Control points: 0.00, 0.33, 0.66, 1.00
Tolerance: Max error 0.56 pixels, approximating curve with segments.
Draw segments in alternating colors?
This demo draws a cubic Bézier curve by approximating it with line segments using the algorithm from Weiyin Ma and Renjiang Zhang's 2006 paper Efficient Piecewise Linear Approximation of Bezier Curves with Improved Sharp Error Bound.
I also derived a check to see if a Bézier curve is monotonically increasing on one axis (the x-axis here), so the curve will be green if it always moves to the right, or orange if it curves to the left at some point. This is useful for constructing curves for animation which use the x-axis as time.