39:
31:
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around 1825. It was commonly used by many map-making agencies of the United States from the time of its proposal until the middle of the 20th century. It is not used much these days, having been replaced by
343:{\displaystyle {\begin{aligned}x&=\cot \varphi \sin \!{\bigl (}\sin \varphi {\bigr )}\\y&=\varphi -\varphi _{0}+\cot \varphi \,{\Bigl (}1-\cos {\bigl (}\sin \varphi {\bigr )}{\Bigr )}\end{aligned}}}
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126:, which uses a single cone to project the globe onto. By using this continuously varying cone, each parallel becomes a
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An interactive Java Applet to study the metric deformations of the
Polyconic Projection
130:
having true scale, contrasting with a conic projection, which can only have one or two
123:
103:
97:
The
American polyconic projection was probably invented by Swiss-American cartographer
59:
1722:
63:
1663:
17:
1572:
520:
127:
83:
1671:
584:
79:
122:
to the Earth at all parallels of latitude. This generalizes the concept of a
1629:
511:
360:
1624:
370:
118:
The
American polyconic projection can be thought of as "rolling" a cone
1485:
119:
90:, which is straight. Often the American polyconic is simply called the
87:
532:
1608:
1405:
1021:
597:
536:
1675:
27:
Map projection historically used for maps of the United States
478:
Flattening the Earth: Two
Thousand Years of Map Projections
521:
Table of examples and properties of all common projections
1683:
70:
beginning early in the 19th century. It belongs to the
149:
1548:
1503:
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1471:
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1142:
1119:
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1034:
976:
926:
913:
868:
840:
757:
748:
648:
619:
610:
342:
331:
267:
176:
1703:
548:
412:, the formulas above are extended so that if
324:
286:
217:
179:
134:at true scale. The scale is also true on the
8:
395:is the latitude chosen to be the origin at
1710:
1696:
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1402:
1093:
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1018:
923:
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616:
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541:
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74:, which consists of map projections whose
34:American polyconic projection of the world
1640:Map projection of the tri-axial ellipsoid
384:is the longitude of the central meridian;
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285:
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150:
148:
37:
29:
470:
480:, John P. Snyder, 1993, pp. 117-122,
7:
1660:
1658:
42:American polyconic projection with
1682:. You can help Knowledge (XXG) by
25:
1662:
1583:Quadrilateralized spherical cube
1263:Quadrilateralized spherical cube
52:cartography of the United States
507:"American polyconic projection"
1172:Lambert cylindrical equal-area
310:
291:
203:
184:
141:The projection is defined by:
1:
1620:Interruption (map projection)
523:, from radicalcartography.net
373:of the point to be projected;
363:of the point to be projected;
108:State Plane Coordinate System
56:American polyconic projection
1258:Lambert azimuthal equal-area
1054:Guyou hemisphere-in-a-square
1044:Adams hemisphere-in-a-square
1750:
1657:
72:polyconic projection class
1615:
1604:
1531:
1414:
1401:
1213:
1030:
1017:
954:
813:
696:
606:
593:
570:
99:Ferdinand Rudolph Hassler
1059:Lambert conformal conic
459:List of map projections
1192:Tobler hyperelliptical
805:Tobler hyperelliptical
731:Space-oblique Mercator
344:
47:
35:
345:
104:conformal projections
62:used for maps of the
41:
33:
1568:Cahill–Keyes M-shape
1428:Chamberlin trimetric
147:
92:polyconic projection
18:Polyconic projection
1635:Tissot's indicatrix
1536:Central cylindrical
1177:Smyth equal-surface
1079:Transverse Mercator
928:General perspective
683:Smyth equal-surface
635:Transverse Mercator
138:of the projection.
44:Tissot's indicatrix
1678:term article is a
1588:Waterman butterfly
1438:Miller cylindrical
1069:Peirce quincuncial
964:Lambert equal-area
716:Gall stereographic
504:Weisstein, Eric W.
