I would love to see Markley’s tetrahedral projection in Geocart.
According to his own text, Markley (being unaware that it already existed) re-invented the tetrahedral conformal projection and created an advantageous arrangement.
Actually, it is already available in Geocart:
– Create the four polyhedron conformal faces with the platonic solid set to Tetrahedron,
– set the projection center of all four to 35°15´51.803˝N, 115°W with a projection spin of 180°,
– duplicate faces #0 and #3,
– arrange them as shown below,
– set the boundary line width of all faces to zero,
– put them together seamlessly,
– export the result, open it in an image processor and cut out the rectangle as shown in the link given above.
The result is a rectangular conformal map that does a good job at keeping the distortions away from land. (Other conformal projections, e.g. the Cahill-Concialdi, are better at this, but at the cost of a more unusual shape.)
- Preparing the map
- prepare-markley-tetrahedral.png (55.34 KiB) Viewed 15108 times
- Areal distortions of Markley’s tetrahedral projection
- tetrahedral-markley-distortion.jpg (58.36 KiB) Viewed 15108 times
- Markley’s tetrahedral projection using a NE2 raster database
- tetrahedral-markley-raster-2.jpg (60.7 KiB) Viewed 15105 times
The trouble of course is the “put them together seamlessly” part.
The seams are almost invisible in the images here, but they are mostly concealed because I rendered larger images that were scaled down. In a high-resolution image they always will be visible due to the interpolated pixel at the border of each face.
So it would be nice to be able to create the full map of Markley’s tetrahedral projection by selecting it from Geocart’s projection menue.
Kind regards,
Tobias
Note: Four hours after I posted this, I saw that the third image was cut in the wrong place, I just uploaded the correct version.