Reverse Engineering a Bezier Curve

Question

Given a few examples of points on a bézier curve , is it possible to develop many possible curves on which these points can lie?

In my particular application, there is a limited set of endpoints that a curve may have, so I want to generate a set of possible curves, list them all and select all those that can end at a valid endpoint.

Some people asked in more detail. I have a set of points that, as I know, are on a quadratic bezier curve, I want to calculate the curve formula and be able to extrapolate new points on the curve.

Answer 1

Bezier curves will always pass through the start and end control points.

If the degree of the curve is equal to the number of sample points, then there will be only one curve that passes through all your points (in the usual case, when all points are different and they do not lie on the bezier curve to a lesser extent).

If the degree of the curve is less, then the number of sample points, then, in the general case, you cannot force the curve to go through all the points (in the usual case).

If the degree of the curve is higher, then the number of sample points, then, in the general case, you can draw an infinite number of curves.

In the wiki article you will find links only to breakpoints, but still I believe that I correctly remember the specified properties and that they i.e. for points on curves.

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