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Mathematica: Generate Surface Equation

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  1. Oct 22, 2013 #1
    Hi there,
    I just began using Mathematica today and I was wondering if there is a way to make the program generate an equation of a surface given a 3d array?

    What I need it to do is to give me an equation of the surface so that given any two variables I can find the value of the third one.

    Any advice will be highly appreciated.

    Here is a screenshot of what the surface looks like:

    attachment.php?attachmentid=63229&stc=1&d=1382478716.png

    And here is the array:

    4 1000 0.10331
    4 1250 0.08479
    4 1500 0.07125
    4 2000 0.05700
    4 3000 0.04133
    4 5000 0.02921
    4 10000 0.01995
    4 15000 0.01660
    4 20000 0.01510
    9 1000 0.11400
    9 1250 0.09476
    9 1500 0.08265
    9 2000 0.06698
    9 3000 0.05201
    9 5000 0.03919
    9 10000 0.02993
    9 15000 0.02630
    9 20000 0.0245
    16 1000 0.12754
    16 1250 0.10901
    16 1500 0.09690
    16 2000 0.08123
    16 3000 0.06555
    16 5000 0.05344
    16 10000 0.04418
    16 15000 0.04235
    16 20000 0.04075
    25 1000 0.14250
    25 1250 0.12683
    25 1500 0.11400
    25 2000 0.09904
    25 3000 0.08336
    25 5000 0.07125
    25 10000 0.06199
    25 15000 0.06070
    25 20000 0.05920
    36 1000 0.16388
    36 1250 0.14963
    36 1500 0.13538
    36 2000 0.12041
    36 3000 0.10474
    36 5000 0.09263
    36 10000 0.08336
    36 15000 0.08250
    36 20000 0.08115
    49 1000 0.19024
    49 1250 0.17100
    49 1500 0.16031
    49 2000 0.14535
    49 3000 0.12968
    49 5000 0.11756
    49 10000 0.10830
    49 15000 0.10750
    49 20000 0.10600
     

    Attached Files:

  2. jcsd
  3. Oct 22, 2013 #2

    SteamKing

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    That's generally a very hard problem, unless you already know the basic equation of the surface.
    In those situations where the basic equation is known, you can use your surface data to fit the equation to the surface using regression techniques. Still a lot of number crunching though, and what if the equation doesn't pass through the surface data in one or more regions?
     
  4. Oct 22, 2013 #3

    Chronos

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    Taming surfaces to keep them from extending beyond where they are intended to go is a black art. I used to model 3D surfaces on an IBM 360 in FORTRAN on punch cards. It was ... educational.
     
  5. Oct 22, 2013 #4
    The equation doesn't have to be perfect, as long as it's a close approximation.
    I found another program that can do this. It has a database of hundreds of basic equations and it fits the best one automatically for you. I was wondering if Mathematica can do this.

    In the case of this example it spat out the following:

    attachment.php?attachmentid=63240&stc=1&d=1382502107.jpg
     

    Attached Files:

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