Tests on spline interpolator in polar coordinates

Functions tests

• \((r,\theta) \mapsto r^p\) with \(0\leq p<4\): interpolation with cubic B-splines supposed to be exact.
• \((r,\theta) \mapsto r^p\) with \(p \geq 4\): interpolation with cubic B-splines supposed to be order 4.
• \((r,\theta) \mapsto r \cos(\theta)\) and \((r,\theta) \mapsto \exp\left(- \frac{(x(r,\theta) - x_0)^2}{2\sigma_x^2} - \frac{(y(r,\theta) - y_0)^2}{2\sigma_y^2} \right)\) : added and interpolation with cubic B-splines supposed to be order 4.

Test the interpolator on mesh points where the errors are supposed to be exact (machine error) and test the interpolator on "pseudo-random" points where the errors are supposed to be order 4 with a cubic B-splines basis.

Python scripts

• test_convergence.py : compute the convergence order in space for the tests where the errors are not supposed to be exact.
• launch the executable for a 64x64 grid and for a 128x128 grid to compare the errors.

• possibility of changing the default sizes by adding the two new sizes (N for NxN grid) at this end of the command (see --help).

• Command to launch the test in this folder: python3 test_convergence.py ../../../build/tests/geometryRTheta/spline_interpolator_rtheta/spline_interpolator_rtheta_tests (N0) (N1)

• display_curves.py : display errors for several grid sizes and compute the slope of the errors for each function.

• Command to launch the test in this folder: python3 display_curves.py ./../../build/tests/geometryRTheta/spline_interpolator_rtheta/spline_interpolator_rtheta_tests