Distances measured along these lines are proportional to the same distance measurement on the curved reference surface. http://www.youtube.com/watch?v=qgErv6M19yY, http://kartoweb.itc.nl/geometrics/Map%20projections/mappro.html Distortion increases by moving away from standard lines. Shape and area are increasingly distorted with distance from the center; in this case, area shrinks relative to its true size. They are expensive to produce, especially in varying sizes (scales). In the secant case the plane intersects the globe along a small circle forming a standard parallel which has true scale. Plate carrée is a case of equirectangular projection with Equator being a standard parallel. [3], In a wide sense, all projections with the point of perspective at infinity (and therefore parallel projecting lines) are considered as orthographic, regardless of the surface onto which they are projected. Maps do not suffer from the above shortcomings and are more practical than globes in most applications. A common method of classification of map projections is according to distortion characteristics - identifying properties that are preserved or distorted by a projection. Equal area projections are useful where relative size and area accuracy of map features is important (such as displaying countries / continents in world maps), as well as for showing spatial distributions and general thematic mapping such as population, soil and geological maps. 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. This perspective projection views the globe from an infinite distance. http://www.quadibloc.com/maps/mapint.htm All in all, it is up to the cartographer to determine what projection is most favorable for its purpose. Maintaining relative areas of features causes distortion in their shapes, which is more pronounced in small-scale maps. Features spherical shape of earth Can only show 1 hemisphere. On a tangent surface to the reference globe, there is no scale distortion at the point (or along the line) of tangency and therefore scale factor is 1. The principal scale or nominal scale of a flat map (the stated map scale) refers to this scale of its generating globe. spun). Orthographic Projection. This projection is useful for presenting individual (This point is not marked with an indicatrix .) central meridian). This can be alternatively stated as ratio of distance on the map to the corresponding distance on the reference globe. : 1 Projections are a subject of several pure mathematical fields, including differential geometry, projective geometry, and manifolds. In planar (also known as azimuthal or zenithal) projections, the reference spherical surface is projected onto a plane. In the secant case, the cylinder intersects the globe; that is the diameter of the cylinder is smaller than the globe’s. There is great distortion towards the borders of the map. Preservation of angles makes conformal map projections suitable for navigation charts, weather maps, topographic mapping, and large scale surveying. Tissot who in 1859 first published his classic analysis of the distortion occurring under a map projection. One way of classifying map projections is by the type of the developable surface onto which the reference sphere is projected. His site has posters of his map, plus maybe the world's only Winkel Tripel-critiquing poetry. Also in most projections there are one or more standard lines along which scale remains constant (true scale). The two axes of the ellipse indicate the directions along which the scale is maximal and minimal at that point on the map. Examples include Lambert Azimuthal Equal-Area, Gnomonic, and azimuthal equidistant projections. However, "map projection" refers specifically to a cartographic projection. For example, a 1:250000 representative fraction scale indicates that 1 unit (e.g. As with Lambert's equal-areal and the stereographic projection, only one hemisphere can be viewed at … This variation of scale can be visualized by Tissot's indicatrix explained in detail below. Since many p… Equal area map projections (also known as equivalent or authalic projection) represent areas correctly on the map. A map projection is needed to show the spherical surface of the earth on a flat map (see What’s a Map Projection? Map scale distortion of a tangent cylindrical projection - SF = 1 along line of tangency, Scale distortion on a tangent surface to the globe. You can create a projcrs object for the orthographic projection using the ESRI authority code 102037. The inverse formulas are particularly useful when trying to project a variable defined on a (λ, φ) grid onto a rectilinear grid in (x, y). A feature that has made Mercator projection especially suited for nautical maps and navigation is the representation of rhumb line or loxodrome (line that crosses meridians at the same angle) as a straight line on the map. The resulting map from this projection looks like a globe (similar to seeing Earth from deep space). Map Projections http://www.flexprojector.com/ In an Orthographic projection, scale is accurate at the center and along any circle circumscribed around the center. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. http://www.radicalcartography.net/index.html?projectionref The selected distortion property depends largely on the purpose of the map. On this type of projection, the meridians are parallel to one another, which is the equivalent of saying that all the parallels of latitude are the same length. Therefore shapes are represented accurately and without distortion for small areas. 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). The idea is to project a small circle (i.e. What? 