Angle determination between pinned curved line.

How to find out the angle ϕ shown in above figure? line is pinned at different points.

[Walter Roberson]

Is the curved line a cubic spline ?

Answer 1

[Roger Stafford]

If s1 is the derivative of the curve on the left at the middle point and s2 the derivative of the curve on the right side at the middle point, the upper angle between the two tangent lines to the curves at that point is given in radians by:

 a  =  mod(atan2(s2-s1,-1-s1*s2),2*pi);

To convert the angle to degrees, multiply this by 180/pi.