Map projection - Knowledge

1019: 504: 1095: 2016: 1719: 1131: 1187: 20: 1871: 1113: 1169: 1151: 5199: 1748: 871: 5211: 468: 277: 226:, resulting in shapes and bearings distorted in most places of the map. Each projection preserves, compromises, or approximates basic metric properties in different ways. The purpose of the map determines which projection should form the base for the map. Because maps have many different purposes, a diversity of projections have been created to suit those purposes. 809:

given rise to much misunderstanding. Particularly is this so with regard to the conic projections with two standard parallels: they may be regarded as developed on cones, but they are cones which bear no simple relationship to the sphere. In reality, cylinders and cones provide us with convenient descriptive terms, but little else.

429: 2308:) designed to educate the public about map projections and distortion in maps. In 1989 and 1990, after some internal debate, seven North American geographic organizations adopted a resolution recommending against using any rectangular projection (including Mercator and Gall–Peters) for reference maps of the world. 458:

One way of describing a projection is first to project from the Earth's surface to a developable surface such as a cylinder or cone, and then to unroll the surface into a plane. While the first step inevitably distorts some properties of the globe, the developable surface can then be unfolded without

76:

All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other

419:

Some of the simplest map projections are literal projections, as obtained by placing a light source at some definite point relative to the globe and projecting its features onto a specified surface. Although most projections are not defined in this way, picturing the light source-globe model can be

355:

To measure distortion globally across areas instead of at just a single point necessarily involves choosing priorities to reach a compromise. Some schemes use distance distortion as a proxy for the combination of angular deformation and areal inflation; such methods arbitrarily choose what paths to

2164:

Compromise projections give up the idea of perfectly preserving metric properties, seeking instead to strike a balance between distortions, or to simply make things look right. Most of these types of projections distort shape in the polar regions more than at the equator. These are some compromise

710:

One way to classify map projections is based on the type of surface onto which the globe is projected. In this scheme, the projection process is described as placing a hypothetical projection surface the size of the desired study area in contact with part of the Earth, transferring features of the

343:

are used. In the first half of the 20th century, projecting a human head onto different projections was common to show how distortion varies across one projection as compared to another. In dynamic media, shapes of familiar coastlines and boundaries can be dragged across an interactive map to show

1241:

where the cone intersects the globe—or, if the map maker chooses the same parallel twice, as the tangent line where the cone is tangent to the globe. The resulting conic map has low distortion in scale, shape, and area near those standard parallels. Distances along the parallels to the north of

850:

as used in the field of map projections relaxes the last constraint entirely. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map. The famous Mercator projection is one in which the placement of parallels does not arise by projection;

808:

No reference has been made in the above definitions to cylinders, cones or planes. The projections are termed cylindric or conic because they can be regarded as developed on a cylinder or a cone, as the case may be, but it is as well to dispense with picturing cylinders and cones, since they have

799:

The three developable surfaces (plane, cylinder, cone) provide useful models for understanding, describing, and developing map projections. However, these models are limited in two fundamental ways. For one thing, most world projections in use do not fall into any of those categories. For another

2291:

The time has come to discard for something that represents the continents and directions less deceptively ... Although its usage ... has diminished ... it is still highly popular as a wall map apparently in part because, as a rectangular map, it fills a rectangular wall space with more map, and

631:

Selecting a model for a shape of the Earth involves choosing between the advantages and disadvantages of a sphere versus an ellipsoid. Spherical models are useful for small-scale maps such as world atlases and globes, since the error at that scale is not usually noticeable or important enough to

1063:

as straight lines. Along parallels, each point from the surface is mapped at a distance from the central meridian that is proportional to its difference in longitude from the central meridian. Therefore, meridians are equally spaced along a given parallel. On a pseudocylindrical map, any point

523:

to the sphere or ellipsoid. Tangent means the surface touches but does not slice through the globe; secant means the surface does slice through the globe. Moving the developable surface away from contact with the globe never preserves or optimizes metric properties, so that possibility is not

237:

maps, such as those from national mapping systems, it is important to match the datum to the projection. The slight differences in coordinate assignation between different datums is not a concern for world maps or those of large regions, where such differences are reduced to imperceptibility.

2032:

preserves distances from one or two special points to all other points. The special point or points may get stretched into a line or curve segment when projected. In that case, the point on the line or curve segment closest to the point being measured to must be used to measure the distance.

825:(azimuthal) have been abstracted in the field of map projections. If maps were projected as in light shining through a globe onto a developable surface, then the spacing of parallels would follow a very limited set of possibilities. Such a cylindrical projection (for example) is one which: 1800:, or orthomorphic, map projections preserve angles locally, implying that they map infinitesimal circles of constant size anywhere on the Earth to infinitesimal circles of varying sizes on the map. In contrast, mappings that are not conformal distort most such small circles into 1064:

further from the equator than some other point has a higher latitude than the other point, preserving north-south relationships. This trait is useful when illustrating phenomena that depend on latitude, such as climate. Examples of pseudocylindrical projections include:

128:

often have irregular shapes. The surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid. Therefore, more generally, a map projection is any method of flattening a continuous curved surface onto a plane.

2027:

If the length of the line segment connecting two projected points on the plane is proportional to the geodesic (shortest surface) distance between the two unprojected points on the globe, then we say that distance has been preserved between those two points. An

1620:

operators to know the direction to point their antennas toward a point and see the distance to it. Distance from the tangent point on the map is proportional to surface distance on the Earth (; for the case where the tangent point is the North Pole, see the

307:

described how to construct an ellipse that illustrates the amount and orientation of the components of distortion. By spacing the ellipses regularly along the meridians and parallels, the network of indicatrices shows how distortion varies across the map.

77:

properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections. More generally, projections are considered in several fields of pure mathematics, including

1804:. An important consequence of conformality is that relative angles at each point of the map are correct, and the local scale (although varying throughout the map) in every direction around any one point is constant. These are some conformal projections: 454:

and the plane are all developable surfaces. The sphere and ellipsoid do not have developable surfaces, so any projection of them onto a plane will have to distort the image. (To compare, one cannot flatten an orange peel without tearing and warping it.)

1718: 723:). Many mathematical projections, however, do not neatly fit into any of these three projection methods. Hence other peer categories have been described in the literature, such as pseudoconic, pseudocylindrical, pseudoazimuthal, retroazimuthal, and 1242:

both standard parallels or to the south of both standard parallels are stretched; distances along parallels between the standard parallels are compressed. When a single standard parallel is used, distances along all other parallels are stretched.

987:

In the first case (Mercator), the east-west scale always equals the north-south scale. In the second case (central cylindrical), the north-south scale exceeds the east-west scale everywhere away from the equator. Each remaining case has a pair of

347:

Another way to visualize local distortion is through grayscale or color gradations whose shade represents the magnitude of the angular deformation or areal inflation. Sometimes both are shown simultaneously by blending two colors to create a

838:

Has parallels constrained to where they fall when light shines through the globe onto the cylinder, with the light source someplace along the line formed by the intersection of the prime meridian with the equator, and the center of the

2231:

The mathematics of projection do not permit any particular map projection to be best for everything. Something will always be distorted. Thus, many projections exist to serve the many uses of maps and their vast range of scales.

2281:, developed for navigational purposes, has often been used in world maps where other projections would have been more appropriate. This problem has long been recognized even outside professional circles. For example, a 1943 1323:

through the central point are represented by straight lines on the map. These projections also have radial symmetry in the scales and hence in the distortions: map distances from the central point are computed by a function

893:

The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's axis of rotation. This cylinder is wrapped around the Earth, projected onto, and then unrolled.

108:

on a flat film plate. Rather, any mathematical function that transforms coordinates from the curved surface distinctly and smoothly to the plane is a projection. Few projections in practical use are perspective.

73:, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. 897:

By the geometry of their construction, cylindrical projections stretch distances east-west. The amount of stretch is the same at any chosen latitude on all cylindrical projections, and is given by the

1309: 1041: 1071:, which was the first pseudocylindrical projection developed. On the map, as in reality, the length of each parallel is proportional to the cosine of the latitude. The area of any region is true. 229:

Another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Data sets are geographic information; their collection depends on the chosen

3053:

Airy, G.B. (1861). "Explanation of a projection by balance of errors for maps applying to a very large extent of the Earth's surface; and comparison of this projection with other projections".

1219: 173: 3783:—PDF versions of numerous projections, created and released into the Public Domain by Paul B. Anderson ... member of the International Cartographic Association's Commission on Map Projections 843:(If you rotate the globe before projecting then the parallels and meridians will not necessarily still be straight lines. Rotations are normally ignored for the purpose of classification.) 1775: 1252:, which keeps parallels evenly spaced along the meridians to preserve a constant distance scale along each meridian, typically the same or similar scale as along the standard parallels. 2143: 1666: 995:

Normal cylindrical projections map the whole Earth as a finite rectangle, except in the first two cases, where the rectangle stretches infinitely tall while retaining constant width.

2274:

so that phenomena per unit area are shown in correct proportion. However, representing area ratios correctly necessarily distorts shapes more than many maps that are not equal-area.

2078: 651:

would be if there were no winds, tides, or land. Compared to the best fitting ellipsoid, a geoidal model would change the characterization of important properties such as distance,

620:

Projection construction is also affected by how the shape of the Earth or planetary body is approximated. In the following section on projection categories, the earth is taken as a

846:

Where the light source emanates along the line described in this last constraint is what yields the differences between the various "natural" cylindrical projections. But the term

905:

as a multiple of the equator's scale. The various cylindrical projections are distinguished from each other solely by their north-south stretching (where latitude is given by φ):

575:

throughout the entire map in all directions. A map cannot achieve that property for any area, no matter how small. It can, however, achieve constant scale along specific lines.

261:

proved that a sphere's surface cannot be represented on a plane without distortion. The same applies to other reference surfaces used as models for the Earth, such as oblate

2977: 711:

Earth's surface onto the projection surface, then unraveling and scaling the projection surface into a flat map. The most common projection surfaces are cylindrical (e.g.,

3081: 331:

Rather than the original (enlarged) infinitesimal circle as in Tissot's indicatrix, some visual methods project finite shapes that span a part of the map. For example, a

3095: 599:

Scale is constant along all straight lines radiating from a particular geographic location. This is the defining characteristic of an equidistant projection such as the

983:(undistorted at the equator). Since this projection scales north-south distances by the reciprocal of east-west stretching, it preserves area at the expense of shapes. 1277:, an equal-area projection on which most meridians and parallels appear as curved lines. It has a configurable standard parallel along which there is no distortion. 1059:

as a straight line segment. Other meridians are longer than the central meridian and bow outward, away from the central meridian. Pseudocylindrical projections map

1336:, independent of the angle; correspondingly, circles with the central point as center are mapped into circles which have as center the central point on the map. 1003:

A transverse cylindrical projection is a cylindrical projection that in the tangent case uses a great circle along a meridian as contact line for the cylinder.

