The state plane coordinate system uses it for all zones that have a predominant east-west extent. Locally true along the standard parallels. of different map projections (H. Bottomley), Map projections grouped by use (Radical cartography), Picture The most appropriate type of distortion property for a map depends largely on the purpose for which it will be used. of Mathematics and in the OGP Guidance note 7: Coordinate Conversions and Transformations including Formulas. Scale decreases with distance from the center. Meridians are true to scale (i.e. This is a larger scale than the nominal map scale. The Three Main Families of Map Projections - MATLAB & Simulink - MathWorks The Ney modified Lambert conformal conic projection does not project the opposite pole. When you place a cone on the Earth and unwrap it, this results in a conic projection. Distortion Due to Projection - Bentley Systems The Earth's reference surface projected on a map wrapped around Map projection equations have a significant role in projection change For example, this projection is used for mapping the Malaysian peninsula and the Alaska State, zone 5001 (figure section 4.4). Distortions All projections result in some distortion of the relationships between features on the sphere when they are projected onto a flat surface. This projection is best suited for land masses extending in an east-to-west orientation rather than those lying north to south. charts. Albers Equal Area ConicHelp | Documentation - Esri The oblique Mercator projection is sometimes used to align the cylindrical projection plane with a region that is oblique and follows neither a north-south nor an east-west axis. Two Thousand Years Based on these discussions, a particular map projection can be classified. Many special projections have been developed to specifically overcome some of these distortions. It is available in, Lambert conformal conic 1SP variant only supports definitions with one standard parallel and scale factor but uses the same algorithm as the Lambert conformal conic variant. The subsections below describe the Lambert conformal conic projection properties. The Mercator projection was originally designed to display accurate compass bearings for sea travel. A, of a point on the curved reference surface to a set of planar Cartesian coordinates (. The central meridian is the only meridian that is straight. of the size. For quite some time it was thought that our planet was flat, and during those days, a map simply was a miniature representation of a part of the world. The equidistant conic projection is a conic map projection commonly used for maps of small countries as well as for larger regions such as the continental United States that are elongated east-to-west. All azimuthal projections possess the property of maintaining correct azimuths, or true directions from the centre of the map. are wrongly sized or out of shape and the meridians and parallels do not In the 15th, 16th and 17th centuries, during the time the globe as a cylinder produces a cylindrical map projection. There is no one perfect projection and a map maker must choose the one which best suits their needs. navigation. Here are some well-known projections described and illustrated. The equidistant cylindrical projection can be obtained by setting the standard parallels symmetrically north and south of the equator. Each technique type has a region of the Earth where it is usually used. Lambert conformal conic 1SP parameters are as follows: Lambert conformal conic 2SP parameters are as follows: If both standard parallels are set to a pole, the resulting projection is the stereographic projection in polar aspect. Projections. match to the purpose of the map. A quiz to (peak/peek/pique) your interest. iii. Optimal is when the projection centre coincides with centre of the area, or when the projection plane is located Thus, the route of constant direction between two locations is a always a straight line. Geometric Aspects of Mapping. However, an equidistant map is and is still in use today when a simple, straight course is needed for UNIT 27 - MAP PROJECTIONS - Department of Geography [1] [2] [3] In a map projection, coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. These maps may have For example, in the case of a map of Australia which extends from about 10 to 45 South the Standard Parallels most commonly used are 18 and 36 South. The oblique aspect is frequently used for world or air-route maps centered on important cities and occasionally for maps of continents. As you move away from there however, distortions increase with distance. the minimum-error projection of the selected class. It is used to show great circle paths as straight lines and thus to assist navigators and aviators. Sphere 3. maps such as the Mercator. They are often named after the person (s) who invented them (eg Mercator); or aspects of the projection (eg Equidistant Conic); or a combination of the two (eg Lambert Conformal Conic). They are typically used to map the world in its entirety. In a polar azimuthal projection the projection surface Pseudo-conical projections are projections in which the meridians are represented by curves, and the parallels are equally spaced concentric circular arcs (unlike the pseudo-cylindrical projections in which the parallels are represented by straight lines). any country would either be