Proximity analysis

<h2 id="distance-measures">Distance measures</h2>
Main article: <a href="/facts/Distance/hbXlaEFk">Distance</a>
All
proximity analysis tools are based on a measure of distance between two locations. This may seen as a simplistic geometric measurement, but the nature of geographic phenomena and geographic activity requires several candidate methods to measure and express distance and distance-related measures.<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a>

<ul><li><a href="/facts/Euclidean_distance/9qDoQKQe">Euclidean distance</a>, the straight-line geometric distance measured on a planar surface. In geographic information systems, this can be easily calculated from locations in a cartesian <a href="/facts/Projected_coordinate_system/YyhuUx2f">Projected coordinate system</a> using the <a href="/facts/Pythagorean_theorem/Lh6x2Kr5">Pythagorean theorem</a>. While it is the simplest method to measure distance, it rarely reflects actual geographic movement.</li>
<li><a href="/facts/Manhattan_distance/zU7gGUPv">Manhattan distance</a>, the distance between two locations in a cartesian (planar) coordinate system along a path that only follows the x and y axes (thus appearing similar to a path through a grid street network such as that of <a href="/facts/Manhattan/fF9JeXjh">Manhattan</a>).</li>
<li><a href="/facts/Geographical_distance/r0a5tbgV"> Geodesic distance</a>, the shortest distance between two locations that stays on the surface of the <a href="/facts/Earth/HLLmDfj0">Earth</a>, following a <a href="/facts/Great_circle/x4fq6eNm">great circle</a>. On a <a href="/facts/Great-circle_distance/s6HNWn8e"> sphere</a>, the formula uses the <a href="/facts/Spherical_law_of_cosines/DYT3Er58">spherical law of cosines</a>, but the method is significantly more difficult on an ellipsoid.</li>
<li>Network distance, a measurement between two locations along a route within a constrained linear space, such as a <a href="/facts/Street_network/6vk6zHBE"> road</a> or utility network.</li>
<li>Abstract distance, a measurement of distance in a space that is only indirectly related to geographic space, or only metaphorically spatial. Examples include <a href="/facts/Social_network/kQg6aEVf">social networks</a> of interpersonal connections, <a href="/facts/Information_spaces/poV16cKW">information spaces</a> of related concepts, and the hypertext network of the <a href="/facts/World_Wide_Web/wvnTrWFq">World Wide Web</a>. Although these are not inherently geographic, projecting them into an abstract space allows geographic tools such as proximity analysis to be used to study them.<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a></li>
<li><a href="/facts/Cost_distance_analysis/SH00UXtG"> Cost distance</a>, a measurement along a route (in any of the above spaces) in which geometric distance is replaced by some other quantity that accumulates along the route (and is thus proportional to distance), called a cost because it generally serves as an undesirable quantity to be minimized.<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> Travel time is the most common cost measurement, but other costs include carbon emissions, fuel consumption, environmental impacts, and construction costs.</li></ul>
<h2 id="techniques">Techniques</h2>
There are a variety of tools, models, and algorithms that incorporate geographic distance, due to the variety of relevant problems and tasks.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a>

<ul><li><a href="/facts/Buffer_(GIS)/jKd2YzBa">Buffers</a>, a tool for determining the region that is within a specified distance of a set of geographic features.</li>
<li><a href="/facts/Cost_distance_analysis/SH00UXtG">Cost distance analysis</a>, algorithms for finding optimal routes through continuous space that minimize distance and/or other location dependent costs.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a></li>
<li><a href="/facts/Voronoi_diagram/AhQY5LD8">Voronoi diagram</a>, also known as Thiessen polygons, an algorithm for partitioning continuous space into a set of regions based on a set of point locations, such that each region consists of locations that are closer to one of the points than any others.<a class="footnote-ref" id="fnref:8" href="#fn:8">8</a></li>
<li><a href="/facts/Distance_decay/fkDmBpbk">Distance decay</a>, based on the <a href="/facts/Inverse_square_law/DxG4T15l">Inverse square law</a>, a mathematical model of how the influence of a phenomenon tends to be inversely proportional to the distance from it. A <a href="/facts/Gravity_model/W3U7dhQM">Gravity model</a> is a similar model.</li>
<li><a href="/facts/Optimal_facility_location/ssbU6ww2"> Location analysis</a>, a set of (usually heuristic) algorithms for finding the optimal locations of a limited set of points (e.g., store locations) that minimize the aggregate distance to another set of points (e.g., customer locations). A commonly used example is <a href="/facts/Lloyd%2527s_algorithm/LuersNRa">Lloyd's algorithm</a>.</li>
<li><a href="/facts/Distance_matrix/2ptk07Y7">Distance matrix</a>, an array containing the distances (Euclidean or otherwise) between any two points in a set. This is frequently used as the independent variable in statistical tests of whether the strength of a relationship is correlated with distance, such as the volume of trade between cities.</li></ul>

