I need to approximate a cubic Bézier curve with a minimal collection of quadratic ones given a maximum acceptable error.
Trying to read up on this problem, it seems like there are about as many approaches as there are people trying to solve it. Everything ranging from using a single curve with the control point being a weighted average of the start, two control, and end point of the cubic with weights -1, 3, 3, -1 respectively, to splitting the curve into an increasing number of equal-sized segments using de Casteljau's algorithm and then approximating every one with the method above, or even starting at one end of the cubic and moving the endpoint of a best-fit quadratic curve along the cubic until the error gets too big and then starting a new quadratic at that point. @Timo even claims it can be done exactly if you split the curve at all its extrema and points of inflection (although I haven't verified this yet): https://stackoverflow.com/questions/2009160/how-do-i-convert-the-2-control-points-of-a-cubic-curve-to-the-single-control-poi/14514491#14514491
Among all these different approaches, is there an accepted gold-standard way of doing this?