# Map Projections

## Orthographic Projection

The orthographic projection is an azimuthal projection suitable for displaying a single hemisphere; the point of perspective is at infinity. 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.

The point of perspective for the orthographic projection is at infinite distance. It depicts a hemisphere of the globe as it appears from outer space, where the horizon is a great circle. The shapes and areas are distorted, particularly near the edges

## Conic Conformal

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 one of seven projections introduced by Johann Heinrich Lambert in 1772.

Conceptually, the projection seats a cone over the sphere of the Earth and projects the surface conformally onto the cone. The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale. That parallel is called the reference parallel or standard parallel.

By scaling the resulting map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them. This gives the map two standard parallels. In this way, deviation from unit scale can be minimized within a region of interest that lies largely between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels.

## Conic Equal Area

Albers Equal Area Conic projection is a conic projection that maintains accurate area measurements. It differs from the Lambert Conformal Conic projection in preserving area rather than shape and in representing both poles as arcs rather than one pole as a single point. (Therefore, the meridians do not converge at the poles.) This projection uses two standard parallels, or secant lines.

First developed by Heinrich Christian Albers in the early nineteenth century for European maps, its biggest success has been for maps of North Americaâ€”specifically, for maps for the conterminous United States. Both poles are represented as arcs rather than as single points.

Latitude lines are unequally spaced concentric circles, whose spacing decreases toward the poles. Scale is true along the secants or standard parallels and constant along all parallels. In order to preserve area, the scale factor of a meridian at any given point is the reciprocal of that along the parallel.

## Conic Equidistant

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. Also known as the simple conic projection, a rudimentary version was described during the 2nd century AD by the Greek astronomer and geographer Ptolemy in his work Geography.

The projection has the useful property that distances along the meridians are proportionately correct, and distances are also correct along two standard parallels that the mapmaker has chosen. The two standard parallels are also free of distortion.

For maps of regions elongated east-to-west (such as the continental United States) the standard parallels are chosen to be about a sixth of the way inside the northern and southern limits of interest. This way distortion is minimized throughout the region of interest.

## Azimuthal Equal Area

The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, but it does not accurately represent angles. It is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. "Zenithal" being synonymous with "azimuthal", the projection is also known as the Lambert zenithal equal-area projection.

The National Atlas of the US uses a Lambert azimuthal equal-area projection to display information in the online Map Maker application, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. It is also used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space.

## Azimuthal Equidistant

The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point.

A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.

## Stereographic

The stereographic projection is another perspective (azimuthal) projection. The point of perspective is on the surface of the sphere, looking in; it is thus commonly used for celestial charts.

The projection is defined on the entire sphere, except at one point: the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it preserves angles at which curves meet.

It is neither isometric nor area-preserving: that is, it preserves neither distances nor the areas of figures.

## Gnomonic

A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints. This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane.

No distortion occurs at the tangent point, but distortion increases rapidly away from it. Less than half of the sphere can be projected onto a finite map. Consequently, a rectilinear photographic lens, which is based on the gnomonic principle, cannot image more than 180 degrees.

## Equirectangular

The equirectangular, or plate carrÃ©e projection, is the simplest possible geographic projection: the identity function. It is neither equal-area nor conformal, but is sometimes used for raster data. See raster reprojection for an example; the source image uses the equirectangular projection.

## Mercator

The Mercator projection is a cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for navigation because it is unique in representing north as up and south as down everywhere while preserving local directions and shapes. The map is thereby conformal.

As a side effect, the Mercator projection inflates the size of objects away from the equator. This inflation is very small near the equator but accelerates with increasing latitude to become infinite at the poles. So, for example, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near the equator, such as Central Africa.

## Transverse Mercator

The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the Universal Transverse Mercator. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent.

## Albers USA

The Albers USA projection is a composite projection of four Albers projections designed to display the forty-eight lower United States alongside Alaska and Hawaii. It scales the area of Alaska by a factor of 0.35x (a lie factor of 3); Hawaii is shown at the same scale as the lower forty-eight. The Albers USA projection does not support rotation or centering.