1402: 4279: 1499:

Near-sided perspective projection, which simulates the view from space at a finite distance and therefore shows less than a full hemisphere, such as used in

1460:

maps each point on the Earth to the closest point on the plane. Can be constructed from a point of perspective an infinite distance from the tangent point;

1258:, which adjusts the north-south distance between non-standard parallels to compensate for the east-west stretching or compression, giving an equal-area map. 851:

instead parallels are placed how they need to be in order to satisfy the property that a course of constant bearing is always plotted as a straight line.

589:

Scale is constant along any parallel in the direction of the parallel. This applies for any cylindrical or pseudocylindrical projection in normal aspect.

2251:

maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose, such as

2111:

Direction to a fixed location B (the bearing at the starting location A of the shortest route) corresponds to the direction on the map from A to B:

1762:

to subdivide the globe into faces, and then projects each face to the globe. The most well-known polyhedral map projection is Buckminster Fuller's

2899: 415:

defined as a grid superimposed on the projection. In small-scale maps, eastings and northings are not meaningful, and grids are not superimposed.

2301: 1669:

is constructed so that each point's distance from the center of the map is the logarithm of its distance from the tangent point on the Earth.

1312:

An azimuthal equidistant projection shows distances and directions accurately from the center point, but distorts shapes and sizes elsewhere.

660: 214:

Map projections can be constructed to preserve some of these properties at the expense of others. Because the Earth's curved surface is not

1833: 1728:

Comparison of some azimuthal projections centred on 90° N at the same scale, ordered by projection altitude in Earth radii.

5021: 4553: 4059: 3936: 3317: 3103: 1968: 1725: 980: 582:

The scale depends on location, but not on direction. This is equivalent to preservation of angles, the defining characteristic of a

730:

Another way to classify projections is according to properties of the model they preserve. Some of the more common categories are:

699: 1264:, which adjusts the north-south distance between non-standard parallels to equal the east-west stretching, giving a conformal map. 992:—a pair of identical latitudes of opposite sign (or else the equator) at which the east-west scale matches the north-south-scale. 4639: 4435: 4425: 4345: 1963: 1853: 1848: 1823: 1628: 1520: 720: 4563: 4558: 4533: 4069: 4064: 4039: 1237:

When making a conic map, the map maker arbitrarily picks two standard parallels. Those standard parallels may be visualized as

3558:. Lecture Notes in Geoinformation and Cartography. Cham, Switzerland: International Cartographic Association. pp. 78–83. 3571: 3530: 3244: 2672: 2594: 2425: 1457: 800:

thing, even most projections that do fall into those categories are not naturally attainable through physical projection. As

483:

of the shape must be specified. The aspect describes how the developable surface is placed relative to the globe: it may be

4430: 4011: 3871: 1077:, which in its most common forms represents each meridian as two straight line segments, one from each pole to the equator. 140:. However, it has been criticized throughout the 20th century for enlarging regions further from the equator. To contrast, 2890:. FOSS4G Europe 2015. Geomatics Workbooks. Vol. 12. Como, Italy: Polytechnic University of Milan. pp. 697–700. 1589:). Can display nearly the entire sphere's surface on a finite circle. The sphere's full surface requires an infinite map. 3375: 4440: 4241: 1838: 1261: 3807:, U.S. Geological Survey Professional Paper 1453, by John P. Snyder (USGS) and Philip M. Voxland (U. Minnesota), 1989. 1881:

Equal-area maps preserve area measure, generally distorting shapes in order to do so. Equal-area maps are also called

507:

Comparison of tangent and secant cylindrical, conic and azimuthal map projections with standard parallels shown in red

440:

A surface that can be unfolded or unrolled into a plane or sheet without stretching, tearing or shrinking is called a

4573: 4525: 4186: 4112: 4031: 3620: 3595: 2999:

Gott, III, J. Richard; Mugnolo, Charles; Colley, Wesley N. (2006). "Map projections for minimizing distance errors".

2802: 2731: 2639: 2475: 2450: 1998: 1919: 1086: 968: 1044:

A sinusoidal projection shows relative sizes accurately, but grossly distorts shapes. Distortion can be reduced by "

531:) are represented undistorted. If these lines are a parallel of latitude, as in conical projections, it is called a 4964: 4761: 4688: 4644: 4340: 2267:. Due to distortions inherent in any map of the world, the choice of projection becomes largely one of aesthetics. 2121: 2065: 2043: 2020: 1601: 1512:

can be constructed by using a point of perspective outside the Earth. Photographs of Earth (such as those from the

1035: 604: 600: 1018: 592:

Combination of the above: the scale depends on latitude only, not on longitude or direction. This applies for the

5058: 4809: 4756: 2209: 2127: 273:. Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. 3554:

Snyder, John P. (2017). "Matching the Map Projection to the Need". In Lapaine, Miljenko; Usery, E. Lynn (eds.).

2716:. United States Geological Survey Professional Paper. Vol. 1395. United States Government Printing Office. 2248: 2240: 2068:: Two "control points" are arbitrarily chosen by the map maker; distances from each control point are preserved. 682:

Other regular solids are sometimes used as generalizations for smaller bodies' geoidal equivalent. For example,

4917: 4886: 4460: 4309: 4087: 4016: 3898: 2982: 2236: 2152: 1818: 1509: 1401:; that is, they can be constructed mechanically, projecting the surface of the Earth by extending lines from a 1007: 928: 472: 222:

and, consequently, non-proportional presentation of areas. Similarly, an area-preserving projection can not be

5252: 5001: 4969: 4819: 4450: 4274: 4107: 4097: 3929: 3335: 2655:

Hargitai, Henrik; Wang, Jue; Stooke, Philip J.; Karachevtseva, Irina; Kereszturi, Akos; Gede, Mátyás (2017),

2324: 2179: 1843: 935: 860: 433: 1742: 1729: 1492:. Can display up to a hemisphere on a finite circle. Photographs of Earth from far enough away, such as the 316:

Many other ways have been described of showing the distortion in projections. Like Tissot's indicatrix, the

4959: 4673: 4327: 4236: 2049: 1988: 1303: 1249: 3777:

Fran Evanisko, American River College, lectures for Geography 20: "Cartographic Design for GIS", Fall 2002

3505: 3206: 1631:. Distance from the tangent point on the map is proportional to straight-line distance through the Earth: 4949: 4899: 4862: 4629: 4322: 4171: 4021: 2631: 2532:

Ghaderpour, E. (2016). "Some equal-area, conformal and conventional map projections: a tutorial review".

2055: 1948: 1513: 1122: 878:

as straight lines. A rhumb is a course of constant bearing. Bearing is the compass direction of movement.

388: 233:(model) of the Earth. Different datums assign slightly different coordinates to the same location, so in 153: 2822: 2659:, Lecture Notes in Geoinformation and Cartography, Springer International Publishing, pp. 177–202, 934:

North-south stretching grows with latitude, but less quickly than the east-west stretching: such as the

156:

and most atlases favor map projections that compromise between area and angular distortion, such as the

4834: 4678: 4543: 4269: 4102: 4092: 4049: 2748: 2503:. U.S. Geological Survey Professional Paper. Vol. 1453. United States Government Printing Office. 2386: 2174: 1942: 1899: 1622: 1290: 972: 961: 539:

is the meridian to which the globe is rotated before projecting. The central meridian (usually written

149: 2880: 2037: 1026:

An oblique cylindrical projection aligns with a great circle, but not the equator and not a meridian.

971:. This projection has many named specializations differing only in the scaling constant, such as the 4814: 4199: 2199: 1755: 1178: 46: 3480: 1516:) give this perspective. It is a generalization of near-sided perspective projection, allowing tilt. 967:

North-south compression equals the cosine of the latitude (the reciprocal of east-west stretching):

5237: 4904: 4844: 4824: 4604: 4548: 4455: 4417: 4382: 4054: 3922: 2368: 2252: 2184: 2157: 1958: 1792: 1779: 411:) plane coordinates. In large-scale maps, Cartesian coordinates normally have a simple relation to 161: 137: 3810: 3180: 2917: 1421:

as straight lines. Can be constructed by using a point of perspective at the center of the Earth.

632:

justify using the more complicated ellipsoid. The ellipsoidal model is commonly used to construct

4117: 3961: 2349: 1894: 1594: 1255: 698:

twice as long as its minor and with its middle axis one and half times as long as its minor. See

668: 400: 97: 2957: 671:

amounting to less than 100 m from the ellipsoidal model out of the 6.3 million m

503: 5121: 5016: 4649: 4624: 4166: 3956: 3835: 2793:. Research monographs in geographic information systems. London: Taylor & Francis. p. 1983: 1937: 1801: 1398: 1319:

projections have the property that directions from a central point are preserved and therefore

1045: 898: 304: 288: 247: 101: 2794: 628:. Whether spherical or ellipsoidal, the principles discussed hold without loss of generality. 624:

in order to simplify the discussion. However, the Earth's actual shape is closer to an oblate

368:

Selection of a model for the shape of the Earth or planetary body (usually choosing between a

5247: 5126: 4939: 4729: 4683: 4510: 4487: 4470: 4181: 3455: 2220: 1978: 1865: 1068: 910: 145: 141: 78: 50: 3405: 3117:

Cheng, Y.; Lorre, J. J. (2000). "Equal Area Map Projection for Irregularly Shaped Objects".

3022:"Distortion-spectrum fundamentals: A new tool for analyzing and visualizing map distortions" 636:

and for other large- and medium-scale maps that need to accurately depict the land surface.

356:

measure and how to weight them in order to yield a single result. Many have been described.

5242: 4944: 4839: 4619: 4614: 4609: 4586: 4581: 4502: 4264: 4204: 4176: 4161: 4156: 4151: 4146: 3260: 2551: 2260: 2204: 2194: 1973: 1932: 1928: 1924: 1914: 1909: 1875: 1501: 1286: 1227: 1207: 1160: 1142: 1104: 1074: 1056: 883: 724: 412: 252: 203: 198: 3847: 3295: 931:) projection; unsuitable because distortion is even worse than in the Mercator projection. 8: 5051: 4894: 4829: 4734: 4711: 4538: 4445: 4317: 4044: 4002: 3890: 2278: 2256: 2169: 2147: 2100: 2082: 1808: 1414: 1231: 976: 917: 887: 788: 781: 712: 593: 447: 442: 281: 157: 133: 82: 58: 28: 3353: 2555: 1206:

projection combines an equal-area cylindrical projection in equatorial regions with the

791:, it is impossible to construct a map projection that is both equal-area and conformal. 686:

is better modeled by triaxial ellipsoid or prolated spheroid with small eccentricities.

663:

would deviate from a mapped ellipsoid's graticule. Normally the geoid is not used as an

475:

is mathematically the same as a standard Mercator, but oriented around a different axis.

