We need to calculate the center of the circle that has the designated radius and passes through both the current position and the target position. This method calculates the following set of equations where [x,y] is the vector from current to target position, d == magnitude of that vector, h == hypotenuse of the triangle formed by the radius of the circle, the distance to the center of the travel vector. A vector perpendicular to the travel vector [-y,x] is scaled to the length of h [-y/d*h, x/d*h] and added to the center of the travel vector [x/2,y/2] to form the new point [i,j] at [x/2-y/d*h, y/2+x/d*h] which will be the center of our arc.