? 1. A line segment has two end points A and B. If this line segment
is to be represented by a cubic Bezier curve model with 4 control
points $P_0$, $P_1$, $P_2$, and $P_3$, prove that $P_0$, $P_1$, $P_2$, and $P_3$ are co
linear.
$P_0$
$P_1$
A
$P_2$
$P_3$
B
r'(0)= 3($P_1$-$P_0$)=$P_3$-$P_0$;
r' (1)=3($P_3$-$P_2$)=$P_3$-$P_0$;
How to rewrite the above equation as an expression for the
points $P_1$ and $P_2$ on the line segment formed by $P_3$ and $P_0$,
which can be found in the exercises of the first lesson.
?2.Construct a quadratic Bezier curve model (equation)
with three control points, $V_0$, $V_1$, and $V_2$.
