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Loximuthal projection

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is the radius of the Earth (in particular if the loxodrome goes straight east, it circles the Earth infinitely many times without getting closer to either pole, so its length is ∞. Let a loxodrome pass through the point whose longitude and latitude are both 0; call this the "central point".
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from the center, and are "true to scale" in the sense that distances measured along such lines are proportional to lengths of the corresponding rhumb lines on the surface of the Earth. It is neither an
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Suppose one starts at the central point and travels a certain distance in a certain direction along this loxodrome and arrives at geographic location . Let
1517: 1049: 555: 432: 328:. If one were to include loxodromes crossing the 180° meridian, one would get infinitely many images of the whole Earth, occupying the entire strip 264: = a half circle. The loxodrome's whole length as it goes from the south pole to the north pole is fairly routinely seen to be 1135: 931: 921: 841: 205: 42: 926: 507: 936: 737: 1069: 1059: 1054: 1029: 1021: 682: 608: 565: 560: 535: 527: 405: 231: 108: 89: 61: 1460: 1257: 1184: 1140: 836: 1305: 1252: 324:, but there is a unique shortest one: the one that does not cross the 180° meridian on its way from the central point to  1413: 1382: 956: 805: 583: 512: 209: 142: 68: 46: 1497: 1465: 1315: 946: 770: 603: 593: 425: 1455: 1169: 823: 732: 1445: 377:. U.S. Geological Survey Professional Paper 1453. Washington, D.C.: U.S. Government Printing Office. pp. 90, 223. 75: 1395: 1358: 1125: 818: 667: 517: 1039: 545: 194: 1330: 1174: 765: 598: 588: 213: 198: 57: 35: 1310: 695: 1044: 550: 1542: 1400: 1340: 1320: 951: 913: 878: 418: 613: 457: 345: 1512: 1145: 1120: 662: 452: 296:)-plane reached by going that same distance in that same direction from the origin (0, 0). Thus 1435: 1179: 1006: 983: 966: 677: 163: 1440: 1335: 1115: 1110: 1105: 1082: 1077: 998: 760: 700: 672: 657: 652: 647: 642: 245: 150: 141:
introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is
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A loxodrome on the surface of the Earth is a curve of constant bearing: it meets every
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Loximuthal projection of the world, central point = 0°E, 30°N. 15° graticule.
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on the map. More than one loxodrome goes from the central point to 
1363: 158: 382: 410: 1486: 1283: 899: 475: 414: 177: 18: 368:; Voxland, Philip M. (1989). "An Album of Map Projections". 1426: 1381: 1372: 1349: 1296: 1239: 1216: 1198: 1158: 1068: 1020: 997: 974: 965: 912: 854: 804: 791: 746: 718: 635: 626: 526: 497: 488: 49:. Unsourced material may be challenged and removed. 260: = a right angle; due west is 336:gives only one copy, occupying a sort of oval. 426: 8: 252:north of east, so, for example, due east is 212:. Unsourced material may be challenged and 16:Pseudocylindrical compromise map projection 1483: 1378: 1293: 1280: 971: 909: 896: 801: 632: 494: 485: 472: 433: 419: 411: 248:at the same angle. Suppose its bearing is 1518:Map projection of the tri-axial ellipsoid 232:Learn how and when to remove this message 109:Learn how and when to remove this message 120: 357: 157:) are shown straight lines, correct in 7: 210:adding citations to reliable sources 47:adding citations to reliable sources 14: 1461:Quadrilateralized spherical cube 1141:Quadrilateralized spherical cube 182: 23: 34:needs additional citations for 1050:Lambert cylindrical equal-area 1: 1498:Interruption (map projection) 256: = 0; due north is 1136:Lambert azimuthal equal-area 932:Guyou hemisphere-in-a-square 922:Adams hemisphere-in-a-square 371:An album of map projections 1559: 308: × . That point 1493: 1482: 1409: 1292: 1279: 1091: 908: 895: 832: 691: 574: 484: 471: 448: 937:Lambert conformal conic 346:List of map projections 288:) be the point in the ( 58:"Loximuthal projection" 1070:Tobler hyperelliptical 683:Tobler hyperelliptical 609:Space-oblique Mercator 126: 406:Loximuthal projection 164:equal-area projection 