I'm designing a game where objects have to move along a series of waypoints. The object has a speed and a maximum turn rate. When moving between points p1 and p2 it will move in a circular curve like so:
a is the angle the object must rotate through. Therefore we can calculate the time it will take to rotate through this angle as
t = a / turn rate.
However, if the object's current speed means it will cover distance
d in quicker than this time, it must slow down on this corner or it will miss p2. I need to calculate the maximum speed it can take this corner at, which means calculating the distance of the curve
d (so I can calculate the maximum corner speed as
d / t).
I think I've figured out
b = 2a, but to determine
d I need to know the radius of the circle. How can I determine it from this information?