</a></li> <li><a href="/facts/House_numbering/VzmnUPng">House numbering</a></li> <li><a href="/facts/Laboratory_frame_of_reference/WdBs8wgh">Laboratory frame of reference</a></li> <li><a href="/facts/Local_reference_frame/WdBs8wgh">Local reference frame</a></li> <li><a href="/facts/Local_tangent_plane_coordinates/q87CmjJI">Local tangent plane coordinates</a></li> <li><a href="/facts/Skeletal_animation/Bab11dVJ">Skeletal animation</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Kolodziej, Krzysztof W.; Hjelm, Johan (2017-12-19). Local Positioning Systems: LBS Applications and Services. CRC Press. ISBN 9781351837972. <a href="9781351837972" target="_blank">9781351837972</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>El-Rabbany, Ahmed (2002). Introduction to GPS: The Global Positioning System. Artech House. ISBN 9781580531832. <a href="9781580531832" target="_blank">9781580531832</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>