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). 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 tangent line is the equator for the equatorial or normal aspect; while in the transverse aspect, the cylinder is tangent along a chosen meridian (i.e. Meridians and parallels intersect at right angles. A tool is built on top of the Interactive Map Projections system that provides a new method of visualizing map projection distortion. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The graticule layout is affected by the choice of the aspect. The size, shape and orientation of the ellipses are changed as the result of projection. [1][2], The orthographic projection has been known since antiquity, with its cartographic uses being well documented. They are hard to transport and store; for example you can not stuff a globe in your backpack while hiking or store it in your car’s glove compartment. In the Orthographic projection (polar aspect), there is a single point of no distortion at the north pole. Measure of scale distortion on map plane can also be quantified by the use of scale factor. Shape 3. The actual scale at a point on map can be obtained by multiplying the nominal map scale by the scale factor. Earth's Magnetic Field Landforms in Google Earth All projections cause distortions in varying degrees; there is no one perfect projection preserving all of the above properties, rather each projection is a compromise best suited for a particular purpose. http://www.youtube.com/watch?v=_XQfRYfxPig&feature=related In this world map equidistant cylindrical projection (also known as plate carrée), Tissot’s ellipses are distorted in size and shape. Orthographic map of the world – coastlines, graticule, and indicatrices: Image title: A map of the world, showing all landmasses with 10° graticule and Tissot's indicatrices of diameter 1,000 km and spacing 30°. It is often used for mapping Polar Regions (with the source located at the opposite pole). Angles, areas, directions, shapes, and distances can become distorted when transformed from a … Since scale distortion varies across the map, distortion ellipses are drawn on the projected map in an array of regular intervals to show the spatial distortion pattern across the map. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. 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. to determine the places of star-rise and star-set. This scale can be measured as the ratio of distance on the globe to the corresponding distance on the Earth. Throughout the globe this scale is constant. Projection method. These parallels are called standard parallels. 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. http://www.btinternet.com/~se16/js/mapproj.htm, "Many ways to see the world": http://www.earthdaytv.net/ Go to "In The Classroom" channel, 4th page Hipparchus used the projection in the 2nd century B.C. For the polar or normal aspect, the cone is tangent along a parallel of latitude or is secant at two parallels. Photogeologic Map of the Moon (wall map) - landmark Lunar map^ - Geographicus - PhotogeologicMoon-usgs-1961.jpg 6,000 × 4,488; 4.78 MB Projections can be further categorized based on their point(s) of contact (tangent or secant) with the reference surface of the Earth and their orientation (aspect). Each indicatrix (ellipse) represents the distortion at the point it is centered on. As an example, the actual scale at a given point on map with scale factor of 0.99860 at the point and nominal map scale of 1:50000 is equal to (1:50000 x 0.99860) = (0.99860 / 50000) = 1:50070 (which is a smaller scale than the nominal map scale). http://www.geometrie.tuwien.ac.at/karto/ Scale factors of less than or greater than one are indicative of scale distortion. This ensures that points on the opposite hemisphere are not plotted: The point should be clipped from the map if cos(c) is negative. Between the secant lines where the surface is inside the globe, features appear smaller than in reality and scale factor is less than 1. The basic problem inherent in any type of map projection is that it will result in some distortion of the ‘ground truth’ of the area being mapped. The polar conic projections are most suitable for maps of mid-latitude (temperate zones) regions with an east-west orientation such as the United States. It is also modeled more accurately as an oblate spheroid or an ellipsoid. Imagine light rays radiating from a source following straight lines. Let’s look at the azimuthal projection in more detail. Azimuthal projections are used often for mapping Polar Regions, the polar aspect of these projections are also referred to as polar azimuthal projections. Interactive Display of Distortion The use of a simple geometric shape is the basis for displaying map projection distortion in an interactive software package created by Brainerd and Pang (1998). True-direction projections are used in applications where maintaining directional relationships are important, such as aeronautical and sea navigation charts. Topographic Maps These kinds of projections distort angles and areas close to the poles. The point of perspective for the orthographic projection is at infinite distance. http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=List_of_supported_map_projections [clarification needed]. Orthographic Map Distortion. homolosine. http://www.youtube.com/watch?v=b1xXTi1nFCo Secant projections lead to less overall map distortion. Orthographic projection (sometimes referred to as orthogonal projection, used to be called analemma ) is a means of representing three-dimensional objects in