It is tricky to manage the extent of a coordinate system when that extent is not an aligned rectangle in another coordinate system.
For example consider Thursday Island, located at:
- 142.2°, -10.2° (WGS84, EPSG:4326) or equivalently,
- 1146km, -1156.5km (Australian Albers projection, EPSG:3577).
- WGS84 Bounds: 108.0000, -45.0000, 155.0000, -10.0000
- Projected Bounds: -2690013.3995, -5098960.4467, 2579169.8548, -1281018.4757
Notice that Thursday Island is well inside of the lat/lon bounds, however it (along with sections of Australian mainland at both Cape York Peninsula and Kakadu) falls outside of the projected bounds.
Say I want to create a web map application using OpenLayers, I need to know the maximum extent of the map in the projected coordinates. The problem is that if I source this information from a standard online reference, I will mistakenly cut off parts of Australia even when choosing a projection that was specifically designed to cover Australia.
Presumably the root cause is that the extent has been represented by an aligned bounding-box and then, rather than transforming the entire boundary of this region precisely (before generating a new bounding box), only two vertices of the box have been properly projected (the bottom-left and top-right corners). Such a method is invalid due to curvature/nonlinearity.
How is this problem normally handled? Is there any authorative source for the extent of a map projection? In particular, is Proj.4 able to report the maximum domain of validity for a transformation? I'd like a solution that works in all cases, including those where the region of validity does not resemble a rectangular coordinate patch (e.g. rHEALPix and QSC).