what is the difference between the blending function and Bernstein Polynomial in Bezier Curves and there role ?
Are they same . what decide the use of which degree to draw a Beizer curve? how the curve can be manipulate using control points?
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the degree of polynomial is tighted to number of control points and continuity ... the bigger the more continuous the patch joints are (position,direction,second derivation,third derivation...) In most cases cubics are enough. The manipulation of control points is not easy for BEZIER because the curve does not go through the points so it is not that intuitive and precise. In worst case You can make an interpolation polynomial of desired curve and transform it to BEZIER or use fitting methods ... Sorry I cant tell you about your first question because I lack the Math knowledge background – Spektre Dec 02 '15 at 09:57
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see [polynomial to BEZIER](http://stackoverflow.com/a/33866901/2521214) and [piecewise linear interpolation/approximation](http://stackoverflow.com/a/30438865/2521214) – Spektre Dec 02 '15 at 10:02