deriving surface equation form data on a table

    i have a table with 3 variables(B/H)= 1,2,3,4,5,6,7,8 and fi= 0,10,20,30 and h which is depend on (B/H) and fi that contains 32 values. for example for fi=0 and (B/H)=1 >>h=1 fi=0 and (B/H)=2 >>h=1.02 ...... fi=30 and (B/H)=8 >>h=14800

>is there any way in MATLAB to get an surface equation for h in terms of (B/H) and fi??

 h:[ 1    1.02  1.11  1.21  1.3   1.4  1.59  1.78      
     1    1.11  1.35  1.62  1.95  2.33 3.34  4.77     
     1.01 1.39  2.12  3.29  5.17  8.29  22    61      
     1.13  2.5  6.36  17.5   50   150  1400  14800 ]

[Walter Roberson]

There are an infinite number of surface equations that would fit the data perfectly. Which one do you want?

[milad babaei]

infinite number of surface equations??would u please explain me more ,what type of equations fit on my data (z=ax+by+c or...)and what should i do in matlab to get that equation???

[Sean de Wolski]

There can be at least one polynomial of order>(number elements) that fits perfectly. Thus from n-> infinity: To infinity and beyond!

[milad babaei]

would u introduce me that polynomial which fits perfectly??

Answer 1

[Andrei Bobrov]

BHv= [1,2,3,4,5,6,7,8];
fiv= [0,10,20,30];
h = rand(length(BHv),length(fiv))*30+10;
[fim BHm] = meshgrid(fiv,BHv);
[XI,YI] = meshgrid(linspace(fiv(1),fiv(end),100),linspace(BHv(1),BHv(end),100));

1 variant use 'interp2'

F1 = @(fi,BH)interp2(fim,BHm,h,fi,BH);
surf(F1(XI,YI))

2 variant use 'TriScatteredInterp'

F = TriScatteredInterp(fim(:),BHm(:),h(:));
figure,surf(F(XI,YI))

[milad babaei]

tnx for your help.what about other h values?

would you please explain how should write this code??

[milad babaei]

i mean i have a table which 32 values for h are specific based on fi and (B/H).so i m thinking that for fitting an surface by equation we should consider those values.