We draw a Bernstein polynomial for an arbitrary number of reference points.

So actually the workspace looks like:


You can specify the number of points (from 2 to 13), and drag any anchor point by watching in real time how the curve changes.
Made for myself, in order to deal with curves of different order.
Basic knowledge is derived from here:

Bernstein Polynomial
Binomial_coefficient
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You can also read about the Bezier curve , which is a special case of the Bernstein polynomial.

Sources are attached, the archive also compiled (Win_X86) exe'shnik.

Archive with source code and exe'shnikom.
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Revision from Vordigont

The class implementing the polynomial is commented out, there will be no problem to be sorted out. Sharpe code.