Directory of Map Projections

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Albers-Lambert homotopy

Parameters: Initial projection, Weight of terminal projection, Standard parallel 1, Standard parallel 2


A very configurable conic-like, equal-area projection that gives a continuum between Albers and Lambert azimuthal equal-area projections. The standard parallels for the Albers do not result in standard parallels in the resulting projection, in general; they describe the source projection only.




Meridians: Complex curves except for straight central meridian.
Parallels: Complex curves.
Poles: Points.


Initial projection: One of “Albers”, “Lambert”, or “Round-trip”. The continuum of projections differs depending on the order. With “round-trip”, the sequence from 0 to ½ goes from Albers to Lambert, and from ½ to 1 goes from Lambert to Albers, yielding a unique projection at every step.
Weight of terminal projection: 0 gives the initial projection; 1 gives the terminal projection; values between give and intermediate projection on the continuum.
Albers standard parallel 1: Configures the Albers as per its usual parameters.
Albers standard parallel 2: Configures the Albers as per its usual parameters.

Similar projections

Albers projection is a limiting form.
Lambert azimuthal equal-area projection is a limiting form.'.


Presented by Daniel “daan” Strebe in 2017 as an example of a completely general system for producing a continuum, or “homotopy”, of equal-area projections between any two existing equal-area projections. Because Albers, a conic projection, is topologically very different than Lambert azimuthal equal-area projection, this was deemed to be a good demonstration of the technique.

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