I have a discrete 2D temperature field, i. e. a dataset of N points (x, y, T). I would like to compute line integrals at fixed radii, $\int_0^{2\pi}T(r,\theta)d\theta$. My first thought was to transform all coordinates into radial coordinates, and then interpolate to a regular grid in $r,\theta$, so the integral would turn into a simple summation. This approach doesn't seem to be ideal, as I lose data at $r=0$. Is there a better way to solve my problem?
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6Have you considered interpolating in x,y coordinates and then evaluating the integral? – Brian Borchers Jan 06 '16 at 15:11
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3Are your $(x,y)$ data points on a uniform grid, or is it an unstructured point cloud? – Wolfgang Bangerth Jan 06 '16 at 20:13
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@WolfgangBangerth The points are on a uniform grid, but stored as a point cloud – akid Jan 07 '16 at 21:45
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@BrianBorchers No... I'll have a look at that. – akid Jan 07 '16 at 21:46
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If the points are on a grid, then interpolating along the points of the circle should be easy. – Wolfgang Bangerth Jan 09 '16 at 02:55
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@BrianBorchers I finally got around to work on this again, and that was exactly the way to go. If you turn your comment into an answer, I'll send some internet points along your way :) – akid Jan 29 '16 at 08:50
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An alternative approach that will help with the situation at $r=0$ is to do the interpolation in $(x,y)$ coordinates first, and then evaluate the integral.
Brian Borchers
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