Snyder equal-area projection

Equal-area polyhedral map projection

Snyder equal-area projection is a polyhedral map projection used in the ISEA (Icosahedral Snyder Equal Area) discrete global grids. It is named for John P. Snyder, who developed the projection in the 1990s.[1]

It is a modified Lambert azimuthal equal-area projection, most often applied to a polyhedral globe consisting of an icosahedron.[2][3]

With the dual tiling system is possible to transform the big triangular faces (gray) into small centered-hexagons (red), and vice versa.

## Use in the ISEA model

[edit]

As stated by Carr at al.,[3] page 32:

The S in ISEA refers to John P. Snyder. He came out of retirement specifically to address projection problems with the original EMAP grid (see Snyder, 1992). He developed the equal area projection that underlies the gridding system.

ISEA grids are simple in concept. Begin with a Snyder Equal Area projection to a regular icosahedron (...) inscribed in a sphere. In each of the 20 equilateral triangle faces of the icosahedron inscribe a hexagon by dividing each triangle edge into thirds (...). Then project the hexagon back onto the sphere using the Inverse Snyder Icosahedral equal area projection. This yields a coarse-resolution equal area grid called the resolution 1 grid. It consists of 20 hexagons on the surface of the sphere and 12 pentagons centered on the 12 vertices of the icosahedron.

## References

[edit]

1. ^ Snyder, J.P. (1992). "An Equal-Area Map Projection for Polyhedral Globes". Cartographica. 29 (1): 10–21\. doi:10.3138/27H7-8K88-4882-1752. (subscription required)
2. ^ "Icosahedral Snyder Equal Area". PROJ. Proj Contributors. 2004-04-04 [n.d.] Retrieved 2024-04-09.
3. ^ a b Carr, D.; Kahn, R.; Sahr, K.; Olsen, T. (1997). "ISEA Discrete Global Grids". Statistical Computing and Statistical Graphics Newsletter. 8 (2/3): 31–39. Retrieved 2024-04-09.

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By surface

| Cylindrical|

| Mercator-conformal|

* Gauss–Krüger
* Transverse Mercator
* Oblique Mercator

|

Equal-area|

* Balthasart
* Behrmann
* Gall–Peters
* Hobo–Dyer
* Lambert
* Smyth equal-surface
* Trystan Edwards

* Cassini
* Central
* Equirectangular
* Gall stereographic
* Gall isographic
* Miller
* Space-oblique Mercator
* Web Mercator

Pseudocylindrical|

| Equal-area|

* Collignon
* Eckert II
* Eckert IV
* Eckert VI
* Equal Earth
* Goode homolosine
* Mollweide
* Sinusoidal
* Tobler hyperelliptical

|

* Kavrayskiy VII
* Wagner VI
* Winkel I and II

Conical|

* Albers
* Equidistant
* Lambert conformal

Pseudoconical|

* Bonne
* Bottomley
* Polyconic
* American
* Chinese
* Werner

Azimuthal
(planar)|

| General perspective|

* Gnomonic
* Orthographic
* Stereographic

|

* Equidistant
* Lambert equal-area

Pseudoazimuthal|

* Aitoff
* Hammer
* Wiechel
* Winkel tripel

By metric

| Conformal|

* Adams hemisphere-in-a-square
* Gauss–Krüger
* Guyou hemisphere-in-a-square
* Lambert conformal conic
* Mercator
* Peirce quincuncial
* Stereographic
* Transverse Mercator

|

Equal-area|

| Bonne|

* Sinusoidal
* Werner

|

Bottomley|

* Sinusoidal
* Werner

Cylindrical|

* Balthasart
* Behrmann
* Gall–Peters
* Hobo–Dyer
* Lambert cylindrical equal-area
* Smyth equal-surface
* Trystan Edwards

Tobler hyperelliptical|

* Collignon
* Mollweide

* Albers
* Briesemeister
* Eckert II
* Eckert IV
* Eckert VI
* Equal Earth
* Goode homolosine
* Hammer
* Lambert azimuthal equal-area
* Quadrilateralized spherical cube
* Strebe 1995

Equidistant in
some aspect|

* Conic
* Equirectangular
* Sinusoidal
* Two-point
* Werner

Gnomonic|

* Gnomonic

Loxodromic|

* Loximuthal
* Mercator

Retroazimuthal
(Mecca or Qibla)|

* Craig
* Hammer
* Littrow

By construction

| Compromise|

* Chamberlin trimetric
* Kavrayskiy VII
* Miller cylindrical
* Natural Earth
* Robinson
* Van der Grinten
* Wagner VI
* Winkel tripel

|

Hybrid|

* Goode homolosine
* HEALPix

Perspective|

| Planar|

* Gnomonic
* Orthographic
* Stereographic

|

* Central cylindrical

Polyhedral|

* AuthaGraph
* Cahill Butterfly
* Cahill–Keyes M-shape
* Dymaxion
* ISEA
* Quadrilateralized spherical cube
* Waterman butterfly

See also

* Interruption (map projection)
* Latitude
* Longitude
* Tissot's indicatrix
* Map projection of the tri-axial ellipsoid

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