Sloped Border
Sloped Border
[Cueball and Blondie are standing on a podium. They are holding a document together between them, filled with unreadable text. On either side of the podium are two informational graphics each on a stand. They are placed a bit behind the back side of the podium. The graphic to the left shows a cross-sectional view of a non-vertical border, shown as a dotted line going up between Cueball and Blondie, who both are standing on the ground. The angle is indicated and noted, and the line tilts towards Blondie's side. The graphic on the right shows a skewed perspective of a similar setup of the non vertical border, shaded so what is behind it becomes gray. There are also some lines on this plane to indicate where it is. It almost looks like a window, but people can move through it. There are also two more persons than on the left, Megan, who is on the same side of the border as Cueball, and another Cueball-like guy standing next to Blondie. Megan is entirely on Cueball's side of the plane, but the other three are positioned so they are intersected by the 'shaded plane' of the border, with the effect that some or most of their bodies are beyond the sloped boundary, in the gray area, but not all. Cueball and Blondie are postureed in a mutual greeting across this border, as the others look on.] Cueball: With this treaty, we are proud to announce the creation of the world's first sloped international border! Angle: 74°
[Caption below frame:] If I'm ever put in charge of a country, I'm going to spend all my time trying to think of new ways to make life a nightmare for GIS people.

Every country has land and sea international borders that demarcate the extent of their territory and their legal jurisdiction. These borders are established through law, treaty, or consensus. Establishing an international border is maintained by present-day customs, immigration, and security checks. Some countries (like Cyprus ) have established a buffer zone outside of their international border in order to gain additional protection during a conflict, and most countries have an offshore Exclusive Economic Zone in order to preserve exclusive proprietorship of marine resources such as oilfields and fishing grounds.
In this comic, Cueball and Blondie have established a "sloped" international border through a treaty. Usually borders are perpendicular to the ground [ citation needed ] so that all the air(space) above the ground belongs to the same country. This is called Air sovereignty . Thus it suffices to define the border on the earth surface, as 1D lines across the curved 2D surface. The precise definition is that a line from the center of the Earth through the point of the border is drawn. Sloped terrain is immaterial to the border of the air sovereignty which is still vertical, even if not perpendicular to the terrain.
If the borders were sloped (with respect to the horizontal ground level) an airplane would need to know its precise height to decide if another country's jurisdiction currently applies. With the help of the Global Positioning System this would be in principle possible, although the height information of GPS is less reliable.  (It might be possible to program a computer to use altitude data from the airplane's altimeter along with latitude and longitude data from the GPS and a relevant ground relief database to make an accurate determination.)
Most countries would not agree to a border that cuts into their airspace and shrinks their territory as the altitude increases; most cases of countries losing area have come about as a result of trying to avert, or losing, an armed conflict. It is entirely possible that Cueball's country has compelled Blondie's country to accept its demands, of which the redrawn border is one. Alternatively, Cueball's country may be deliberately reducing its own airspace purely because it will cause problems.
There is at least one famous case of a border being affected by elevation: the Franco-Swiss border bisects the staircase of the Hotel Arbez . Hence, although part of the upper floor is geographically in France, the entire floor is Swiss territory, because it is only accessible through Switzerland.
The mathematical computation for an angled air sovereignty seems relatively straight-forward at low level and could be expressed with a single line of code or a single equation, although the people acting on the information are likely unfamiliar with code and equations and likely use tools with completely no support for sloped borders.  The mention of curvatures in the title text may reveal some emergent problems that need accounting for.
A totally straight line drawn far enough upwards at an angle will find the surface of the Earth curving away beneath it (not even considering terrain undulations) and the angle to the local vertical will reduce as it continues, tending towards vertical as you head towards infinite altitude.
Alternately (although it seems this is not the case) the profile of the sloped border may be assumed to remain at a constant angle to the shifting vertical, in which case it describes a certain form of spiral (which will eventually loop around the earth).
A third option is that it gains altitude at a constant rate, with respect to the passage of land measured on its surface track, to form a different spiral , in which case it will still loop around the Earth but at an angle that increasingly tends towards horizontal.
While the comic doesn't mention this, such a boundary should probably also extend underground, in the opposite direction. (The straight-line version, if implemented, will eventually reach a depth at which it is tangential to the radius and then rise back through the surface an equal distance further around the planet.)  This would then impact, at practical depths for such things, planning rights for property foundations and, at deeper levels, mining rights for minerals.
Practically an upper-limit to a nation's claim (somewhat below satellites, e.g. the Karman Line) and a lower limit (well before reaching the Earth's mantle) will prevent many of these complications, together with intersections with other (probably vertical) 'territorial volume' borders that will supercede in any compound claims to ownership. - However, it is still very important to specify exactly which curve (i.e. with respect to what) the boundary is designed to respecting.
"GIS" refers to geographic information system , a set of tools and methods for capturing, analyzing and presenting spatial and geographic data. While altitude is already an (optional) element in the blocks of information, people developing these systems would be inconvenienced by the additional requirements demanded by the border described in the comic.
It is possible this comic is inspired by such boundary disputes as the Beaufort Sea 'wedge' which, while in this case perpendicular to the surface, suffers from alternative interpretations of how to extend it from the shoreline out towards international waters.
[Cueball and Blondie are standing on a podium. They are holding a document together between them, filled with unreadable text. On either side of the podium are two informational graphics each on a stand. They are placed a bit behind the back side of the podium. The graphic to the left shows a cross-sectional view of a non-vertical border, shown as a dotted line going up between Cueball and Blondie, who both are standing on the ground. The angle is indicated and noted, and the line tilts towards Blondie's side. The graphic on the right shows a skewed perspective of a similar setup of the non vertical border, shaded so what is behind it becomes gray. There are also some lines on this plane to indicate where it is. It almost looks like a window, but people can move through it. There are also two more persons than on the left, Megan, who is on the same side of the border as Cueball, and another Cueball-like guy standing next to Blondie. Megan is entirely on Cueball's side of the plane, but the other three are positioned so they are intersected by the 'shaded plane' of the border, with the effect that some or most of their bodies are beyond the sloped boundary, in the gray area, but not all. Cueball and Blondie are postureed in a mutual greeting across this border, as the others look on.] Cueball: With this treaty, we are proud to announce the creation of the world's first sloped international border! Angle: 74°
[Caption below frame:] If I'm ever put in charge of a country, I'm going to spend all my time trying to think of new ways to make life a nightmare for GIS people.
