171:
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136:
598:
31:
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593:{\displaystyle {\begin{aligned}\cos {\frac {\rho }{R}}&=\sin \varphi _{0}\sin \varphi +\cos \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)\\\tan \theta &={\frac {\cos \varphi \sin \left(\lambda -\lambda _{0}\right)}{\cos \varphi _{0}\sin \varphi -\sin \varphi _{0}\cos \varphi \cos \left(\lambda -\lambda _{0}\right)}}\end{aligned}}}
958:
135:
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to point the antenna. The map can also be used in one way communication. For example if the operator is looking to receive signals from a distant radio station, this type of projection could help identify the direction of the distant radio station. In order for the map to be useful, the map should be
742:
being approximately 40,000 km (24,855 mi), the maximum distance that can be displayed on an azimuthal equidistant projection map is half the circumference, or about 20,000 km (12,427 mi). For distances less than 10,000 km (6,214 mi) distortions are minimal. For distances
728:
84:(direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly.
289:
750:
lies on land and the map is extended to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle. This is shown in the example of two maps centered about
321:
996:
Azimuthal equidistant projection maps can also be useful to show ranges of ballistic missiles, as demonstrated by the map centered on North Korea showing the country's missile range.
1585:
973:. The operator simply finds on the map the location of the target transmitter or receiver (i.e. the other antenna being communicated with) and uses the map to determine the
80:. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct
636:
1081:
1062:
662:
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10,000â15,000 km (6,214â9,321 mi) the distortions are moderate. Distances greater than 15,000 km (9,321 mi) are severely distorted.
2327:
1859:
1365:
1242:
142:
1945:
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1005:
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as a map of the Flat Earth, particularly due to its use in the UN flag and its depiction of
Antarctica as a ring around the edge of the Earth.
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is arbitrary, so it is most convenient to assign it the value of 0. This assignment significantly simplifies the equations for
2115:
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103:
for star maps in some holy books, the earliest text describing the azimuthal equidistant projection is an 11th-century work by
2223:
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1615:
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that the line subtends from the vertical is the azimuth angle. The distance from the center point to another projected point
845:
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and some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii.
204:
referring to longitude. All points along a given azimuth will project along a straight line from the center, and the angle
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David A. KING (1996), "Astronomy and
Islamic society: Qibla, gnomics and timekeeping", in Roshdi Rashed, ed.,
739:
1423:
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150:
118:
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1955:
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hence there is not much significant distortion of land masses for the Los
Angeles centered map except for
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provides a class for performing azimuthal equidistant projections centered at any point on the ellipsoid.
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969:. This type of projection allows the operator to easily determine in which direction to point their
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2017:
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1350:
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An interactive Java Applet to study the metric deformations of the
Azimuthal Equidistant Projection
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60:
1999:
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between them on the globe. By this description, then, the point on the plane specified by (
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used it for an inset of the north polar regions in sheet 13 and legend 6 of his well-known
978:
723:{\displaystyle \rho =R\left({\frac {\pi }{2}}-\varphi \right),\qquad \theta =\lambda ~~}
110:
An example of this system is the world map by âAli b. Ahmad al-Sharafi of Sfax in 1571.
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A point on the globe is chosen as "the center" in the sense that mapped distances and
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775:
100:
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1209:
Animated US National
Weather Service Wind Data for Azimuthal equidistant projection
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217:
989:
An azimuthal equidistant projection centered on North Korea along with ranges of
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17:
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centered as close as possible about the location of the operator's antenna.
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If the azimuthal equidistant projection map is centered about a point whose
182:
directions from that point to any other point will be correct. That point, (
121:. In France and Russia this projection is named "Postel projection" after
2312:
879:
302:) of the point on the globe, and its latitude and longitude coordinates (
1214:
1079:
Edward S. Kennedy, 1996, Mathematical geography, in Roshdi Rashed, ed.,
2173:
1202:
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912:
179:
81:
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857:
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1215:
Generate an
Azimuthal equidistant projection from any point on Earth
158:
The polar azimuthal equidistant projection has also been adopted by
1191:
965:
Azimuthal equidistant projection maps can be useful in terrestrial
174:
Tissot's indicatrix applied to the azimuthal equidistant projection
977:
needed to point the operator's antenna. The operator would use an
957:
956:
901:
169:
1220:
1109:"Fact Check: The UN Flag Does NOT Show Flat Earth | Lead Stories"
91:
contains an example of a polar azimuthal equidistant projection.
2296:
2093:
1709:
1285:
1224:
284:{\displaystyle x=\rho \sin \theta ,\qquad y=-\rho \cos \theta }
196:), will project to the center of a circular projection, with
1037:
Flattening the earth: two thousand years of map projections
1186:
Table of examples and properties of all common projections
125:, who used it for a map in 1581. Many modern star chart
961:
An azimuthal equidistant projection centered on Sydney
774:, causing the Taipei centered map to severely distort
665:
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770:. On the other hand, Taipei's antipode is near the
68:
containing a polar azimuthal equidistant projection
722:
630:
592:
283:
129:use the polar azimuthal equidistant projection.
