51:
145:
The Hotine oblique
Mercator (also known as the rectified skew orthomorphic or 'RSO' projection) projection has approximately constant scale along the geodesic of conceptual tangency. Hotine's work was extended by Engels and Grafarend in 1995 to make the geodesic of conceptual tangency have true
78:: for the normal Mercator, the axis of the cylinder coincides with the polar axis and the line of tangency with the equator. For the transverse Mercator, the axis of the cylinder lies in the equatorial plane, and the line of tangency is any chosen meridian, thereby designated the
20:
112:
Both projections can have constant scale on the line of tangency (the equator for the normal
Mercator and the central meridian for the transverse). For the ellipsoidal form, several developments in use do not have constant scale along the line (which is a
759:
133:
is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. For maps of smaller regions, an
121:
Since the standard great circle of the oblique
Mercator can be chosen at will, it may be used to construct highly accurate maps (of narrow width) anywhere on the globe.
66:) Mercator projection. They share the same underlying mathematical construction and consequently the oblique Mercator inherits many traits from the normal Mercator:
1501:
1033:
539:
416:
1119:
915:
905:
825:
910:
491:
354:
87:
Both projections may be modified to secant forms, which means the scale has been reduced so that the cylinder slices through the model globe.
180:
The Space-oblique
Mercator projection is a generalization of the oblique Mercator projection to incorporate time evolution of a satellite
920:
721:
1053:
1043:
1038:
1013:
1005:
666:
592:
549:
544:
519:
511:
208:
175:
1444:
1241:
1168:
1124:
820:
1289:
1236:
1526:
1397:
1366:
940:
789:
567:
496:
203:
54:
Comparison of tangent and secant forms of normal, oblique and transverse
Mercator projections with standard parallels in red
1481:
1449:
1299:
930:
754:
587:
577:
409:
1439:
1153:
807:
716:
1429:
1379:
1342:
1109:
802:
651:
1023:
529:
1314:
1158:
749:
582:
572:
1294:
679:
1028:
534:
42:, the oblique Mercator delivers high accuracy in zones less than a few degrees in arbitrary directional extent.
1384:
1324:
1304:
935:
897:
862:
402:
597:
441:
193:
50:
1496:
1129:
1104:
646:
436:
1419:
1209:
1163:
990:
967:
950:
661:
1424:
1319:
1099:
1094:
1089:
1066:
1061:
982:
744:
684:
656:
641:
636:
631:
626:
80:
255:
Engels, J.; Grafarend, E. (1995). "The oblique
Mercator projection of the ellipsoid of revolution".
1374:
1309:
1214:
1191:
1018:
925:
797:
524:
482:
198:
134:
91:
35:
1246:
857:
562:
330:
272:
38:. The oblique version is sometimes used in national mapping systems. When paired with a suitable
1531:
1173:
1114:
1084:
1079:
995:
972:
852:
847:
766:
711:
689:
350:
311:
241:
959:
739:
370:
342:
303:
264:
233:
331:"The Hotine Rectified Skew Orthomorphic Projection (Oblique Mercator Projection) Revisited"
19:
130:
1411:
1357:
1334:
1281:
1269:
1224:
1201:
1183:
1143:
885:
839:
776:
731:
703:
611:
473:
461:
425:
147:
75:
71:
59:
39:
31:
1520:
276:
234:
163:
98:
1434:
307:
181:
346:
291:
446:
213:
102:
315:
1491:
159:
1486:
155:
114:
1347:
268:
151:
137:
must be chosen if greater accuracy is required; see next section.
49:
394:
329:
Grafarend, E. W.; Engels, J. (2001). Benciolini, Battista (ed.).
1470:
1267:
883:
459:
398:
1410:
1365:
1356:
1333:
1280:
1223:
1200:
1182:
1142:
1052:
1004:
981:
958:
949:
896:
838:
788:
775:
730:
702:
619:
610:
510:
481:
472:
335:
IV Hotine-Marussi
Symposium on Mathematical Geodesy
371:"The Malaysian CRS Monster :: Mike Meredith"
337:. International Association of Geodesy Symposia.
410:
8:
290:Glasscock, J.T.C.; Kubik, K. (1990-09-01).
240:. U.S. Government Printing Office. p.
129:In constructing a map on any projection, a
1467:
1362:
1277:
1264:
955:
893:
880:
785:
616:
478:
469:
456:
417:
403:
395:
1502:Map projection of the tri-axial ellipsoid
18:
224:
58:The oblique Mercator projection is the
341:. Berlin, Heidelberg: Springer: 122.
