The Robinson projection is a good example of a map projection that balances area and shape distortion and is seen as a good compromise, being adopted by the National Geographic Society for general purpose word maps. Map scale distortion of a secant cylindrical projection - SF = 1 along secant lines, Scale distortion on a secant surface to the globe. For example, it may be constant along any given parallel. Elevation Profile
Geokov Education
geostac@gmail.com April 7, 2008: Map Projection Distortions. It can also be produced in digital form for online use. http://www.youtube.com/watch?v=e2jHvu1sKiI&feature=rec-LGOUT-exp_fresh+div-1r-3-HM
Map Projections - A Working Manual (USGS PP 1395, John P. Snyder, 1987)
it measures highest to 90 degrees at the north pole or 90 degrees at the south pole, lines of longitude are called meridians. In contrast, KADIS-700k [18] contains 140,000pristine images and distorted images were derived using 25different distortion types at 5 intensity levels but MOS values are not given in this database. Grades: 6 th, 7 th, 8 th, 9 th, 10 th, 11 th, 12 th. In transverse aspect, the cylinder is oriented perpendicular to the Earth’s axis with its center located on a chosen meridian (a line going through the poles). If you have a map projection that preserves one, it will distort the other two The so-called ‘flat-Earth map’ is claimed to be distortion-free, and some flat-Earthers take that as proof of its correctness. For the polar or normal aspect, the cone is tangent along a parallel of latitude or is secant at two parallels. It is often used for mapping Polar Regions (with the source located at the opposite pole). In addition to the previous distortion types mentioned, which are inherent to the optical design of a lens, improper system alignment can also result in keystone distortion, which is a manifestation of parallax (shown in Figure 7a and 7b). The same applies to other reference surfaces used as models for the Earth, such as oblate spheroids, ellipsoids and geoids.Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. Equal area map projections (also known as equivalent or authalic projection) represent areas correctly on the map. http://www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf
Disadvantages for maps depicting the entire world with regards to either shape, distance, relative size, and direction. The Robinson projection is unique. Tissot’s indicatrices are all circular (shape preserved) in this world map Mercator projection, however they vary in size (area distorted). Scale factor is the ratio of actual scale at a location on map to the principal (nominal) map scale (SF = actual scale / nominal scale). The Robinson projection balances area and shape distortion. In cylindrical projections, the reference spherical surface is projected onto a cylinder wrapped around the globe. Four Types of Map Distortion. In reality, a map can only be distortion-free if the actual shape it represents is also flat. Basic types of map projection. © Eric Gaba – Wikimedia Commons user: Sting. When the lake guardians are unable to handle both of them, Giratina comes and swoops on Cyrus to stop him from destroying both worlds. Map Scale
Each indicatrix (ellipse) represents the distortion at the point it is centered on. It is also modeled more accurately as an oblate spheroid or an ellipsoid. Robinson projection © Eric Gaba – Wikimedia Commons user: geographic coordinates (latitude, longitude), http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html, http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=List_of_supported_map_projections, http://www.radicalcartography.net/index.html?projectionref, http://en.wikipedia.org/wiki/List_of_map_projections, http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html, http://mathworld.wolfram.com/topics/MapProjections.html, http://www.giss.nasa.gov/tools/gprojector/, http://www.uff.br/mapprojections/mp_en.html, http://demonstrations.wolfram.com/WorldMapProjections/, http://demonstrations.wolfram.com/DistortionsInMapProjections/, http://www.btinternet.com/~se16/js/mapproj.htm, http://www.youtube.com/watch?v=2LcyMemJ3dE&feature=related, http://www.youtube.com/watch?v=e2jHvu1sKiI&feature=rec-LGOUT-exp_fresh+div-1r-3-HM, http://www.youtube.com/watch?v=_XQfRYfxPig&feature=related, http://www.youtube.com/watch?NR=1&v=EPbQQNrBIgo, http://www.youtube.com/watch?v=AI36MWAH54s&feature=related, http://www.youtube.com/watch?v=b1xXTi1nFCo, http://www.youtube.com/watch?v=qgErv6M19yY, http://kartoweb.itc.nl/geometrics/Map%20projections/mappro.html, http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html, Map Projections - A Working Manual (USGS PP 1395, John P. Snyder, 1987), http://www.ec-gis.org/sdi/publist/pdfs/annoni-etal2003eur.pdf, https://courseware.e-education.psu.edu/projection/index.html. The cartogram is now the final type of thematic map you will need to know for the exam and when it comes to these maps, remember they tend to focus more on expressing the data than the geography. It is a compromise projection; it does not eliminate any type of distortion, but it keeps the levels of all types of distortion relatively low over most of the map. The polar aspect yields parallels of latitude as concentric circles around the center of the map, and meridians projecting as straight lines from this center. The distortion is minimal around the point of tangency in the tangent case, and close to the standard parallel in the secant case. A map derived from a secant projection surface has less overall distortion than a map from a tangent surface. central meridian). Gravity. A scale factor of 0.99950 at a given location on the map indicates that 999.5 meters on the map represents 1000 meters on the reference globe. Distance between points may become increased or decreased ex. In gnomonic maps great circles are displayed as straight lines. Equidistant projections are used in air and sea navigation charts, as well as radio and seismic mapping. http://www.uff.br/mapprojections/mp_en.html
