where (10) represents the theorem of Pythagoras, while (11) states that the slope of the line between the two waypoints is constant. These equations are solved in the following, temporarily dropping the time dependence of the variables for notational convenience. Denote the difference between the x- and y-position of the two waypoints as Ax = xk+1 - xk and Ay = yk+1 - yk , respectively. The equations are first solved analytically assuming that | Ax| >0 and secondly for the case Ax = 0. Case 1: |Ax| >0 Equation (11) results in when choosing to solve for yint . For simplicity and brevity in the calculations to follow, denote
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