E_Bezier

Normally the quadratic Bezier through three points A,B,C is:

I found an alternative that has some nice properties I'm calling the E_Bezier also through points A,B,C:

Both the Bezier and the E_Bezier are defined over the interval t=0..1, and equal A at t=0 and C at t=1, but the E_Bezier has the property that at t=1/2, it equals exactly B, which is not the case for the Bezier curve...

The acceleration of the E_Bezier curve is exactly double the acceleration of the Bezier curve...

I called it the E_Bezier because it spends "E" qual time between points A and B and points B and C...

**I might continue with an update for higher order than quadratic E_Bezier**