The set of all such lines is itself a space, called the real projective plane in mathematics. This is equivalent to preservation of angles, the defining characteristic of a conformal map.
North-south compression equals the cosine of the latitude the reciprocal of east-west stretching: A rhumb is a course of constant bearing. For another thing, even most projections that do fall into those categories are not naturally attainable through physical projection.
Construction of a map projection[ edit ] The creation of a map projection involves two steps: In practice the projection is often Equal area projection to the hemisphere centered at that point; the other hemisphere can be mapped separately, using a second projection centered at the antipode.
Sinusoidalwhich was the first pseudocylindrical projection developed. On the other hand, the projection does not preserve angular relationships Equal area projection curves on the sphere. On the map, as in reality, the length of each parallel is proportional to the cosine of the latitude.
Another consideration in the configuration of a projection is its compatibility with data sets to be used on the map. Other meridians are longer than the central meridian and bow outward, away from the central meridian. Mercatorconic e. Some possible properties are: No mapping between a portion of a sphere and the plane can preserve both angles and areas.
In the first case Mercatorthe east-west scale always equals the north-south scale. Auxiliary latitudes are often employed in projecting the ellipsoid. Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods.
Pseudocylindrical projections map parallels as straight lines. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map.
Bearing is the compass direction of movement. Pseudocylindrical projections represent the central meridian as a straight line segment. For one thing, most world projections in use do not fall into any of those categories.
On a pseudocylindrical map, any point further from the equator than some other point has a higher latitude than the other point, preserving north-south relationships. The ellipsoidal model is commonly used to construct topographic maps and for other large- and medium-scale maps that need to accurately depict the land surface.
The scale depends on location, but not on direction. When many planes are being plotted together, plotting poles instead of traces produces a less cluttered plot. Scale is constant along all straight lines radiating from a particular geographic location. The east-west scale matches the north-south scale: Thus the Lambert azimuthal projection lets us plot directions as points in a disk.
The cylindric perspective or central cylindrical projection; unsuitable because distortion is even worse than in the Mercator projection. Researchers in structural geology use the Lambert azimuthal projection to plot crystallographic axes and faces, lineation and foliation in rocks, slickensides in faultsand other linear and planar features.
Transformation of geographic coordinates longitude and latitude to Cartesian x,y or polar plane coordinates. Preserving direction azimuthal or zenithala trait possible only from one or two points to every other point  Preserving shape locally conformal or orthomorphic Preserving area equal-area or equiareal or equivalent or authalic Preserving distance equidistanta trait possible only between one or two points and every other point Preserving shortest route, a trait preserved only by the gnomonic projection Because the sphere is not a developable surface, it is impossible to construct a map projection that is both equal-area and conformal.
Distortion can be reduced by "interrupting" the map. This trait is useful when illustrating phenomena that depend on latitude, such as climate.
The famous Mercator projection is one in which the placement of parallels does not arise by "projection"; instead parallels are placed how they need to be in order to satisfy the property that a course of constant bearing is always plotted as a straight line.
Once a choice is made between projecting onto a cylinder, cone, or plane, the aspect of the shape must be specified.Define equal-area projection. equal-area projection synonyms, equal-area projection pronunciation, equal-area projection translation, English dictionary definition of equal-area projection.
a map projection in which regions on the earth's surface that are of equal area are represented as equal. An equal area projection is a map projection that shows regions that are the same size on the Earth the same size on the map but may distort the shape, angle, and/or scale.
GIS Software Maptitude Mapping Software gives you all of the tools, maps, and data you need to analyze and understand how geography affects you and your business. Cylindrical equal-area projection The Lambert cylindrical equal-area projection with Tissot's indicatrix of deformation In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.
Many map projections can then be grouped by a particular developable surface: cylinder, cone, or plane.
Equal areas—A map projection is equal area if every part, as well as the whole, has the same area as the corresponding part on the Earth, at the same reduced scale. No flat map can be both equal area and conformal.
An equal-area projection is not necessarily equidistant; in fact, in order to preserve area, at any point the scale distortion in a given direction must be the inverse of the scale distortion in the orthogonal direction. For instance, in the conventional aspect of Mollweide's projection the horizontal scale is slightly too low along the Equator, and.
an equal-area projection map of the globe; oceans are distorted in order to minimize the distortion of the continents Sanson-Flamsteed projection, sinusoidal projection an equal-area map projection showing parallels and the equator as straight lines and other meridians as curved; used to map.Download