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Quadratic Bezier curves don't quite have enough independent degrees of freedom. With cubic curves, there's a simple method: you put the two endpoints at arbitra
by teraflop 9y ago
Quadratic Bezier curves don't quite have enough independent degrees of freedom. With cubic curves, there's a simple method: you put the two endpoints at arbitrary nearby points on the curve, and then the other two control points are determined by the derivatives at those points.
See https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Derivative https://en.wikipedia.org/wiki/B%C3%A9zier_curve#Derivative
- ttoinou 9y agoExactly. You can even have your own formulae for 3rd order polynomial interpolating curve (no need to go through the "original" formulae)
- iTokio 9y agoSorry I meant cubic, control points can just be points of the original curve with a catmull rom spline. So an easy method is just to remove the point with the minimal error contribution and iterate until a given threshold. But the cost is too high for large curves.