monotone interpolation given two points and their derivatives

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Is there an algorithm or implementation? I have searched the monotone cubic interpolation or monotone piecewise cubic interpolation. It seems that both the two methods cannot preserve the derivatives at the two given points. I am not really sure about this, because I am not a mathematician. Can you provide some information or ideas? Anything will be greatly appreciated.

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I just found Bézier curve meet my requirements perfectly and is really simple for implementation.