Mapping Points, Zones, etc on a Sphere

[WILL]

Ok i might throw some ideas:
- First thought came that sphere can consist of spherified cube; say a cube with NxN grid on each of 6 sides and vertices moved so they are from equal length out of center. This divides sphere more evenly into "tiles". Each side is 90 degrees away from each other.

I'm not sure I quite grasp the purpose of creating a cube for the sake of simulating a sphere... :scratch:

- Day night calculation. 2 parameters needed: Earth rotation angle, Earth angle towards sun.

I assumed that day/night would probably be the easiest of them all, heck if I went 2D then it would be a simple matter of using the day/night texture too if I wanted.

- Positioning, i'd place every object using 3D coordinates instead of 2D even when it's surface of sphere. That way it is easier to calculate distances and pathing. Note that paths still aren't linear; earth isn't flat Path creates an arc instead of line.. not bothered to draw it, formula might be easy to make.

This seems like it might be the toughest way to do this. Nevermind that my math is weak in this area, but the fact that determaning zones would be a royal pain, no?

But you have a very good point about the non-flat earth. I know the kind of arch that a path of that size would make having looked at a few charts that plot stuff like that in the Navy, etc... I do believe that there must be a way to calculate a path in 2D though.

- Zones/continents could propably be made of arrays of 3D points forming the outlines. Bit tricky checking if object is in area. Only other choice i can think of would be marking each "tile" with zone info, however this is very rough solution. Even as rough solution it could still be used as pre-calculation, narrowing down the choices quickly.

I think this is what kills me wanting to do 3D entirely. It's already my weak area and this blows what I know out of the water. So it looks like full calculations 3D are out.


I do want to have a 3D representation if I can manage it though. So I guess the only 3D calculations I'll need at from 2 to 3. This does leave the open question of how does one calculate a path simulating the curvature of the earth, given the radius/diameter of the earth across a 2D plane. Gives me something to Google for I guess.

[User137]

Here's image explaining the spherified cube:
http://i8.tinypic.com/67qxyjb.png

Sounds like you got some interesting 3D maths to study Vectors and matrices are much fun when you get to know them better.

[WILL]

Ah ha! looky what I found

Distance = Radius * acos( cos(Lat1)*cos(Lat2)*cos((Long1-Long2)) + sin(Lat1)*sin(Lat2) )

Ok I've got my distance function... Put simply it uses the great-circle formula to figure it out.

Now... I think what I'm aiming for is to figure out how to get a 2D vector from my current point to the destination point. I'd obviously be updating this vector each iteration of my main game loop to get an accurate simulated curve.


btw, I think that I'm going to stick with knots and lat/long for my co-ordinate system. It'll be easiest for both development and the players to wrap their heads around. (Has worked for hundreds of years so far, right? )

[WILL]

Ok this is really killing me. I can't find a direct answer anywhere, is this such a rare thing to look for?

Best I could find is: this and this. :?


What I need to know is how do I plot on an orthographic map of the 'real' shortest movement from one point to another on the surface of a sphere in the form of a simple 2D vector?

I imagine that I'll need an equation that takes the current point, the destination point, the radius of the earth and speed to provide me with a pair of 2D VelX and VelY values. So I guess 2 equations then.

Anyone know how to do this?

I should be able to create results similar to something like this...

[jdarling]