Knowledge (XXG)

Cahill–Keyes projection

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36: 28: 80: 20: 67:. The projection was designed to achieve a number of desirable characteristics, namely symmetry of component maps (octants), scalability allowing the map to continue to work well even at high resolution, uniformity of 642: 91:, 10,000 km lengths for each of its octants' three main joined edges, and an M-shape Master-Map profile. The resulting map comprises 8 octants. Each octant is an 71:, metric-based joining edges, minimized distortion compared to a globe, and an easily understood orientation to enhance general usability and teachability. 1384: 916: 422: 299: 1002: 798: 788: 708: 793: 374: 803: 604: 936: 926: 921: 896: 888: 549: 475: 432: 427: 402: 394: 27: 79: 1327: 1124: 1051: 1007: 703: 87:
The Cahill–Keyes projection was designed with four fundamental considerations in mind: visual fidelity to a globe, proportional
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divides each half-octant into twelve zones, each of which has different formulae for coordinate calculations.
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Diagram by Duncan Webb showing the construction of one octant of a Cahill–Keyes projection
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in 1975. The projection is a refinement of an earlier 1909 projection by
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The Cahill–Keyes projection with Tissot's indicatrix of deformation.
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with three segments per side. One side runs along the
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Example of the projection used by The New York Times
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Gene Keyes's Cahill-Keyes and Cahill resource index
43:2012 by Duncan Webb using Cahill–Keyes projection. 268:D3.js Implementation of Cahill–Keyes Projection 293: 8: 1350: 1245: 1160: 1147: 838: 776: 763: 668: 499: 361: 352: 339: 300: 286: 278: 1385:Map projection of the tri-axial ellipsoid 78: 34: 26: 18: 162: 7: 16:Polyhedral compromise map projection 193:Stockton, Nick (December 9, 2013). 170:Lobner, Peter (December 23, 2016). 14: 220:Keyes, Gene (December 30, 2009). 1328:Quadrilateralized spherical cube 1008:Quadrilateralized spherical cube 174:. The Lyncean Group of San Diego 917:Lambert cylindrical equal-area 23:Cahill–Keyes map of the world. 1: 1365:Interruption (map projection) 1003:Lambert azimuthal equal-area 799:Guyou hemisphere-in-a-square 789:Adams hemisphere-in-a-square 1426: 1360: 1349: 1276: 1159: 1146: 958: 775: 762: 699: 558: 441: 351: 338: 315: 39:Political World Map for 804:Lambert conformal conic 136:List of map projections 49:Cahill–Keyes projection 937:Tobler hyperelliptical 550:Tobler hyperelliptical 476:Space-oblique Mercator 84: 44: 32: 24: 103:converge towards the 82: 38: 30: 22: 1313:Cahill–Keyes M-shape 1173:Chamberlin trimetric 146:Bernard J. S. Cahill 93:equilateral triangle 1380:Tissot's indicatrix 1281:Central cylindrical 922:Smyth equal-surface 824:Transverse Mercator 673:General perspective 428:Smyth equal-surface 380:Transverse Mercator 1333:Waterman butterfly 