two dimensions. Only the center of the map is free of distortion. Equidistant projections are used in air and sea navigation charts, as well as radio and seismic mapping. A straight line drawn on the Mercator map represents an accurate compass bearing. Here the area distortion is more pronounced as we move towards the poles. These projections are named azimuthal due to the fact that they preserve direction property from the center point of the projection. As a result of preserving angles and shapes, area or size of features are distorted in these maps. A classic example of area exaggeration is the comparison of land masses on the map, where for example Greenland appears bigger than South America and comparable in size to Africa, while in reality it is about one-eight the size of S. America and one-fourteenth the size of Africa. http://www.youtube.com/watch?v=AI36MWAH54s&feature=related Gall-Peters cylindrical equal-area projection Tissot's indicatrix Tissot’s indicatrices are all circular (shape preserved) in this world map Mercator projection, however they vary in size (area distorted). Scale is true (scale factor = 1) and there is no distortion along standard parallels. Distortion increases with distance from the point (or line) of tangency. The cone can be situated over the North or South Pole. About, Gall-Peters cylindrical equal-area projection Tissot's indicatrix, Mercator - conformal projection Tissot's indicatrix, Equirectangular (equidistant cylindrical) projection Tissot's indicatrix. Their shape represents the distortion of an imaginary circle on the spherical surface after being projected on the map plane. In transverse aspect of planar projections, the plane is oriented perpendicular to the equatorial plane. Keep in mind that while some projections use a geometric process, in reality most projections use mathematical equations to transform the coordinates from a globe to a flat surface. This aspect produces a map with meridians radiating out as straight lines from the cone’s apex, and parallels drawn as concentric arcs perpendicular to meridians. Circular shapes of the same size indicate preservation of properties with no distortion occurring. In map projection we try to represent a good model of any part of the earth in its true shape and dimension. Examples of cylindrical projections include Mercator, Transverse Mercator, Oblique Mercator, Plate Carré, Miller Cylindrical, Cylindrical equal-area, Gall–Peters, Hobo–Dyer, Behrmann, and Lambert Cylindrical Equal-Area projections. http://www.giss.nasa.gov/tools/gprojector/ The normal polar aspect yields parallels as concentric circles, and meridians projecting as straight lines from the center of the map. Great circles passing through the center point are drawn as straight lines. I'm not sure I want to reproject to an orthographic projection. As stated above spherical bodies such as globes can represent size, shape, distance and directions of the Earth features with reasonable accuracy. No map can be both conformal and equal area. http://www.csiss.org/map-projections/, USGS Decision Support System: http://mcmcweb.er.usgs.gov/DSS/ http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. Equirectangular (equidistant cylindrical) projection Tissot's indicatrix Many properties can be measured on the earth's surface independently of its geography. The ellipses are usually centered at the intersection of meridians and parallels. Globes are not suitable for use at large scales, such as finding directions in a city or following a hiking route, where a more detailed image is essential. The areas of features on the map are proportional to their areas on the reference surface of Earth. Projection was introduced by Max Eckert (at time of its publication known as Max Eckert-Greifendorff) in 1935. Whenever one type of distortion is minimized, there will be corresponding increases in the distortion of one or more of the other properties. Distortion will vary in at least one of each of the above properties depending on the projection used, as well as the scale of the map, or the spatial extent that is mapped. Compass Basics Distance 6. 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. In transverse aspect, the two standard lines run north-south parallel to meridians. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the p… It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The Orthographic projection is an azimuthal projection. Latitude and Longitude A highly refined map designed by Renaissance polymath Albrecht Dürer and executed by Johannes Stabius appeared in 1515.[2]. Contact Us | Some examples are Albers Equal-Area Conic, Cylindrical Equal Area, Sinusoidal Equal Area, and Lambert Azimuthal Equal Area projections. A map projection is the transformation of Earth’s curved surface (or a portion of) onto a two-dimensional flat surface by means of mathematical equations. Stereographic projection is a conformal projection, that is over small areas angles and therefore shapes are preserved. Bearing 5. Some of these properties are: 1. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective (or azimuthal) projection, in which the sphere is projected onto a tangent plane or secant plane. http://en.wikipedia.org/wiki/List_of_map_projections During such transformation, the angular geographic coordinates (latitude, longitude) referencing positions on the surface of the Earth are converted to Cartesian coordinates (x, y) representing position of points on a flat map. 