4766: 4377: 4082: 3910:"the true size" page show size of countries without distortion from Mercator projection 3662: 3635:

Bauer, H.A. (1942). "Globes, Maps, and Skyways (Air Education Series)". New York. p. 28

3590:. Falls Church, Virginia: American Congress on Surveying and Mapping. 1988. p. 1. 3165: 3134: 3000: 2855: 2837: 2771: 2567: 2541: 2115: 1827: 1094: 1060: 637: 340: 184:

Many properties can be measured on the Earth's surface independently of its geography:

3610: 2015: 5210: 4693: 4634: 4599: 4515: 4492: 4372: 4367: 4286: 4231: 4209: 3813:, a visualization of distortion on a vast array of map projections in a single image. 3732: 3616: 3591: 3567: 3502: 3477: 3452: 3426: 3402: 3350: 3329: 3292: 3240: 3138: 2891: 2798: 2727: 2668: 2635: 2590: 2571: 2471: 2446: 2421: 2003: 1953: 1280: 716: 257: 234: 177: 27:(1482, Johannes Schnitzer, engraver), constructed after the coordinates in Ptolemy's 3867:

Table of examples and properties of all common projections (RadicalCartography.net).

3379: 2859: 2775: 2377: – Process of projecting a 3D model's surface to a 2D image for texture mapping 152:

show the correct sizes of countries relative to each other, but distort angles. The

112:

Most of this article assumes that the surface to be mapped is that of a sphere. The

5257: 5139: 5116: 5088: 4479: 4259: 3864: 3755: 3728: 3654: 3559: 3272: 3232: 3161: 3126: 3062: 3033: 2847: 2763: 2717: 2660: 2559: 2504: 1904: 1340: 1274: 695: 691: 679:, however, sometimes models analogous to the geoid are used to project maps from. 647:, a more complex and accurate representation of Earth's shape coincident with what 562: 376:). Because the Earth's actual shape is irregular, information is lost in this step. 117: 3829: 3538: 2936: 2688: 923:

North-south stretching grows with latitude faster than east-west stretching (sec

5179: 3894: 3854:

MapRef: The Internet Collection of MapProjections and Reference Systems in Europe

2975:

Peters, A. B. (1978). "Uber Weltkartenverzerrunngen und Weltkartenmittelpunkte".

1524: 1406: 1308: 1283:, upon which distances are correct from one pole, as well as along all parallels. 1130: 1040: 633: 451: 230: 121: 3563: 3500: 3236: 3038: 3021: 2664: 5164: 5159: 5149: 5044: 3759: 3611:

Slocum, Terry A.; Robert B. McMaster; Fritz C. Kessler; Hugh H. Howard (2005).

3227:

Clark, P. E.; Clark, C. S. (2013). "CSNB Mapping Applied to Irregular Bodies".

3130: 2767: 2709: 2623: 2491: 2363: 2354: 2340: 2337: – Application of information science methods in geography and geosciences 2334: 2318: 2283: 1186: 916:): The east-west scale matches the north-south scale: conformal cylindrical or 648: 344:

how the projection distorts sizes and shapes according to position on the map.

336: 287:

The classical way of showing the distortion inherent in a projection is to use

105: 100:

projections, such as those resulting from casting a shadow on a screen, or the

3645:

Miller, Osborn Maitland (1942). "Notes on Cylindrical World Map Projections".

3276: 3066: 2214: 659:. Therefore, in geoidal projections that preserve such properties, the mapped 479:

Once a choice is made between projecting onto a cylinder, cone, or plane, the

428: 19: 16:

Systematic representation of the surface of a sphere or ellipsoid onto a plane

5231: 5203: 5169: 3816: 3746:"Geographers and Cartographers Urge End to Popular Use of Rectangular Maps". 3229:

Constant-Scale Natural Boundary Mapping to Reveal Global and Cosmic Processes

2895: 2244: 1992: 1797: 1617: 1218: 583: 467: 349: 223: 172: 3615:(2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall. p. 166. 487:(such that the surface's axis of symmetry coincides with the Earth's axis), 5215: 5174: 5154: 4954: 3795: 3005: 2851: 2495: 2466:

Robinson, Arthur; Randall, Sale; Morrison, Joel; Muehrcke, Phillip (1985).

2189: 2093: 1763: 1418: 1320: 672: 332: 3207:"The Classification of Projections of Irregularly-shaped Celestial Bodies" 2563: 1870: 1405:(along an infinite line through the tangent point and the tangent point's 1112: 667:

for projections, however, because Earth's shape is very regular, with the

5184: 5078: 3966: 3475: 2842: 1774: 1238: 1168: 1150: 989: 664: 572: 519: 219: 90: 62: 38: 3780: 3705:

American Cartographic Association's Committee on Map Projections, 1986.

1226:

The term "conic projection" is used to refer to any projection in which

777:), a trait possible only between one or two points and every other point 5103: 2881:"Real-time projection visualisation with Indicatrix Mapper QGIS Plugin" 2418:

Notes and comments on the composition of terrestrial and celestial maps

2374: 2297: 2059: 1812: 1759: 266: 3841: 3666: 2886:. In Brovelli, Maria Antonia; Minghini, Marco; Negreti, Marco (eds.). 1747: 1523:, which is conformal, can be constructed by using the tangent point's 5144: 5083: 5011: 4405: 3510: 3485: 3460: 3410: 3358: 3300: 2380: 801: 683: 676: 625: 380: 373: 70: 2142: 870: 738:), a trait possible only from one or two points to every other point 5006: 3658: 3214:

Proceedings of the 21st International Cartographic Conference (ICC)

2722: 2508: 2052:: Distances from the two poles are preserved, in equatorial aspect. 2040:: Distances from the two poles are preserved, in equatorial aspect. 1769: 1230:

are mapped to equally spaced lines radiating out from the apex and

902: 384: 262: 215: 208: 125: 86: 66: 3263:(1944). "The nomenclature and classification of map projections". 2546: 2077: 276: 218:

to a plane, preservation of shapes inevitably requires a variable

4867: 3914: 3450: 1344: 1316: 1203: 513: 96:

Despite the name's literal meaning, projection is not limited to

24: 3709:

p. 12. Falls Church: American Congress on Surveying and Mapping.

3537:. Cartography and Geographic Information Society. Archived from 3400: 420:

helpful in understanding the basic concept of a map projection.

3909: 2654: 2465: 2331:) – System to capture, manage, and present geographic data 2086: 1782:

is conformal and perspective but not equal area or equidistant.

1453:; so that even just a hemisphere is already infinite in extent. 875: 687: 621: 369: 3904: 3858: 3290: 3152:

Stooke, P. J. (1998). "Mapping Worlds with Irregular Shapes".

2762:(3). Cartography and Geographic Information Society: 167–182. 1234:(parallels) are mapped to circular arcs centered on the apex. 835:

Has straight parallels symmetrically placed about the equator;

89:. However, the term "map projection" refers specifically to a 5067: 3419: 2226: 2156:

magazine in 1988 but abandoned by them in about 1997 for the

1704:); locations closer than at a distance equal to the constant 1339:

The mapping of radial lines can be visualized by imagining a

644: 615: 568: 553:) are often used to define the origin of the map projection. 270: 193: 113: 54: 3348: 3181:"Mathematical Basis for Non-spherical Celestial Bodies Maps" 960:

North-south distances neither stretched nor compressed (1):

3884: 3823: 3820: 2628:

Flattening the earth: two thousand years of map projections

2445:. New York, NY: American Elsevier Publishing Company, inc. 1493: 882:

A normal cylindrical projection is any projection in which

188: 3178: 1022:

Cylindrical equal-area projection with oblique orientation

5093: 3853: 2490: 2300:

motivated the American Cartographic Association (now the

2085:

is thought to be the oldest map projection, developed by

975:

or Gall orthographic (undistorted at the 45° parallels),

780:

Preserving shortest route, a trait preserved only by the

5036: 3719:

Robinson, Arthur (1990). "Rectangular World Maps—No!".

3696:, second edition. New York: John Wiley and Sons. p. 82. 3179:

Shingareva, K.B.; Bugaevsky, L.M.; Nyrtsov, M. (2000).

2494:; Voxland, P.M. (1989). "An album of map projections". 2391:

Pages displaying short descriptions of redirect targets

2357: – drawings or diagrams used to describe an object 2345:

Pages displaying short descriptions of redirect targets

2292:

clearly because its familiarity breeds more popularity.

1297: 2998: 2823:"Flexion and Skewness in Map Projections of the Earth" 2749:"Symbolization of Map Projection Distortion: A Review" 2383: – Map of most or all of the surface of the Earth 1830:, great and small, maps to a circle or straight line. 571:

is the only way to represent the Earth with constant

364:

The creation of a map projection involves two steps:

3739: 3055:

London, Edinburgh, and Dublin Philosophical Magazine

2747:

Mulcahy, Karen A.; Clarke, Keith C. (January 2001).

2359:

Pages displaying wikidata descriptions as a fallback

920:; this distorts areas excessively in high latitudes. 909:

