I'm trying to interpolate a curve using cubic splines and three points in the x-y plane. I have some troubles finding the equation for the middle point such that the normal vectors in point P0 is always perpendicular to the x-axis, given any angle between the yellow line and the x-axis. See figure: Spline curve
P0 is always known, P1 is given by:
P_1 = [r1*cos(beta); r1*sin(beta)], where r1 is the the length of the yellow line and beta is the angle between the yellow line and the x-axis. In the image above I have experimentally found the equations for P2, which is:
P2 = [0.75*P1_x; 0.25*P1_y]. But this only works if beta is 45 degrees. I've tried to reverse engineer it but I failed miserably. How would I go about finding the equations for P2?
Best regards MC