Tetrahedral Snyder Equal Area

Added in version 9.9.

Snyder's equal-area mapping [Snyder1992] applied to the four faces of a regular tetrahedron and unfolded into a planar net.

The tetrahedron is subdivided into 4 × 6 = 24 right sub-triangles, and each sub-triangle is mapped independently using the area-preserving Snyder construction.

See Polyhedral Snyder Equal Area projections for the shared theory.

Classification	Polyhedral, equal area
Available forms	Forward and inverse, spherical and ellipsoidal
Defined area	Global
Alias	tsea
Domain	2D
Input type	Geodetic coordinates
Output type	Projected coordinates

proj-string: +proj=tsea

Nets

The default net (shown above) follows Snyder's Figure 8. An alternative +net=triangle layout is available, and +dual maps onto the tetrahedron's vertices rather than its faces:

triangle

The south-cap face sits at the centre, with its three neighbours fanned around it.

proj-string: +proj=tsea +net=triangle

dual

The tetrahedron is self-dual, so the net keeps the same outline.

proj-string: +proj=tsea +dual

Parameters

Note

All parameters are optional.

+net=<name>

Selects the planar unfolding. Accepted values: tsea, triangle.

Defaults to tsea.

+dual

Unfolds onto self-dual tetrahedron net.

+orient_lat=<value>

Geodetic latitude of the polyhedron's first vertex, in degrees. Together with +orient_lon and +azi this fully constrains the 3D pose of the polyhedron on the sphere.

Defaults to 90.0.

+orient_lon=<value>

Longitude of the polyhedron's first vertex, in degrees. Together with +orient_lat and +azi this fully constrains the 3D pose of the polyhedron on the sphere.

Defaults to 0.0.

+azi=<value>

Azimuth from the polyhedron's first vertex to its second, in degrees clockwise. Together with +orient_lat and +orient_lon this fully constrains the 3D pose of the polyhedron on the sphere.

Defaults to 0.0.

+lat_0=<value>

Geodetic latitude of the geographic point that should land at the projected origin (0, 0). Used together with +lon_0; the pair translates the projected output without rotating the polyhedron. +x_0 / +y_0 are applied on top of this translation.

When unset, the projected origin falls on the unfold's root face instead (its centroid in general, or its bounding-box centre for +proj=isea) rather than at a fixed lat / lon.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lat_0=1.570796r

See Projection Units for more information.

+lon_0=<value>

Geodetic longitude of the geographic point that should land at the projected origin (0, 0). Used together with +lat_0; the pair translates the projected output without rotating the polyhedron. +x_0 / +y_0 are applied on top of this translation.

When unset, the projected origin falls on the unfold's root face instead (its centroid in general, or its bounding-box centre for +proj=isea) rather than at a fixed lat / lon.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lon_0=1.570796r

See Projection Units for more information.

+x_0=<value>

False easting, easting at false origin or easting at projection centre (naming and meaning depend on the projection method). Always in meters.

Defaults to 0.0.

+y_0=<value>

False northing, northing at false origin or northing at projection centre (naming and meaning depend on the projection method). Always in meters.

Defaults to 0.0.

+ellps=<value>

The name of a built-in ellipsoid definition.

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

Defaults to "GRS80".

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.