Better function sampler with adaptive algorithm to choose additional sample points

[szdytom]

Maybe we shoule initially evaluate f at a number of equally spaced sample points specified by samples, then use an adaptive algorithm to choose additional sample points, subdividing a given interval at most max-recursion times.

Since it is connected with straight lines between sampled points, I think we can test for every index i if $\left|y_i - \frac{y_{i-1}+y_{i+1}}{2}\right|\le \text{error threshold}$, if not, add 2 more samples at $\frac{x_{i-1}+x_i}2$ and $\frac{x_i+x_{i+1}}2$, then do recursion down and repeat this process.

[liuguangxi]

Perhaps we can broaden our thinking further. For smooth curves, we can even approximate them using piecewise cubic Bezier curves, which will result in much fewer sampling points.