Peirce Quincuncial
The Peirce Quincuncial projection is a conformal map projection
that transforms the circle of the northern hemisphere into a square,
and the southern hemisphere split into four triangles arranged
around the square to form a quincunx. The resulting projection
is a regular diamond shape or can be rotated to form a square.
The resulting tile can be infinitely tessellated. Though this implementation
defaults to a central meridian of 0, it is more common to use a central
meridian of around 25 to optimise the distortions. Peirce's original
published map from 1879 used a central meridian of approx -70.
The diamond and square versions can be produced using the
+shape=diamond
and +shape=square
options respectively.
This implementation includes an alternative lateral projection
which places hemispheres side-by-side (+shape=horizontal
or
+shape=vertical
). Combined with a general oblique transformation,
this can be used to produced a Grieger Triptychial projection
(see example below).
Classification |
Miscellaneous |
Available forms |
Forward spherical projection |
Defined area |
Global |
Alias |
peirce_q |
Domain |
2D |
Input type |
Geodetic coordinates |
Output type |
Projected coordinates |
Parameters
Note
All parameters are optional.
- +lon_0=<value>
Central meridian/longitude of natural origin, longitude of origin or longitude of false origin (naming and meaning depend on the projection method).
Defaults to 0.0.
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.
- +shape=square/diamond/horizontal/vertical/nhemisphere/shemisphere
Added in version 9.0.
Defaults to diamond.
Warning
This option was wrongly introduced introduced in 8.2.1 with the
type
name, which was inappropriate as it conflicted with the+type=crs
general hint.Indicates the shape of transformation applied to the southern hemisphere:
square
anddiamond
represent the traditional quincuncial form suggested by Peirce with the southern hemisphere divided into 4 triangles and reflected outward from the northern hemisphere. Thesquare
shape is rotated by 45 degrees to produce the conventional square presentation. The origin lies at the centre of the square or diamond.By contrast, the
horizontal
andvertical
forms reflect the southern hemisphere laterally across the x or y axis respectively to produce a rectangular form. The origin lies at the centre of the rectangle.The other two types,
nhemisphere
andshemisphere
, discard latitudes of less than 0 or more than 0, respectively, to allow single hemispheres to be selected. The origin lies at the centre of the square or diamond.
- +scrollx=<value>
For
horizontal
shape allows a scalar circular scroll of resulting x coordinates to shift sections of the projection to the other horizontal side of the map.Defaults to 0.0. Must be a scale between -1.0 and 1.0.
- +scrolly=<value>
For
vertical
shape allows a scalar circular scroll of resulting y coordinates to shift sections of the projection to the other vertical side of the map.Defaults to 0.0. Must be a scale between -1.0 and 1.0.
- +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.
- +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.