Variation Diminishing Property for Bézier Curves

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.

SNAPSHOTS

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DETAILS

The variation diminishing property also applies to rational Bézier curves.
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