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edited Mar 23, 2017 at 10:53

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vx = {{{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}ConstantArray[1, {1, 1, 15, 15, 1}}5}; ] vyvx = {{{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}ConstantArray[3, {3, 3, 35, 35, 3}}5}; ] vzvy = {{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}ConstantArray[2, {2, 2, 25, 25, 2}}5}; ] together = ArrayReshape[Transpose[Flatten /@ {vx, vy, vz}], {5, 5, 5, 3}] interpolation = ListInterpolation[together] ListVectorPlot3D[together] VectorPlot3D[interpolation[x, y, z], {x, 1, 5}, {y, 1, 5}, {z, 1, 5}]

vx = {{{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}};  vy = {{{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}};  vz = {{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}};  together = ArrayReshape[Transpose[Flatten /@ {vx, vy, vz}], {5, 5, 5, 3}] interpolation = ListInterpolation[together] ListVectorPlot3D[together] VectorPlot3D[interpolation[x, y, z], {x, 1, 5}, {y, 1, 5}, {z, 1, 5}]

vx = ConstantArray[1, {5, 5, 5}] vx = ConstantArray[3, {5, 5, 5}] vy = ConstantArray[2, {5, 5, 5}] together = ArrayReshape[Transpose[Flatten /@ {vx, vy, vz}], {5, 5, 5, 3}] interpolation = ListInterpolation[together] ListVectorPlot3D[together] VectorPlot3D[interpolation[x, y, z], {x, 1, 5}, {y, 1, 5}, {z, 1, 5}]

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asked Mar 22, 2017 at 23:26

Tomi

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Interpolation of Discrete 3D Vector Field

I have a vector field with discrete values and I want to interpolate these values to create a differentiable vector field.

I have matrices which give the vector values of the velocity - $vx, vy, vz$. They have dimensions of $(5,5,5)$. I put these together to get a vector field which looks like $(vx,vy,vz)$ with dimensions $(5,5,5,3)$ i.e. each coordinate has a vector at it.

But the interpolation function on this matrix doesn't seem to work.

interpolation = ListInterpolation[together]

No errors here, but when I plot it I get a blank graph, whereas from the "raw" data I get what I would expect.

All Code:

vx = {{{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}}; vy = {{{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}}; vz = {{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}}; together = ArrayReshape[Transpose[Flatten /@ {vx, vy, vz}], {5, 5, 5, 3}] interpolation = ListInterpolation[together] ListVectorPlot3D[together] VectorPlot3D[interpolation[x, y, z], {x, 1, 5}, {y, 1, 5}, {z, 1, 5}]

From ListVectorPlot:

From VectorPlot3D (interpolation):