Shape preserving properties of the generalised Ball basis (Q806935)

The second author has recently modified Bernstein polynomials to obtain a new basis for polynomials of degrees up to an odd number that can be used in the definition of curves from a control polygon. These polynomials are easier to evaluate than Bernstein polynomials. The authors show that the curve defined by a given polygon can be obtained as a Bézier curve of a polygon obtained from the given one by an edge-cutting algorithm. The new description of curves is therefore as stable as the Bézier description but less easily manipulated.