1183:Miller cylindrical 814:Peirce quincuncial 709:Lambert equal-area 461:Gall stereographic 247:Gene Keyes Website 85: 59:first proposed by 45: 33: 25: 1397: 1396: 1393: 1392: 1345: 1344: 1341: 1340: 1289: 1288: 1142: 1141: 1138: 1137: 1021: 1020: 758: 757: 754: 753: 717: 716: 605:Lambert conformal 581: 580: 495:Pseudocylindrical 489: 488: 151:Octant projection 1417: 1351: 1308:Cahill Butterfly 1246: 1226:Goode homolosine 1161: 1148: 1113: 1112:(Mecca or Qibla) 993:Goode homolosine 839: 777: 764: 669: 664: 535:Goode homolosine 500: 385:Oblique Mercator 362: 353: 340: 302: 295: 288: 279: 250: 239: 233: 232: 230: 228: 217: 211: 210: 208: 206: 190: 184: 183: 181: 179: 167: 1425: 1424: 1420: 1419: 1418: 1416: 1415: 1414: 1410:Map projections 1400: 1399: 1398: 1389: 1356: 1337: 1285: 1272: 1235: 1212: 1198:Van der Grinten 1155: 1153:By construction 1134: 1111: 1110: 1102: 1079: 1061: 1042:Equirectangular 1028: 1017: 954: 931: 927:Trystan Edwards 883: 860: 828: 771: 750: 723:Pseudoazimuthal 713: 695: 662: 661: 654: 609: 577: 573:Winkel I and II 554: 485: 466:Gall isographic 456:Equirectangular 437: 433:Trystan Edwards 389: 347: 334: 311: 306: 259: 254: 253: 240: 236: 226: 224: 219: 218: 214: 204: 202: 192: 191: 187: 177: 175: 169: 168: 164: 159: 117: 77: 17: 12: 11: 5: 1423: 1421: 1413: 1412: 1402: 1401: 1395: 1394: 1391: 1390: 1388: 1387: 1382: 1377: 1372: 1367: 1361: 1358: 1357: 1354: 1347: 1346: 1343: 1342: 1339: 1338: 1336: 1335: 1330: 1325: 1320: 1315: 1310: 1305: 1299: 1297: 1291: 1290: 1287: 1286: 1284: 1283: 1277: 1274: 1273: 1271: 1270: 1265: 1260: 1254: 1252: 1243: 1237: 1236: 1234: 1233: 1228: 1222: 1220: 1214: 1213: 1211: 1210: 1205: 1200: 1195: 1190: 1185: 1180: 1178:Kavrayskiy VII 1175: 1169: 1167: 1157: 1156: 1151: 1144: 1143: 1140: 1139: 1136: 1135: 1133: 1132: 1127: 1122: 1116: 1114: 1108:Retroazimuthal 1104: 1103: 1101: 1100: 1095: 1089: 1087: 1081: 1080: 1078: 1077: 1071: 1069: 1063: 1062: 1060: 1059: 1054: 1049: 1044: 1039: 1033: 1031: 1027:Equidistant in 1023: 1022: 1019: 1018: 1016: 1015: 1010: 1005: 1000: 995: 990: 985: 980: 975: 970: 965: 959: 956: 955: 953: 952: 947: 941: 939: 933: 932: 930: 929: 924: 919: 914: 909: 904: 899: 893: 891: 885: 884: 882: 881: 876: 870: 868: 862: 861: 859: 858: 853: 847: 845: 836: 830: 829: 827: 826: 821: 816: 811: 806: 801: 796: 791: 785: 783: 773: 772: 767: 760: 759: 756: 755: 752: 751: 749: 748: 743: 738: 733: 727: 725: 719: 718: 715: 714: 712: 711: 706: 700: 697: 696: 694: 693: 688: 683: 677: 675: 666: 656: 655: 653: 652: 647: 646: 645: 640: 630: 625: 619: 617: 611: 610: 608: 607: 602: 597: 591: 589: 583: 582: 579: 578: 576: 575: 570: 565: 563:Kavrayskiy VII 559: 556: 555: 553: 552: 547: 542: 537: 532: 527: 522: 517: 512: 506: 504: 497: 491: 490: 487: 486: 484: 483: 478: 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641: 639: 636: 635: 634: 631: 629: 626: 624: 621: 620: 618: 616: 615:Pseudoconical 612: 606: 603: 601: 598: 596: 593: 592: 590: 588: 584: 574: 571: 569: 566: 564: 561: 560: 557: 551: 548: 546: 543: 541: 538: 536: 533: 531: 528: 526: 523: 521: 518: 516: 513: 511: 508: 507: 505: 501: 498: 496: 492: 482: 479: 477: 474: 472: 469: 467: 464: 462: 459: 457: 454: 452: 