http://www.youtube.com/watch?v=qgErv6M19yY, http://kartoweb.itc.nl/geometrics/Map%20projections/mappro.html
Maps do not suffer from the above shortcomings and are more practical than globes in most applications. http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=List_of_supported_map_projections
Map Legend Symbols
This map projection shows Greenland as the same size as Argentina, and not as the size of all of South America. Where the piece of paper touches the globe there is no distortion on the map; it is an exact reflection of the globe. Map distortion glitch type. Distortion increases with distance from the point (or line) of tangency. As a result of this feature, angles drawn on this type of map are correct. types of map projections and to observe the distortions associated with each one, and (b) an interactive tool in the form of a floating ring for 2D overlayed information, and a floating cone for 3D overlayed information to highlight the nature and magnitude of distortions present in different map projections. Another major concern that drives the choice of a projection is the compatibility of data sets (geographic information). However while there are changes in the ellipses, their north-south axis has remained equal in length. This thematic map type is appropriate for this presentation because it does not systematically distort area. http://demonstrations.wolfram.com/DistortionsInMapProjections/
The shape of the Earth is represented as a sphere. Subjects: Earth Sciences, Geography. In conformal map projections (also known as orthomorphic or autogonal projection) local angles are preserved; that is angles about every point on the projected map are the same as the angles around the point on the curved reference surface. In transverse aspect of conical projections, the axis of the cone is along a line through the equatorial plane (perpendicular to Earth’s polar axis). Transverse and oblique aspects are seldom used. But this is not the case as the Earth is a sphere. http://mathworld.wolfram.com/topics/MapProjections.html
Today, it is usually the job of the cartographer or editor to choose a suitable map projection, taking into account the purpose of the map. The choice of a projection for a map depends on such factors as the purpose for which the map will be used, the area being mapped, and the map’s scale (distortion is more pronounced in small-scale mapping). The plane in planar projections may be tangent to the globe at a single point or may be secant. In this aspect the cone’s apex is situated along the polar axis of the Earth, and the cone is tangent along a single parallel of latitude or secant at two parallels. In normal or equatorial aspect, the cylinder is oriented (lengthwise) parallel to the Earth’s polar axis with its center located along the equator (tangent or secant). This would mean that features lying on the 20th parallel are equally distorted, features on the 40th parallel are equally distorted … In normal aspect of cylindrical projection, the secant or standard lines are along two parallels of latitude equally spaced from equator, and are called standard parallels. Critics of the map – and similar projections – suggest that distortion reinforces a sense of colonialist superiority. There are no map projections that can maintain a perfect scale throughout the entire projection because they are taking a sphereoid and forcing it onto a flat surface. http://www.geometrie.tuwien.ac.at/karto/
Map Distortion. There are two main types of dot distribution maps; one-to-one and one-to-many. In conical or conic projections, the reference spherical surface is projected onto a cone placed over the globe. http://www.csiss.org/map-projections/, USGS Decision Support System: http://mcmcweb.er.usgs.gov/DSS/
As mentioned above, there is no distortion along standard lines as evident in following figures. Very lately, Ponomarenko et al. The distortion pattern of a projection can be visualized by distortion ellipses, which are known as Tissot's indicatrices. Properties Conformal Preserves angles locally, implying that local shapes are not distorted and that local scale is … Although they can represent size, shape, distance and directions of the Earth features with reasonable accuracy, globes are not practical or suitable for many applications. The best way to describe how a map projection works is by imagining a piece of paper (the map) being laid over the Earth (or a globe) to obtain the latitude and longitude lines for the map. © Eric Gaba – Wikimedia Commons user: Sting. Many types of distortion employ clipping behaviour, but when we talk about clipping in music production, we’re usually referring to basic hard and soft clipping. 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