ummmmm......

 

If you take two circles(make it three one to represent the earth) and you scale them in one axis with respect to the rotation achieved you will find you have a complete representation of a polar system. No where in this system is there any suggestion of a mans orientation. So now and correct me if I'm wrong there is no exception for there being any rotation of a man on a diagonal traverse as opposed to a movement solely in longitude or latitude especially being that with the use of the Sine law you are essentially breaking the diagonal traverse into these two respective transformations. Unless of course you are intentionally integrating this behaviour into your system in which case I misread your posts....

 

Three ellipses and a bunch of numbers would be easily created using C# and WPF IMHO :\

Imagine standing on the equator (I forgot to mention that part) and you go east or west, your angle relative to the north pole is pi/2 and the same at all times. Now imagine standing anwhere and going north, again your angle to the north pole always stays at 0 untill you cross the north pole.

 

This time you are standing 10 meters from the north pole, you travel at an angle of pi/2 10 meters. You are now further away from the north pole but not as much further as if you have traveled directly away from it (angle of pi).

 

Your angle relative to the north pole is different from when you started, it is your final_angle. To be the same as the angle variable in this case the man would have had to move in a curve, but he didn't he moved in a straight line.

Edited June 25, 201015 yr by alan2here