No warning if extents past limits are clipped

[kdpenner]

Description

TransverseMercator has two properties bounding map units:

cartopy/lib/cartopy/crs.py

Lines 856 to 862 in 2148e13

	@property
	def x_limits(self):
	return (-2e7, 2e7)
	@property
	def y_limits(self):
	return (-1e7, 1e7)

I'd like to see past these boundaries, but set_xlim and set_ylim don't work as expected.

import cartopy.crs as ccrs
import matplotlib.pyplot as plt

tmerc_crs_plt = ccrs.TransverseMercator(approx=False)
region_proj = [-5e6, 5e6, -5e6, 2e7]
x1, x2, y1, y2 = region_proj

fig = plt.figure(figsize=(20, 7))
ax3 = fig.add_subplot(1, 2, 1, projection=tmerc_crs_plt)
ax3.set_extent(region_proj, crs=tmerc_crs_plt)
ax3.coastlines()

ax5 = fig.add_subplot(1, 2, 2, projection=tmerc_crs_plt)
ax5.set_xlim(x1, x2)
ax5.set_ylim(y1, y2)
ax5.coastlines()

plt.show()

On the left, the top is clipped to 1e7 without warning. On the right, setting 2e7 creates whitespace instead of moving the spine and plotting the additional data.

It seems like these properties are used all over---what are the consequences of changing them?

[blazing216]

The x_limits and y_limits are used to define the boundary. Everything outside the boundary is clipped.

cartopy/lib/cartopy/crs.py

Lines 848 to 854 in 7c75f5a

	@property
	def boundary(self):
	x0, x1 = self.x_limits
	y0, y1 = self.y_limits
	return sgeom.LinearRing([(x0, y0), (x0, y1),
	(x1, y1), (x1, y0),
	(x0, y0)])

I think you have to change the value hard-coded in the x_limits and y_limits if you want to go beyond the limits. The largest I can go is x_limits to (-1.671e7, 1.671e7) and y_limits to (-2e7, 2e7). Beyond that, the map is blank. It gives you something similar to https://en.wikipedia.org/wiki/File:MercTranSph.png

[dopplershift]

There's definitely a sensible max for these coords, based on the PROJ docs. We could probably do better and make them something like y = +/- scale_factor * radius * np.pi/2 and x = +/- scale_factor * radius * const. I tried to come up with a value for const, but it seems like it depends on how small and increment of points I use, so it doesn't seem to be converging.

[QuLogic]

The defined area from the docs is Global, with full accuracy within 3900 km of the central meridian, though it's only 0.1mm at 7000km. In fact, before Transverse Mercator was replaced with etmerc (or, approx=True right now), there was much more severe distortion as you went out further.

Vertically, Mercator extends to infinity at the pole, but Transverse Mercator is the opposite, and we need to pick a cut off point for x.

[kdpenner]

I changed the title of the PR to better reflect the issue. I expected to see the extent I passed or a warning, not a silent clip to the hard coded limits. In part because I didn't know they existed.

@dopplershift I changed the limits as part of #1739

@QuLogic where do the docs mention the chosen area? the x and y limits as they are now---x = (-2e7, 2e7), y = (-1e7, 1e7)---include regions that don't have an inverse transformation.

[blazing216]

Instead of setting a cut off for x and y, maybe it is better to set the cut off for longitude and latitude.

The reason I proposed that is because some projections, e.g. Transverse Mercator, do not work properly beyond certain limits. They may project some points that should be outside the x, y limits inside. Hence, those points cannot be cut off properly. They are projected incorrectly because you transform those projected points back, the resulting longitude and latitude are not the same as the original ones.

I saw there are some latitude limits set for Mercator. I guess it is used to cut off the geometries before projection?

You may see an example when plotting coastlines with TransverseMercator(central_longitude=-40.9). The line across South America is from a wrong projection of a segment from Africa.

If I understand it correctly, _project_segment uses a clear way to split a line segment at the 'timeline'. However, looks like it assumes the projections work properly for all the longitude and latitudes, which is not true. Maybe adding a check of the validity of the projected points can be helpful.

cartopy/lib/cartopy/trace.pyx

Lines 539 to 544 in 7c75f5a

	else:
	t_current = t_max
	p_current = p_max
	state = get_state(p_current, gp_domain, handle)
	if state == POINT_IN:
	lines.new_line()

[kdpenner]

@blazing216 Transverse Mercator has holes which are centered on the equator and (-90-central_longitude, 90+central_longitude). A simple cutoff will not work. #1739 fixes your example, but my guess is that a solution in trace.pyx will be better than mine.