Since seven years later, Geocart still doesn’t offer that feature, I guess there a no plans to add it?
Oh, definitely on the backlog, but, well… priorities, and mmummbblemmmrmph blah blah, and it’s hard, and…
But yes, actually, it’s fairly hard in Geocart’s raster architecture. I built in provision for it at the lowest levels of the data structures from the beginning of Geocart 3, so adding it in the future won’t require messy changes at that level, but it’s still no cakewalk.
One fundamental distinction between a projection you can extend beyond normalized range from one you cannot, is that an extensible projection projects longitudes as a monotonic function, whereas nonextensible one project longitudes as functions that are periodic beyond [-180°…180°). Hence, Mollweide (or any cylindric and pseudocylindric projection) can be extended indefinitely because the longitude appears as a simple multiplier in its generating formulae.
Meanwhile something like Hammer is more complicated. The longitudinal value gets scaled, but then periodic functions (sine, cosine) are applied, and so there is a limit to how far it can be extended. That limit is specific to each projection, and so in order to enable longitudinal extension, every projection would need to declare how far it can be extended. How far it can be extended may depend on parameterization: Hammer, for example, uses ½ as the longitudinal duplication factor in canonical form, but you can change that value, and changing that value changes the extent to which you can repeat swaths of the earth. This implies a bunch of code, custom to each projection formula, to solve an equation that may have no closed form solution.
If that were not hard enough, the extension could fundamentally change the topology of the boundary. Because the boundary description is, itself, another piece of custom programming, the complexity starts spiraling out of control when you consider parameterization’s contribution to boundary changes. The projection code also has to make sure the resulting topology is coherent: Does the projection wrap back on itself and start overlapping? That would be the normal case for an azimuthal projection, which you cannot extend at all. Azimuthals are easy; you just mark them as non-extensible, but there are lots of projections that can be extended “some amount”, but how much is not obvious, both from the perspective of periodicity in the functions applied to the longitude, as well as the perspective of topological coherency.
Long explanation. I hope that helps. Yes, I could just enable longitude extension for easy classes (cylindric, pseudocylindric) and leave the rest for incremental updates. Even there I have hard problems to solve because the map is no longer bijective. That complicates a lot of underlying machinery that depends on bijection. Geocart depends heavily on numerical computation of projection inverse in order to achieve its beautiful raster imaging. Numerical inverse is already incredibly messy in the domain of map projections, but if you complicate it further with something like,
x ≠
f ⁻¹∙
f (
x), well, ouch!
Happy 2018!
— daan