7:
292:"Map projections used in S.E. Asia"
146:scale. The Hotine is the standard
141:Hotine oblique Mercator projection
14:
209:Space-oblique Mercator projection
176:Space-oblique Mercator projection
170:Space-oblique Mercator projection
34:is an adaptation of the standard
1445:Quadrilateralized spherical cube
1125:Quadrilateralized spherical cube
236:Map projections—A Working Manual
105:is independent of direction and
1034:Lambert cylindrical equal-area
308:10.1080/00050326.1990.10438681
204:Transverse Mercator projection
1:
1482:Interruption (map projection)
1120:Lambert azimuthal equal-area
916:Guyou hemisphere-in-a-square
906:Adams hemisphere-in-a-square
347:10.1007/978-3-642-56677-6_20
90:Both exist in spherical and
46:Standard and oblique aspects
23:oblique Mercator projection.
1548:
173:
125:Spherical oblique Mercator
109:shapes are well preserved;
1477:
1466:
1393:
1276:
1263:
1075:
892:
879:
816:
675:
558:
468:
455:
432:
232:Snyder, John P. (1987).
921:Lambert conformal conic
194:List of map projections
1054:Tobler hyperelliptical
667:Tobler hyperelliptical
593:Space-oblique Mercator
162:. It was developed by
55:
24:
1527:Conformal projections
97:Both projections are
53:
22:
1430:Cahill–Keyes M-shape
1290:Chamberlin trimetric
62:of the standard (or
1497:Tissot's indicatrix
1398:Central cylindrical
1039:Smyth equal-surface
941:Transverse Mercator
790:General perspective
545:Smyth equal-surface
497:Transverse Mercator
296:Australian Surveyor
199:Mercator projection
36:Mercator projection
1450:Waterman butterfly
1300:Miller cylindrical
931:Peirce quincuncial
826:Lambert equal-area
578:Gall stereographic
269:10.1007/BF00863417
257:Journal of Geodesy
56:
25:
1514:
1513:
1510:
1509:
1462:
1461:
1458:
1457:
1406:
1405:
1259:
1258:
1255:
1254:
1138:
1137:
875:
874:
871:
870:
834:
833:
722:Lambert conformal
698:
697:
612:Pseudocylindrical
606:
605:
356:978-3-642-56677-6
135:ellipsoidal model
1539:
1468:
1425:Cahill Butterfly
1363:
1343:Goode homolosine
1278:
1265:
1230:
1229:(Mecca or Qibla)
1110:Goode homolosine
956:
894:
881:
786:
781:
652:Goode homolosine
617:
502:Oblique Mercator
479:
470:
457:
419:
412:
405:
396:
385:
384:
382:
381:
367:
361:
360:
326:
320:
319:
287:
281:
280:
252:
246:
245:
239:
229:
81:central meridian
29:oblique Mercator
1547:
1546:
1542:
1541:
1540:
1538:
1537:
1536:
1517:
1516:
1515:
1506:
1473:
1454:
1402:
1389:
1352:
1329:
1315:Van der Grinten
1272:
1270:By construction
1251:
1228:
1227:
1219:
1196:
1178:
1159:Equirectangular
1145:
1134:
1071:
1048:
1044:Trystan Edwards
1000:
977:
945:
888:
867:
840:Pseudoazimuthal
830:
812:
779:
778:
771:
726:
694:
690:Winkel I and II
671:
602:
583:Gall isographic
573:Equirectangular
554:
550:Trystan Edwards
506:
464:
451:
428:
423:
393:
388:
379:
377:
369:
368:
364:
357:
328:
327:
323:
289:
288:
284:
254:
253:
249:
231:
230:
226:
222:
190:
178:
172:
143:
127:
48:
17:
12:
11:
5:
1545:
1543:
1535:
1534:
1529:
1519:
1518:
1512:
1511:
1508:
1507:
1505:
1504:
1499:
1494:
1489:
1484:
1478:
1475:
1474:
1471:
1464:
1463:
1460:
1459:
1456:
1455:
1453:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1416:
1414:
1408:
1407:
1404:
1403:
1401:
1400:
1394:
1391:
1390:
1388:
1387:
1382:
1377:
1371:
1369:
1360:
1354:
1353:
1351:
1350:
1345:
1339:
1337:
1331:
