Chamberlin trimetric projection
Encyclopedia
The Chamberlin trimetric projection is a map projection
where three points are fixed on the globe
and the points on the sphere
are mapped onto a plane by triangulation
. It was developed in 1946 by Wellman Chamberlin for the National Geographic Society
.
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 area being mapped.
National Geographic Society maps have often used this projection for representations of many of the continents.
As originally implemented, the projection algorithm
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
and longitude
, 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
.
The Chamberlin trimetric projection is not equidistant, not conformal, inequivalent, and not azimuthal. Rather, the projection strikes a balanced compromise between each of these distortions. This projection is not appropriate for mapping the entire sphere.
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
where three points are fixed on the globe
Globe
A globe is a three-dimensional scale model of Earth or other spheroid celestial body such as a planet, star, or moon...
and the points on the sphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...
are mapped onto a plane by triangulation
Triangulation
In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly...
. It was developed in 1946 by Wellman Chamberlin for the National Geographic Society
National Geographic Society
The National Geographic Society , headquartered in Washington, D.C. in the United States, is one of the largest non-profit scientific and educational institutions in the world. Its interests include geography, archaeology and natural science, the promotion of environmental and historical...
.
Chamberlin was chief cartographer
Cartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
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 area being mapped.
National Geographic Society maps have often used this projection for representations of many of the continents.
As originally implemented, the projection algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
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
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
and longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
, 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
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...
for a spherical earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
.
The Chamberlin trimetric projection is not equidistant, not conformal, inequivalent, and not azimuthal. Rather, the projection strikes a balanced compromise between each of these distortions. This projection is not appropriate for mapping the entire sphere.
External links
- The Chamberlin Trimetric Projection - Implementations of the projection using MatlabMATLABMATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
scripts. - The Chamberlin Trimetric Projection - Notes on the projection from a cartographyCartographyCartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
class at Colorado State UniversityColorado State UniversityColorado State University is a public research university located in Fort Collins, Colorado. The university is the state's land grant university, and the flagship university of the Colorado State University System.The enrollment is approximately 29,932 students, including resident and...
. - National Geographic Map Collection - Many examples of National Geographic Society maps employing the Chamberlin Trimetric Projection can be seen here.