I figured this would go here because I need to figure this out for a mod I'm writing for MineCraft.

 

 

How do you determine the length of the arc s given only the radius r, and the lengths t and e?

 

Basically the player has free movement in the X and Y direction and the Z (vertical) offset e is calculated by applying the pythagorean theorem to the xy offset(t) and the radius ( sqrt(r^2 - t^2) = e). I need s to determine the resistance the player encounters when attempting to swing to the given point. Of course I also still need to calculate X and Y momentum, but I can't even start on that until I figure this out.

First theta = arctan(t/(r-e)), and then the arclength s =r*theta, where theta is measured in radians.

Thanks a bunch, it seems to work great:

 

 

Now to get working on the (pseudo) physics.