1330:
1328:
1327:
1322:
1317:
1312:
1307:
1302:
1297:
1295:Kavrayskiy VII
1292:
1286:
1284:
1274:
1273:
1268:
1261:
1260:
1257:
1256:
1253:
1252:
1250:
1249:
1244:
1239:
1233:
1231:
1225:Retroazimuthal
1221:
1220:
1218:
1217:
1212:
1206:
1204:
1198:
1197:
1195:
1194:
1188:
1186:
1180:
1179:
1177:
1176:
1171:
1166:
1161:
1156:
1150:
1148:
1144:Equidistant in
1140:
1139:
1136:
1135:
1133:
1132:
1127:
1122:
1117:
1112:
1107:
1102:
1097:
1092:
1087:
1082:
1076:
1073:
1072:
1070:
1069:
1064:
1058:
1056:
1050:
1049:
1047:
1046:
1041:
1036:
1031:
1026:
1021:
1016:
1010:
1008:
1002:
1001:
999:
998:
993:
987:
985:
979:
978:
976:
975:
970:
964:
962:
953:
947:
946:
944:
943:
938:
933:
928:
923:
918:
913:
908:
902:
900:
890:
889:
884:
877:
876:
873:
872:
869:
868:
866:
865:
860:
855:
850:
844:
842:
836:
835:
832:
831:
829:
828:
823:
817:
814:
813:
811:
810:
805:
800:
794:
792:
783:
773:
772:
770:
769:
764:
763:
762:
757:
747:
742:
736:
734:
728:
727:
725:
724:
719:
714:
708:
706:
700:
699:
696:
695:
693:
692:
687:
682:
680:Kavrayskiy VII
676:
673:
672:
670:
669:
664:
659:
654:
649:
644:
639:
634:
629:
623:
621:
614:
608:
607:
604:
603:
601:
600:
595:
590:
585:
580:
575:
570:
565:
559:
556:
555:
553:
552:
547:
542:
537:
532:
527:
522:
516:
514:
508:
507:
505:
504:
499:
494:
488:
486:
476:
466:
465:
460:
453:
452:
450:
449:
444:
439:
433:
430:
429:
426:Map projection
424:
422:
421:
414:
407:
399:
392:
391:External links
389:
387:
386:
362:
355:
321:
302:(3): 265–270.
282:
263:(1–2): 38–50.
247:
223:
221:
218:
217:
216:
211:
206:
201:
196:
189:
186:
174:Main article:
171:
168:
166:in the 1940s.
148:map projection
142:
139:
126:
123:
119:
118:
117:) of tangency.
110:
101:, so that the
95:
88:
85:
60:oblique aspect
47:
44:
40:geodetic datum
32:map projection
16:Map projection
15:
13:
10:
9:
6:
4:
3:
2:
1544:
1533:
1530:
1528:
1525:
1524:
1522:
1503:
1500:
1498:
1495:
1493:
1490:
1488:
1485:
1483:
1480:
1479:
1476:
1469:
1465:
1451:
1448:
1446:
1443:
1441:
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1417:
1415:
1413:
1409:
1399:
1396:
1395:
1392:
1386:
1385:Stereographic
1383:
1381:
1378:
1376:
1373:
1372:
1370:
1368:
1364:
1361:
1359:
1355:
1349:
1346:
1344:
1341:
1340:
1338:
1336:
1332:
1326:
1325:Winkel tripel
1323:
1321:
1318:
1316:
1313:
1311:
1308:
1306:
1305:Natural Earth
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1287:
1285:
1283:
1279:
1275:
1271:
1266:
1262:
1248:
1245:
1243:
1240:
1238:
1235:
1234:
1232:
1226:
1222:
1216:
1213:
1211:
1208:
1207:
1205:
1203:
1199:
1193:
1190:
1189:
1187:
1185:
1181:
1175:
1172:
1170:
1167:
1165:
1162:
1160:
1157:
1155:
1152:
1151:
1149:
1147:
1141:
1131:
1128:
1126:
1123:
1121:
1118:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1085:Briesemeister
1083:
1081:
1078:
1077:
1074:
1068:
1065:
1063:
1060:
1059:
1057:
1055:
1051:
1045:
1042:
1040:
1037:
1035:
1032:
1030:
1027:
1025:
1022:
1020:
1017:
1015:
1012:
1011:
1009:
1007:
1003:
997:
994:
992:
989:
988:
986:
984:
980:
974:
971:
969:
966:
965:
963:
961:
957:
954:
952:
948:
942:
939:
937:
936:Stereographic
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
903:
901:
899:
895:
891:
887:
882:
878:
864:
863:Winkel tripel
861:
859:
856:
854:
851:
849:
846:
845:
843:
841:
837:
827:
824:
822:
819:
818:
815:
809:
