25:
1915:
17:
37:
515:
317:
360:
187:
198:
603:
510:{\displaystyle {\begin{aligned}\varphi &=\cot \varphi _{1}+\varphi _{1}-\rho \\\lambda &=\lambda _{0}+{\frac {\rho }{\cos \varphi }}\arctan \left({\frac {x}{\cot \varphi _{1}-y}}\right)\end{aligned}}}
365:
203:
105:
1148:
100:
312:{\displaystyle {\begin{aligned}\rho &=\cot \varphi _{1}+\varphi _{1}-\varphi \\E&={\frac {(\lambda -\lambda _{0})\cos \varphi }{\rho }}\end{aligned}}}
1960:
91:, but progressively distorts away from those regions. Thus, it best maps "t"-shaped regions. It has been used extensively for maps of Europe and Asia.
1890:
1422:
928:
805:
526:
1508:
1304:
1294:
1214:
1299:
880:
1309:
1110:
1442:
1432:
1427:
1402:
1394:
1055:
981:
938:
933:
908:
900:
711:
80:
in 1696. Both
Sylvanus and Honter's usages were approximate, however, and it is not clear they intended to be the same projection.
1833:
1630:
1557:
1513:
1209:
1979:
1678:
1625:
739:
1953:
1786:
1755:
1329:
1178:
956:
885:
773:
1870:
1838:
1688:
1319:
1143:
976:
966:
798:
24:
1828:
1542:
1196:
1105:
731:
1818:
1768:
1731:
1498:
1191:
1040:
890:
1412:
918:
1984:
1703:
1547:
1138:
971:
961:
1946:
1683:
1068:
1417:
923:
1773:
1713:
1693:
1324:
1286:
1251:
791:
986:
830:
673:
1885:
1518:
1493:
1035:
825:
29:
1808:
1598:
1552:
1379:
1356:
1339:
1050:
657:
619:
182:{\displaystyle {\begin{aligned}x&=\rho \sin E\\y&=\cot \varphi _{1}-\rho \cos E\end{aligned}}}
1813:
1708:
1488:
1483:
1478:
1455:
1450:
1371:
1133:
1073:
1045:
1030:
1025:
1020:
1015:
661:
348:
84:
347:
Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the
1763:
1698:
1603:
1580:
1407:
1314:
1186:
913:
871:
1635:
1246:
951:
77:
1562:
1503:
1473:
1468:
1384:
1361:
1241:
1236:
1155:
1100:
1078:
707:
653:
634:
73:
1930:
735:
69:
652:). The Bonne projection can be seen as an intermediate projection in the unwinding of a
1800:
1746:
1723:
1670:
1658:
1613:
1590:
1572:
1532:
1274:
1228:
1165:
1120:
1092:
1000:
862:
850:
814:
88:
65:
49:
1973:
1914:
778:
1823:
774:
An interactive Java Applet to study the metric deformations of the Bonne
Projection
767:
16:
751:
1922:
835:
68:(1727–1795), the projection was in use prior to his birth, in 1511 by Sylvanus,
36:
726:
649:
645:
598:{\displaystyle \rho =\pm {\sqrt {x^{2}+\left(\cot \varphi _{1}-y\right)^{2}}}}
752:
Between the
Sinusoidal projection and the Werner: an alternative to the Bonne
1880:
1875:
1736:
630:
83:
The Bonne projection maintains accurate shapes of areas along the
783:
1859:
1656:
1272:
848:
787:
1926:
704:
Flattening the Earth: Two
Thousand Years of Map Projections
768:
Table of examples and properties of all common projections
742:
Professional Paper 1395, John P. Snyder, 1987, pp. 138–140
20:
Bonne projection of the world, standard parallel at 45°N.
1934:
529:
363:
201:
103:
351:
and the standard latitude shapes are not distorted.
1799:
1754:
1745:
1722:
1669:
1612:
1589:
1571:
1531:
1441:
1393:
1370:
1347:
1338:
1285:
1227:
1177:
1164:
1119:
1091:
1008:
999:
899:
870:
861:
618:Special cases of the Bonne projection include the
597:
509:
311:
181:
337:is the longitude of the central meridian, and
1954:
799:
8:
697:
695:
693:
691:
689:
344:is the standard parallel of the projection.
1961:
1947:
1856:
1751:
1666:
1653:
1344:
1282:
1269:
1174:
1005:
867:
858:
845:
806:
792:
784:
1891:Map projection of the tri-axial ellipsoid
660:; an alternative intermediate would be a
587:
570:
545:
539:
528:
484:
468:
440:
431:
401:
388:
364:
362:
281:
265:
239:
226:
202:
200:
154:
104:
102:
35:
23:
15:
685:
7:
1911:
1909:
354:The inverse projection is given by:
40:World map by Bernard Sylvanus, 1511
1933:. You can help Knowledge (XXG) by
728:Map Projections - A Working Manual
14:
64:projection. Although named after
1913:
1834:Quadrilateralized spherical cube
1514:Quadrilateralized spherical cube
48:is a pseudoconical equal-area
1423:Lambert cylindrical equal-area
779:Bonne Projection (wolfram.com)
287:
268:
94:The projection is defined as:
1:
1871:Interruption (map projection)
770:, from radicalcartography.net
1509:Lambert azimuthal equal-area
1305:Guyou hemisphere-in-a-square
1295:Adams hemisphere-in-a-square
2001:
1908:
1866:
1855:
1782:
1665:
1652:
1464:
1281:
1268:
1205:
1064:
947:
857:
844:
821:
702:John Parr Snyder (1993).
