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Possible Duplicate:
Error measurement between given perfect 2D shape and freeform shape drawn by user

I am programming (with vectors) an application which requires a user to draw line according to certain data. Then the user will click a check button which will grade the users drawing to the actual data line. So I am wondering how would I go about grading the accuracy of the two lines?

So far what I have been able to do is interpolate the entire line of both the user line and the actual line. So that the user lines data can match with the actual line data.

What is my next step in finding the accuracy of the user line to the actual line?

I can't use area because the line the user draws is not linear, its freeform.

Heres an image of what i mean:

enter image description here

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    why can't you use area? The less the area, the better the users line as compared to yours?2011-12-05
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    "I can't use area because the line the user draws is not linear, its freeform." but there is no case in my application where the line is just a line, it could be shaped along the x and y positive axis.2011-12-05
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    I think I get what you mean. How about randomly choosing points on the users line and then finding the [root mean square error](http://en.wikipedia.org/wiki/Root-mean-square_deviation) from yours?2011-12-05
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    I'll read that then, i uploaded a photo of what i mean if it helps2011-12-05
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    From your image, I think Area will work.2011-12-05

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Lets say user line is $g(x)$ and line drawn by you is $f(x)$

Then grade can be made be inversely proportional to

$$\displaystyle \sum_{x=a}^{b} (g(x)-f(x))^2$$

This is commonly used function.

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    I will see how this works out for me.2011-12-05
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    @John, this is RMS applied in a slightly different manner.2011-12-05
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    I rather like the RMSE better nyways. @picakhu post it as your answer as an answer, so i can give you credit.2011-12-05
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    @John, I would have to elaborate on how you should use it, and I am not sure which approach is best. I think it is better that I do not get credit for it, I do not deserve it.2011-12-05
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    This just avoids taking the root and average. So it saves computation. We are using this in stanford ml-class online. :) @picakhu is right its just RMS squared times number of points!2011-12-05