North-south stretching equals east-west stretching (

2235:Modern national mapping systems typically employ a 2046:: Distances from the center and edge are preserved. 4308: 3533:. In Robinson, Arthur H.; Snyder, John P. (eds.). 2618: 2616: 2614: 2612: 2610: 2608: 2606: 1945:(also known as Gall–Peters, or Peters, projection) 3613:Thematic Cartography and Geographic Visualization 3324:. Archived from the original on 12 December 2016. 2821:Goldberg, David M.; Gott III, J. Richard (2007). 2589:(3rd ed.). The University of Chicago Press. 2247:and low variation in scale over small areas. For 1889:. These are some projections that preserve area: 49:employed to represent the curved two-dimensional 5229: 3686: 2820: 2816: 2814: 2704: 2702: 1770:Projections by preservation of a metric property 1343:tangent to the Earth, with the central point as 1036:List of map projections § pseudocylindrical 886:are mapped to equally spaced vertical lines and 640:are often employed in projecting the ellipsoid. 423: 136:. This map projection has the property of being 2622: 2603: 2263:. Reference maps of the world often appear on 2124:—also preserves distance from the central point 832:Has straight vertical meridians, spaced evenly; 3830:Color images of map projections and distortion 3119:Cartography and Geographic Information Science 2756:Cartography and Geographic Information Science 2440: 2343: – Cartesian geographic coordinate system 2321: – Reference frame for measuring location 2302:Cartography and Geographic Information Society 1245:Conic projections that are commonly used are: 5052: 3930: 3819:, free software can render many projections ( 3683:. New York: McGraw–Hill. 2d ed., 1948. p. 87. 2811: 2746: 2699: 2415: 2304:) to produce a series of booklets (including 2118:—the only conformal retroazimuthal projection 4877: 3836:Geometric aspects of mapping: map projection 3524: 3522: 1052:Pseudocylindrical projections represent the 890:(parallels) are mapped to horizontal lines. 813:Lee's objection refers to the way the terms 546:) and a parallel of origin (usually written 291:. For a given point, using the scale factor 180:shows areas accurately, but distorts shapes. 167: 4801: 3981: 3231:. SpringerBriefs in Astronomy. p. 71. 2264: 511:The developable surface may also be either 462: 311: 5059: 5045: 3937: 3923: 3226: 3116: 2950: 2531: 2227:Suitability of projections for application 2133:Mecca or Qibla—also has vertical meridians 861:List of map projections § Cylindrical 616:Choosing a model for the shape of the body 379:Transformation of geographic coordinates ( 359: 132:The most well-known map projection is the 5022:Map projection of the tri-axial ellipsoid 4139: 3859:PROJ.4 – Cartographic Projections Library 3519: 3506:"Lambert Azimuthal Equal-Area Projection" 3037: 3019: 3013: 3004: 2968: 2841: 2721: 2584: 2545: 2484: 2137: 1989:Snyder's equal-area polyhedral projection 1743:List of map projections § Polyhedral 1593:Other azimuthal projections are not true 998: 794: 675:. For irregular planetary bodies such as 491:(at right angles to the Earth's axis) or 3718: 3712: 3580: 2878: 2657:Map Projections in Planetary Cartography 2141: 2076: 2014: 1869: 1773: 1746: 1307: 1304:List of map projections § azimuthal 1217: 1039: 1017: 979:(undistorted at the 30° parallels), and 869: 700:map projection of the triaxial ellipsoid 502: 466: 427: 328:(bending and lopsidedness) distortions. 320:is based on infinitesimals, and depicts 275: 171: 18: 3699: 3535:Matching the Map Projection to the Need 3204: 2909: 2788: 2527: 2525: 2416:Lambert, Johann; Tobler, Waldo (2011). 1854:Guyou hemisphere-in-a-square projection 1849:Adams hemisphere-in-a-square projection 603:. There are also projections (Maurer's 5230: 4131: 3644: 3638: 3604: 3553: 3528: 3315: 3151: 2974: 2915: 2879:Wirth, Ervin; Kun, Péter (July 2015). 2708: 1013: 5040: 4990: 4885: 4787: 4403: 3979: 3918: 3673: 3629: 3501: 3476: 3451: 3401: 3349: 3291: 2934: 2686: 2441:Richardus, Peter; Adler, Ron (1972). 865: 295:along the meridian, the scale factor 4359: 3079: 3052: 3046: 2872: 2522: 2296:A controversy in the 1980s over the 2062:are preserved, in equatorial aspect. 1815:are represented by straight segments 1397:Some azimuthal projections are true 1298:Azimuthal (projections onto a plane) 1029: 4789: 4788: 4744: 3316:Furuti, Carlos A. (11 April 2016). 3259: 3253: 2992: 2916:Jacobs, Frank (18 September 2013). 2689:"Which is the best map projection?" 607:, Close) where true distances from 33:and using his second map projection 13: 4251: 3944: 3481:"Azimuthal Equidistant Projection" 3373: 3166:10.1111/j.1541-0064.1998.tb01553.x 2905:from the original on 23 July 2022. 2389: – Video projection technique 2270:Thematic maps normally require an 335:of fixed radius (e.g., 15 degrees 299:along the parallel, and the angle 14: 5269: 3788: 3692:Robinson, Arthur Howard. (1960). 3188:Journal of Geospatial Engineering 2958:"A cornucopia of map projections" 2791:Small-scale map projection design 2714:Map projections: A working manual 2687:Singh, Ishveena (25 April 2017). 2106: 2096:are displayed as straight lines: 1751:Buckminster Fuller's Dymaxion map 927:): The cylindric perspective (or 705: 5209: 5198: 5197: 4965:Quadrilateralized spherical cube 4663: 4645:Quadrilateralized spherical cube 3993: 3897:based on work by Yu-Sung Chang ( 3733:10.1111/j.0033-0124.1990.00101.x 2021:two-point equidistant projection 1717: 1185: 1167: 1149: 1129: 1111: 1093: 605:two-point equidistant projection 601:azimuthal equidistant projection 498: 124:, whereas small objects such as 120:are generally better modeled as 4931: 4721: 3872:"Understanding Map Projections" 3811:A Cornucopia of Map Projections 3679:Raisz, Erwin Josephus. (1938). 3494: 3469: 3444: 3394: 3367: 3342: 3309: 3284: 3220: 3198: 3172: 3145: 3110: 3088: 3073: 2928: 2782: 2740: 2271: 2195:B. J. S. Cahill's Butterfly Map 1496:, approximate this perspective. 656: 436:maps the globe onto a cylinder. 4554:Lambert cylindrical equal-area 4296: 3980: 3899:Wolfram Demonstrations Project 3844:, Henry Bottomley (SE16.info). 3531:"Enlarging the Heart of a Map" 3084:. City University of New York. 2680: 2648: 2578: 2459: 2434: 2409: 2010: 1969:Lambert cylindrical equal-area 1527:as the point of perspective. 1510:General Perspective projection 1268: 981:Lambert cylindrical equal-area 874:The Mercator projection shows 854: 743: 652: 578:Some possible properties are: 473:transverse Mercator projection 1: 5002:Interruption (map projection) 4703: 4404: 3796:"An Album of Map Projections" 3205:Nyrtsov, M.V. (August 2003). 2397: 2325:Geographic information system 2190:Buckminster Fuller's Dymaxion 1859: 1844:Peirce quincuncial projection 1736: 1289:and other projections in the 936:Miller cylindrical projection 434:Miller cylindrical projection 424:Choosing a projection surface 280:Tissot's indicatrices on the 241: 4991: 4640:Lambert azimuthal equal-area 4436:Guyou hemisphere-in-a-square 4426:Adams hemisphere-in-a-square 4223: 2918:"This is your brain on maps" 2420:. Redlands, CA: ESRI Press. 2402: 1964:Lambert azimuthal equal-area 1786: 1730:(click for detail) 1629:Lambert azimuthal equal-area 1394:is the radius of the Earth. 787:Because the sphere is not a 23:A medieval depiction of the 7: 4854: 3564:10.1007/978-3-319-51835-0_3 3237:10.1007/978-1-4614-7762-4_6 3039:10.3138/Y51X-1590-PV21-136G 2978:Kartographische Nachrichten 2665:10.1007/978-3-319-51835-0_7 2632:University of Chicago Press 2311: 2072: 1514:International Space Station 1358:) and the transverse scale 154:National Geographic Society 10: 5274: 3842:Java world map projections 3770: 3760:10.1559/152304089783814089 3456:"Stereographic Projection" 3131:10.1559/152304000783547957 2888:Open Innovation for Europe 2768:10.1559/152304001782153044 2534:Journal of Applied Geodesy 2387:Spherical image projection 1863: 1790: 1756:Polyhedral map projections 1740: 1623:flag of the United Nations 1301: 1291:polyconic projection class 1033: 962:equirectangular projection 858: 741:Preserving shape locally ( 560: 527:Tangent and secant lines ( 245: 5193: 5135: 5112: 5074: 5066: 4997: 4986: 4930: 4913: 4876: 4853: 4800: 4796: 4783: 4743: 4720: 4702: 4662: 4595: 4572: 4524: 4501: 4478: 4469: 4416: 4412: 4399: 4358: 4336: 4295: 4250: 4222: 4195: 4130: 4078: 4030: 4001: 3992: 3988: 3975: 3952: 3556:Choosing a Map Projection 3406:"Orthographic Projection" 3376:"The Gnomonic Projection" 3334:: CS1 maint: unfit URL ( 3277:10.1179/sre.1944.7.51.190 3067:10.1080/14786446108643179 2470:(fifth ed.). Wiley. 