I'm trying to understand how to calculate the midpoint of a turning circle. In the attached picture, my unit is at location U. I want to compute the trajectory of the unit as it turns toward the starred location.
I understand that to achieve this I need to know the location of point P, whose coordinates are (a,b). I also understand that I can do this using some simple trig:
a = x - cos(theta) * r
b = y - sin(theta) * r
My problem is that I do not know the value of the angle Theta which sits between the sides of the right-triangle named "R" and "X-A". All I know is:
The radius of the turning circle.
The orientation of the unit.
How can I solve this problem and others like it more generally?