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Add two vector fields if they are based on different mesh points?

Posted 10 months ago
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Hi,

I have n number different 3D vector fields which are partially overlaying on each-other, but not at the same mesh points. Let's say n=2 and

vField1={{{x11,y11,z11},{vx11,vy11,vz11}},{{x12,y12,z12},{vx12,vy12,vz12}},....,{{x1m,y1m,z1m},{vx1m,vy1m,vz1m}}} 

and

vField2={{{x21,y21,z21},{vx21,vy21,vz21}},{{x22,y22,z22},{vx22,vy22,vz22}},....,{{x2m,y2m,z2m},{vx2m,vy2m,vz2m}}}

where {x1i,y1i,z1i} != {x2i,y2i,z2i} are the coordinate points and {vx1i,vy1i,vz1i}=={vx2i,vy2i,vz2i} are the vector coordinates at the given space points. {x1i,y1i,z1i} and {x2i,y2i,z2i} might be very far from each-other space-wise, other {x2j,y2j,z2j} points surely can be much closer to {x1i,y1i,z1i} in the 3D space. My thinking is to interpolate the two fields above the union of the two 3D coordinate sets and then discretize them over some third {x3i,y3i,z3i} mesh where {i,1,m} and finally add them over this third mesh. However it looks too complicated to me. Also there are regions in coordinate space where vField1 or vField2 are non-existent or very spar and any interpolation can be very wacky. I hope for a more elegant way, if there is one already in existence. Thanks ahead, János

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