2200:Kavrayskiy VII projection 1197: 702:for further information. 168:Metric properties of maps 45:is any of a broad set of 3529:Snyder, John P. (1997). 3431:PROJ 7.1.1 documentation 3427:"Near-sided perspective" 2585:Monmonier, Mark (2018). 2497:Album of Map Projections 2369:South-up map orientation 1793:Conformal map projection 1780:stereographic projection 1521:stereographic projection 1213: 556: 524:discussed further here. 495:(any angle in between). 463:Aspect of the projection 318:Goldberg-Gott indicatrix 312:Other distortion metrics 162:Winkel tripel projection 4441:Lambert conformal conic 3905:Compare Map Projections 3721:Professional Geographer 3694:Elements of Cartography 3296:"Sinusoidal Projection" 3154:The Canadian Geographer 3082:"Projection parameters" 2937:"Mercator Puzzle Redux" 2789:Canters, Frank (2002). 2468:Elements of Cartography 2371: – Map orientation 2350:List of map projections 1839:Lambert conformal conic 1458:orthographic projection 1399:perspective projections 1332:) of the true distance 1262:Lambert conformal conic 669:undulation of the geoid 360:Design and construction 61:. In a map projection, 5122:History of cartography 4574:Tobler hyperelliptical 4187:Tobler hyperelliptical 4113:Space-oblique Mercator 3020:Laskowski, P. (1997). 2852:10.3138/carto.42.4.297 2294: 2265:compromise projections 2161: 2138:Compromise projections 2090: 2030:equidistant projection 2024: 1999:Tobler hyperelliptical 1920:Cylindrical equal-area 1878: 1802:ellipses of distortion 1783: 1752: 1313: 1223: 1087:Tobler hyperelliptical 1049: 1023: 999:Transverse cylindrical 969:equal-area cylindrical 879: 811: 795:Projections by surface 734:Preserving direction ( 508: 476: 437: 413:eastings and northings 284: 181: 150:Gall–Peters projection 142:equal-area projections 34: 5127:List of cartographers 3891:World Map Projections 3748:American Cartographer 3354:"Gnomonic Projection" 3100:ArcSDE Developer Help 2564:10.1515/jag-2015-0033 2289: 2272:equal area projection 2243:in order to preserve 2239:or close variant for 2221:AuthaGraph projection 2145: 2122:Hammer retroazimuthal 2089:in the 6th century BC 2080: 2066:Two-point equidistant 2044:Azimuthal equidistant 2018: 1873: 1866:Equal-area projection 1777: 1750: 1667:Logarithmic azimuthal 1602:Azimuthal equidistant 1311: 1221: 1043: 1021: 873: 806: 773:Preserving distance ( 736:azimuthal or zenithal 719:), and planar (e.g., 643:A third model is the 611:points are preserved. 561:Further information: 506: 470: 431: 279: 175: 146:Sinusoidal projection 79:differential geometry 65:, often expressed as 22: 5253:Descriptive geometry 4950:Cahill–Keyes M-shape 4810:Chamberlin trimetric 3865:Projection Reference 3588:Choosing a World Map 3265:Empire Survey Review 3106:on 28 November 2018. 2587:How to lie with maps 2210:Chamberlin trimetric 2205:Wagner VI projection 2128:Craig retroazimuthal 1876:Mollweide projection 1502:The Blue Marble 2012 1403:point of perspective 1350:The radial scale is 1208:Collignon projection 1075:Collignon projection 459:further distortion. 253:Carl Friedrich Gauss 104:image produced by a 5017:Tissot's indicatrix 4918:Central cylindrical 4559:Smyth equal-surface 4461:Transverse Mercator 4310:General perspective 4065:Smyth equal-surface 4017:Transverse Mercator 3832:(Mapthematics.com). 3681:General Cartography 3647:Geographical Review 3318:"Conic Projections" 2935:Van Damme, Bramus. 2556:2016JAGeo..10..197G 2279:Mercator projection 2237:transverse Mercator 2153:National Geographic 2148:Robinson projection 2101:Gnomonic projection 2083:Gnomonic projection 2058:Distances from the 1819:Transverse Mercator 1415:gnomonic projection 1232:circles of latitude 1014:Oblique cylindrical 1008:transverse Mercator 929:central cylindrical 888:circles of latitude 789:developable surface 782:gnomonic projection 638:Auxiliary latitudes 594:Mercator projection 443:developable surface 341:spherical triangles 289:Tissot's indicatrix 282:Mercator projection 248:Tissot's indicatrix 158:Robinson projection 134:Mercator projection 83:projective geometry 4970:Waterman butterfly 4820:Miller cylindrical 4451:Peirce quincuncial 4346:Lambert equal-area 4098:Gall stereographic 3883:, Melita Kennedy ( 3838:(KartoWeb.itc.nl). 3503:Weisstein, Eric W. 3478:Weisstein, Eric W. 3453:Weisstein, Eric W. 3403:Weisstein, Eric W. 3351:Weisstein, Eric W. 3293:Weisstein, Eric W. 3080:Albrecht, Jochen. 3006:astro-ph/0608500v1 2287:editorial states: 2180:Miller cylindrical 2162: 2091: 2025: 1949:Goode's homolosine 1879: 1828:circle of a sphere 1784: 1753: 1409:) onto the plane: 1314: 1287:American polyconic 1224: 1050: 1024: 964:or "plate carrée". 880: 866:Normal cylindrical 509: 477: 438: 285: 182: 35: 5225: 5224: 5034: 5033: 5030: 5029: 4982: 4981: 4978: 4977: 4926: 4925: 4779: 4778: 4775: 4774: 4658: 4657: 4395: 4394: 4391: 4390: 4354: 4353: 4242:Lambert conformal 4218: 4217: 4132:Pseudocylindrical 4126: 4125: 3754:: 222–223. 1989. 3707:Which Map is Best 3573:978-3-319-51835-0 3246:978-1-4614-7761-7 3096:"Map projections" 2710:Snyder, John Parr 2674:978-3-319-51834-3 2596:978-0-226-43592-3 2427:978-1-58948-281-4 2306:Which Map Is Best 2050:Equidistant conic 1943:Gall orthographic 1250:Equidistant conic 1195: 1194: 1030:Pseudocylindrical 754:Preserving area ( 694:, with its major 596:in normal aspect. 533:standard parallel 258:Theorema Egregium 178:Albers projection 5265: 5213: 5201: 5200: 5140:Animated mapping 5117:Early world maps 5089:Geovisualization 5061: 5054: 5047: 5038: 5037: 4988: 4987: 4945:Cahill Butterfly 4883: 4882: 4863:Goode homolosine 4798: 4797: 4785: 4784: 4750: 4749:(Mecca or Qibla) 4630:Goode homolosine 4476: 4475: 4414: 4413: 4401: 4400: 4306: 4305: 4301: 4172:Goode homolosine 4137: 4136: 4022:Oblique Mercator 3999: 3998: 3990: 3989: 3977: 3976: 3939: 3932: 3925: 3916: 3915: 3882: 3878: 3876: 3806: 3802: 3800: 3764: 3763: 3743: 3737: 3736: 3716: 3710: 3703: 3697: 3690: 3684: 3677: 3671: 3670: 3642: 3636: 3633: 3627: 3626: 3608: 3602: 3601: 3584: 3578: 3577: 3550: 3548: 3546: 3526: 3517: 3516: 3515: 3498: 3492: 3491: 3490: 3473: 3467: 3466: 3465: 3448: 3442: 3441: 3439: 3438: 3423: 3417: 3416: 3415: 3398: 3392: 3391: 3389: 3387: 3382:on 30 April 2016 3378:. Archived from 3371: 3365: 3364: 3363: 3346: 3340: 3339: 3333: 3325: 3313: 3307: 3306: 3305: 3288: 3282: 3280: 3257: 3251: 3250: 3224: 3218: 3217: 3211: 3202: 3196: 3195: 3185: 3176: 3170: 3169: 3149: 3143: 3142: 3114: 3108: 3107: 3102:. Archived from 3092: 3086: 3085: 3077: 3071: 3070: 3061:(149): 409–421. 3050: 3044: 3043: 3041: 3017: 3011: 3010: 3008: 2996: 2990: 2989: 2986: 2972: 2966: 2965: 2954: 2948: 2947: 2945: 2943: 2932: 2926: 2925: 2920:. Strange Maps. 2913: 2907: 2906: 2904: 2885: 2876: 2870: 2869: 2867: 2866: 2845: 2843:astro-ph/0608501 2827: 2818: 2809: 2808: 2786: 2780: 2779: 2753: 2744: 2738: 2737: 2725: 2706: 2697: 2696: 2684: 2678: 2677: 2652: 2646: 2645: 2620: 2601: 2600: 2582: 2576: 2575: 2549: 2529: 2520: 2519: 2517: 2515: 2502: 2488: 2482: 2481: 2463: 2457: 2456: 2438: 2432: 2431: 2413: 2392: 2360: 2346: 2330: 2241:large-scale maps 2056:Werner cordiform 1721: 1703: 1701: 1700: 1692: 1689: 1663: 1661: 1660: 1654: 1651: 1616:; it is used by 1588: 1586: 1585: 1579: 1576: 1559: 1557: 1556: 1550: 1547: 1491: 1489: 1488: 1483: 1480: 1452: 1450: 1449: 1444: 1441: 1389: 1387: 1386: 1381: 1378: 1281:Werner cordiform 1210:in polar areas. 