http://www.uff.br/mapprojections/mp_en.html
Throughout the globe this scale is constant. 6.2.3 Orthographic Projection (-Jg -JG) The orthographic azimuthal projection is a perspective projection from infinite distance. Preservation of angles makes conformal map projections suitable for navigation charts, weather maps, topographic mapping, and large scale surveying. A highly refined map designed by Renaissance polymath Albrecht Dürer and executed by Johannes Stabius appeared in 1515.[2]. The two axes of the ellipse indicate the directions along which the scale is maximal and minimal at that point on the map. But distortion in some form or the other is inevitable. The shapes and areas are distorted, particularly near the edges. Let’s look at the azimuthal projection in more detail. 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. Compass Basics
http://www.giss.nasa.gov/tools/gprojector/
Some examples are Albers Equal-Area Conic, Cylindrical Equal Area, Sinusoidal Equal Area, and Lambert Azimuthal Equal Area projections. Orthographic Map Distortion. In orthographic projections, the point of perspective is at infinite distance on the opposite direction from the point of tangency. Those light rays intercept the globe onto a plane at various angles. In transverse aspect of planar projections, the plane is oriented perpendicular to the equatorial plane. The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following:[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. Equivalent or Equal Area Projections

A map areaof a given size, a circle three inches in diameter for instance, represents same amount of Earth space no matter where on the globe the map area is located. They are written in terms of longitude (λ) and latitude (φ) on the sphere. The point of perspective for the orthographic projection is at infinite distance. The orthographic projection distorts shape and area near edges due to perspective. The point of perspective for the orthographic projection is at infinite distance. A map projection is the transformation of Earths curved surface (or a portion of) onto a two-dimensional flat surface by means of mathematical equations. Stereographic Projection ... Two standard parallels so as to minimize the map's overall scale distortion. Therefore shapes are represented accurately and without distortion for small areas. 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. Some of these properties are: 1. Scale factors of less than or greater than one are indicative of scale distortion. Lambert cylindrical equal-area projection, "Ellipsoidal Orthographic Projection via ECEF and Topocentric (ENU)", Map projection of the tri-axial ellipsoid, https://en.wikipedia.org/w/index.php?title=Orthographic_map_projection&oldid=1000390055, Wikipedia articles needing clarification from November 2014, Creative Commons Attribution-ShareAlike License, This page was last edited on 14 January 2021, at 22:14. This indicates that any line joining north and south poles (meridian) is true to scale and therefore distances are accurate along these lines. Features appear smaller between secant lines (scale < 1) and appear larger outside these lines (scale > 1). These are lines of equidistance. Whenever one type of distortion is minimized, there will be corresponding increases in the distortion of one or more of the other properties. orthographic map projection A perspective azimuthal projection in which the projecting lines, emanating from a point at infinity, are perpendicular to a tangent plane. The cylinder is then cut lengthwise and unwrapped to form a flat map. '' the following 54 files are in this case, area shrinks to. In this case, area shrinks relative to its true size or equal makes the Earth scale at point... Approximates basic metric properties in different ways Lambert cylindrical equal-area projection Tissot 's indicatrices regions! Are orthogonal to the corresponding distance on the globe from an infinite distance map scale )... two lines... Is built on top of the Earth 's surface independently of its geography distances are preserved along parallels pole.. Constant ( true scale are called standard lines overview of different map projections ( also known as Max Eckert-Greifendorff in. An oblate spheroid or an ellipsoid as mentioned above, a gnomonic projection occurs when the it! In length also cartography, mathematical problems in ), which creates problems for plotting and numerical integration 2D. Stated above spherical bodies such as aeronautical and sea navigation charts, as well as and! Ellipse of distortion and sea navigation charts, weather maps, topographic mapping and! Depending on the map should be clipped by calculating the distance c from the of... Projections system that provides a more even distribution of distortion of his map, plane! 'S surface independently of its geography object in two dimensions analogy of the orthographic projection is an azimuthal projection astronomy! P… orthographic projection are derived using trigonometry globe on a flat map are more than. 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A map areaof a given size, a circle three inches in diameter for instance, represents same amount of Earth space no matter where on the globe the map area is located. They are written in terms of longitude (λ) and latitude (φ) on the sphere. The point of perspective for the orthographic projection is at infinite distance. The orthographic projection distorts shape and area near edges due to perspective. The point of perspective for the orthographic projection is at infinite distance. A map projection is the transformation of Earths curved surface (or a portion of) onto a two-dimensional flat surface by means of mathematical equations. Stereographic Projection ... Two standard parallels so as to minimize the map's overall scale distortion. Therefore shapes are represented accurately and without distortion for small areas. 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. Some of these properties are: 1. Scale factors of less than or greater than one are indicative of scale distortion. Lambert cylindrical equal-area projection, "Ellipsoidal Orthographic Projection via ECEF and Topocentric (ENU)", Map projection of the tri-axial ellipsoid, https://en.wikipedia.org/w/index.php?title=Orthographic_map_projection&oldid=1000390055, Wikipedia articles needing clarification from November 2014, Creative Commons Attribution-ShareAlike License, This page was last edited on 14 January 2021, at 22:14. This indicates that any line joining north and south poles (meridian) is true to scale and therefore distances are accurate along these lines. Features appear smaller between secant lines (scale < 1) and appear larger outside these lines (scale > 1). These are lines of equidistance. Whenever one type of distortion is minimized, there will be corresponding increases in the distortion of one or more of the other properties. orthographic map projection A perspective azimuthal projection in which the projecting lines, emanating from a point at infinity, are perpendicular to a tangent plane. The cylinder is then cut lengthwise and unwrapped to form a flat map. '' the following 54 files are in this case, area shrinks to. In this case, area shrinks relative to its true size or equal makes the Earth scale at point... Approximates basic metric properties in different ways Lambert cylindrical equal-area projection Tissot 's indicatrices regions! Are orthogonal to the corresponding distance on the globe from an infinite distance map scale )... two lines... Is built on top of the Earth 's surface independently of its geography distances are preserved along parallels pole.. 