4.4 Mercator projection This direct cylindrical projection is in conformity, and transforms the curves into lines. The projection of the meridian lines and the parallels thus gives a grid. This projection deforms considerably the areas close to the poles, and is to be used with prudence for all the areas which are not close to Ecuador. It should not be confused with the projection UTM, which is a cylindrical transverse. The famous conformal cylindrical projection. It is excellent for the limited purpose of marine navigation and very poor for thematic presentation. a) Selection of corresponding ellipsoid in the study zone b) Selection of the ellipsoid for the study zone Savamer 9.02 ©IRD User manual - 5 4.5 Cylindrical projection In the case of a cylindrical projection, the surface of projection is a tangent or secant cylinder with the model of the ground: ¾ UTM ¾ Mercator conformal ¾ Gauss conformal ¾ Equi rectangular (Not available) ¾ Transverse Mercator (Not available) ¾ Miller (Not available) 4.5.1 UTM projection The UTM system applies the Transverse Mercator projection to mapping the world, using 60 pre-defined standard zones to supply parameters. The Universal Transverse Mercator system of projections deals with this by defining 60 different standard projections, each one of which is a different Transverse Mercator projection that is slightly rotated to use a different meridian as the central line of tangency. UTM zones are six degrees wide. Each zone exists in a North and South variant 4.5.2 Cylindrical Mercator conformal projection The Mercator projection is a conformal projection. On a conformal projection, the scale is constant in all directions about each point but scale varies from point to point on the map. If we consider the parallels, on cylindrical projections, east-west scale increases as we move towards the poles. Assuming tangent case, only the Equator is represented true to scale. All other parallels are longer on the map than they are on the globe. In the extreme case, the pole is subject to an infinite degree of distortion since it has been stretching into a line having the same length as the Equator, although it is a point on the globe. Since east- west scale is increasing as we move toward the poles, we must increase north-south scale by an equal amount in order to obtain a conformal projection. Savamer 9.02 ©IRD User manual - 5 4.5.3 Gauss conformal projection The Gauss Conformal is useful for star maps of the kind that show how the sky appears at a particular time on a particular day of the year, because the resulting map can be equally useful for people who live at any latitude. 4.5.4 Equirectangular projection (Not available) The Equirectangular map projection is a modification of the geographic projection, with the longitude lines (meridians) spaced closer together, forming rectangles with the latitude lines (parallels) instead of squares. In this projection, there are two standard parallels, resulting in less distortion at mid latitudes, but causing distortion at the Equator. Savamer 9.02 ©IRD User manual - 5 4.5.5 Transverse mercator projection (Not available) This is the transverse aspect of the mercator projection. The Mercator projection has little distortion near the Equator. By using the transverse aspect, that property of low distortion runs north-south instead of east-west, so that some areas which would have high distortion in the normal Mercator projection could be projected with less distortion 4.5.6 Miller projection (Not available) A cylindrical projection that is neither conformal nor equal-area. A compromise between the Mercator and other cylindrical projection that attempts to eliminate some of the scale exaggeration of the Mercator. This is used for world maps and in several atlases, including the National Atlas of the United States prepared by USGS in 1970 Savamer 9.02 ©IRD User manual - 5 4.6 Pseudo cylindrical projection (Not available) Projection that, in the normal aspect, has straight parallel lines for parallels and on which the meridians are (usually) equally spaced along parallels, as they are on a cylindrical projection, but on which the meridians are curved. 4.7 Conical projection A method of projecting maps of parts of the earth's spherical surface on a surrounding cone, which is then flattened to a plane surface having concentric circles as parallels of latitude and radiating lines from the apex as meridians. It is carried out while placing a cone on the sphere, and by projecting the points of the sphere on the surface of the cone. The surface of projection is a tangent or secant cone: • Lambert • Albers equivalent • Polyconic projection (Not available) • Equidistant projection(Not available) Savamer 9.02 ©IRD User manual - 5 4.7.1 Lambert Conical projection The Lambert conformal conic projection is analogous to the Mercator projection. Both are conformal projections, meaning that at any point, scale is constant in all