Derivative and integrate a path

[pRototype]

Feature request:
Topic discussed in Inkscape forum: "http://www.inkscapeforum.com/viewtopic.php?f=28&t=16138"
An example (hand made) drawing can be found there in first post (that is by me, have a different username on that forum)

Say I have a path that start on left and going toward right.
I would like Inkscape to be able to make a derivate path out of the original path. Also it would be great if there was possible to be able to create an integral path from the original path.

I do not expect the integral or derivate output path to be absolutely excact in mathematically terms. A close aproximation would be enough.

For me, the reasons to be able to create a derivate and intregral is this:
I spend some time drawing voltage/time curves. When making timing diagrams, there is always a need for both derivate the curve as well as integrate it. Most cases just for understanding the result. Drawing the derivates and integrals of a curve by hand means I have to guess a lot. Having this to happens automatically would really make my work easier and spare me for some time.
I'm sure I can find more reasons to wish for this.

One aditional feature that would also be possible to include (that use integration) is to being able to put out a pont that is a paths center of gravity (or you call it mass center?).

[su_v (suv-lp)]

Attaching sample file retrieved from forum topic.

[Alvin Penner (apenner)]

I wonder if this could be added in as an option in the existing Extensions->Render->Function Plotter routine, which is written in Python.
- for example, maybe the original path could be specified as a standard svg path element, with beziers and arcs and so on, and then Function Plotter could do the derivative, etc.

[Johan Engelen (johanengelen)]

I think this is easy to implement as an LPE. However, it needs thought on how to handle all kinds of input paths. For example, what's the output for a circle?