<ul><li><a href="/facts/Transport_network_analysis/xtFgRh60">Transport network analysis</a>, a set of algorithms and tools for solving a number of distance routing problems when travel is constrained to a network of one-dimensional lines, such as roads and utility networks.<a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> For example, the common task of finding the shortest route from point A to point B, which is typically solved using <a href="/facts/Dijkstra%2527s_algorithm/ehun88jl">Dijkstra's algorithm</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://pro.arcgis.com/en/pro-app/latest/tool-reference/analysis/an-overview-of-the-proximity-toolset.htm">Proximity tools</a> in Esri <a href="/facts/ArcGIS/pYPJ9GD5">ArcGIS</a></li>
<li><a href="http://www.postgis.org/docs/ST_DWithin.html">OGC ST_DWithin function</a> (<a href="/facts/PostGIS/a3vdt50J">PostGIS</a> implementation)</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Blinn, Charles R., Lloyd P. Queen, and Les W. Maki, "Geographic Information Systems: A Glossary." Archived 2010-03-22 at the Wayback Machine <a href="http://www.extension.umn.edu/distribution/naturalresources/components/DD6097hr.html" target="_blank">http://www.extension.umn.edu/distribution/naturalresources/components/DD6097hr.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Sarkar, D. "FC-42 - Distance Operations". GIS&T Body of Knowledge. UCGIS. Retrieved 5 January 2023. <a href="https://gistbok.ucgis.org/bok-topics/distance-operations" target="_blank">https://gistbok.ucgis.org/bok-topics/distance-operations</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Sarkar, D. "FC-42 - Distance Operations". GIS&T Body of Knowledge. UCGIS. Retrieved 5 January 2023. <a href="https://gistbok.ucgis.org/bok-topics/distance-operations" target="_blank">https://gistbok.ucgis.org/bok-topics/distance-operations</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Agarwal, Pragya; Skupin, André (2008). Self-organizing maps: Applications in geographic information science. Wiley. ISBN 9780470021675. <a href="9780470021675" target="_blank">9780470021675</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">"How cost distance tools work". ArcGIS Pro Documentation. Esri. Retrieved 5 January 2023. <a href="https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/how-the-cost-distance-tools-work.htm" target="_blank">https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/how-the-cost-distance-tools-work.htm</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">de Smith, Michael J.; Goodchild, Michael F.; Longley, Paul A. (2018). "4.4 Distance Operations". Geospatial Analysis: A Comprehensive Guide to Principles, Techniques, and Software Tools (6th ed.). <a href="https://www.spatialanalysisonline.com/HTML/index.html?distance_operations.htm" target="_blank">https://www.spatialanalysisonline.com/HTML/index.html?distance_operations.htm</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">"How cost distance tools work". ArcGIS Pro Documentation. Esri. Retrieved 5 January 2023. <a href="https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/how-the-cost-distance-tools-work.htm" target="_blank">https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-analyst/how-the-cost-distance-tools-work.htm</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">"25.1.18.81 Voronoi polygons". QGIS 3.22 Documentation. OSGEO. Retrieved 5 January 2023. <a href="https://docs.qgis.org/3.22/en/docs/user_manual/processing_algs/qgis/vectorgeometry.html#voronoi-polygons" target="_blank">https://docs.qgis.org/3.22/en/docs/user_manual/processing_algs/qgis/vectorgeometry.html#voronoi-polygons</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">"Network Analyst solvers". ArcGIS Pro Documentation. Esri. Retrieved 5 January 2023. <a href="https://pro.arcgis.com/en/pro-app/latest/help/analysis/networks/network-analyst-solver-types.htm" target="_blank">https://pro.arcgis.com/en/pro-app/latest/help/analysis/networks/network-analyst-solver-types.htm</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
</ol>

Proximity analysis open-in-new

Proximity analysis