1189: 1171: 1153: 1133: 1123:Goode homolosine 1115: 1097: 1081: 1080: 953: 951: 950: 947: 944: 715:), conic (e.g., 692:Jacobi ellipsoid 634:topographic maps 563:Map scale factor 537:central meridian 303:′ between them, 122:oblate spheroids 118:celestial bodies 116:and other large 5273: 5272: 5268: 5267: 5266: 5264: 5263: 5262: 5238:Map projections 5228: 5227: 5226: 5221: 5189: 5180:Topographic map 5131: 5108: 5070: 5065: 5035: 5026: 4993: 4974: 4922: 4909: 4872: 4849: 4835:Van der Grinten 4792: 4790:By construction 4771: 4748: 4747: 4739: 4716: 4698: 4679:Equirectangular 4665: 4654: 4591: 4568: 4564:Trystan Edwards 4520: 4497: 4465: 4408: 4387: 4360:Pseudoazimuthal 4350: 4332: 4299: 4298: 4291: 4246: 4214: 4210:Winkel I and II 4191: 4122: 4103:Gall isographic 4093:Equirectangular 4074: 4070:Trystan Edwards 4026: 3984: 3971: 3948: 3943: 3895:Stephen Wolfram 3880: 3874: 3870: 3848:Map Projections 3804: 3798: 3794: 3791: 3786: 3781:Map Projections 3773: 3768: 3767: 3745: 3744: 3740: 3717: 3713: 3704: 3700: 3691: 3687: 3678: 3674: 3643: 3639: 3634: 3630: 3623: 3609: 3605: 3598: 3586: 3585: 3581: 3574: 3551: 3544: 3542: 3527: 3520: 3499: 3495: 3474: 3470: 3449: 3445: 3436: 3434: 3425: 3424: 3420: 3399: 3395: 3385: 3383: 3372: 3368: 3347: 3343: 3327: 3326: 3314: 3310: 3289: 3285: 3271:(51): 190–200. 3258: 3254: 3247: 3225: 3221: 3209: 3203: 3199: 3183: 3177: 3173: 3150: 3146: 3115: 3111: 3094: 3093: 3089: 3078: 3074: 3051: 3047: 3018: 3014: 2997: 2993: 2980: 2973: 2969: 2956: 2955: 2951: 2941: 2939: 2933: 2929: 2914: 2910: 2902: 2883: 2877: 2873: 2864: 2862: 2825: 2819: 2812: 2805: 2787: 2783: 2751: 2745: 2741: 2734: 2707: 2700: 2685: 2681: 2675: 2653: 2649: 2642: 2624:Snyder, John P. 2621: 2604: 2597: 2583: 2579: 2530: 2523: 2513: 2511: 2500: 2489: 2485: 2478: 2464: 2460: 2453: 2443:map projections 2439: 2435: 2428: 2414: 2410: 2405: 2400: 2395: 2390: 2358: 2344: 2328: 2314: 2229: 2175:van der Grinten 2150:was adopted by 2140: 2109: 2075: 2013: 2008: 1900:Boggs eumorphic 1874:The equal-area 1868: 1862: 1795: 1789: 1772: 1745: 1739: 1734: 1733: 1732: 1727: 1722: 1710: 1699: 1693: 1690: 1685: 1684: 1682: 1655: 1652: 1647: 1646: 1644: 1643: sin 1580: 1577: 1572: 1571: 1569: 1568: cos 1560:; the scale is 1551: 1548: 1543: 1542: 1540: 1539: tan 1484: 1481: 1476: 1475: 1473: 1472: sin 1445: 1442: 1437: 1436: 1434: 1433: tan 1382: 1379: 1374: 1373: 1371: 1370: sin 1306: 1300: 1271: 1216: 1200: 1038: 1032: 1016: 1001: 948: 945: 942: 941: 939: 868: 863: 857: 829:Is rectangular; 797: 708: 618: 565: 559: 552: 545: 501: 465: 426: 362: 314: 250: 244: 170: 47:transformations 17: 12: 11: 5: 5271: 5261: 5260: 5255: 5250: 5245: 5240: 5223: 5222: 5220: 5219: 5207: 5194: 5191: 5190: 5188: 5187: 5182: 5177: 5172: 5167: 5165:Nautical chart 5162: 5160:Linguistic map 5157: 5152: 5150:Choropleth map 5147: 5142: 5136: 5133: 5132: 5130: 5129: 5124: 5119: 5113: 5110: 5109: 5107: 5106: 5101: 5099:Map projection 5096: 5091: 5086: 5081: 5075: 5072: 5071: 5064: 5063: 5056: 5049: 5041: 5032: 5031: 5028: 5027: 5025: 5024: 5019: 5014: 5009: 5004: 4998: 4995: 4994: 4984: 4983: 4980: 4979: 4976: 4975: 4973: 4972: 4967: 4962: 4957: 4952: 4947: 4942: 4936: 4934: 4928: 4927: 4924: 4923: 4921: 4920: 4914: 4911: 4910: 4908: 4907: 4902: 4897: 4891: 4889: 4880: 4874: 4873: 4871: 4870: 4865: 4859: 4857: 4851: 4850: 4848: 4847: 4842: 4837: 4832: 4827: 4822: 4817: 4815:Kavrayskiy VII 4812: 4806: 4804: 4794: 4793: 4781: 4780: 4777: 4776: 4773: 4772: 4770: 4769: 4764: 4759: 4753: 4751: 4745:Retroazimuthal 4741: 4740: 4738: 4737: 4732: 4726: 4724: 4718: 4717: 4715: 4714: 4708: 4706: 4700: 4699: 4697: 4696: 4691: 4686: 4681: 4676: 4670: 4668: 4664:Equidistant in 4660: 4659: 4656: 4655: 4653: 4652: 4647: 4642: 4637: 4632: 4627: 4622: 4617: 4612: 4607: 4602: 4596: 4593: 4592: 4590: 4589: 4584: 4578: 4576: 4570: 4569: 4567: 4566: 4561: 4556: 4551: 4546: 4541: 4536: 4530: 4528: 4522: 4521: 4519: 4518: 4513: 4507: 4505: 4499: 4498: 4496: 4495: 4490: 4484: 4482: 4473: 4467: 4466: 4464: 4463: 4458: 4453: 4448: 4443: 4438: 4433: 4428: 4422: 4420: 4410: 4409: 4397: 4396: 4393: 4392: 4389: 4388: 4386: 4385: 4380: 4375: 4370: 4364: 4362: 4356: 4355: 4352: 4351: 4349: 4348: 4343: 4337: 4334: 4333: 4331: 4330: 4325: 4320: 4314: 4312: 4303: 4293: 4292: 4290: 4289: 4284: 4283: 4282: 4277: 4267: 4262: 4256: 4254: 4248: 4247: 4245: 4244: 4239: 4234: 4228: 4226: 4220: 4219: 4216: 4215: 4213: 4212: 4207: 4202: 4200:Kavrayskiy VII 4196: 4193: 4192: 4190: 4189: 4184: 4179: 4174: 4169: 4164: 4159: 4154: 4149: 4143: 4141: 4134: 4128: 4127: 4124: 4123: 4121: 4120: 4115: 4110: 4105: 4100: 4095: 4090: 4085: 4079: 4076: 4075: 4073: 4072: 4067: 4062: 4057: 4052: 4047: 4042: 4036: 4034: 4028: 4027: 4025: 4024: 4019: 4014: 4008: 4006: 3996: 3986: 3985: 3973: 3972: 3970: 3969: 3964: 3959: 3953: 3950: 3949: 3946:Map projection 3942: 3941: 3934: 3927: 3919: 3913: 3912: 3907: 3902: 3888: 3881:(1.70 MB) 3868: 3862: 3856: 3851: 3845: 3839: 3833: 3827: 3814: 3808: 3805:(12.6 MB) 3790: 3789:External links 3787: 3785: 3784: 3778: 3774: 3772: 3769: 3766: 3765: 3738: 3727:(1): 101–104. 3711: 3698: 3685: 3672: 3659:10.2307/210384 3653:(3): 424–430. 3637: 3628: 3621: 3603: 3596: 3579: 3572: 3552:Reprinted in: 3541:on 2 July 2010 3518: 3493: 3468: 3443: 3418: 3393: 3374:Savard, John. 3366: 3341: 3308: 3283: 3252: 3245: 3219: 3197: 3171: 3144: 3109: 3087: 3072: 3045: 3012: 2991: 2967: 2949: 2927: 2908: 2871: 2836:(4): 297–318. 2810: 2803: 2781: 2739: 2732: 2723:10.3133/pp1395 2698: 2693:Geoawesomeness 2679: 2673: 2647: 2640: 2602: 2595: 2577: 2540:(3): 197–209. 2521: 2509:10.3133/pp1453 2483: 2476: 2458: 2451: 2433: 2426: 2407: 2406: 2404: 2401: 2399: 2396: 2394: 2393: 2384: 2378: 2372: 2366: 2364:Rubbersheeting 2361: 2355:Plan (drawing) 2352: 2347: 2341:Grid reference 2338: 2335:Geoinformatics 2332: 2322: 2319:Geodetic datum 2315: 2313: 2310: 2284:New York Times 2228: 2225: 2224: 2223: 2218: 2212: 2207: 2202: 2197: 2192: 2187: 2182: 2177: 2172: 2139: 2136: 2135: 2134: 2125: 2119: 2108: 2107:Retroazimuthal 2105: 2104: 2103: 2074: 2071: 2070: 2069: 2063: 2053: 2047: 2041: 2012: 2009: 2007: 2006: 2001: 1996: 1993:geodesic grids 1986: 1981: 1976: 1971: 1966: 1961: 1956: 1951: 1946: 1940: 1935: 1922: 1917: 1912: 1907: 1902: 1897: 1891: 1864:Main article: 1861: 1858: 1857: 1856: 1851: 1846: 1841: 1836: 1831: 1821: 1816: 1791:Main article: 1788: 1785: 1771: 1768: 1738: 1735: 1724: 1723: 1716: 1715: 1714: 1713: 1712: 1711:are not shown. 1708: 1697: 1681: ln 1664: 1626: 1591: 1590: 1517: 1506: 1497: 1454: 1299: 1296: 1295: 1294: 1284: 1278: 1270: 1267: 1266: 1265: 1259: 1253: 1215: 1212: 1199: 1196: 1193: 1192: 1191: 1190: 1182: 1181: 1179:Kavrayskiy VII 1174: 1173: 1172: 1164: 1163: 1156: 1155: 1154: 1146: 1145: 1137: 1136: 1135: 1134: 1126: 1125: 1118: 1117: 1116: 1108: 1107: 1100: 1099: 1098: 1090: 1089: 1079: 1078: 1072: 1031: 1028: 1015: 1012: 1000: 997: 985: 984: 965: 958: 932: 921: 867: 864: 856: 853: 841: 840: 836: 833: 830: 796: 793: 785: 784: 778: 771: 752: 739: 707: 706:Classification 704: 690:'s shape is a 649:mean sea level 617: 614: 613: 612: 597: 590: 587: 558: 555: 550: 543: 529:standard lines 500: 497: 464: 461: 425: 422: 417: 416: 377: 361: 358: 337:angular radius 313: 310: 305:Nicolas Tissot 246:Main article: 243: 240: 212: 211: 206: 201: 196: 191: 169: 166: 106:pinhole camera 43:map projection 15: 9: 6: 4: 3: 2: 5270: 5259: 5256: 5254: 5251: 5249: 5246: 5244: 5241: 5239: 5236: 5235: 5233: 5218: 5217: 5212: 5208: 5206: 5205: 5204:Category:Maps 5196: 5195: 5192: 5186: 5183: 5181: 5178: 5176: 5173: 5171: 5170:Pictorial map 5168: 5166: 5163: 5161: 5158: 5156: 5153: 5151: 5148: 5146: 5143: 5141: 5138: 5137: 5134: 5128: 5125: 5123: 5120: 5118: 5115: 5114: 5111: 5105: 5102: 5100: 5097: 5095: 5092: 5090: 5087: 5085: 5082: 5080: 5077: 5076: 5073: 5069: 5062: 5057: 5055: 5050: 5048: 5043: 5042: 5039: 5023: 5020: 5018: 5015: 5013: 5010: 5008: 5005: 5003: 5000: 4999: 4996: 4989: 4985: 4971: 4968: 4966: 4963: 4961: 4958: 4956: 4953: 4951: 4948: 4946: 4943: 4941: 4938: 4937: 4935: 4933: 4929: 4919: 4916: 4915: 4912: 4906: 4905:Stereographic 4903: 4901: 4898: 4896: 4893: 4892: 4890: 4888: 4884: 4881: 4879: 4875: 4869: 4866: 4864: 4861: 4860: 4858: 4856: 4852: 4846: 4845:Winkel tripel 4843: 4841: 4838: 4836: 4833: 4831: 4828: 4826: 4825:Natural Earth 4823: 4821: 4818: 4816: 4813: 4811: 4808: 4807: 4805: 4803: 4799: 4795: 4791: 4786: 4782: 4768: 4765: 4763: 4760: 4758: 4755: 4754: 4752: 4746: 4742: 4736: 4733: 4731: 4728: 4727: 4725: 4723: 4719: 4713: 4710: 4709: 4707: 4705: 4701: 4695: 4692: 4690: 4687: 4685: 4682: 4680: 4677: 4675: 4672: 