directions about the point. As a result, shapes of small areas are represented with minimal distortion but shapes of larger areas are distorted because of changes in scale from point to point. As with the Mercator projection, the Lambert conformal projection is constructed by adjusting the spacing of the parallels so that the stretching of the map in the east-west direction is exactly matched by stretching in the north-south direction. The projection can be constructed using either one or two standard parallels. Use of two standard parallels is more common because it gives a better distribution of distortion over the entire map. The Lambert conformal projection is extensively used for maps of Canada and Ontario. The different types of Lambert projection is explained above in the menu Lambert projection 4.7.2 Albers equivalent projection Albers projection is constructed by modifying the spacing of parallels to obtain an equivalent projection. The meridians are represented the same as on the simple conic, but the spacing between parallels is adjusted to maintain constant area scale. Areas the size of Canada or the United States can be mapped with little distortion of distances and shapes. The Alber's projection is extensively used in the United States as the basis for state plane co-ordinate systems used for topographic maps. Savamer 9.02 ©IRD User manual - 5 4.7.3 Polyconic projection (Not available) The polyconic projection is neither conformal nor equivalent; it is a compromise projection that attempts to minimize all distortions while not eliminating any particular type of distortion. The Polyconic projection shows meridians curved, not straight. Mathematically, it is projected onto cones tangent to each parallel of latitude (an infinite number of cones tangent to an infinite number of parallels). 4.7.4 Equidistant projection (Not available) The Equidistant Conic projection is commonly used in the spherical form in atlases for maps of small countries. It can also cover large areas, and was used to map the Soviet Union. 4.8 Azimuthal projection Azimuthal projections are projections to a plane placed tangent to the globe at a point. In normal (or polar) aspect, the point of tangency is either the north or south pole and meridians of longitude are represented as radial straight lines through the pole while parallels of latitude appear as concentric circles. Distortion in the map increases with distance from the point of tangency. Since distortion is minimal near the point of tangency, Savamer 9.02 ©IRD User manual - 5 azimuthal projections are useful for representing areas having approximately equal extents in the north-south and east-west directions. The azimuth projections which results from the perspective projection of a portion of the terrestrial sphere on a tangent level with the sphere, starting from a point given (ex: polar stereography with the sky charts or the charts of the polar areas.....). 4.8.1 Azimuthal Stereographic projection The sterographic projection positions the light source at the antipode of the point of tangency. Thus if the north pole is the point of tangency, the light source would be at the south pole. The spacing of parallels increases with distance from the pole, but not as rapidly as was the case with the gnomonic projection. As a result, deformation of areas and angles is less severe and it is possible to show an area of up to about 135 degrees from the pole on one map, although stereographic projections are usually limited to showing one hemisphere. The stereographic projection is a conformal projection and is commonly used for maps of the polar region. The stereographic projection also has an important special property: with the exception of great circles passing through the pole, circles on the globe appear as circles or circular arcs on the map. This makes the stereographic projection useful for representing radial phenomena such as shock waves from earthquakes. Savamer 9.02 ©IRD User manual - 5 4.8.2 Azimuthal orthographic projection The orthographic projection assumes that the light source is an infinite distance from the point of tangency, resulting in the rays of light being parallel to each other and perpendicular to the projection surface. The resulting projection can show only one hemisphere. The spacing between parallels decreases towards the Equator. The orthographic projection has no special properties but it does approximate a perspective view of the Earth from outer space. It is therefore useful for visualizing spatial relationships. 4.8.3 Universal polar stereographic projection (Not available) This is a perspective projection on a plane tangent to either the North or South Pole. It is conformal, being free from angular distortion. Additionally, all great and small circles are either straight lines or circular arcs on this projection. Scale is true along latitudes 87 degrees, 7 minutes N or S, and is constant along any other parallel.