An exact representation of a circle requires a degree 2 rational Bézier curve. ![]() Wikipedia (technically, Thomas Herter and Klaus Lott) tells us that a. A degree 2 polynomial Bézier curve can only represent a parabola. A detailed explanation of Bzier curves, and how to do the many things that we. Rational Bézier curves are useful for lots of reasons. If the weights of the control points are all 1, the rational Bézier reduces to a standard polynomial Bézier curve. The blending functions are rational polynomials, or the ratio of two polynomials. P ( t ) = ∑ i = 0 n B i n ( t ) P i = ∑ i = 0 n ( n i ) ( 1 − t ) n − i t i P i Blending functions are functions of the parameter of the curve and depending on their equations, they can change the shape of the curve.Ī standard n-degree Bézier curve is defined as follows: The shape of the resulting curve is determined by blending functions. ![]() In the example at left, they are the labeled points. It depends on certain control points that often mimic the shape of the resulting curve.
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