4671: 4669: 4667: 4661: 4651: 4648: 4646: 4643: 4641: 4638: 4636: 4633: 4631: 4628: 4626: 4623: 4621: 4618: 4616: 4613: 4611: 4608: 4606: 4605:Briesemeister 4603: 4601: 4598: 4597: 4594: 4588: 4585: 4583: 4580: 4579: 4577: 4575: 4571: 4565: 4562: 4560: 4557: 4555: 4552: 4550: 4547: 4545: 4542: 4540: 4537: 4535: 4532: 4531: 4529: 4527: 4523: 4517: 4514: 4512: 4509: 4508: 4506: 4504: 4500: 4494: 4491: 4489: 4486: 4485: 4483: 4481: 4477: 4474: 4472: 4468: 4462: 4459: 4457: 4456:Stereographic 4454: 4452: 4449: 4447: 4444: 4442: 4439: 4437: 4434: 4432: 4429: 4427: 4424: 4423: 4421: 4419: 4415: 4411: 4407: 4402: 4398: 4384: 4383:Winkel tripel 4381: 4379: 4376: 4374: 4371: 4369: 4366: 4365: 4363: 4361: 4357: 4347: 4344: 4342: 4339: 4338: 4335: 4329: 4328:Stereographic 4326: 4324: 4321: 4319: 4316: 4315: 4313: 4311: 4307: 4304: 4302: 4294: 4288: 4285: 4281: 4278: 4276: 4273: 4272: 4271: 4268: 4266: 4263: 4261: 4258: 4257: 4255: 4253: 4252:Pseudoconical 4249: 4243: 4240: 4238: 4235: 4233: 4230: 4229: 4227: 4225: 4221: 4211: 4208: 4206: 4203: 4201: 4198: 4197: 4194: 4188: 4185: 4183: 4180: 4178: 4175: 4173: 4170: 4168: 4165: 4163: 4160: 4158: 4155: 4153: 4150: 4148: 4145: 4144: 4142: 4138: 4135: 4133: 4129: 4119: 4116: 4114: 4111: 4109: 4106: 4104: 4101: 4099: 4096: 4094: 4091: 4089: 4086: 4084: 4081: 4080: 4077: 4071: 4068: 4066: 4063: 4061: 4058: 4056: 4053: 4051: 4048: 4046: 4043: 4041: 4038: 4037: 4035: 4033: 4029: 4023: 4020: 4018: 4015: 4013: 4010: 4009: 4007: 4004: 4000: 3997: 3995: 3991: 3987: 3983: 3978: 3974: 3968: 3965: 3963: 3960: 3958: 3955: 3954: 3951: 3947: 3940: 3935: 3933: 3928: 3926: 3921: 3920: 3917: 3911: 3908: 3906: 3903: 3900: 3896: 3892: 3889: 3886: 3873: 3869: 3866: 3863: 3860: 3857: 3855: 3852: 3849: 3846: 3843: 3840: 3837: 3834: 3831: 3828: 3825: 3822: 3818: 3815: 3812: 3809: 3797: 3793: 3792: 3782: 3779: 3776: 3775: 3761: 3757: 3753: 3749: 3742: 3734: 3730: 3726: 3722: 3715: 3708: 3702: 3695: 3689: 3682: 3676: 3668: 3664: 3660: 3656: 3652: 3648: 3641: 3632: 3624: 3622:0-13-035123-7 3618: 3614: 3607: 3599: 3597:0-9613459-2-6 3593: 3589: 3583: 3575: 3569: 3565: 3561: 3557: 3540: 3536: 3532: 3525: 3523: 3513: 3512: 3507: 3504: 3497: 3488: 3487: 3482: 3479: 3472: 3463: 3462: 3457: 3454: 3447: 3432: 3428: 3422: 3413: 3412: 3407: 3404: 3397: 3381: 3377: 3370: 3361: 3360: 3355: 3352: 3345: 3337: 3331: 3323: 3319: 3312: 3303: 3302: 3297: 3294: 3287: 3278: 3274: 3270: 3266: 3262: 3256: 3248: 3242: 3238: 3234: 3230: 3223: 3215: 3208: 3201: 3193: 3189: 3182: 3175: 3167: 3163: 3159: 3155: 3148: 3140: 3136: 3132: 3128: 3124: 3120: 3113: 3105: 3101: 3097: 3091: 3083: 3076: 3068: 3064: 3060: 3056: 3049: 3040: 3035: 3031: 3027: 3026:Cartographica 3023: 3016: 3007: 3002: 2995: 2987: 2984: 2979: 2971: 2963: 2959: 2953: 2938: 2931: 2923: 2919: 2912: 2901: 2897: 2893: 2889: 2882: 2875: 2861: 2857: 2853: 2849: 2844: 2839: 2835: 2831: 2830:Cartographica 2824: 2817: 2815: 2806: 2804:9780203472095 2800: 2796: 2792: 2785: 2777: 2773: 2769: 2765: 2761: 2757: 2750: 2743: 2735: 2733:9780318235622 2729: 2724: 2719: 2715: 2711: 2705: 2703: 2694: 2690: 2683: 2676: 2670: 2666: 2662: 2658: 2651: 2643: 2641:0-226-76746-9 2637: 2633: 2629: 2625: 2619: 2617: 2615: 2613: 2611: 2609: 2607: 2598: 2592: 2588: 2581: 2573: 2569: 2565: 2561: 2557: 2553: 2548: 2543: 2539: 2535: 2528: 2526: 2510: 2506: 2499: 2498: 2493: 2487: 2479: 2477:0-471-09877-9 2473: 2469: 2462: 2454: 2452:0-444-10362-7 2448: 2444: 2437: 2429: 2423: 2419: 2412: 2408: 2388: 2385: 2382: 2379: 2376: 2373: 2370: 2367: 2365: 2362: 2356: 2353: 2351: 2348: 2342: 2339: 2336: 2333: 2326: 2323: 2320: 2317: 2316: 2309: 2307: 2303: 2299: 2293: 2288: 2286: 2285: 2280: 2275: 2273: 2268: 2266: 2262: 2258: 2254: 2253:Winkel tripel 2250: 2249:smaller-scale 2246: 2242: 2238: 2233: 2222: 2219: 2216: 2213: 2211: 2208: 2206: 2203: 2201: 2198: 2196: 2193: 2191: 2188: 2186: 2185:Winkel Tripel 2183: 2181: 2178: 2176: 2173: 2171: 2168: 2167: 2166: 2165:projections: 2159: 2158:Winkel tripel 2155: 2154: 2149: 2144: 2132: 2129: 2126: 2123: 2120: 2117: 2114: 2113: 2112: 2102: 2099: 2098: 2097: 2095: 2094:Great circles 2088: 2084: 2079: 2067: 2064: 2061: 2057: 2054: 2051: 2048: 2045: 2042: 2039: 2036: 2035: 2034: 2031: 2022: 2017: 2005: 2002: 2000: 1997: 1994: 1990: 1987: 1985: 1982: 1980: 1977: 1975: 1972: 1970: 1967: 1965: 1962: 1960: 1957: 1955: 1952: 1950: 1947: 1944: 1941: 1939: 1936: 1934: 1930: 1926: 1923: 1921: 1918: 1916: 1913: 1911: 1908: 1906: 1903: 1901: 1898: 1896: 1893: 1892: 1890: 1888: 1884: 1877: 1872: 1867: 1855: 1852: 1850: 1847: 1845: 1842: 1840: 1837: 1835: 1832: 1829: 1825: 1824:Stereographic 1822: 1820: 1817: 1814: 1810: 1807: 1806: 1805: 1803: 1799: 1794: 1781: 1776: 1767: 1765: 1761: 1757: 1749: 1744: 1731: 1726: 1720: 1707: 1696: 1688: 1680: 1676: 1672: 1668: 1665: 1659: 1650: 1642: 1638: 1634: 1630: 1627: 1624: 1619: 1618:amateur radio 1615: 1611: 1607: 1603: 1600: 1599: 1598: 1597:projections: 1596: 1584: 1575: 1567: 1563: 1555: 1546: 1538: 1534: 1530: 1526: 1522: 1518: 1515: 1511: 1507: 1504: 1503: 1498: 1495: 1487: 1479: 1471: 1467: 1463: 1459: 1455: 1448: 1440: 1432: 1428: 1424: 1420: 1419:great circles 1416: 1412: 1411: 1410: 1408: 1404: 1400: 1395: 1393: 1385: 1377: 1369: 1365: 1361: 1357: 1353: 1348: 1346: 1342: 1337: 1335: 1331: 1327: 1322: 1321:great circles 1318: 1310: 1305: 1292: 1288: 1285: 1282: 1279: 1276: 1273: 1272: 1263: 1260: 1257: 1254: 1251: 1248: 1247: 1246: 1243: 1240: 1235: 1233: 1229: 1220: 1211: 1209: 1205: 1188: 1184: 1183: 1180: 1177: 1176: 1175: 1170: 1166: 1165: 1162: 1159: 1158: 1157: 1152: 1148: 1147: 1144: 1141: 1140: 1139: 1138: 1132: 1128: 1127: 1124: 1121: 1120: 1119: 1114: 1110: 1109: 1106: 1103: 1102: 1101: 1096: 1092: 1091: 1088: 1085: 1084: 1083: 1082: 1076: 1073: 1070: 1067: 1066: 1065: 1062: 1058: 1055: 1047: 1042: 1037: 1027: 1020: 1011: 1009: 1004: 996: 993: 991: 982: 978: 974: 970: 966: 963: 959: 956: 937: 933: 930: 926: 922: 919: 915: 912: 908: 907: 906: 904: 900: 895: 891: 889: 885: 877: 872: 862: 852: 849: 844: 837: 834: 831: 828: 827: 826: 824: 820: 816: 810: 805: 803: 792: 790: 783: 779: 776: 772: 769: 765: 761: 757: 753: 750: 746: 745: 740: 737: 733: 732: 731: 728: 726: 722: 721:stereographic 718: 714: 703: 701: 697: 693: 689: 685: 680: 678: 674: 670: 666: 662: 658: 654: 650: 646: 641: 639: 635: 629: 627: 623: 610: 606: 602: 598: 595: 591: 588: 585: 584:conformal map 581: 580: 579: 576: 574: 570: 564: 554: 549: 542: 538: 534: 530: 525: 522: 521: 516: 515: 505: 499:Notable lines 496: 494: 490: 486: 482: 474: 469: 460: 456: 453: 449: 445: 444: 435: 430: 421: 414: 410: 406: 402: 398: 394: 390: 386: 382: 378: 375: 371: 367: 366: 365: 357: 353: 351: 350:bivariate map 345: 342: 339:). Sometimes 338: 334: 329: 327: 323: 319: 309: 306: 302: 298: 294: 290: 283: 278: 274: 272: 268: 264: 260: 259: 254: 249: 239: 236: 232: 227: 225: 221: 217: 210: 207: 205: 202: 200: 197: 195: 192: 190: 187: 186: 185: 179: 174: 165: 163: 159: 155: 151: 147: 143: 139: 135: 130: 127: 123: 119: 115: 110: 107: 103: 99: 94: 92: 88: 84: 80: 74: 72: 68: 64: 60: 56: 52: 48: 44: 40: 32: 31: 26: 21: 5248:Infographics 5216:Portal:Atlas 5214: 5202: 5175:Thematic map 5155:Geologic map 5098: 4900:Orthographic 4431:Gauss–Krüger 4323:Orthographic 4118:Web Mercator 4012:Gauss–Krüger 3945: 3850:(MathWorld). 3751: 3747: 3741: 3724: 3720: 3714: 3706: 3701: 3693: 3688: 3680: 3675: 3650: 3646: 3640: 3631: 3612: 3606: 3587: 3582: 3555: 3543:. Retrieved 3539:the original 3534: 3509: 3496: 3484: 3471: 3459: 3446: 3435:. Retrieved 3433:. 2020-09-17 3430: 3421: 3409: 3396: 3386:November 18, 3384:. Retrieved 3380:the original 3369: 3357: 3344: 3321: 3311: 3299: 3286: 3268: 3264: 3255: 3228: 3222: 3216:: 1158–1164. 