808:Stereographic
806:
804:
801:
799:
796:
795:
793:
791:
787:
784:
782:
774:
768:
765:
761:
758:
756:
753:
752:
751:
748:
746:
743:
741:
738:
737:
735:
733:
732:Pseudoconical
729:
723:
720:
718:
715:
713:
710:
709:
707:
705:
701:
691:
688:
686:
683:
681:
678:
677:
674:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
624:
622:
618:
615:
613:
609:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
560:
557:
551:
548:
546:
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
517:
515:
513:
509:
503:
500:
498:
495:
493:
490:
489:
487:
484:
480:
477:
475:
471:
467:
463:
458:
454:
448:
445:
443:
440:
438:
435:
434:
431:
427:
420:
415:
413:
408:
406:
401:
400:
397:
390:
376:
375:mmeredith.net
372:
366:
363:
358:
352:
348:
344:
340:
336:
332:
325:
322:
317:
313:
309:
305:
301:
297:
293:
286:
283:
278:
274:
270:
266:
262:
258:
251:
248:
243:
238:
237:
228:
225:
219:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
191:
187:
185:
183:
177:
169:
167:
165:
164:Martin Hotine
161:
157:
153:
149:
140:
138:
136:
132:
124:
122:
116:
111:
108:
104:
100:
96:
93:
89:
86:
83:
82:
77:
73:
69:
68:
67:
65:
61:
52:
45:
43:
41:
37:
33:
30:
21:
1380:Orthographic
911:Gauss–Krüger
803:Orthographic
598:Web Mercator
501:
492:Gauss–Krüger
378:. Retrieved
374:
365:
338:
334:
324:
299:
295:
285:
260:
256:
250:
235:
227:
182:ground track
179:
144:
128:
120:
106:
79:
63:
57:
28:
26:
1358:Perspective
1146:some aspect
1130:Strebe 1995
1105:Equal Earth
1024:Gall–Peters
1006:Cylindrical
821:Equidistant
717:Equidistant
647:Equal Earth
530:Gall–Peters
474:Cylindrical
214:Scale (map)
103:point scale
92:ellipsoidal
76:cylindrical
72:projections
1521:Categories
1420:AuthaGraph
1412:Polyhedral
1282:Compromise
1210:Loximuthal
1202:Loxodromic
1164:Sinusoidal
1014:Balthasart
991:Sinusoidal
968:Sinusoidal
951:Equal-area
662:Sinusoidal
620:Equal-area
520:Balthasart
512:Equal-area
485:-conformal
462:By surface
380:2021-10-28
220:References
1492:Longitude
1320:Wagner VI
1169:Two-point
1100:Eckert VI
1095:Eckert IV
1090:Eckert II
1067:Mollweide
1062:Collignon
1029:Hobo–Dyer
983:Bottomley
898:Conformal
886:By metric
777:Azimuthal
750:Polyconic
745:Bottomley
685:Wagner VI
657:Mollweide
642:Eckert VI
637:Eckert IV
632:Eckert II
627:Collignon
535:Hobo–Dyer
316:0005-0326
277:121405050
160:Singapore
99:conformal
94:versions.
1532:Geocodes
1487:Latitude
1472:See also
1435:Dymaxion
1375:Gnomonic
1310:Robinson
1215:Mercator
1192:Gnomonic
1184:Gnomonic
1019:Behrmann
926:Mercator
798:Gnomonic
780:(planar)
755:American
525:Behrmann
483:Mercator
188:See also
156:Malaysia
150:used in
115:geodesic
1348:HEALPix
1247:Littrow
858:Wiechel
760:Chinese
704:Conical
568:Central
563:Cassini
540:Lambert
437:History
1367:Planar
1335:Hybrid
1242:Hammer
1174:Werner
1115:Hammer
1080:Albers
996:Werner
973:Werner
853:Hammer
848:Aitoff
767:Werner
712:Albers
588:Miller
447:Portal
353:
314:
275:
158:, and
152:Brunei
131:sphere
64:Normal
1237:Craig
1154:Conic
960:Bonne
740:Bonne
273:S2CID
107:local
70:Both
1440:ISEA
442:List
351:ISBN
312:ISSN
74:are
27:The
343:doi
339:122
304:doi
265:doi
1523::
373:.
349:.
333:.
310:.
300:35
298:.
294:.
271:.
261:70
259:.
242:70
184:.
154:,
418:e
411:t
404:v
383:.
359:.
345::
318:.
306::
279:.
267::
244:.
84:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
