Variation Diminishing Property for Bézier Curves

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This Demonstration illustrates the variation diminishing property for planar polynomial Bézier curves: the number of intersection points of any straight line with a Bézier curve (blue points) is at most the number of intersection points of the same straight line with the control polygon of the curve (red points). The parameter controls the angle and the parameter controls the height of the straight line.

Contributed by: Isabelle Cattiaux-Huillard (March 2011)
Open content licensed under CC BY-NC-SA



The variation diminishing property also applies to rational Bézier curves.

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