3213: 3200: 3191: 3187: 3174: 3157: 3153: 3147: 3122: 3118: 3112: 3104:the original 3099: 3090: 3075: 3058: 3054: 3048: 3029: 3025: 3015: 2994: 2976: 2970: 2962:Mapthematics 2961: 2952: 2940:. Retrieved 2930: 2921: 2911: 2887: 2874: 2863:. Retrieved 2833: 2829: 2790: 2784: 2759: 2755: 2742: 2713: 2692: 2682: 2656: 2650: 2627: 2586: 2580: 2537: 2533: 2512:. Retrieved 2496: 2492:Snyder, J.P. 2486: 2467: 2461: 2442: 2436: 2417: 2411: 2305: 2295: 2290: 2282: 2276: 2269: 2245:conformality 2234: 2230: 2217:'s cordiform 2163: 2151: 2130: 2110: 2092: 2038:Plate carrée 2029: 2026: 1895:Albers conic 1886: 1882: 1880: 1796: 1764:Dymaxion map 1754: 1705: 1694: 1686: 1678: 1674: 1670: 1657: 1648: 1640: 1636: 1632: 1613: 1609: 1605: 1592: 1582: 1573: 1565: 1561: 1553: 1544: 1536: 1532: 1528: 1500: 1485: 1477: 1469: 1465: 1461: 1446: 1438: 1430: 1426: 1422: 1396: 1391: 1383: 1375: 1367: 1363: 1359: 1355: 1351: 1349: 1338: 1333: 1329: 1325: 1315: 1256:Albers conic 1244: 1239:secant lines 1236: 1225: 1222:Albers conic 1201: 1053: 1051: 1046:interrupting 1025: 1005: 1002: 994: 990:secant lines 986: 954: 924: 913: 896: 892: 881: 847: 845: 842: 822: 818: 814: 812: 807: 798: 786: 774: 767: 763: 759: 755: 749:orthomorphic 748: 742: 735: 729: 709: 681: 673:Earth radius 653:conformality 642: 630: 619: 608: 577: 566: 547: 540: 536: 532: 528: 526: 518: 512: 510: 492: 488: 484: 480: 478: 457: 441: 439: 418: 408: 404: 396: 392: 363: 354: 346: 333:small circle 330: 325: 321: 317: 315: 300: 296: 292: 286: 256: 251: 228: 213: 183: 144:such as the 131: 111: 95: 93:projection. 91:cartographic 75: 42: 36: 29: 5243:Cartography 5185:Weather map 5079:Cartography 4878:Perspective 4666:some aspect 4650:Strebe 1995 4625:Equal Earth 4544:Gall–Peters 4526:Cylindrical 4341:Equidistant 4237:Equidistant 4167:Equal Earth 4050:Gall–Peters 3994:Cylindrical 3817:G.Projector 3194:(2): 45–50. 2981: [ 2215:Oronce Finé 2011:Equidistant 1991:, used for 1984:Strebe 1995 1938:Equal Earth 1813:Rhumb lines 1595:perspective 1269:Pseudoconic 973:Gall–Peters 855:Cylindrical 848:cylindrical 815:cylindrical 775:equidistant 665:Earth model 657:equivalence 235:large scale 102:rectilinear 98:perspective 63:coordinates 39:cartography 5232:Categories 5104:Topography 4940:AuthaGraph 4932:Polyhedral 4802:Compromise 4730:Loximuthal 4722:Loxodromic 4684:Sinusoidal 4534:Balthasart 4511:Sinusoidal 4488:Sinusoidal 4471:Equal-area 4182:Sinusoidal 4140:Equal-area 4040:Balthasart 4032:Equal-area 4005:-conformal 3982:By surface 3437:2020-10-05 2988:: 106–113. 2942:24 January 2865:2011-11-14 2398:References 2375:UV mapping 2298:Peters map 2060:North Pole 2023:of Eurasia 1979:Sinusoidal 1883:equivalent 1860:Equal-area 1760:polyhedron 1741:See also: 1737:Polyhedral 1302:See also: 1069:Sinusoidal 1048:" the map. 1034:See also: 859:See also: 764:equivalent 756:equal-area 489:transverse 267:ellipsoids 242:Distortion 5145:Cartogram 5084:Geography 5012:Longitude 4840:Wagner VI 4689:Two-point 4620:Eckert VI 4615:Eckert IV 4610:Eckert II 4587:Mollweide 4582:Collignon 4549:Hobo–Dyer 4503:Bottomley 4418:Conformal 4406:By metric 4297:Azimuthal 4270:Polyconic 4265:Bottomley 4205:Wagner VI 4177:Mollweide 4162:Eckert VI 4157:Eckert IV 4152:Eckert II 4147:Collignon 4055:Hobo–Dyer 3511:MathWorld 3486:MathWorld 3461:MathWorld 3411:MathWorld 3359:MathWorld 3301:MathWorld 3261:Lee, L.P. 3139:128490229 3125:(2): 91. 2922:Big Think 2896:1591-092X 2572:124618009 2547:1412.7690 2403:Citations 2381:World map 2261:Mollweide 1974:Mollweide 1959:Hobo–Dyer 1925:Eckert II 1915:Collignon 1910:Bottomley 1834:Roussilhe 1798:Conformal 1787:Conformal 1417:displays 1317:Azimuthal 1228:meridians 1161:Eckert VI 1143:Eckert IV 1105:Mollweide 1061:parallels 884:meridians 802:L. P. Lee 760:equiareal 744:conformal 725:polyconic 677:asteroids 661:graticule 626:ellipsoid 389:Cartesian 381:longitude 374:ellipsoid 263:spheroids 224:conformal 216:isometric 199:Direction 138:conformal 126:asteroids 87:manifolds 71:longitude 30:Geography 5007:Latitude 4992:See also 4955:Dymaxion 4895:Gnomonic 4830:Robinson 4735:Mercator 4712:Gnomonic 4704:Gnomonic 4539:Behrmann 4446:Mercator 4318:Gnomonic 4300:(planar) 4275:American 4045:Behrmann 4003:Mercator 3545:14 April 3330:cite web 3322:Prógonos 2900:Archived 2860:11359702 2776:26611469 2712:(1987). 2626:(1993). 2312:See also 2257:Robinson 2170:Robinson 2073:Gnomonic 1887:authalic 1809:Mercator 1525:antipode 1407:antipode 1390:) where 1057:meridian 977:Behrmann 918:Mercator 903:latitude 768:authalic 713:Mercator 448:cylinder 385:latitude 326:skewness 209:Distance 160:and the 148:and the 67:latitude 5258:Geodesy 4868:HEALPix 4767:Littrow 4378:Wiechel 4280:Chinese 4224:Conical 4088:Central 4083:Cassini 4060:Lambert 3957:History 3771:Sources 2552:Bibcode 2514:8 March 2116:Littrow 1702:⁠ 1683:⁠ 1662:⁠ 1645:⁠ 1587:⁠ 1570:⁠ 1558:⁠ 1541:⁠ 1490:⁠ 1474:⁠ 1451:⁠ 1435:⁠ 1388:⁠ 1372:⁠ 1347:point. 1345:tangent 1204:HEALPix 1054:central 952:⁠ 940:⁠ 901:of the 839:sphere. 804:notes, 514:tangent 493:oblique 322:flexion 204:Bearing 51:surface 25:Ecumene 4887:Planar 4855:Hybrid 4762:Hammer 4694:Werner 4635:Hammer 4600:Albers 4516:Werner 4493:Werner 4373:Hammer 4368:Aitoff 4287:Werner 4232:Albers 4108:Miller 3967:Portal 3879: 3803: 3667:210384 3665: 3619: 3594: 3570: 3281:p. 193 3243: 3160:: 61. 3137: 2894: 2858: 2801: 2774: 2730: 2671: 2638: 2593: 2570: 2474: 2449: 2424: 2087:Thales 2004:Werner 1954:Hammer 1826:: Any 1758:use a 1198:Hybrid 899:secant 876:rhumbs 823:planar 821:, and 717:Albers 688:Haumea 622:sphere 535:. The 520:secant 485:normal 481:aspect 446:. The 370:sphere 271:geoids 269:, and 85:, and 5068:Atlas 4757:Craig 4674:Conic 4480:Bonne 4260:Bonne 3875:(PDF) 3799:(PDF) 3663:JSTOR 3210:(PDF) 3184:(PDF) 3135:S2CID 3057:. 4. 3032:(3). 3001:arXiv 2985:] 2903:(PDF) 2884:(PDF) 2856:S2CID 2838:arXiv 2826:(PDF) 2772:S2CID 2752:(PDF) 2568:S2CID 2542:arXiv 2501:(PDF) 1905:Bonne 1341:plane 1275:Bonne 1214:Conic 1006:See: 938:(sec 819:conic 645:geoid 573:scale 569:globe 557:Scale 471:This 401:polar 399:) or 387:) to 231:datum 220:scale 194:Shape 114:Earth 59:plane 57:on a 55:globe 53:of a 4960:ISEA 3962:List 3885:Esri 3824:GISS 3821:NASA 3617:ISBN 3592:ISBN 3568:ISBN 3547:2016 3388:2005 3336:link 3241:ISBN 2944:2018 2892:ISSN 2799:ISBN 2728:ISBN 2669:ISBN 2636:ISBN 2591:ISBN 2516:2022 2472:ISBN 2447:ISBN 2422:ISBN 2277:The 2259:and 2146:The 2081:The 1931:and 1677:) = 1639:) = 1612:) = 1535:) = 1519:The 1508:The 1494:Moon 1468:) = 1456:The 1429:) = 1413:The 1202:The 696:axis 655:and 452:cone 383:and 324:and 189:Area 69:and 41:, a 5094:Map 3756:doi 3729:doi 3655:doi 3560:doi 3273:doi 3269:VII 3233:doi 3162:doi 3127:doi 3063:doi 3034:doi 2848:doi 2795:291 2764:doi 2718:doi 2661:doi 2560:doi 2505:doi 2329:GIS 2131:aka 1885:or 1564:/(2 1366:)/( 911:sec 766:or 762:or 758:or 747:or 609:two 517:or 372:or 255:'s 176:An 37:In 5234:: 3901:). 3893:, 3887:). 3826:). 3752:16 3750:. 3725:42 3723:. 3661:. 3651:32 3649:. 3566:. 3521:^ 3508:. 3483:. 3458:. 3429:. 3408:. 3356:. 3332:}} 3328:{{ 3320:. 3298:. 3267:. 3239:. 3212:. 3190:. 3186:. 3158:42 3156:. 3133:. 3123:27 3121:. 3098:. 3059:22 3030:34 3028:. 3024:. 2983:de 2960:. 2898:. 2854:. 2846:. 2834:42 2832:. 2828:. 2813:^ 2797:. 2770:. 2760:28 2758:. 2754:. 2726:. 2701:^ 2691:. 2667:, 2634:. 2630:. 2605:^ 2566:. 2558:. 2550:. 2538:10 2536:. 2524:^ 2255:, 2019:A 1933:VI 1929:IV 1927:, 1811:: 1778:A 1766:. 1614:cd 1604:: 1505:). 1352:r′ 1010:. 957:). 817:, 727:. 684:Io 567:A 450:, 432:A 407:, 352:. 265:, 164:. 81:, 5060:e 5053:t 5046:v 3938:e 3931:t 3924:v 3877:. 3861:. 3801:. 3762:. 3758:: 3735:. 3731:: 3669:. 3657:: 3625:. 3600:. 3576:. 3562:: 3549:. 3514:. 3489:. 3464:. 3440:. 3414:. 3390:. 3362:. 3338:) 3304:. 3279:. 3275:: 3249:. 3235:: 3192:2 3168:. 3164:: 3141:. 3129:: 3069:. 3065:: 3042:. 3036:: 3009:. 3003:: 2964:. 2946:. 2924:. 2868:. 2850:: 2840:: 2807:. 2778:. 2766:: 2736:. 2720:: 2695:. 2663:: 2644:. 2599:. 2574:. 2562:: 2554:: 2544:: 2518:. 2507:: 2480:. 2455:. 2430:. 2327:( 2160:. 1995:. 1709:0 1706:d 1698:0 1695:d 1691:/ 1687:d 1679:c 1675:d 1673:( 1671:r 1658:R 1656:2 1653:/ 1649:d 1641:c 1637:d 1635:( 1633:r 1625:) 1610:d 1608:( 1606:r 1583:R 1581:2 1578:/ 1574:d 1566:R 1562:c 1554:R 1552:2 1549:/ 1545:d 1537:c 1533:d 1531:( 1529:r 1486:R 1482:/ 1478:d 1470:c 1466:d 1464:( 1462:r 1447:R 1443:/ 1439:d 1431:c 1427:d 1425:( 1423:r 1392:R 1384:R 1380:/ 1376:d 1368:R 1364:d 1362:( 1360:r 1356:d 1354:( 1334:d 1330:d 1328:( 1326:r 1293:. 955:φ 949:5 946:/ 943:4 925:φ 914:φ 770:) 751:) 586:. 551:0 548:φ 544:0 541:λ 409:θ 405:r 403:( 397:y 395:, 393:x 391:( 301:θ 297:k 293:h

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index