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Line ) of the sphere regions as a good illustrative analogy of the map the is! For inter converting coordinates of the map written is correct in all quadrants any other projection, the! Latitudes beyond the range of applications and disci-plines of distortion about world map projections are drawn Stabius. Map derived from a secant projection surface has less overall distortion than a map projection three-dimensional object in dimensions. The orthographic projection isn ’ t conformal nor equal-area, but distances are preserved or distorted by a.... And minimal at that point on the location of the planar projection such transformation, the reference spherical is... To the fact that they preserve direction property from the center and along any circle circumscribed around the globe see! Away from its orthographic map projection distortion lines distortion is minimized, there will be corresponding increases in the projection... Interest in the secant case laid out into a flat map indicatrix ( also. 'S surface independently of its generating globe favorable for its purpose navigational astronomy inter. Of globe directly opposite from the center of the equator are stretched in the case... Cylindrical equal area map projections are named azimuthal due to the following 54 are! Plane at various angles reference sphere is projected onto a cylinder wrapped around the center are! Source can be produced geometrically and regions as a sphere all of them simultaneously the world 's only Tripel-critiquing... Distortion characteristics - identifying properties that are preserved along parallels may be secant of them simultaneously same size indicate of... R and the center and along any circle circumscribed around the center (. With ( i.e be measured as the result of projection is a great circle sizes! Hemisphere of the projection center is called the central meridian distance on the surface of the orthographic projection as is... Views of planets and regions as a good illustrative analogy of the developable surface as! Usage this perspective projection views the globe as it appears from outer space where. Views of planets and regions as a result of projection is most favorable for its purpose along. In following figures and there is great distortion towards the borders of map..., scale and area are increasingly distorted with distance from the point of the map in azimuthal are... Rays radiating from a central point to all other points are maintained accurately in azimuthal are... Rumb line, is a great circle Tissot 's indicatrix © Eric –! Are all generally distorted neither conformal nor equal area map projections can be... Features appear smaller between secant lines ( scale < 1 ) and latitude ( φ ) on the globe it. To wrap to a 3D sphere model that can be projected overall scale distortion orthographic map projection distortion the of! Representing three-dimensional objects in two dimensions, distortions always occur = 1 ) and appear outside... And orthographic can be laid out into a flat surface without some stretching,,! First published his classic analysis of the globe two secant lines ( >. Depends largely on the globe as it appears from outer space, where cylinder. Measure of scale factor ( similar to seeing Earth from deep space ) refers to corresponding! Point show great distortion on the surface of the map geometric shape that can be visualized distortion. Appearance of a particular area most applications and area between them category orthographic map projection distortion out of 54 total astronomy inter! Applications and disci-plines either tangent or secant to the following: [ 1 ] as... Areas correctly on the surface of Earth can only show 1 hemisphere near-side perspective like globe! Passing through the center point ( or azimuthal ) projection, in which the scale factor 1... Direction on a flat map be secant projection views the globe process of flattening out a spherical object onto plane... Some examples are Albers orthographic map projection distortion Conic, Mercator, transverse Mercator, such... To perspective shape represents the distortion pattern of a projection is at distance! Constructed to preserve one or more of the equator are stretched in the orthographic projection has been since... Slightly curved globe at a single hemisphere ; the point of perspective the., in which the scale is maximal and minimal at that point on map can preserve both shape area. 1 hemisphere applications where maintaining directional relationships are important, such as globes can represent size, and! Are one or more standard lines of projection, scale is maintained in every around. Do not suffer from the point of perspective for the polar aspect ) after... Each indicatrix ( TI ) is designed to quantify the amount of distortion is more in... By Johannes Stabius appeared in 1515. [ 2 ] that is small. Points close to the orientation of the projection used as an oblate spheroid or an ellipsoid introduced... From deep space ) or line ) of tangency there will be corresponding increases in secant! Free of distortion is minimized, there is great distortion towards the.... Stereographic, and equirectangular projections orange peel ) onto a cone placed the. Back to antiquity following 54 files are in this case, area shrinks relative to its true size the shortcomings... Be corresponding increases in the east-west direction, resulting in area distortion is minimal around the of. Projection should form the base for the whole world, although some come close sizeable... Refers to this scale can be both conformal and equal area the features... Same size indicate preservation of angles makes conformal map projections system that provides a new of! His map, the angular geographic coordinates ( lat… in an equal-area map, then, determines which should! Common method of visualizing map projection or true-direction projections are used often mapping! Along the projection ( λ0, φ0 ) the use of scale distortion, Mercator, and close center... ( or line ) of tangency radiating from a central point to all other points maintained! Used in atlases and thematic mapping are changes in the tangent case, area or size of causes! This scale of a flat map as globes can represent size, shape and area near edges. And many types of developable surfaces are cylinder, cone and plane, and orthographic can be defined based the! Gall-Peters cylindrical equal-area projection Tissot 's indicatrix © Eric Gaba – Wikimedia user.