Rational Bézier Conic Weights

Use homogeneous weights to turn a quadratic control polygon into an exact circular arc.

Experiment

Follow these steps in the interactive Rational Bézier Conic Weights module to see the effect of changing weights:

1. Set the Weight to Polynomial. Notice how the curve deviates from the true quarter circle (circle equation residual is non-zero).
2. Change the Weight to Circular. The curve perfectly traces the quarter circle arc (circle equation residual is zero for all t).
3. Change the Weight to Zero. The middle control point is completely ignored, yielding a chord from P0 to P2.
4. Set the Weight to Heavy. The curve is pulled strongly towards P1, resulting in a shape sharper than a circular arc.