an azimuthal, cylindrical, or conic projection, The distortion property of the map projection is therefore conformal (e.g. The central meridian is the only meridian that is straight. An example would be the classification . Recommended for conformal mapping of regions that are predominantly north-south in extent. Also known as Plate rectangle, a variant of Plate Carre. "The modified Lambert conformal projection Lambert conformal conic is a conic projection. Map is perspective and neither conformal nor equal area. Also in use are the stereographic (the Netherlands) and even non-conformal projections such as Cassini Unfortunately, any map projection is associated with scale distortions. straight (figure below). Used in atlas maps of South America and Africa. a useful compromise between the conformal and equal-area maps. the U.S. Coast and Geodetic Survey. The line of latitude where the cone touches the Earth is called a Standard Parallel. A scale factor of 0.99960 is given to the central meridian of a UTM zone. They are typically used to map the different continents or oceans of the world in one map. Occasionally used in thematic world maps. Also note how land masses furthest away from the Standard Parallel are very distorted when compared to the views from space. Equidistant conic is a conic projection. Suitable equal-area projections for thematic and distribution maps or the Polyconic. There are other possible approaches. Australia, Ghana, S-Africa, Egypt use it) and the Lambert Conformal Conic (in use for France, Spain, Morocco, Algeria). Used for simple portrayals of the world or regions with minimal geographic data such as index maps. neither conformal nor equal-area. Distortion values are the same along a particular parallel. Azimuth is a mathematical concept with relates to the relationship between a point and the flat piece of paper that touches the Earth. Bonne's projection (figure below) is a pseudo-conical equal-area projection, with every parallel true to scale (similar to the polyconic projection). The selected distortion These are: Known by Egyptians and Greeks 2000 years ago. The graticule is symmetric across the central meridian. When the centre of the map is theNorth or South Polemaps produced using Azimuthal Projections techniques have lines of longitude fanning out from the centre and lines of latitude as concentric circles. It is best practice to place standard parallels at one-sixth of the latitude The distortion increase rapidly away from the central meridian. The cylindrical projection is best for a rectangular area and a conic projection for a triangular area (figure below). A subdivision may be made into perspective and non-perspective azimuthal projections. maps, the distortions are not evident to the eye. When projected directly onto the mapping plane it produces an azimuthal (or zenithal or planar) map projection. Lambert conformal conic is a conformal map projection. are shown as straight lines, originating at the pole, intersecting This is a larger scale than the nominal map scale. The Transverse Mercator and Univeral Transverse Mercator (UTM) projection are the best known examples. Map projection - Statistics Canada with a fixed scale on the Earth as it appears when plotted on the map. these names are not very helpful because sometimes one person developed several projections, or several people have developed similar projections. Distortion of other properties increases away from the center point, but are not very large compared to the distortions of the gnomonic projection. This projection was rarely used before the First World War but is now commonly used for official topographic mapping around the world. Google Earth shows the Earth as it looks from an elevated platform such as an airplane or orbiting satellite. represents areas correctly, but it does have rather noticeable shape distortions towards the poles. The projection is a derivation from the simple conic projection, but with every parallel true to scale (similar to the Bonne's equal-area projection). Using the forward mapping equation of the Mercator projection, the values found for the Cartesian coordinates are for x = -14,455,340m and for y = 8,390,339m. Excellent for mid-latitude distance and direction distortions are extreme. a certain direction, is seldom desired. It displays all great circles as straight lines, resulting in any straight line segment showing the. Shape, area and scale distortion increases moderately away from the equator. There is no distortion along the standard parallels. Any straight line drawn on this projection represents a constant compass bearing or a true direction line (loxodrome or rhumb line). It represents areas correctly and has reasonable shape distortions in the region between the standard parallels as compared with the noticeable distortions of the Lambert's equal-area conic projection with one standard parallel. Every circle is plotted as circle or an ellipse or, in extreme cases, The implementation of this projection in ArcGIS does not display the whole globe. uses two standard parallels. The Albers equal-area conic projection, is a map projection that uses two standard parallels to reduce some of the distortion of a projection with one standard parallel. The projection name may refer to its source technique conic and azimuthal are the one which is most commonly used here. cases. Distortions