17:
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base points. Chamberlin did not specify how to handle this case, but it would be determined by which definition of triangle center is chosen, as noted next. In the remaining case, which is most of the map, connecting the three points of intersection of the circles by line segments creates a small triangle. The position of
128:. Rather, the projection was conceived to minimize distortion of distances everywhere with the side-effect of balancing between areal equivalence and conformality. This projection is not appropriate for mapping the entire sphere because the outer boundary would loop and overlap itself in most configurations.
76:
minimally enclosing the area to be mapped. These points are mapped at the correct distance from each other according to the map’s chosen scale; aside from arbitrary rotation and translation, the position of the three points on the plane are unambiguous because a triangle is determined by the lengths
89:
from the base point. The three circles will always intersect at one, two, or three points. Intersecting at one point happens only at the base points, which are already mapped and therefore need no further processing. Intersecting at two points happens only along the straight line between two mapped
56:
for the
Society from 1964 to 1971. The projection's principal feature is that it compromises between distortions of area, direction, and distance. A Chamberlin trimetric map therefore gives an excellent overall sense of the region being mapped. Many
109:, with shorelines and other features then mapped by interpolation. Based on the principles of the projection, precise, but lengthy, mathematical formulas were later developed for calculating this projection by
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20:
A map of Africa using the
Chamberlin trimetric projection. The three red dots indicate the selected "base" locations: (22°N, 0°), (22°N, 45°E), (22°S, 22.5°E). 10°
229:
Christensen, Albert H.J. (1992). "The
Chamberlin Trimetric Projection". Vol. 19, no. 2. Cartography and Geographic Information Science. pp. 88–100.
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248:
Bretterbauer, Kurt (1989). "Die trimetrische
Projektion von W. Chamberlin". Vol. 39, no. 2. Kartographische Nachrichten. pp. 51–55.
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are calculated. Using each of the three mapped base points as center, a circle is drawn with radius equal to the scale spherical distance of
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A Chamberlin trimetric projection map was originally obtained by graphically mapping points at regular intervals of
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In some cases, the
Chamberlin trimetric projection is difficult to distinguish visually from the Lambert
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The Round Earth on Flat Paper: Map
Projections Used by Cartographers
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98:. Chamberlin did not specify which definition of center to use.
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Flattening the earth: two thousand years of map projections
81:, the spherical distances from each of the base points to
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begins with the selection of three base points to form a
48:. It was developed in 1946 by Wellman Chamberlin for the
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261:"Notes on Mapping, Projections and Data Analysis"
171:. Washington, D.C.: National Geographic Society.
120:The Chamberlin trimetric projection is neither
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290:- Implementations of the projection using
68:As originally implemented, the projection
1419:Map projection of the tri-axial ellipsoid
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7:
162:
160:
36:where three points are fixed on the
298:The Chamberlin Trimetric Projection
288:The Chamberlin Trimetric Projection
14:
300:- Notes on the projection from a
1362:Quadrilateralized spherical cube
1042:Quadrilateralized spherical cube
145:Two-point equidistant projection
59:National Geographic Society maps
133:azimuthal equal-area projection
77:of its sides. To map any point
30:Chamberlin trimetric projection
951:Lambert cylindrical equal-area
1:
1399:Interruption (map projection)
1037:Lambert azimuthal equal-area
833:Guyou hemisphere-in-a-square
823:Adams hemisphere-in-a-square
259:Dushaw, Brian (2009-12-18).
167:Chamberlin, Wellman (1947).
201:University of Chicago Press
135:centered on the same area.
50:National Geographic Society
44:are mapped onto a plane by
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235:10.1559/152304092783786609
96:the center of the triangle
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306:Colorado State University
195:Snyder, John P. (1997).
838:Lambert conformal conic
52:. Chamberlin was chief
971:Tobler hyperelliptical
584:Tobler hyperelliptical
510:Space-oblique Mercator
40:and the points on the
25:
65:use this projection.
