Re: Surface integral
- To: mathgroup at smc.vnet.net
- Subject: [mg9801] Re: [mg9774] Surface integral
- From: Wouter Meeussen <vdmcc at vandemoortele.be>
- Date: Fri, 28 Nov 1997 05:35:14 -0500
- Sender: owner-wri-mathgroup at wolfram.com
>Date: Tue, 25 Nov 1997 16:59:42
>To: Yves Verbandt <yverband at ulb.ac.be>
>From: Wouter Meeussen <vdmcc at vandemoortele.be>
To: mathgroup at smc.vnet.net
>Subject: [mg9801] Re: [mg9774] Surface integral
>Cc: mathgroup at smc.vnet.net
>
>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.
Oops,
NIntegrate[Evaluate at Sqrt[(1+D[fun[x,y],x]^2)(1+D[fun[x,y],y]^2)],{x,0,Pi/3
},{y,0,
Pi/3 }]
might be better,
still, check it!
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