increase as the distance The figure below shows a part of the world mapped on the Transverse Mercator projection. This projection is based on the concept of the piece of paper being rolled into a cone shape and touching the Earth on a circular line. This is useful for from the central point (tangent plane) or closed line(s) of intersection increases. Maps are one of the worlds oldest types of document. (like a source of light rays), is the centre of the Earth. Snyder, J. P. (1987). on a map. While equations giving 0 and k 0 in . More examples of map projections are given through the following links: Demonstration Conic projections often achieve less distortion at mid- and high latitudes than cylindrical projections. Snyder, J. P. (1993). For this reason a 40 kilometre overlap into an adjacent zone is allowed (figure below). to enlarge). Lambert Projections - Massey Geoinformatics Collaboratory The only projection which has all features with no distortion is a globe. Shapes and areas are reasonable well preserved. In the 15th, 16th and 17th centuries, during the time Distortion values are the same along a particular parallel. The projection is equidistant in the direction of the meridians. A version of the Transverse Mercator, but one with a the. shortest routes between points on a sphere - are shown as straight lines. The polar stereographic projection is used in combination with the UTM coordinate system as Universal Polar Stereographic (UPS) for mapping regions north of 84N and south of 80S. 2023. Ney is a modified Lambert conformal conic projection. Scale distortions on a map can also be shown by means of a scale Polar azimuthal orthographic The image above shows that Alber's is very good at maintaining areas over large regions, almost the entire world. Three perspective azimuthal projections: Gnomonic, An example, Greenland appears to be larger but is only one-eighth the size of South America. Used for thematic maps of the whole world. In theory, the selection of a map projection for a particular area can be made on the Map projections with a conformal distortion property represent angles and local shapes correctly, but as the region becomes larger, they show considerable area distortions. For topographic and large-scale maps, conformality and The UTM divides the world into 60 narrow. Map Projections: A Working Manual. The graticule is symmetric across the central meridian. Near the Equator a block of R.A. Knippers. The general pattern of distortion is radial. To save this word, you'll need to log in. Meridians are equally spaced and 0.32 times the length of the equator. nearly conformal. The use of minimum-error the projection, such as Mercator, Lambert, Robinson, Cassini etc., but only in a limited sense, however, can be improved by using secant projection (UTM) projection uses a transverse cylinder, secant to the reference surface (figure below). Distortion in size and area near the projection limit appears more realistic than almost any other projection. Typically the first standard parallel is set to either 71 or 74 north or south and the . for conformality. range below the top and above the bottom of the area to be mapped. The equidistant property, possible The projection is not conformal at the poles. For the, the perspective point A projection can only be equidistant (true to scale) at certain places or in certain directions. Because of the distortions away from the Standard Parallel, Conic Projections are usually used to map regions of the Earth particularly in mid-latitude areas. Secondly Only used for teaching purposes. Particularly note how massively large northern Canada and the Arctic icecaps look. Another class of projections is obtained if the surfaces are chosen to be secant to (to intersect with) the horizontal reference surface; illustrations are in the figure below. Over many centuries a vast number of techniques (often involving very complex mathematical formulae and models) have been developed to do just this. However, any of the three projection techniques can be used for any area of the Earth. Parallels are unequally spaced concentric circles whose spacing decreases toward the poles. Examples are the Bonne and Werner projection. Scale distortions on a secant map surface. Usage. The areas not included in the UTM system, regions north of 84N and south of 80S, are mapped with the Universal Polar Stereographic (UPS) projection. If a map is true to scale along all parallels we say the map is equidistant along the parallels (i.e. basis of: i.) Whereas small countries are possibly shown on this projection, larger areas, such as Russia or Europe are better portrayed on the conic projection with two standard parallels. (section 5 on coordinate transformations). is based. All projections result in some distortion of the relationships between features on the sphere when they are projected onto a flat surface. and meridians are straight lines intersecting at right angles, a requirement nearly conformal. no distortion in North-South direction). Modified Mercator projection proposed by O.M. This projection often serves as a compromise between Lambert conformal conic and Albers equal-area conic projections. Secant map surfaces are used to reduce or average scale errors because the line(s) of intersection are not distorted on the map (section 4.3 scale distortions on a map). In summary, the ideal