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?
6
-
6$\begingroup$ Have you considered interpolating in x,y coordinates and then evaluating the integral? $\endgroup$– Brian BorchersCommented Jan 6, 2016 at 15:11
-
3$\begingroup$ Are your $(x,y)$ data points on a uniform grid, or is it an unstructured point cloud? $\endgroup$– Wolfgang BangerthCommented Jan 6, 2016 at 20:13
-
$\begingroup$ @WolfgangBangerth The points are on a uniform grid, but stored as a point cloud $\endgroup$– akidCommented Jan 7, 2016 at 21:45
-
$\begingroup$ @BrianBorchers No... I'll have a look at that. $\endgroup$– akidCommented Jan 7, 2016 at 21:46
-
$\begingroup$ If the points are on a grid, then interpolating along the points of the circle should be easy. $\endgroup$– Wolfgang BangerthCommented Jan 9, 2016 at 2:55
|
Show 1 more comment
1 Answer
$\begingroup$
$\endgroup$
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.
answered Jan 29, 2016 at 15:56