I know this might not be so easy to implement but it would increase the value of freehand shapes a lot if the functions created this way could be used as input for a custom tool.
An example of the use of this:
As a teacher I often want to have a function that "goes something like this". The freehand shapes are almost perfect for this. It is a huge disadvantage though that the tangent tool does not work for this kind of functions. To overcome this I do one of two things:
Create a function (f) with the freehand tool
Create a point (A) on f
g(x)=Polynomial[A,(x(A)-0.1,f(x(A)-0.1)),(x(A)+0.1,f(x(A)+0.1))] (this is rough of course but it is all I need)
Tangent[A,g].
OR
Create a function (f) with the freehand tool
g(x)=FitPoly[f,5] (this is very often enough)
Create point (A) on g
Tangent[A,g].
The problem is that this is a bit cumbersome in class and a custom tool would be great.
Best regards,
Mikkel
I like this idea 
Nice idea, we could just implement (approx) tangents for Freehand Functions for you :)
Here's a mockup of what it would look like - do the values of the sliders give a nice result for the sort of functions you would use?
It seems you have forgotten an attachment.
Thanks :)
http://tube.geogebra.org/st...
Here's a preview of the real thing:
http://tube.geogebra.org/st...
First of all, thanks a lot for looking into this.
"The real thing" looks great and personally I would mostly use this for rather smooth functions so this will be perfect.
Regarding the values of the sliders I think there is some kind of bug when the order is set to 3 or 4. At least the tangent is not very close to the point A.
Generally I think one should avoid using more points than order+1 (including A) because otherwise the tangent won't pass through A and that will look stupid. For my purpose I don't think it will be necessary to use polynomials of higher degree than 5.
As I said this is great work but I still think it could be useful in general to be able to use freehand functions in a custom tool.
ps just added a Toolbar so you can try it out for different functions (use the Freehand Tool then the Tangent Tool) :)
As far as I can tell it works great. At least it does what I need. Typically I would just draw something that looks like a polynomial of degree 3-5 meaning "some function" so I don't need anything fancier than this. Weird functions doesn't do well on smartboards anyway.
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