I would like to fit a Cubic Bezier Curve in a rectangle, and wondering how to get the 2nd and 3rd control points's Y value, illustrated below:
(Sorry the rectangle is bit distorted.) Basically, given the position of first point (x1, y1), fourth point (x4, y4), and the height of middle point h, how can I get the y2 and y3 from this curve?
curve generated using: http://demofox.org/bezcubic.html
Thank you for any reply in advance.
$$ \vec{B}(1/2)=\Sigma_{i=0}^3 \phi_{3,i}\vec{b_i} $$ $$ B_y(t=1/2)=\phi_{3,0}*b_{0,y}+\phi_{3,1}*b_{1,y}+\phi_{3,2}*b_{2,y}+\phi_{3,3}*b_{3,y}\\ =\phi_{3,1}*b_{1,y}+\phi_{3,2}*b_{2,y}\\ =\binom{3}{1}t^1(1-t)^{3-1}*b_{1,y}+\binom{3}{2}t^2(1-t)^{3-2}*b_{2,y} \\ =3*(1/2)^3*b_{1,y}+3*(1/2)^3*b_{2,y}=3*(1/2)^2*b_{1,y}=50 $$ $$ b_{1,y}=b_{2,y}=200/3 $$