How to translate and rotate mesh in cartesian coordinate systems

[keixthb]

Modeling the Lüneburg Lens Antenna Using OpenEMS

Background

Hello! I hope you are all doing well!

I am doing some research on antennas--particularly the lüneburg lens. I am trying to recreate the results of this experiment using pyems. So far, I have been able to successfully generate a .stl file and have it attached below:

luneburg.stl.zip

Using your horn antenna example, I am able to load the luneburg.stl file with the following script, run a simulation, and view the results in paraview, just by modifying the file name in python and loading the new mesh.

New Simulation

In the LuneburgLensGenerator repo mentioned above, the maintainers mentioned that they tested their design in CST and in the lab--using a horn antenna. I am able to get close to their setup using this script:

luneburg.py

#!/usr/bin/env python3

import os
import sys
import numpy as np
from pyems.utilities import print_table
from pyems.port import RectWaveguidePort
from pyems.simulation import Simulation
from pyems.field_dump import FieldDump
from pyems.structure import standard_waveguides
from pyems.coordinate import Coordinate3, Box3, Axis
from pyems.mesh import Mesh
from pyems.nf2ff import NF2FF

unit = 1e-3
freq = np.linspace(5.3e9, 5.9e9, 501)
sim = Simulation(freq=freq, unit=unit)

metal = sim.csx.AddMetal("metal")
stl = metal.AddPolyhedronReader(filename=os.path.abspath("horn-antenna.stl"))
stl.ReadFile()



new_metal = sim.csx.AddMetal("metal")
new_stl = new_metal.AddPolyhedronReader(filename=os.path.abspath("luneburg.stl"))
new_stl.ReadFile()

wg = standard_waveguides["WR159"]
wg.set_unit(unit)
wg_len = 10
port = RectWaveguidePort(
    sim=sim,
    box=Box3(
        Coordinate3(-wg.a / 2, -wg.b / 2, -wg_len),
        Coordinate3(wg.a / 2, wg.b / 2, 0),
    ),
    propagation_axis=Axis("z"),
    excite=True,
)
port.add_metal_shell(thickness=5)

mesh = Mesh(
    sim=sim,
    metal_res=1 / 20,
    nonmetal_res=1 / 10,
    smooth=(1.5, 1.5, 1.5),
    min_lines=5,
    expand_bounds=((16, 16), (16, 16), (8, 24)),
)
field_dump = FieldDump(sim=sim, box=mesh.sim_box(include_pml=False))
nf2ff = NF2FF(sim=sim)

if os.getenv("_PYEMS_PYTEST"):
    sys.exit(0)

sim.run()
sim.view_field()

s11 = sim.s_param(1, 1)
print_table(
    np.concatenate(([sim.freq / 1e9], [s11])),
    col_names=["freq", "s11"],
    prec=[4, 4],
)

theta = np.arange(-90, 90, 1)
phi = np.arange(0, 360, 1)

nf2ff.calc(theta=theta, phi=phi)

horn_width = 109.9e-3
horn_height = 80e-3
effective_aperture = horn_height * horn_width
print(nf2ff.directivity(effective_aperture))
print("gain: {:.2f} dB".format(nf2ff.gain()))

rad_phi0 = nf2ff.radiation_pattern(phi=0)
rad_phi90 = nf2ff.radiation_pattern(phi=90)

print("phi0")
print_table(
    np.concatenate(([theta], [rad_phi0])),
    col_names=["theta", "gain"],
    prec=[4, 4],
)

print("phi90")
print_table(
    np.concatenate(([theta], [rad_phi90])),
    col_names=["theta", "gain"],
    prec=[4, 4],
)

..which generates the following results:

..but if we compare this to the setup mentioned in their repo:

..we can visually see, the lens is translated too far in the negative-z direction, and the orientation is rotated.

Question:

Is there a way to easily perform linear transformations on the .stl files--such as translation and rotation--so that we can achieve a similar mesh that was used in the experiment mentioned above? I would think that it would be a relatively straightforward task; however, I am not familiar with the pymesh and openEMS / CSXCAD api.

Thank you so much for your time!

[matthuszagh]

Cool application.

I'm on vacation until June 9 and can take a more detailed look after then.

In the meantime, take a look at apply_transform. Or, the underlying CSXCAD API (eg AddTransform). This can be applied to your new_stl. I think the OpenEMS creator used to have examples of constructing transforms, but I'm not finding them at the moment. You may simply have to read the CSXCAD API for them. But, arbitrary linear transforms are possible.

Good luck and let me know how it goes!