The Chamberlin trimetric projection is a

map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...

where three points are fixed on the

globe A globe is a spherical model of Earth, of some other celestial body, or of the celestial sphere. Globes serve purposes similar to maps, but unlike maps, they do not distort the surface that they portray except to scale it down. A model glo ...

and the points on the

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...

are mapped onto a plane by triangulation. It was developed in 1946 by Wellman Chamberlin for the

National Geographic Society The National Geographic Society (NGS), headquartered in Washington, D.C., United States, is one of the largest non-profit scientific and educational organizations in the world. Founded in 1888, its interests include geography, archaeology, an ...

. Chamberlin was chief cartographer for the Society from 1964 to 1971. The projection's principal feature is that it compromises between distortions of area, direction, and distance. A Chamberlin trimetric map therefore gives an excellent overall sense of the region being mapped. Many National Geographic Society maps of single

continents A continent is any of several large landmasses. Generally identified by convention rather than any strict criteria, up to seven geographical regions are commonly regarded as continents. Ordered from largest in area to smallest, these seven ...

use this projection. As originally implemented, the projection

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

begins with the selection of three points near the outer boundary of the area to be mapped. From these three base points, the true distances to a point on the mapping area are calculated. The distances from each of the three base points are then drawn on the plane by compass circles. Unlike triangulation on a plane where three such compass circles will intersect at a unique point, the compass circles from a sphere do not intersect precisely at a point. A small triangle is generated from the intersections, and the center of this triangle is calculated as the mapped point. A Chamberlin trimetric projection map was originally obtained by graphically mapping points at regular intervals of

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

and

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...

, with shorelines and other features then mapped by interpolation. Based on the principles of the projection, precise, but lengthy, mathematical formulas were later developed for calculating this projection by computer for a

spherical earth Spherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. ...

. The Chamberlin trimetric projection is neither conformal nor equal-area. Rather, the projection was conceived to minimize distortion of distances everywhere with the side-effect of balancing between areal equivalence and conformality. This projection is not appropriate for mapping the entire sphere because the outer boundary would loop and overlap itself in most configurations. In some cases, the Chamberlin trimetric projection is difficult to distinguish visually from the Lambert

azimuthal equal-area projection 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 ...

centered on the same area.

References

External links

The Chamberlin Trimetric Projection
- Implementations of the projection using

Matlab MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementa ...

scripts.
The Chamberlin Trimetric Projection
- Notes on the projection from a

cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an i ...

class at Colorado State University. {{DEFAULTSORT:Chamberlin Trimetric Projection Map projections

See also

References

External links