758:. The antipode for Los Angeles is in the south
945: Purple circles: 15,000 km radius circles
228:) will be projected to Cartesian coordinates:
49:An azimuthal equidistant projection about the
34:An azimuthal equidistant projection about the
1236:
1082:Encyclopedia of the History of Arabic Science
1063:Encyclopedia of the History of Arabic Science
8:
784:Sample azimuthal equidistant projection maps
939: Red circles: 10,000 km radius circles
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1442:
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1192:Online Azimuthal Equidistant Map Generator
294:The relationship between the coordinates (
2328:Map projection of the tri-axial ellipsoid
680:
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603:When the center point is the north pole,
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59:
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29:
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1006:Lambert azimuthal equal-area projection
7:
27:Azimuthal equidistant map projection
1146:. Professional Paper 1453. Denver:
25:
2271:Quadrilateralized spherical cube
1951:Quadrilateralized spherical cube
829:
790:
147:Azimuthal equidistant projection
134:
74:azimuthal equidistant projection
1039:. University of Chicago Press.
704:
259:
99:While it may have been used by
1860:Lambert cylindrical equal-area
1:
2308:Interruption (map projection)
1188:, from radicalcartography.net
310:) is given by the equations:
53:extending all the way to the
38:extending all the way to the
1946:Lambert azimuthal equal-area
1742:Guyou hemisphere-in-a-square
1732:Adams hemisphere-in-a-square
967:point to point communication
151:(click for detail)
1143:An Album of Map Projections
2369:
740:circumference of the Earth
200:referring to latitude and
160:21st century Flat Earthers
89:flag of the United Nations
2303:
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2219:
2102:
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1901:
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1642:
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1384:
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1016:Modern flat Earth beliefs
846:ArgentinaâParaguay border
772:ArgentinaâParaguay border
1035:SNYDER, John P. (1997).
991:their different missiles
920:
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854:
815:
78:azimuthal map projection
2353:Equidistant projections
1747:Lambert conformal conic
1066:, Vol. 1, p. 128â184 .
1011:List of map projections
166:Mathematical definition
1880:Tobler hyperelliptical
1493:Tobler hyperelliptical
1419:Space-oblique Mercator
1089:, London and New York.
1070:, London and New York.
993:
962:
724:
632:
631:{\displaystyle \pi /2}
594:
285:
175:
69:
57:
42:
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173:
63:
48:
33:
2256:CahillâKeyes M-shape
2116:Chamberlin trimetric
663:
614:
317:
235:
2323:Tissot's indicatrix
2224:Central cylindrical
1865:Smyth equal-surface
1767:Transverse Mercator
1616:General perspective
1371:Smyth equal-surface
1323:Transverse Mercator
971:directional antenna
836:Map centered about
797:Map centered about
2276:Waterman butterfly
2126:Miller cylindrical
1757:Peirce quincuncial
1652:Lambert equal-area
1404:Gall stereographic
1138:Voxland, Philip M.
1098:Snyder 1997, p. 29
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145:Comparison of the
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1548:Lambert conformal
1524:
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1438:Pseudocylindrical
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688:
584:
338:
115:Gerardus Mercator
101:ancient Egyptians
16:(Redirected from
2360:
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2251:Cahill Butterfly
2189:
2169:Goode homolosine
2104:
2091:
2056:
2055:(Mecca or Qibla)
1936:Goode homolosine
1782:
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1707:
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1478:Goode homolosine
1443:
1328:Oblique Mercator
1305:
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1160:. Archived from
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979:electric rotator
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805:is in the south
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123:Guillaume Postel
21:
18:Polar projection
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2141:Van der Grinten
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2096:By construction
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2004:
1985:Equirectangular
1971:
1960:
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1870:Trystan Edwards
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1666:Pseudoazimuthal
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1516:Winkel I and II
1497:
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1409:Gall isographic
1399:Equirectangular
1380:
1376:Trystan Edwards
1332:
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1150:. p. 228.
1134:Snyder, John P.
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1113:leadstories.com
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2121:Kavrayskiy VII
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1506:Kavrayskiy VII
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1217:from ns6t.net.
