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S2

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Classification

Miscellaneous

Available forms

Forward and inverse, ellipsoidal

Defined area

Global

Alias

s2

Domain

2D

Input type

Geodetic coordinates

Output type

Projected coordinates

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New in version 8.2.

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The S2 projection, like the Quadrilateralized Spherical Cube (QSC) projection, projects +a sphere surface onto the six sides of a cube:

+Quadrilateralized Spherical Cube +

S2 was created by Google to represent geographic data on the whole earth. The documentation can be found +at S2 Geometry It works by first +projecting a point on the sphere to a face of the cube. These are called u,v-coordinates, and they are in [-1,1] x [-1,1]. +This step is followed by a non-linear transformation to normalize the area of rectangles on the sphere. There are three +different choices available for this transformation, meaning that S2 is a family of projections. The final output is in +s,t-coordinates, which are in [0,1] x [0,1]. +See the comments in S2 Code +for an explanation of the tradeoff between speed and area-preservation. Note that the projection is azimuthal when “none” or +“linear” is selected for the area-normalization, but it is not azimuthal when “quadratic” or “tangent” is chosen. See +S2’s Earthcube page +to visualize the unfolded cube and the orientation of each face.

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In this implementation, the cube side is selected by choosing one of the following six projection centers:

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+lat_0=0 +lon_0=0

front cube side

+lat_0=0 +lon_0=90

right cube side

+lat_0=0 +lon_0=180

back cube side

+lat_0=0 +lon_0=-90

left cube side

+lat_0=90

top cube side

+lat_0=-90

bottom cube side

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The specific transformation can be chosen with the UVtoST parameter:

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+UVtoST=linear

fastest, no normalization

+UVtoST=quadratic

fast, good normalization

+UVtoST=tangent

slowest, best normalization

+UVtoST=none

returns u,v-coordinates

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Furthermore, this implementation allows the projection to be applied to ellipsoids. +A preceding shift to a sphere is performed automatically; see [LambersKolb2012] for details. +The output of the projection is in s,t-coordinates ([0,1] x [0,1]), so only the +eccentricity of the ellipse is taken into account: the absolute value of the axes does +not affect the output.

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Usage

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The following example uses S2 on the right face:

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echo 90 0 | ../bin/proj +proj=s2 +lat_0=0 +lon_0=90 +ellps=WGS84 +UVtoST=linear
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+0.5 0.5
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Explanation:

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  • S2 projection is selected with +proj=s2.

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  • The WGS84 ellipsoid is specified with +ellps=WGS84.

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  • The cube side is selected with +lat_0=... +lon_0=....

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  • The normalization transformation is selected with +UVtoST=....

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Parameters

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Note

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All parameters for the projection are optional.

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++lon_0=<value>
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Longitude of projection center.

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Defaults to 0.0.

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++lat_0=<value>
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Latitude of projection center.

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Defaults to 0.0.

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++ellps=<value>
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The name of a built-in ellipsoid definition.

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See Ellipsoids for more information, or execute +proj -le for a list of built-in ellipsoid names.

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Defaults to “GRS80”.

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++UVtoST=<value>
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The area-normalization transformation. Choose from {linear, quadratic, tangent, none}

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Defaults to “quadratic”.

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++x_0=<value>
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False easting.

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Defaults to 0.0.

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++y_0=<value>
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False northing.

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Defaults to 0.0.

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Further reading

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  1. S2’s Website

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