However, the importance of conformality can be overemphasised. Notice that areas close to the equator have very little distortion. Conformality the exponential function, and world map projections timothy g. Can have the properites of equidistance, conformality or equal area. Lambert conic conformal projection, the central parallels are spaced. The department of defense replaced wpg with the conformal utm system in the 1940s. The lambert azimuthal equalarea projection is mathematically based on a plane tangent to the earth. Georeferencing, map projections, cartographic conceptsmap projectionscoordinate systemsdatum.
Pdf cylindrical projection conformality of triaxial ellipsoid. This projection was developed to provide a conformal map of alaska with. The selected distortion property depends largely on the purpose of the map. Some of the most popular world map projections in use today were devised in this manner. What is the difference between equivalent map projection. Commonly, a map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Although the projection procedure inevitably introduces systematic spatial distortions, particular types of distortion can be minimized to suit the geographic scope and intended use of the map data. Adaptive composite map projections bernhard jenny abstractall major web mapping services use the web mercator projection. The map scale may be expressed in three ways and the pictorial representation of these three types is shown in the figure. Maptitude mapping software gives you all of the tools, maps, and data you need to analyze and understand how geography affects you and your business.
The traditional plate carree projection uses the equator as the standard parallel. This projection is one of the best for middle latitudes. The focal point is at the opposite pole of the sphere. Distortions of the map characteristics conformality, distance, direction, scale, and area always result from a map projection. Five map projections showing a variety of shapes and sizes of land masses when different projection systems are applied. It is perpendicular to the direction of gravity pull.
Meridians lines of longitude and parallels lines of latitude. Conformalitya map projection is conformal when at any point the scale is the same in every direction. Although conformality is a local property, distortions are usually minimized within the immediate vicinity of the conformal points. Scale along the equator or standard parallels is true. Other conformal maps, sometimes called orthomorphic. Lines of latitude and longitude are parallel intersecting at 90 degrees.
The most common example is the mercator map, a twodimensional representation of the surface of the earth that preserves compass directions. Mar 06, 2018 integrated system of map projections and ultimately led to development of both spcs and the universal transverse mercator utm system. Depending on the purpose of the map, some distortions are acceptable and others are not. The family is referred to as the lambert conic conformal projections. Scale increases perpendicular to the radii toward the periphery. A map projection is a way to flatten a globe s surface into a plane in order to make a map. A map projection is a geometric function that transforms the earths curved, ellipsoidal surface onto a flat, 2dimensional plane. Understanding map projections landing page for kartoweb.
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on earth a sphere or an ellipsoid is preserved in the image of the projection, i. The state plane coordinate system uses this projection for all zones that have a greater eastwest extent. Projected on a map formed into a cone gives a conical map projection. This booklet provides a conceptual introduction to map projections and geographic reference systems.
What is a conformal projection conformal projection. Map projections map, department of the interior, u. The classical approach to map projections is to obtain an explicit pair of equations relating places on the earth to locations on a map. A conic projection that preserves shape as its name implies, the projection wasnt appreciated for nearly a century after its invention. Map projection and coordinates chiang mai university. How the projections major property conformality, equivalence, etc. About map projectionthe classification of map projection. Since the earth is roughly the shape of an oblate spheroid, map projections are necessary for creating maps of the earth or parts of the earth that are represented on a plane such as a piece of paper or a computer screen. The parallels in the lambert conformal conic projection are concentric circles, while the. Conformal radiotherapy, radiosurgery and treatment planning, iop publishing, page 335, some are realizable in practical computational times. Lambert conformal conic projection, whereas states. The mercator and stereographic projections, and many in.
Therefore, meridians and parallels intersect at right angles and the shapes of very small areas and angles with very short sides are preserved. Feb 29, 2008 the three classes of map projections are cylindrical, conical and azimuthal. Then, given the conditions for a particular map projection, the particular conformal mapping equations are derived. The short the short investigation reported here was undertaken to explore this. It begins with the basics of differential geometry and conformal mapping. The lambert conformal conic projection was also developed by johann lambert around 1772. Map projections for satellite tracking a new series of map projections, on which satellite groundtracks are shown as straight lines, are derived. When projected on a planar map it produces an azimuthal or zenithal map projections. Ifa 5 b for all locations, then angles between lines on the globe are maintained after projection. Map projection is the process of systematically transforming positions on the earths spherical surface to a flat map while maintaining spatial relationships. For example, if two roads cross each other at a 39 angle, then their images on a map.
The azimuthal map projection is angular given three points on a map a, b, and c the azimuth from point b to point c dictates the angle someone would have to. What is a conformal projection conformal projection definition. A better map projection is needed for interactive smallscale maps, which allow the user to adjust scale and the geographic area displayed. The sixth section, the special properties of a map projection, discusses the features of conformality, equivalency and equal distance. Longitude lines are actually radii of the same circles that define the latitude. The earths surface projected on a map wrapped around the globe as a cylinder produces the cylindrical map projection. The stereographic map projection is conformal but not. Imagine placing the movie screen around the globe in a cylinder shape. Identify the complex plane c with the x,yplane in r3. Manual by lev bugayevskiy and john snyder, ball state. Since the mass of the earth is not uniform at all points, and the direction of gravity changes, the shape of the geoid is irregular. A map projection is used to portray all or part of the round earth on a flat surface. Introduction d uring the past 15 years, images of the earth have been obtained from satellites for many purposes such as meteorology and detection of resources.