1310:Lambert conformal conic
674:List of map projections
1980:Equal-area projections
1443:Tobler hyperelliptical
1056:Tobler hyperelliptical
982:Space-oblique Mercator
754:, Henry Bottomley 2002
599:
511:
313:
183:
41:
33:
28:Bonne projection with
21:
658:Sinusoidal projection
620:sinusoidal projection
600:
512:
314:
184:
52:, sometimes called a
39:
27:
19:
1819:Cahill–Keyes M-shape
1679:Chamberlin trimetric
662:Bottomley projection
527:
361:
199:
101:
1886:Tissot's indicatrix
1787:Central cylindrical
1428:Smyth equal-surface
1330:Transverse Mercator
1179:General perspective
934:Smyth equal-surface
886:Transverse Mercator
608:taking the sign of
30:Tissot's indicatrix
1929:term article is a
1839:Waterman butterfly
1689:Miller cylindrical
1320:Peirce quincuncial
1215:Lambert equal-area
967:Gall stereographic
734:2010-07-01 at the
629:is zero (i.e. the
595:
507:
505:
330:is the longitude,
309:
307:
179:
177:
58:modified Flamsteed
54:dépôt de la guerre
42:
34:
22:
1985:Cartography stubs
1942:
1941:
1903:
1902:
1899:
1898:
1851:
1850:
1847:
1846:
1795:
1794:
1648:
1647:
1644:
1643:
1527:
1526:
1264:
1263:
1260:
1259:
1223:
1222:
1111:Lambert conformal
1087:
1086:
1001:Pseudocylindrical
995:
994:
654:Werner projection
644:is 90° (i.e. the
635:Werner projection
593:
497:
456:
326:is the latitude,
303:
89:standard parallel
1992:
1963:
1956:
1949:
1917:
1910:
1857:
1814:Cahill Butterfly
1752:
1732:Goode homolosine
1667:
1654:
1619:
1618:(Mecca or Qibla)
1499:Goode homolosine
1345:
1283:
1270:
1175:
1170:
1041:Goode homolosine
1006:
891:Oblique Mercator
868:
859:
846:
808:
801:
794:
785:
755:
749:
743:
724:
718:
717:
699:
604:
602:
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596:
594:
592:
591:
586:
582:
575:
574:
550:
549:
540:
516:
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508:
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502:
498:
496:
489:
488:
469:
457:
455:
441:
436:
435:
406:
405:
393:
392:
349:central meridian
318:
316:
315:
310:
308:
304:
299:
286:
285:
266:
244:
243:
231:
230:
188:
186:
185:
180:
178:
159:
158:
85:central meridian
76:before 1700 and
46:Bonne projection
2000:
1999:
1995:
1994:
1993:
1991:
1990:
1989:
1970:
1969:
1968:
1967:
1906:
1904:
1895:
1862:
1843:
1791:
1778:
1741:
1718:
1704:Van der Grinten
1661:
1659:By construction
1640:
1617:
1616:
1608:
1585:
1567:
1548:Equirectangular
1534:
1523:
1460:
1437:
1433:Trystan Edwards
1389:
1366:
1334:
1277:
1256:
1229:Pseudoazimuthal
1219:
1201:
1168:
1167:
1160:
1115:
1083:
1079:Winkel I and II
1060:
991:
972:Gall isographic
962:Equirectangular
943:
939:Trystan Edwards
895:
853:
840:
817:
812:
764:
759:
758:
750:
746:
736:Wayback Machine
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258:
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251:
235:
222:
209:
197:
196:
176:
175:
150:
137:
131:
130:
111:
99:
98:
32:of deformation.