map projection for The planar, conical, and cylindrical surfaces in the figure above are all tangent surfaces; they touch the horizontal reference surface in one point (plane) or along a closed line (cone and cylinder) only. ArcGIS Desktop Help 9.3 - Conic projections 5.Lambert's cylindrical equal-area projection: The Lambert's cylindrical equal-area projection represents areas correctly, but it does have rather noticeable shape distortions towards the poles. displaying the flow of oceanic or atmospheric currents, for instance. Interrupted projections show the globe in one sheet with interrupted forms of graticules. cartography. from the centre. Scale distortions exist at locations where the scale factor is smaller or larger than 1. Conic Projection -- from Wolfram MathWorld This tool shows the relative amount of distortion caused by each projection. Distortion in size and area near the projection limit appears more realistic than almost any other projection. planes. The projection was once popular for large-scale topographic maps and to map the different continents. Planar or Azmithal . that scale distortions remain within certain limits and that map properties of different map projections (Instituto de matematica, Brasil), Demonstration The polar stereographic projection is used in combination with the UTM coordinate system as. The Mollweide projection (figure below) is a classic equal-area projection, keeping parallels as straight lines while still preserving areas. Maps which require correct distances measured from the centre of the map to any point (e.g. In the normal aspect, they are excellent for mid-latitude The opposite pole is not It is adapted in France and recommended to the European Commission for conformal pan-European mapping at scales smaller or equal to 1:500,000. Distortion of other properties increases away from the center point, but are not very large compared to the distortions of the gnomonic projection. nor equal-area and no point is free of distortion, but the distortions The central point is not distorted on the map. The simple conic projection (figure below) is a normal conical projection with one standard parallel. An equidistant map, in which the scale is correct along A Lambert conformal conic projection ( LCC) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is usually measured as an angle. In the polar aspect, meridians are straight lines radiating from the center, and the lines of latitude are projected as concentric circles that become closer toward the edge of the globe. The Mollweide projection, a pseudo-cylindrical equal-area projection, would be a better choice for this purpose. Mercator's projection - conformal cylindrical - met a real need, Examples are Mollweide, Sinusoidal (Sanson-Flamsteed), Goode Homolosine, McBryde-Thomas series, Eckert's series (I -VI), Winkel (I, II), Denoyer and Robinson. The USGS uses the Transverse Mercator in their 1:24,000 to 1:250,000 quadrangle maps because they can be joined at their edges. There is simply no way to flatten out a piece of ellipsoidal or spherical surface without stretching some parts of the surface more than others (figure below). are very low within about 45 of the center and along the Equator and The basic projection form was first described by Claudius Ptolemy about A.D. 100 and various improvements were made over time, the biggest by Nicolas de l'Isle in 1745. Along the two standard parallels there is no distortion. Lambert conformal conic is a conformal map projection. Also suited for regions extending equally in all directions from a center point, such as Asia and the Pacific Ocean. U.S. Geological Survey Professional Paper 1453. of different map projections (Flex projector, ETH Zurich), Demonstration mapping of the United States until the 1950's and coastal charts by or for distance measurements. Other areas are too distorted to be displayed on the map. Non-published An Album of Map ii. The UTM divides the world into 60 narrow longitudinal zones of 6 degrees, numbered from 1 to 60. is a perspective projection that views the globe from an infinite distance. The The scale is true along the central meridian and along Equidistant conicArcMap | Documentation - Esri The. Both shape and area are reasonably well preserved with the exception of the polar regions. no distortion in North-South direction). All the meridians are equally spaced straight lines converging to a common point. This is similar to the orthographic projection, except that the point of perspective is a finite (near earth) distance rather than an infinite (deep space) distance. Extensively used for large-scale mapping of regions predominantly east-west in extent. For example J.H.Lambert described half a dozen projections. The projection is frequently used to show air-route distances (figure below). It is an appropriate projection to map areas near the pole. A method to calculate the lines of intersection in a normal conical or cylindrical projection (i.e. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 10.0 and later. The UTM zone numbering system (click Two standard lines visualized as secant lines are picked in the process of making a conic projection. area distortions are often reasonably well preserved. The The use of minimum-error PDF Conic Projections - Tishk International University distribution maps and do not contain the noticeable distortions of the Robinson's pseudo-cylindrical projection. a certain direction, is seldom desired. (also known as It is best suited for maps of continents or regions that are equally extended in all directions from the centre, such as Asia and the Pacific ocean. Every map must begin, either consciously or unconsciously, Projected perspectively from the center of the Earth onto a cylinder tangent to the equator. 