19:
1347:Cahill–Keyes M-shape
1207:Chamberlin trimetric
265:staff.washington.edu
1414:Tissot's indicatrix
1315:Central cylindrical
956:Smyth equal-surface
858:Transverse Mercator
707:General perspective
462:Smyth equal-surface
414:Transverse Mercator
94:′ is determined by
1367:Waterman butterfly
1217:Miller cylindrical
848:Peirce quincuncial
743:Lambert equal-area
495:Gall stereographic
74:spherical triangle
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639:Lambert conformal
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529:Pseudocylindrical
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210:978-0-226-76747-5
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1342:Cahill Butterfly
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1260:Goode homolosine
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1146:(Mecca or Qibla)
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569:Goode homolosine
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1232:Van der Grinten
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1187:By construction
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1076:Equirectangular
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961:Trystan Edwards
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757:Pseudoazimuthal
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607:Winkel I and II
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500:Gall isographic
490:Equirectangular
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467:Trystan Edwards
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34:map projection
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649:Pseudoconical
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46:triangulation
43:
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31:
23:
18:
1297:Orthographic
1206:
828:Gauss–Krüger
720:Orthographic
515:Web Mercator
409:Gauss–Krüger
268:. Retrieved
264:
254:
243:
196:
168:
130:
119:
100:
91:
86:
82:
78:
67:
54:cartographer
29:
27:
1275:Perspective
1063:some aspect
1047:Strebe 1995
1022:Equal Earth
941:Gall–Peters
923:Cylindrical
738:Equidistant
634:Equidistant
564:Equal Earth
447:Gall–Peters
391:Cylindrical
302:cartography
1337:AuthaGraph
1329:Polyhedral
1199:Compromise
1127:Loximuthal
1119:Loxodromic
1081:Sinusoidal
931:Balthasart
908:Sinusoidal
885:Sinusoidal
868:Equal-area
579:Sinusoidal
537:Equal-area
437:Balthasart
429:Equal-area
402:-conformal
379:By surface
270:2022-09-08
177:B000WTCPXE
151:References
126:equal-area
63:continents
61:of single
1409:Longitude
1237:Wagner VI
1086:Two-point
1017:Eckert VI
1012:Eckert IV
1007:Eckert II
984:Mollweide
979:Collignon
946:Hobo–Dyer
900:Bottomley
815:Conformal
803:By metric
694:Azimuthal
667:Polyconic
662:Bottomley
602:Wagner VI
574:Mollweide
559:Eckert VI
554:Eckert IV
549:Eckert II
544:Collignon
452:Hobo–Dyer
304:class at
122:conformal
107:longitude
70:algorithm
22:graticule
1438:Category
1404:Latitude
1389:See also
1352:Dymaxion
1292:Gnomonic
1227:Robinson
1132:Mercator
1109:Gnomonic
1101:Gnomonic
936:Behrmann
843:Mercator
715:Gnomonic
697:(planar)
672:American
442:Behrmann
400:Mercator
294:scripts.
139:See also
111:computer
103:latitude
1265:HEALPix
1164:Littrow
775:Wiechel
677:Chinese
621:Conical
485:Central
480:Cassini
457:Lambert
354:History
1284:Planar
1252:Hybrid
1159:Hammer
1091:Werner
1032:Hammer
997:Albers
913:Werner
890:Werner
770:Hammer
765:Aitoff
684:Werner
629:Albers
505:Miller
364:Portal
292:Matlab
207:
175:
113:for a
42:sphere
1154:Craig
1071:Conic
877:Bonne
657:Bonne
38:globe
32:is a
1357:ISEA
359:List
205:ISBN
173:ASIN
124:nor
105:and
28:The
231:doi
1440::
263:.
219:^
203:.
199:.
185:^
159:^
117:.
335:e
328:t
321:v
308:.
273:.
237:.
233::
213:.
179:.
92:P
87:P
83:P
79:P
24:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