12:
11:
5:
1998:
1996:
1988:
1987:
1982:
1972:
1971:
1966:
1965:
1958:
1951:
1943:
1940:
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1900:
1897:
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1726:
1720:
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1701:
1696:
1691:
1686:
1684:Kavrayskiy VII
1681:
1675:
1673:
1663:
1662:
1657:
1650:
1649:
1646:
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1642:
1641:
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1620:
1614:Retroazimuthal
1610:
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1575:
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1533:Equidistant in
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1113:
1108:
1103:
1097:
1095:
1089:
1088:
1085:
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1076:
1071:
1069:Kavrayskiy VII
1065:
1062:
1061:
1059:
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1053:
1048:
1043:
1038:
1033:
1028:
1023:
1018:
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815:Map projection
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762:External links
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66:Rigobert Bonne
50:map projection
13:
10:
9:
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3:
2:
1997:
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1981:
1978:
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1798:
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1775:
1774:Stereographic
1772:
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1765:
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1729:
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1721:
1715:
1714:Winkel tripel
1712:
1710:
1707:
1705:
1702:
1700:
1697:
1695:
1694:Natural Earth
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1474:Briesemeister
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1325:Stereographic
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1296:
1293:
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1253:
1252:Winkel tripel
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1234:
1232:
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1226:
1216:
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1197:Stereographic
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1190:
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1127:
1126:
1124:
1122:
1121:Pseudoconical
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713:0-226-76747-7
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63:
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55:
51:
47:
38:
31:
26:
18:
1935:expanding it
1920:
1905:
1769:Orthographic
1348:
1300:Gauss–Krüger
1192:Orthographic
1128:
987:Web Mercator
881:Gauss–Krüger
747:
727:
722:
703:
638:
623:
617:
609:
607:
519:
353:
346:
338:
331:
327:
323:
321:
191:
93:
82:
61:
57:
53:
45:
43:
1923:cartography
1747:Perspective
1535:some aspect
1519:Strebe 1995
1494:Equal Earth
1413:Gall–Peters
1395:Cylindrical
1210:Equidistant
1106:Equidistant
1036:Equal Earth
919:Gall–Peters
863:Cylindrical
633:), and the
1974:Categories
1809:AuthaGraph
1801:Polyhedral
1671:Compromise
1599:Loximuthal
1591:Loxodromic
1553:Sinusoidal
1403:Balthasart
1380:Sinusoidal
1357:Sinusoidal
1340:Equal-area
1051:Sinusoidal
1009:Equal-area
909:Balthasart
901:Equal-area
874:-conformal
851:By surface
680:References
650:South Pole
1881:Longitude
1709:Wagner VI
1558:Two-point
1489:Eckert VI
1484:Eckert IV
1479:Eckert II
1456:Mollweide
1451:Collignon
1418:Hobo–Dyer
1372:Bottomley
1287:Conformal
1275:By metric
1166:Azimuthal
1139:Polyconic
1134:Bottomley
1074:Wagner VI
1046:Mollweide
1031:Eckert VI
1026:Eckert IV
1021:Eckert II
1016:Collignon
924:Hobo–Dyer
577:−
568:φ
564:
537:±
531:ρ
491:−
482:φ
478:
462:
453:φ
450:
443:ρ
429:λ
418:λ
411:ρ
408:−
399:φ
386:φ
382:
369:φ
301:ρ
297:φ
294:
279:λ
275:−
272:λ
249:φ
246:−
237:φ
224:φ
220:
207:ρ
170:
164:ρ
161:−
152:φ
148:
125:
119:ρ
78:Coronelli
74:De l'Isle
72:in 1561,
1876:Latitude
1861:See also
1824:Dymaxion
1764:Gnomonic
1699:Robinson
1604:Mercator
1581:Gnomonic
1573:Gnomonic
1408:Behrmann
1315:Mercator
1187:Gnomonic
1169:(planar)
1144:American
914:Behrmann
872:Mercator
732:Archived
668:See also
87:and the
62:Sylvanus
1927:mapping
1737:HEALPix
1636:Littrow
1247:Wiechel
1149:Chinese
1093:Conical
957:Central
952:Cassini
929:Lambert
826:History
656:into a
637:, when
631:Equator
622:, when
60:, or a
1756:Planar
1724:Hybrid
1631:Hammer
1563:Werner
1504:Hammer
1469:Albers
1385:Werner
1362:Werner
1242:Hammer
1237:Aitoff
1156:Werner
1101:Albers
977:Miller
836:Portal
710:
520:where
459:arctan
192:where
70:Honter
1921:This
1626:Craig
1543:Conic
1349:Bonne
1129:Bonne
646:North
1931:stub
1829:ISEA
831:List
740:USGS
708:ISBN
322:and
44:The
1925:or
648:or
561:cot
475:cot
447:cos
379:cot
291:cos
217:cot
167:cos
145:cot
122:sin
1976::
738:,
706:.
688:^
664:.
615:.
56:,
1962:e
1955:t
1948:v
1937:.
807:e
800:t
793:v
716:.
642:1
639:φ
627:1
624:φ
613:1
610:φ
589:2
584:)
580:y
572:1
557:(
552:+
547:2
543:x
534:=
500:)
494:y
486:1
471:x
466:(
438:+
433:0
425:=
403:1
395:+
390:1
376:=
342:1
339:φ
335:0
332:λ
328:λ
324:φ
288:)
283:0
269:(
263:=
256:E
241:1
233:+
228:1
214:=
173:E
156:1
142:=
135:y
128:E
116:=
109:x
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