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I would like to allow user interactivity similar to this Javascript demo in a Matplotlib plot. I have a fairly good idea of how I can do this with a slider widget, but I would prefer direct interaction with the curve. What tools are available? It does not have to be a web app, it can be a simple interactivity built into the plot.

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One of the better ways I've seen is to use the mpld3 library (github link, which does a pretty good job at embedding matplotlib into D3.js.

The upside is that interactivity comes from javascript.
The downside is that interactivity comes from javascript.

I take this as an example of Atwood's Law.

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Looks promising. Have not heard of Atwood's law. Interesting. Thanks.
Question: say the user modifies a curve in the plot; are there tools to allow for the new curve to be written back to a python variable (either the original one or a new one)?

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