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36:
1734:Cartography stubs
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860:Lambert conformal
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750:Pseudocylindrical
744:
743:
16:(Redirected from
1741:
1712:
1705:
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1666:
1659:
1606:
1563:Cahill Butterfly
1501:
1481:Goode homolosine
1416:
1403:
1368:
1367:(Mecca or Qibla)
1248:Goode homolosine
1094:
1032:
1019:
924:
919:
790:Goode homolosine
755:
640:Oblique Mercator
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410:division by zero
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136:central meridian
124:conic projection
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1729:Map projections
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1453:Van der Grinten
1410:
1408:By construction
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1297:Equirectangular
1283:
1272:
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1182:Trystan Edwards
1138:
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978:Pseudoazimuthal
968:
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828:Winkel I and II
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721:Gall isographic
711:Equirectangular
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688:Trystan Edwards
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86:except for the
46:of deformation.
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1433:Kavrayskiy VII
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1363:Retroazimuthal
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564:Map projection
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496:External links
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60:map projection
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1523:Stereographic
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1463:Winkel tripel
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1443:Natural Earth
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1001:Winkel tripel
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870:Pseudoconical
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64:United States
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32:
19:
1684:expanding it
1669:
1654:
1518:Orthographic
1049:Gauss–Krüger
941:Orthographic
892:
736:Web Mercator
630:Gauss–Krüger
510:
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128:circular arc
117:
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55:
49:
1672:cartography
1496:Perspective
1284:some aspect
1268:Strebe 1995
1243:Equal Earth
1162:Gall–Peters
1144:Cylindrical
959:Equidistant
855:Equidistant
785:Equal Earth
668:Gall–Peters
612:Cylindrical
114:Description
68:its regions
1723:Categories
1558:AuthaGraph
1550:Polyhedral
1420:Compromise
1348:Loximuthal
1340:Loxodromic
1302:Sinusoidal
1152:Balthasart
1129:Sinusoidal
1106:Sinusoidal
1089:Equal-area
800:Sinusoidal
758:Equal-area
658:Balthasart
650:Equal-area
623:-conformal
600:By surface
465:References
80:concentric
1630:Longitude
1458:Wagner VI
1307:Two-point
1238:Eckert VI
1233:Eckert IV
1228:Eckert II
1205:Mollweide
1200:Collignon
1167:Hobo–Dyer
1121:Bottomley
1036:Conformal
1024:By metric
915:Azimuthal
888:Polyconic
883:Bottomley
823:Wagner VI
795:Mollweide
780:Eckert VI
775:Eckert IV
770:Eckert II
765:Collignon
673:Hobo–Dyer
512:MathWorld
408:To avoid
361:longitude
320:φ
317:
302:λ
298:−
295:λ
282:
276:−
262:φ
259:
244:φ
240:−
237:φ
213:φ
210:
195:λ
191:−
188:λ
171:φ
168:
132:parallels
82:circular
76:parallels
1625:Latitude
1610:See also
1573:Dymaxion
1513:Gnomonic
1448:Robinson
1353:Mercator
1330:Gnomonic
1322:Gnomonic
1157:Behrmann
1064:Mercator
936:Gnomonic
918:(planar)
893:American
663:Behrmann
621:Mercator
453:See also
371:latitude
78:are non-
1676:mapping
1486:HEALPix
1385:Littrow
996:Wiechel
898:Chinese
842:Conical
706:Central
701:Cassini
678:Lambert
575:History
419:, then
369:is the
359:is the
352:where:
120:tangent
106:in the
88:equator
50:In the
1505:Planar
1473:Hybrid
1380:Hammer
1312:Werner
1253:Hammer
1218:Albers
1134:Werner
1111:Werner
991:Hammer
986:Aitoff
905:Werner
850:Albers
726:Miller
585:Portal
484:
54:, the
1670:This
1375:Craig
1292:Conic
1098:Bonne
878:Bonne
58:is a
1680:stub
1578:ISEA
580:List
482:ISBN
436:and
84:arcs
66:and
1674:or
441:= −
417:= 0
314:sin
279:cos
256:cot
207:sin
174:sin
165:cot
1725::
509:.
449:.
428:−
424:=
110:.
94:.
1711:e
1704:t
1697:v
1686:.
556:e
549:t
542:v
529:.
515:.
488:.
446:0
443:φ
439:y
433:0
430:λ
426:λ
422:x
415:φ
404:.
401:0
398:λ
392:0
389:φ
381:0
378:λ
367:φ
357:λ
332:)
325:)
311:]
306:0
292:[
287:(
273:1
268:(
253:+
248:0
234:=
227:y
218:)
204:]
199:0
185:[
180:(
162:=
155:x
20:)
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