How to determine t value of original cubic bezier curve after subdivide such curve twice with each t = 0.5?

Question

Take this as initial cubic bezier, first subdivide with t=0.5 get point K, then I want to further subdivide the second half cubic bezier KJGD, get a point, let's say M.

My question is: If I subdivide the original cubic bezier ABCD at the point of M, what is the t value? is it 0.5 + 0.5 * 0.5 = 0.75? (first t=0.5 plus half (0.5) of the second part (0.5))

I use c++ as programming language.

Answer 1

If S0 is your original split point (0.5 in your case), and S1 is the split on the second curve (again, 0.5 in your case), then yes, your split point on the original curve is:

S0+(1-S0)*S1,

0.5+(1-0.5)*0.5 == 0.75.

Answer 2

This is not subdividing the curve but its recursive De_Casteljau algorithm to compute the value (point on BEZIER) from t so the value of t is never changing if you used t=0.5 it stays the same all the way ...

If you want to obtain t of closest point on BEZIER to some point M then you need a reverse process see:

• Is it possible to express "t" variable from Cubic Bezier Curve equation?