As discussed in #4758 (comment) (including an advanced eC prototype of all the necessary pieces), it would be great to be able to support e.g.
+proj=polyhedral +polyhedron={4,3} +net=0,1,2,3,4,5
(specifying a Cubic Snyder Equal-Area projection).
The +polyhedron could support:
- common name,
- extended Schlafli symbol, or
- extended Wythoff symbol
(code already written for this in prototype).
The +net would support the current internal face indices, and could automatically switch between the kis or meta operation based on how many faces are listed. We should validate the net, and also support a default unfolding if no net is specified (code already written for this in the prototype as well).
In addition, we should introduce a +transform parameter (or individual parameters as in +proj=affine) allowing e.g., to define the 5x6 rhombic/icosahedral space in the form of applying an affine transformation (rotation/shearing/scaling) to the icosahedral net, or other arbitrary rotation to the net (without a need for +proj=pipeline which is not well supported in many contexts).
We could have various examples of these projections, including IVEA (felixpalmer#3) and R. Buckminster Fuller's Dymaxion orientation (aka Airocean) for ISEA/IVEA keeping all land contiguous (particularly useful since ST_Area() for any land polygons will then yield correct values, rather than crossing interruptions with e.g, ISEA/IVEA or DSEA).
As discussed in #4758 (comment) (including an advanced eC prototype of all the necessary pieces), it would be great to be able to support e.g.
+proj=polyhedral +polyhedron={4,3} +net=0,1,2,3,4,5(specifying a Cubic Snyder Equal-Area projection).
The
+polyhedroncould support:(code already written for this in prototype).
The
+netwould support the current internal face indices, and could automatically switch between the kis or meta operation based on how many faces are listed. We should validate the net, and also support a default unfolding if no net is specified (code already written for this in the prototype as well).In addition, we should introduce a
+transformparameter (or individual parameters as in+proj=affine) allowing e.g., to define the 5x6 rhombic/icosahedral space in the form of applying an affine transformation (rotation/shearing/scaling) to the icosahedral net, or other arbitrary rotation to the net (without a need for+proj=pipelinewhich is not well supported in many contexts).We could have various examples of these projections, including IVEA (felixpalmer#3) and R. Buckminster Fuller's Dymaxion orientation (aka Airocean) for ISEA/IVEA keeping all land contiguous (particularly useful since
ST_Area()for any land polygons will then yield correct values, rather than crossing interruptions with e.g, ISEA/IVEA or DSEA).