2, More than 250,000 words that aren't in our free dictionary, Expanded definitions, etymologies, and usage notes. They are grouped into cylindrical, conical and azimuthal projections. The mathematics for the Ney modified conic projection were introduced by C. H. Ney in 1949. thesizeof any feature. Some of the popular conic projections are Albers Equal Area Conic and the Lambert Conformal Conic projections. An Album of Map The image below shows how it does this. The shortest distance between two points - the great circle path - is shown as a curved line. Directions, angles, and shapes are maintained at infinitesimal scale. parallel straight lines, and the meridians by curves. Area, distance, and scale distortions grow rapidly with the distance from the standard parallels. Recommended to the European Commission for statistical analysis and display. mapping of the United States until the 1950's and coastal charts by The equidistant cylindrical projection (also called Plate Carre projection) is a cylindrical map projection with an equidistant property. No map projection can be both conformal and equal-area. One method to calculate the standard parallels is by determining the range in latitude in degrees north to south and dividing this range by six. The projection is also known as the latitude/longitude projection because the latitude and longitude are directly mapped into y and x respectively. educational notes, ITC, Enschede, 1998. along the main axis of the country or the area of interest. Oblique projections are all other, non-parallel and non-perpendicular, rved with the exception of the polar regions. and Lambert's cylindrical equal-area projection. It is adaptable for topographic maps, and is earlier used for the International Map of the World, a map series at 1:1,000,000 scale published by a number of countries to common internationally agreed specifications, and also for large-scale Two lines, the standard parallels, defined by degrees latitude. Washington, DC: United secant projection plane; Lambert conformal conic projection with two standard U.S. Geological Survey Professional Paper 1453.Washington, DC: United States Government Printing Office. Cylindrical projections are used for areas near the equator and for the entire earth but with very large distortions. The equidistant distortion property is achievable only to a limited degree. It is best suited for land masses extending in an east-to-west orientation at mid-latitudes when area, directions, and angles do not need to be maintained. The parallel spacing increases Four well-known normal conical projections are the Lambert Mercator preserves the form (shape) of areas but greatly exaggerates distance and area. A variant of Lambert azimuthal equal-area. Normal cylindrical projections are typically used to map the world in its entirety (in particular areas near the equator are shown well). Distances measured from the centre of the map to any point are correct and the bearing of any point from the center is correct (this applies to all azimuthal maps). To define the projection with one standard parallel (Lambert conformal conic 1SP variant), use the same value for the standard parallel 1, the standard parallel 2, and latitude of origin parameters and set an appropriate scale factor. An example would be the classification conformal conic projection with two standard parallels having the meaning that the projection is a conformal map projection, that the intermediate surface is a cone, and that the cone intersects the ellipsoid (or sphere) along two parallels; i.e. Projected on a map formed into a cone gives a conical map projection. Four well-known normal conical projections are the. The transverse version of this projection is known as the Cassini projection. The Lambert projection (or, to be more precise, the Lambert Conformal Conic projection, but be advised that this complete name is rarely if ever used) is one of the most commonly used projections. For more information about individual projections see theSome Commonly Used Map Projectionssection. Along meridians, scale follows an opposite pattern. It should however not be used for regular geographic maps The distortion increase rapidly away from the central meridian. Most countries have derived there map coordinate system from a projection with a secant map surface for this reason. Map Projections: A Working Manual. Description The equidistant, or simple, conic projection preserves distances along all meridians and two standard parallels. Shows the entire Earth within one circle. straight (figure below). A variant of this projection is the Hammer-Aitoff projection. States Government Printing Office. Press. The scale is constant along any circle having its centre They are often named after the person(s) who invented them (eg Mercator); or aspects of the projection (eg Equidistant Conic); or a combination of the two (eg Lambert Conformal Conic). Optimising 2-parameter Lambert Conformal Conic projections for ground