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Diffstat (limited to 'docs/source/operations/projections/peirce_q.rst')
| -rw-r--r-- | docs/source/operations/projections/peirce_q.rst | 79 |
1 files changed, 76 insertions, 3 deletions
diff --git a/docs/source/operations/projections/peirce_q.rst b/docs/source/operations/projections/peirce_q.rst index 86445ea1..cf972932 100644 --- a/docs/source/operations/projections/peirce_q.rst +++ b/docs/source/operations/projections/peirce_q.rst @@ -4,6 +4,23 @@ 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 +``+type=diamond`` and ``+type=square`` options respectively. +This implementation includes an alternative lateral projection +which places hemispheres side-by-side (``+type=horizontal`` or +``+type=vertical``). Combined with a general oblique transformation, +this can be used to produced a Grieger Triptychial projection +(see example below). + +---------------------+----------------------------------------------------------+ | **Classification** | Miscellaneous | +---------------------+----------------------------------------------------------+ @@ -21,12 +38,33 @@ Peirce Quincuncial +---------------------+----------------------------------------------------------+ -.. figure:: ./images/peirce_q.png +.. figure:: ./images/peirce_q_square.png + :width: 500 px + :align: center + :alt: Peirce Quincuncial (Square) + + proj-string: ``+proj=peirce_q +lon_0=25 +type=square`` + +.. figure:: ./images/peirce_q_diamond.png + :width: 500 px + :align: center + :alt: Peirce Quincuncial (Diamond) + + proj-string: ``+proj=peirce_q +lon_0=25 +type=diamond`` + +.. figure:: ./images/peirce_q_horizontal.png + :width: 500 px + :align: center + :alt: Peirce Quincuncial (Horizontal) + + proj-string: ``+proj=peirce_q +lon_0=25 +type=horizontal`` + +.. figure:: ./images/grieger_triptychial.png :width: 500 px :align: center - :alt: Peirce Quincuncial + :alt: Grieger Triptychial - proj-string: ``+proj=peirce_q`` + proj-string: ``+proj=pipeline +step +proj=ob_tran +o_proj=peirce_q +o_lat_p=-45 +o_lon_p=45 +o_type=horizontal +o_scrollx=-0.25 +step +proj=affine +s11=-1 +s12=0 +s21=0 +s22=-1`` Parameters ################################################################################ @@ -35,6 +73,41 @@ Parameters .. include:: ../options/lon_0.rst +.. option:: +type=square/diamond/horizontal/vertical/nhemisphere/shemisphere + + .. versionadded:: 8.2.1 + + *Defaults to diamond.* + + Indicates the type of transformation applied to the southern hemisphere: + ``square`` and ``diamond`` represent the traditional quincuncial form suggested + by Peirce with the southern hemisphere divided into 4 triangles and reflected + outward from the northern hemisphere. The ``square`` type 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`` and ``vertical`` 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`` and ``shemisphere``, 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. + +.. option:: +scrollx=<value> + + For ``horizontal`` type 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.* + +.. option:: +scrolly=<value> + + For ``vertical`` type 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.* + .. include:: ../options/R.rst .. include:: ../options/x_0.rst |