Re: [Matplotlib-users] find the projected distance between two curves

[G. A. <gio...@gm...>]

Thanks Andrew, conceptually it's clear. Now I have to code it :)
I will have a look to SimPy, and also to SciPy/NumPy

I will let you know how it's going on.

2009/2/20 Andrew Straw <str...@as...>:
> G. Allegri wrote:
>>
>> Hi Andrew.
>> With dist(point_i,polynomial_curve) do you mean point_i belonging to
>> the Line 2 set of points and pol_curve as Line 1?
>
> yes
>
>>  In this case it
>> could be reasonably ok for me. How can I derive the closed form for
>> dist()? Excuse my ignorance with geometry....
>>
>
> Take the equation for line 1parameterized by s. Something like f(s) = (x,y)
> = (as**2 + bs +c, ds**2 + es + f ) for your polynomial model. Now, the
> distance for that point on line 1 from point i is dist(point_i, f(s)), where
> dist can be Euclidean distance, for example.
>
> So, the question is what value of s minimizes the distance. Since this
> function will be smallest at an inflection, just take the derivative of your
> distance function and solve for it to be equal to zero. Hopefully this
> function will be convex and you'll have only one zero, which will tell you
> the value of s where distance is a minimum. Otherwise, pick the inflection
> at the closest distance. Finally, repeat for all points i and sum the
> results.
>
> Hopefully that helps on the conceptual side. Sympy will be more useful than
> matplotlib on the coding side...
>