Recreating this image of an atomic set
TeX - LaTeX Asked by Ramanujan on April 19, 2021
On slide 24 of this talk one finds this image
which is supposed to depict the atomic set e^{i phi} [ 1, e^{2 pi i f}, e^{4 pi i f}, … e^{2 (n – 1) pi i f}]^T for phi in [0, 2 pi) and f in [0, 1).
I am suspecting that only the real parts of the first three components of the vector is plotted for different phi values but that is not quite it.
I would be grateful if someone could identify what exactly is plotted and how to achieve the colouring on the surface.
MWE
documentclass[tikz]{standalone}
usepackage{pgfplots}
begin{document}
begin{tikzpicture}
begin{axis}[grid = major, view={-30}{30}]
addplot3[variable=t,samples = 60,domain=0:1]
({cos(2 * pi * deg(t))},{cos(4 * pi * deg(t))}, {cos(6 * pi * deg(t))});
end{axis}
end{tikzpicture}
end{document}
One Answer
As @Symbol 1 said, It seems that the plot corresponds to the real part of three successive elements + the convex hull.
I've tried it in Matlab and the closest graph corresponds to [cos(2*pi*f+phi),cos(4*pi*f+phi),cos(6*pi*f+phi)] and phi=pi/2 and f in [0,1]
Here is the result:
This is generated by the following Matlab code:
f=0:0.01:1;
phi=pi/2;
xx=cos(2*pi*f+phi);
yy=cos(4*pi*f+phi);
zz=cos(6*pi*f+phi);
[k1] = convhull(xx,yy,zz);
trimesh(k1,xx,yy,zz)
hold on
plot3(cos(2*pi*f+phi),cos(4*pi*f+phi),cos(6*pi*f+phi),'r','linewidth',2)
with Jet colormap option.
You can use matlab2tikz to get the LaTeX code and you can plot it using pgfplots package. Here is my attempt:
I've modified the Latex code:
- removed the plot of the three elements (red curve in the previous illustration)
- Changed opacity from 1 to 0.95.
Here is the LaTeX main file:
documentclass[border=0.2cm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.11}
begin{document}
input{atomicSet}
end{document}
and the illustration file, named atomicSet.tex:
begin{tikzpicture}
begin{axis}[%
width=3.743in,
height=2.983in,
scale only axis,
colormap/jet,
xmin=-1,
xmax=1,
ymin=-1,
ymax=1,
zmin=-1,
zmax=1,
view={-37.5}{30},
grid,
]
addplot3[area legend,opacity=0.95, table/row sep=crcr, patch, shader=flat corner, fill=white, patch table with point meta={%
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}]
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};
end{axis}
end{tikzpicture}%
Correct answer by LaTeXdraw-com on April 19, 2021
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