The Bézier curve is defined by:
$$C(t)=\sum_{i=0}^{n} {{n}\choose{i}} t^i (1-t)^{n-i} P_i$$
where the $P_i$ are the control points.
I am trying to write it down in Mathematica. What I have is:
p0 = {0, 0};
p1 = {1, 1};
p2 = {2, 1};
p3 = {3, -1};
p = {p0, p1, p2, p3};
c[t_, n_] := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(n\)]\(Binomial[n, i]
\*SuperscriptBox[\(t\), \(i\)]
\*SuperscriptBox[\((1 - t)\), \(n - i\)] p[\([i]\)]\)\)
I can't manage to get a proper list for plotting. Can anyone please advise on how to correctly formulate the equations?