Curve fitting with derivatives Is there any tool to do curve fitting with derivative values? I.e. I have a bunch of values of the function at certain points, a bunch of values of the function's derivative at certain points, a bunch of values of the function's second derivative at certain points, and I want to find the simplest function that obeys these constraints.
 A: Suppose you have $n+1$ constraints on function values and derivatives. You should be able to satisfy these constraints with a polynomial of degree $n$, since this will have $n+1$ coefficients $a_0, \ldots, a_n$. Each constraint will give you a linear equation involving $a_0, \ldots, a_n$. Pass these equations to your favorite linear solver, and you will (usually) get a solution. I say "usually" because sometimes the linear system will not be solvable. The conditions for solvability are complicated. If you want to understand them, look up the topic of "Hermite interpolation".
A: If you're asking "can you find a function given its derivative and an initial value?" then the answer is yes (presuming the derivative is integrable), and this is precisely the fundamental theorem of calculus.
If you have only some values of the derivative, and an initial value of the function, then you can estimate the shape of the original curve, and this is Euler's method.
A: Have a look at Hermite basis polynomials (that must not be confused with the "classical" Hermite polynomials): they can be substituted to Bernstein basis polynomials, classical for Bezier curves.
