I am sketching out a new simulation that will involve thousands of ships moving around on Earth's oceans and interacting over long periods of time. So, lots of "intersection detection" for sensor and communications ranges, as well as region detection for various environmental conditions. We'll assume a spherical earth, not WGS84. This is an event-step simulation that spits out metrics, not a real time game or anything like that.
A question is to use Cartesian coordinates (Earth-Centered, Earth-Fixed) or Geodic/polar coordinates. With polar coordinates a ship's track would be internally represented as a series of lat/lon waypoints with times and a great circle paths between them. With a Cartesian representation the waypoints would be connected with polyline renderings of the great circle between them.
The reason this is a question is I suspect that by sticking to a Cartesian data model it becomes possible to use various geometry libraries that are performance tuned, and even offer up SIMD/GPU performance advantages. The polar coordinates would probably be the more natural way to proceed if writing everything from scratch. But I suspect that by keeping things Cartesian I will have greater access to better and faster libraries. Is this an invalid line of thought? Another consideration is that I know polar coordinate calculations tend to get really screwy when near the poles.
Just curious if somebody with experience could save me a whole lot of time prototyping some scenarios both ways.
It often works well to represent directions as unit vectors instead of angles. Rotation of a vector by another angle becomes a 2x2 or 3x3 matmul (efficient with SIMD, but still more expensive than an FP add of two numbers in radians), but you very rarely need sin/cos.
You may occasionally want atan2 to get an angle, but usually not inside tight loops.
Intersection-detection can be very efficient (with SIMD) for XYZ coordinates given another XYZ + range. I'm not sure how efficiently you could check which lat/lon pairs were within range of a given point, not a problem I've looked at.
IDK what kind of stuff you'd find in existing libraries, or what you'd want to do with it.