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 diameter of the cylinder is equal to the diameter of the globe. http://demonstrations.wolfram.com/DistortionsInMapProjections/ Scale Map projections can be constructed to preserve one or some of these properties, though not all of them simultaneously. In conical or conic projections, the reference spherical surface is projected onto a cone placed over the globe. On a secant surface to the reference globe, there is no distortion along the standard lines (lines of intersection) where SF = 1. Orthographic Planar projection. It depicts a hemisphere of the globe as it appears from outer space. (This point is not marked with an indicatrix .) I am using a 3D modeling program (Cinema 4D) to wrap a sphere with a 2MB "Blue Marble" image (equirectangular projection) from NASA. In the tangent case, the cylinder’s circumference touches the reference globe’s surface along a great circle (any circle having the same diameter as the sphere and thus dividing it into two equal halves). Every projection has strengths and weaknesses. These characteristics include distance, direction, shape, and area. Distortion. The meridians are vertical and equally spaced; the parallels of latitude are horizontal straight lines parallel to the equator with their spacing increasing toward the poles. In the Orthographic projection (polar aspect), there is a single point of no distortion at the north pole. [2], The earliest surviving maps on the projection appear as woodcut drawings of terrestrial globes of 1509 (anonymous), 1533 and 1551 (Johannes Schöner), and 1524 and 1551 (Apian). In cylindrical projections, the reference spherical surface is projected onto a cylinder wrapped around the globe. Map scale distortion of a secant cylindrical projection - SF = 1 along secant lines, Scale distortion on a secant surface to the globe. Projection appears to have straight parallels, but they are actually slightly curved. 1961 U.S.G.S. However, the name analemma, which also meant a sundial showing latitude and longitude, was the common name until François d'Aguilon of Antwerp promoted its present name in 1613. Scale factor of 2 indicates that the actual map scale is twice the nominal scale; if the nominal scale is 1:4million, then the map scale at the point would be (1:4million x 2) = 1:2million. The formulas for the spherical orthographic projection are derived using trigonometry. Direct application of the orthographic projection yields scattered points in (x, y), which creates problems for plotting and numerical integration. Width: 1600: Height: 1600 Terms & Conditions | In equidistant map projections, accurate distances (constant scale) are maintained only between one or two points to every other point on the map. https://courseware.e-education.psu.edu/projection/index.html, Site Map | Albers Equal Area Conic Projection. Points close to center point show great distortion on the map. The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following:[1]. The tangent and secant lines are important since scale is constant along these lines (equals that of the globe), and therefore there is no distortion (scale factor = 1). 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. Mercator - conformal projection Tissot's indicatrix Those light rays intercept the globe onto a plane at various angles. http://mathworld.wolfram.com/topics/MapProjections.html Stereographic maps have a point of projection on the side of Earth opposite the plane’s point of tangency; the point of projection for an orthographic map is at infinity. Maps do not suffer from the above shortcomings and are more practical than globes in most applications. As mentioned above, there is no distortion along standard lines as evident in following figures. In gnomonic maps great circles are displayed as straight lines. small enough so that the distortion remains relatively uniform across the circle’s extent) and to measure its distorted shape on the projected map. Meridians and parallels are perpendicular to each other. The light rays travel as parallel lines. The orthographic projection is used for perspective views of planets and regions as a means of presenting a three-dimensional object in two dimensions. The orthographic projection is neither conformal nor equal-area. Because you can't display 3D surfaces perfectly in two dimensions, distortions always occur. The Orthographic map projection is one of the oldest; it was used by Egyptians and Greeks thousands of years ago. The degree and kinds of distortion vary with the projection used in making a map of a particular area. This indicates that any line joining north and south poles (meridian) is true to scale and therefore distances are accurate along these lines. One solution is to start from the (x, y) projection plane and construct the image from the values defined in (λ, φ) by using the inverse formulas of the orthographic projection. For example: projcrs(102037,'Authority','ESRI') . Three projections, namely gnomonic, stereographic and orthographic can be defined based on the location of the perspective point or the light source. Extreme polar distortion Cuts off at 80 degree N and S Rhumb Lines are straight Still used for nautical charts (maps) ... 1 anywhere on map going E-W - line of latidtude Equidistanct in east-west direction. Cylindrical projection - tangent and secant equatorial aspect © USGS. The orthographic projection is an azimuthal projection suitable for displaying a single hemisphere; the point of perspective is at infinity. Geokov Map maker To avoid this distortion, various methods have been devised and many types of projections are drawn. At two parallels Albrecht Dürer and executed by Johannes Stabius appeared in 1515. 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