Calculating triple integral between two surfaces gained with TriScatteredInterp or griddata

I am trying to calculate a triple integral of a function over a body defined as an intersection of two surfaces which I get interpolating data points using TriScatteredInterp or griddata, so they are functions z1(x,y) and z2(x,y). Actually, it is a calculation of the gravitational potential of a homogenous body of completely irregular shape at a point outside of it. The problem is in defining integral limits. Integration over a thetraedron is completed with no problems at all, but as I try to use my functions as lower and upper limits I always encounter errors.

Could you help me, please?

Thank you. Ivan

[Kiran]

Hello,

seems like the nit.zip has been deleted from the website. Will you please send me the same which I need urgently.

Thanks

Answer 1

[the cyclist]

Rather than trying to code the integration limits as functions, could you instead integrate over fixed intervals, but include a term in the integrand that makes it zero when it lies outside the desired limits?

In response to your answers (which would have been better positioned as comments on my answer), I have included the following code. It calculates the volume of a cube (of side length 2) and a sphere (of diameter 2). The sphere calculation uses the method I suggested, and seems to work fine.

% Volume of cube
f1 = @(x,y,z) ones(size(x))
Q1 = triplequad(f1,-1,1,-1,1,-1,1)

% Volume of sphere
f2 = @(x,y,z) ones(size(x)) .* (x.^2+y.^2+z.^2)<1
Q2 = triplequad(f2,-1,1,-1,1,-1,1)

Answer 2

[Ivan]

Thank you very much, works. Actually I tried that yesterday, but obviously I had made some mistakes in defining function. Also I'm using function numint3 from nit.zip from the following link: http://www-users.math.umd.edu/users/jmr/241/mfiles/ which is described here: http://www-users.math.umd.edu/~jmr/241/tripleint.html and it works very well.

[Kiran]

Hello,

seems like the nit.zip has been deleted from the website. Will you please send me the same which I need urgently.

Thanks

Answer 3

[Ivan]

Actually it still doesn't work. Using numint3 I do get a result which is always the same, independantly of the integrand. Triplequad returns an error. Any other ideas?

[the cyclist]

I've responded with an edited answer.