Conformal map projections conformality was recognized as an important and desirable property for map projections used. Pdf cylindrical projection conformality of triaxial. This is a poor choice for maps of the entire globe or areas of the size of continents or larger countries because the mercator projection shows medium and higher latitudes with extreme. All map projections distort the surface in some fashion. The short the short investigation reported here was undertaken to explore this topic with respect to the. Conformality, the exponential function, and world map. Tobler, michigan, usa with 3 figures and 6 tables abstract.
Pdf it is proved that the projection of a triaxial ellipsoid with rectilinear meridians orthogonal to the rectilinear equator cannot be strictly. All projections of a sphere on a plane necessarily distort the surface in some way and to some extent. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. A sound knowledge of map projections and grids requires an understanding of the mathematical nature of projections and the size and shape of the earth, since in our context. Gis software maptitude mapping software gives you all of the tools, maps, and data you need to analyze and understand how geography affects you and your business. Adaptive composite map projections geovisualization. Bipolar oblique conic conformal summary table general notes. Due to the many uses of maps and the vast range of scales at which they are created, no single map projection serves well for all purposes. For example, if two roads cross each other at a 39 angle, then their images on a map with a conformal projection cross at a 39 angle. This map projection, now mathematically developed, is nearly confor ma1. That conforms, especially to the shape of something. On conformal map projections, the scale depends on location only and not direction. His main research interests are operator theory and. Project map data onto a flat surface touching the globe usually tangent to the globe, but may be secant tangent point is focus of the projection ags 722 22003 conic projections conic projection tangent to the globe along a line of latitude distortion increases away from the standard parallel conic projections are used for midlatitude.
Conformality the preservation of angles is a property illsuited to. Jun 06, 2017 map projection a map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. Oct 05, 2019 cartography, of a map projection that preserves relative angles over small scales, at all but a limited number of distinct points. There is no limit to the number of possible map projections. Stereographic projection is conformal let s2 x,y,z. What is the difference between equivalent map projection and. Special cases include the mercator map and the stereographic. This requires a systematic transformation of the latitudes and longitudes of locations from the surface of the globe into locations on a plane.
The mercator and stereographic projections, and many in between daniel daners revised version, july 29, 2011 abstract we consider a family of conformal angle preserving projections of the sphere onto the plane. In a lambert conformal conic map projection, latitude lines are unequally spaced arcs that are portions of concentric. In cartography, a map projection is a way to flatten a globes surface into a plane in order to make a map. Some distortions of conformality, distance, direction, and area always result from this process. In order to portray the surface of a round body on a twodimensional flat plane, you must first define a developable surface i. The classification of map projection next to their property equivalence, equidistance, conformality, map projections can be discribed in terms of their class azimuthal, cylindrical, conical and aspect normal, transverse, oblique.
Conformal parallels unequally spaced, distance increases away from equator loxodromes or rhumb lines are straight all straight lines on the map are lines of constant azimuth the image of the poles are at infinity used for navigation and regions near equator. Each rectangular grid cell has the same size, shape, and area. The mercator and stereographic projections, and many in between. Blending world map projections bernhard jenny, oregon state university, usa tom patterson, us national park service, usa abstract. Locally, conformality preserves shapes, but for larger areas. Conformalitywhen the scale of a map at any point on the map is the same in any direction, the projection is conformal. The idea of designing a new map projection via combination of two projections is well established. It is the only projection that can accurately represent both areas and true direction from the center of the projection. A map projection is used to portray all or part of the. For example, while the sansonflamsteed projection is conformal along the equator and central. The stereographic map projection is most useful for maps of polar regions for navigation purposes or large continentsized areas of similar extent in all directions. The geoid is defined as the surface of the earths gravity field, which is approximately the same as mean sea level. Map projection a map projection is a systematic transformation of the latitudes and longitudes of locations on the surface of a sphere or an ellipsoid into locations on a plane. It is the representation of the objects and information on a curved surface in a plane using mathematical and geometric relations.
Conformal map, in mathematics, a transformation of one graph into another in such a way that the angle of intersection of any two lines or curves remains unchanged. Georeferencing, map projections, cartographic concepts map. Because designing projections always involves compromises, a projection by necessity must distort geographic shapes, often grossly. The stereographic map projection is another ancient projection, dating back to the second century b. A sphere, unlike a polyhedron, cone, or cylinder, cannot be reformed into a plane. The albers projection is an example of a conic map projection. Ground truth for the future august 2019 page 3 map projection types and conformality when a map projection is associated with a specific geometric reference frame i. On an equivalent map projection preserves the area of. Since there is no practical use for conformal world maps, conformal. On a conformal map projection the local shape of the maps features are preserved, the lines of longitude and latitude meet at right angles. This simple cylindrical projection converts the globe into a cartesian grid. Geodesy map projections, datums, and coordinate systems. Modern national mapping systems typically employ a transverse mercator or close variant for largescale maps in order to preserve conformality and low variation in scale over small areas. The alternative projection must minimize space distortion and be applicable for all map scales, all geographic latitudes, and all map formats.
It is similar to the albers conic equal area projection except that lambert conformal conic portrays shape more accurately than area. Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. The three classes of map projections are cylindrical, conical and azimuthal. In summary, the ideal map projection for any country would either be an azimuthal, cylindrical, or conic projection, depending on the shape of the area, with a secant projection plane located along the main axis of the country or the area of interest.
Pdf in this paper, we introduce some known map projections from a. In a lambert conformal conic map projection, latitude lines are unequally spaced arcs that are portions of concentric circles. Georeferencing, map projections, cartographic concepts. Webb, the physics of three dimensional radiation therapy. A conformal projection is a map projection that favors preserving the shape of features on the map but may greatly distort the size of features. Map projections and coordinates a map projection is any method of representing the surface of a sphere or other threedimensional body on a plane.