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1180:External links
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2151:Winkel tripel
2149:
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2139:
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2131:Natural Earth
2129:
2127:
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1911:Briesemeister
1909:
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1894:
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1689:Winkel tripel
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1558:Pseudoconical
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1203:GeographicLib
1201:
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1187:
1184:
1183:
1179:
1164:on 2010-07-01
1163:
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976:
975:azimuth angle
972:
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925:
917:
914:
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839:
832:
820:
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811:
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779:
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776:South America
773:
769:
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83:
79:
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67:
62:
56:
52:
47:
41:
37:
32:
19:
2206:Orthographic
1737:GaussâKrĂźger
1646:
1629:Orthographic
1424:Web Mercator
1318:GaussâKrĂźger
1166:. Retrieved
1162:the original
1142:
1128:
1117:. Retrieved
1115:. 2022-09-12
1112:
1103:
1094:
1080:
1075:
1061:
1056:
1036:
1030:
995:
964:
953:Applications
844:is near the
807:Indian Ocean
760:Indian Ocean
745:
737:
653:
646:
639:
604:
602:
307:
303:
299:
295:
293:
225:
221:
218:great circle
209:
205:
201:
197:
190:
183:
177:
156:
146:
127:planispheres
112:
109:
98:
86:
73:
71:
2184:Perspective
1972:some aspect
1956:Strebe 1995
1931:Equal Earth
1850:GallâPeters
1832:Cylindrical
1647:Equidistant
1543:Equidistant
1473:Equal Earth
1356:GallâPeters
1300:Cylindrical
799:Los Angeles
764:East Africa
752:Los Angeles
2246:AuthaGraph
2238:Polyhedral
2108:Compromise
2036:Loximuthal
2028:Loxodromic
1990:Sinusoidal
1840:Balthasart
1817:Sinusoidal
1794:Sinusoidal
1777:Equal-area
1488:Sinusoidal
1446:Equal-area
1346:Balthasart
1338:Equal-area
1311:-conformal
1288:By surface
1168:2018-03-29
1119:2024-02-04
1085:, Vol. 1,
1022:References
819:California
768:Madagascar
734:Limitation
214:arc length
55:North Pole
51:South Pole
40:South Pole
36:North Pole
2318:Longitude
2146:Wagner VI
1995:Two-point
1926:Eckert VI
1921:Eckert IV
1916:Eckert II
1893:Mollweide
1888:Collignon
1855:HoboâDyer
1809:Bottomley
1724:Conformal
1712:By metric
1603:Azimuthal
1576:Polyconic
1571:Bottomley
1511:Wagner VI
1483:Mollweide
1468:Eckert VI
1463:Eckert IV
1458:Eckert II
1453:Collignon
1361:HoboâDyer
1087:Routledge
1068:Routledge
891:Argentina
738:With the
712:λ
706:θ
694:φ
691:−
683:π
667:ρ
618:π
570:λ
566:−
563:λ
555:
549:φ
546:
534:φ
530:
524:−
521:φ
518:
506:φ
502:
483:λ
479:−
476:λ
468:
462:φ
459:
443:θ
440:
419:λ
415:−
412:λ
404:
398:φ
395:
383:φ
379:
370:φ
367:
355:φ
351:
333:ρ
328:
279:θ
276:
270:ρ
267:−
254:θ
251:
245:ρ
105:al-Biruni
2347:Category
2313:Latitude
2298:See also
2261:Dymaxion
2201:Gnomonic
2136:Robinson
2041:Mercator
2018:Gnomonic
2010:Gnomonic
1845:Behrmann
1752:Mercator
1624:Gnomonic
1606:(planar)
1581:American
1351:Behrmann
1309:Mercator
1140:(1989).
1000:See also
880:Paraguay
840:, whose
801:, whose
216:along a
119:1569 map
2174:HEALPix
2073:Littrow
1684:Wiechel
1586:Chinese
1530:Conical
1394:Central
1389:Cassini
1366:Lambert
1263:History
924:Uruguay
913:Bolivia
610:equals
212:is the
180:azimuth
95:History
82:azimuth
2193:Planar
2161:Hybrid
2068:Hammer
2000:Werner
1941:Hammer
1906:Albers
1822:Werner
1799:Werner
1679:Hammer
1674:Aitoff
1593:Werner
1538:Albers
1414:Miller
1273:Portal
1154:
1051:, p.29
1043:
943:
937:
922:
911:
900:
889:
878:
869:Brazil
867:
858:Taiwan
856:
838:Taipei
817:
756:Taipei
754:, and
718:
715:
76:is an
2063:Craig
1980:Conic
1786:Bonne
1566:Bonne
902:Chile
2266:ISEA
1268:List
1152:ISBN
1148:USGS
1041:ISBN
766:and
656:to:
652:and
638:and
87:The
72:The
552:cos
543:cos
527:sin
515:sin
499:cos
465:sin
456:cos
437:tan
401:cos
392:cos
376:cos
364:sin
348:sin
325:cos
273:cos
248:sin
2349::
1136:;
1111:.
778:.
306:,
189:,
107:.
1244:e
1237:t
1230:v
1211:.
1199:.
1171:.
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709:=
702:,
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686:2
677:(
673:R
670:=
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650:u
647:Ď
643:0
640:Îť
626:2
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574:0
559:(
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450:=
429:)
423:0
408:(
387:0
373:+
359:0
345:=
336:R
308:Îť
304:Ď
300:Ď
298:,
296:θ
264:=
261:y
257:,
242:=
239:x
226:Ď
224:,
222:θ
210:Ď
206:θ
202:Îť
198:Ď
194:0
191:Îť
187:0
184:Ď
20:)
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