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.
AFTERWORD Beizer curves were invented in 1960 by a FRENCH duo ' Paul de Casteljao' and ' Beizer'. they worked for automobile compaines named RENAULT and CITREON