449: 447: 444: 443: 440: 434: 431: 429: 426: 424: 421: 419: 416: 414: 411: 409: 406: 404: 401: 400: 398: 396: 392: 386: 383: 381: 378: 376: 373: 372: 370: 367: 363: 360: 358: 354: 350: 346: 341: 337: 331: 328: 326: 323: 321: 318: 317: 314: 310: 303: 298: 296: 291: 289: 284: 283: 280: 274: 271: 269: 266: 264: 261: 260: 256: 248: 244: 238: 235: 223: 216: 213: 200: 196: 189: 186: 173: 166: 163: 156: 152: 149: 147: 144: 142: 139: 137: 134: 132: 129: 127: 124: 122: 119: 118: 114: 112: 110: 106: 102: 98: 94: 90: 81: 74: 72: 70: 66: 62: 58: 54: 50: 42: 37: 29: 21: 1312: 1263:Orthographic 794:Gauss–Krüger 686:Orthographic 481:Web Mercator 375:Gauss–Krüger 249:, 2010-08-20 246: 241:Gene Keyes, 237: 225:. Retrieved 215: 203:. Retrieved 201:. Condé Nast 198: 188: 176:. Retrieved 165: 141:Dymaxion map 86: 75:Construction 48: 46: 1241:Perspective 1029:some aspect 1013:Strebe 1995 988:Equal Earth 907:Gall–Peters 889:Cylindrical 704:Equidistant 600:Equidistant 530:Equal Earth 413:Gall–Peters 357:Cylindrical 227:January 22, 205:January 22, 178:January 22, 121:Cartography 55:compromise 1303:AuthaGraph 1295:Polyhedral 1165:Compromise 1093:Loximuthal 1085:Loxodromic 1047:Sinusoidal 897:Balthasart 874:Sinusoidal 851:Sinusoidal 834:Equal-area 545:Sinusoidal 503:Equal-area 403:Balthasart 395:Equal-area 368:-conformal 345:By surface 157:References 61:Gene Keyes 53:polyhedral 1375:Longitude 1203:Wagner VI 1052:Two-point 983:Eckert VI 978:Eckert IV 973:Eckert II 950:Mollweide 945:Collignon 912:Hobo–Dyer 866:Bottomley 781:Conformal 769:By metric 660:Azimuthal 633:Polyconic 628:Bottomley 568:Wagner VI 540:Mollweide 525:Eckert VI 520:Eckert IV 515:Eckert II 510:Collignon 418:Hobo–Dyer 126:World map 109:graticule 101:meridians 1404:Category 1370:Latitude 1355:See also 1318:Dymaxion 1258:Gnomonic 1193:Robinson 1098:Mercator 1075:Gnomonic 1067:Gnomonic 902:Behrmann 809:Mercator 681:Gnomonic 663:(planar) 638:American 408:Behrmann 366:Mercator 115:See also 89:geocells 69:geocells 1231:HEALPix 1130:Littrow 741:Wiechel 643:Chinese 587:Conical 451:Central 446:Cassini 423:Lambert 320:History 97:equator 1250:Planar 1218:Hybrid 1125:Hammer 1057:Werner 998:Hammer 963:Albers 879:Werner 856:Werner 736:Hammer 731:Aitoff 650:Werner 595:Albers 471:Miller 330:Portal 1120:Craig 1037:Conic 843:Bonne 623:Bonne 199:Wired 51:is a 1323:ISEA 325:List 229:2020 207:2020 180:2020 105:pole 47:The 1406:: 245:, 197:. 41:CE 301:e 294:t 287:v 231:. 209:. 182:.

Index




CE
polyhedral
map projection
Gene Keyes
Bernard Cahill
geocells

geocells
equilateral triangle
equator
meridians
pole
graticule
Cartography
World map
Map projection
List of map projections
Dymaxion map
Bernard J. S. Cahill
Octant projection
"Polyhedral Projections Improve the Accurately of Mapping the Earth on a 2D Surface"
"Get to Know a Projection: Gene Keyes' 40-Year Quest for the Perfect Map"
"Notes on Re-designing B.J.S. Cahill's Butterfly World Map"
"Cahill-Keyes Octant Graticule: Principles and Specifications"
Gene Keyes's Cahill-Keyes and Cahill resource index
D3.js Implementation of Cahill–Keyes Projection
Example of the projection used by The New York Times

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