1
$\begingroup$

A Bézier curve $Q$ has control points $P_0 = (0,0,0)$, $P_1 = (0,1,0)$, $P_2 = (1,1,0)$ and $P_3 = (2,0,0)$. What point is $Q(\frac12)$?

$\endgroup$
3
$\begingroup$

The equation of the Bézier curve is $$ Q(t) = (1-t)^3P_0 + 3t(1-t)^2P_1 + 3t^2(1-t)P_2 + t^3P_3 $$ Setting $t=\tfrac12$ gives $$ Q(\tfrac12) = \tfrac18 P_0 + \tfrac38 P_1 + \tfrac38 P_2 + \tfrac18 P_3 $$ Then substitute your known control points.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.