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Math Help - Difference similarity shape, length, width, height, regardless of scale, most similar

  1. #1
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    Difference similarity shape, length, width, height, regardless of scale, most similar

    Lets say you have a rectangular prism.
    Model: LxWxH: 192 x 210 x 212


    various rectangular prisms L,W,H
    186,205,204
    186,206,205
    188,210,206
    191,209,210
    188,208,209
    185,207,208
    197,204,207
    199,211,214
    210,192,212 (should be farthest from a match)
    384,420,424 (should be perfect match)


    How would you pick the one that most closely matches the proportions of the original shape? scale does not matter, only proportions


    In the above data set I added one with the same dimensions but in a different order, also a couple where the width is greater than the height.
    The solving method should show those value as the least similar.
    I also added one that has the exact same dimensions as the original only doubled, it should return the closest match.(perfet match, although there wont usually be a perfect match)


    when its two dimensions its much simpler, you could just divide the length/width and pick which ever number is closest to the result of the original model.


    I dont need a solution, these numbers are just examples, I am just wanting to know what equation you would use to solve this type of problem.
    I am working on a software project where I will need to do a lot of work comparing the difference between sets of numbers.
    Last edited by xinlo; January 30th 2013 at 06:07 PM.
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  2. #2
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    Re: Difference similarity shape, length, width, height, regardless of scale, most sim

    Hey xinlo.

    For this problem you might want to use a metric where d(x,y) = SQRT((x0-y0)^2 + (x1-y1)^2 + (x2-y2)^2) where (x0,x1,x2) is LWH for item 1 and (y0,y1,y2) is LWH for item 2.

    Smaller value indicates closer fit.

    This is a very crude way of doing it but it does provide a starting point.
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  3. #3
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    Re: Difference similarity shape, length, width, height, regardless of scale, most sim

    When I tried that just now but

    384,420,424 got a value of 354.835173 and it should have been the closest match, should I normalize the values based on the height, or maybe there is another way.
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  4. #4
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    Re: Difference similarity shape, length, width, height, regardless of scale, most sim

    Well the metric I gave was a standard one but you may want to add to or change it based on the actual attribute you are looking for (i.e. incorporate the nature of the ratio into the metric).
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  5. #5
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    Re: Difference similarity shape, length, width, height, regardless of scale, most sim

    yep, i am only looking for geometric similarity, with the objects in question facing the same direction

    As far as I can tell once normalized this works excellent! Thank you so very much

    here is how I normalized it, and it seems to be exactly what I needed. Just hope the way I am normalizing it is the correct way to go about it, so nothing creeps up on me when im not expecting it.

    The reason I normalized it is because the scale of the object does not matter only geometric similarity.

    =SQRT((x0/x2-y0/y2)^2 + (x1/x2-y1/y2)^2 + (x2/x2-y2/y2)^2)


    x0,x1,x2 = 192,210,212 = 0
    --------------------------------------------
    y0,y1,y2 = 384,420,424 = 0
    y0,y1,y2 = 191,209,210 = 0.006062527
    y0,y1,y2 = 188,208,209 = 0.007700726
    y0,y1,y2 = 186,206,205 = 0.014407578
    y0,y1,y2 = 186,205,204 = 0.015581448
    y0,y1,y2 = 185,207,208 = 0.016883492
    y0,y1,y2 = 199,211,214 = 0.024675823
    y0,y1,y2 = 188,210,206 = 0.029679298
    y0,y1,y2 = 197,204,207 = 0.046307593
    y0,y1,y2 = 210,192,212 = 0.120074736
    Last edited by xinlo; January 30th 2013 at 10:33 PM.
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