Re: Surface integral
- To: mathgroup at smc.vnet.net
- Subject: [mg9799] Re: [mg9774] Surface integral
- From: Wouter Meeussen <vdmcc at vandemoortele.be>
- Date: Fri, 28 Nov 1997 05:35:13 -0500
- Sender: owner-wri-mathgroup at wolfram.com
At 12:07 25.11.97 -0500, Yves Verbandt wrote:
>Deat Mathematica experts,
>
>Can anyone help me with the calculation of a surface in 3D which is
>given by a list of {x,y,z} values? Perhaps there is an adaptation of
>ListIntegrate somewhere out there?
>
>Thank you,
>***************************************** Yves Verbandt
>Universit=E9 Libre de Bruxelles
>Biomedical Physics Laboratory
>cp. 613/3, Route de Lennik 808,
>1070 Bruxelles, BELGIUM
>tel. +-322-555.61.63
>fax. +-322-555.61.62
>email yverband at ulb.ac.be
>****************************************
>
>
>
Yves,
what's wrong with constructing an interpolation function : data3D= your
{x,y,z} - table, for instance :
N at Table[Sin[i j],{i,0,Pi,Pi/5},{j,0,Pi,Pi/5}];
fun=ListInterpolation[data3D,{{0,Pi},{0,Pi}},InterpolationOrder->3];
now, you can treat fun as any other function :
fun[1.1,1.3] is 0.981797
just like :
Sin[1.1 1.3] is 0.990105
Now, you can check the interpolation by plotting it:
Plot3D[fun[x,y],{x,0,Pi },{y,0,Pi }]
So, if you know how to calculate a surface integral, you can get there
.. I would guess something along :
NIntegrate[Evaluate at Sqrt[(1+D[fun[x,y],x])(1+D[fun[x,y],y])],{x,0,Pi/3
},{y,0, Pi/3 }]
but you'd better check that,
wouter.
NV Vandemoortele Coordination Center Oils & Fats Applied Research
Prins Albertlaan 79
Postbus 40
B-8870 Izegem (Belgium)
Tel: +/32/51/33 21 11
Fax: +/32/51/33 21 75
vdmcc at vandemoortele.be