135:loximuthal projection 124: 1446:Cahill–Keyes M-shape 1306:Chamberlin trimetric 246:parallel of latitude 206:improve this section 43:improve this article 1513:Tissot's indicatrix 1414:Central cylindrical 1055:Smyth equal-surface 957:Transverse Mercator 806:General perspective 561:Smyth equal-surface 513:Transverse Mercator 1466:Waterman butterfly 1316:Miller cylindrical 947:Peirce quincuncial 842:Lambert equal-area 594:Gall stereographic 316:) is the image of 127: 1530: 1529: 1526: 1525: 1478: 1477: 1474: 1473: 1422: 1421: 1275: 1274: 1271: 1270: 1154: 1153: 891: 890: 887: 886: 850: 849: 738:Lambert conformal 714: 713: 628:Pseudocylindrical 622: 621: 242: 241: 234: 145:by the fact that 119: 118: 111: 93: 1550: 1484: 1441:Cahill Butterfly 1379: 1359:Goode homolosine 1294: 1281: 1246: 1245:(Mecca or Qibla) 1126:Goode homolosine 972: 910: 897: 802: 797: 668:Goode homolosine 633: 518:Oblique Mercator 495: 486: 473: 435: 428: 421: 412: 393: 392: 390: 389: 376: 362: 267: 237: 230: 226: 223: 217: 186: 178: 114: 107: 103: 100: 94: 92: 51: 27: 19: 1558: 1557: 1553: 1552: 1551: 1549: 1548: 1547: 1543:Map projections 1533: 1532: 1531: 1522: 1489: 1470: 1418: 1405: 1368: 1345: 1331:Van der Grinten 1288: 1286:By construction 1267: 1244: 1243: 1235: 1212: 1194: 1175:Equirectangular 1161: 1150: 1087: 1064: 1060:Trystan Edwards 1016: 993: 961: 904: 883: 856:Pseudoazimuthal 846: 828: 795: 794: 787: 742: 710: 706:Winkel I and II 687: 618: 599:Gall isographic 589:Equirectangular 570: 566:Trystan Edwards 522: 480: 467: 444: 439: 402: 397: 396: 387: 385: 374: 366:Snyder, John P. 364: 363: 359: 354: 342: 271: csc  265: 238: 227: 221: 218: 203: 187: 176: 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Retrieved 370: 360: 333: 329: 325: 321: 317: 313: 309: 305: 301: 297: 293: 289: 285: 281: 276: 272: 268: 261: 257: 253: 249: 243: 228: 219: 204:Please help 192: 153:and central 134: 128: 105: 96: 86: 79: 72: 65: 53: 41:Please help 36:verification 33: 1374:Perspective 1162:some aspect 1146:Strebe 1995 1121:Equal Earth 1040:Gall–Peters 1022:Cylindrical 837:Equidistant 733:Equidistant 663:Equal Earth 546:Gall–Peters 490:Cylindrical 174:Description 131:cartography 1436:AuthaGraph 1428:Polyhedral 1298:Compromise 1226:Loximuthal 1218:Loxodromic 1180:Sinusoidal 1030:Balthasart 1007:Sinusoidal 984:Sinusoidal 967:Equal-area 678:Sinusoidal 636:Equal-area 536:Balthasart 528:Equal-area 501:-conformal 478:By surface 388:2019-02-18 352:References 147:loxodromes 69:newspapers 1508:Longitude 1336:Wagner VI 1185:Two-point 1116:Eckert VI 1111:Eckert IV 1106:Eckert II 1083:Mollweide 1078:Collignon 1045:Hobo–Dyer 999:Bottomley 914:Conformal 902:By metric 793:Azimuthal 766:Polyconic 761:Bottomley 701:Wagner VI 673:Mollweide 658:Eckert VI 653:Eckert IV 648:Eckert II 643:Collignon 551:Hobo–Dyer 193:does not 168:conformal 1537:Category 1503:Latitude 1488:See also 1451:Dymaxion 1391:Gnomonic 1326:Robinson 1231:Mercator 1208:Gnomonic 1200:Gnomonic 1035:Behrmann 942:Mercator 814:Gnomonic 796:(planar) 771:American 541:Behrmann 499:Mercator 340:See also 155:latitude 151:meridian 1364:HEALPix 1263:Littrow 874:Wiechel 776:Chinese 720:Conical 584:Central 579:Cassini 556:Lambert 453:History 292:,  214:removed 199:sources 159:azimuth 83:scholar 1383:Planar 1351:Hybrid 1258:Hammer 1190:Werner 1131:Hammer 1096:Albers 1012:Werner 989:Werner 869:Hammer 864:Aitoff 783:Werner 728:Albers 604:Miller 463:Portal 275:where 133:, the 85:  78:  71:  64:  56:  1253:Craig 1170:Conic 976:Bonne 756:Bonne 375:(PDF) 137:is a 90:JSTOR 76:books 1456:ISEA 458:List 197:any 195:cite 166:nor 62:news 379:doi 208:by 129:In 45:by 1539:: 170:. 434:e 427:t 420:v 391:. 381:: 334:p 330:R 326:p 322:p 318:p 314:p 312:( 310:f 306:R 302:p 300:( 298:f 294:y 290:x 286:p 284:( 282:f 277:R 273:θ 269:R 266:π 262:θ 258:θ 254:θ 250:θ 235:) 229:( 224:) 220:( 216:. 202:. 112:) 106:( 101:) 97:( 87:· 80:· 73:· 66:· 39:.

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"Loximuthal projection"
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cartography
map projection
characterized
loxodromes
meridian
latitude
azimuth
equal-area projection
conformal

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parallel of latitude
List of map projections

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