Is there a way to determine if all points of a bezier curve are visible from an endpoint? For instance, if you're given a cubic bezier curve in the plane: $\textbf C(t) = \sum_{i=0}^3 B_i^3(t) \textbf P^i$ would any of the rays from $\textbf P^0$ to $\textbf C(t)$ intersect the curve at any other point?

So I want to know if the following has 0 or >=1 #solutions:

all the rays from the origin: $\textbf L(s) := s { \textbf a}$

$\textbf C(0) = \textbf L(0) = {\textbf 0}$

$\textbf C(t1) = \textbf L(s1) = s1 { \textbf a}$

$\textbf C(t2) = \textbf L(s2) = s2 { \textbf a}$

this appears to have 4 equations in 5 unknowns (${ \textbf a}$ can be normalized)?

where $B_i^3$ is the Bernstein basis: $B_i^3(t) = C(3,i)(1-t)^{3-i}t^i$

thanks!