Try moving the Base points and notice how the curves can be manipulated. C is a LINEAR combination of A1 and A2. Like wise Locus C1 is a parabolic ( 2nd DEGREE) BEIZER curve. And finally Locus of point 'O' is a CUBIC ( 3rd Degree) Polynomial. Move the points to see the effects of the tangents. All the points are linked to the slider A. Move it and SEE the EFFECT.