page_title: Map projection
section_title: Equidistant
hierarchical_section_title: Map projection / Projections by preservation of a metric property / Equidistant
caption_attribution_description: English: Eurasia on two-point equidistant projection. 15° graticule; two anchor points are (45°N, 40°E), (30°N, 110°E). Imagery is a derivative of NASA’s Blue Marble summer month composite with oceans lightened to enhance legibility and contrast. Image created with the Geocart map projection software.
context_page_description: In cartography, a map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane.
  All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. Every distinct map projection distorts in a distinct way, by definition. The study of map projections is the characterization of these distortions. There is no limit to the number of possible map projections.
  Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. However, "map projection" refers specifically to a cartographic projection.
context_section_description: If the length of the line segment connecting two projected points on the plane is proportional to the geodesic (shortest surface) distance between the two unprojected points on the globe, then we say that distance has been preserved between those two points. An equidistant projection preserves distances from one or two special points to all other points. The special point or points may get stretched into a line or curve segment when projected. In that case, the point on the line or curve segment closest to the point being measured to must be used to measure the distance.
  Plate carrée: Distances from the two poles are preserved, in equatorial aspect.
  Azimuthal equidistant: Distances from the center and edge are preserved.
  Equidistant conic: Distances from the two poles are preserved, in equatorial aspect.
  Werner cordiform Distances from the North Pole are preserved, in equatorial aspect.
  Two-point equidistant: Two "control points" are arbitrarily chosen by the map maker; distances from each control point are preserved.
caption: A two-point equidistant projection of Eurasia
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