Tikz/Pgf - Surf plot with smooth color transition
3
I am drawing a surf 3d plot in Tikz/Pgf using gnuplot. This surface need to be projected on a plane, which can be achieved by adding another surf plot.
The thing is that the transition between colors, in both surf plots actually is not very smooth, despite using
shader=interp
One possibility is to increase the number of samples however building becomes slow and I cannot exceed 75 samples.
An example code can be found right next
documentclass{standalone}
usepackage{pgfplots}
usepackage{tikz}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf,
samples=51,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(x**2+y**2)};
end{axis}
end{tikzpicture}
end{document}
and the result of this code is the following image
Any idea on how to make a smoother transition from color to color?
tikz-pgf pgfplots 3d gnuplot smooth
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
add a comment |
3
I am drawing a surf 3d plot in Tikz/Pgf using gnuplot. This surface need to be projected on a plane, which can be achieved by adding another surf plot.
The thing is that the transition between colors, in both surf plots actually is not very smooth, despite using
shader=interp
One possibility is to increase the number of samples however building becomes slow and I cannot exceed 75 samples.
An example code can be found right next
documentclass{standalone}
usepackage{pgfplots}
usepackage{tikz}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf,
samples=51,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(x**2+y**2)};
end{axis}
end{tikzpicture}
end{document}
and the result of this code is the following image
Any idea on how to make a smoother transition from color to color?
tikz-pgf pgfplots 3d gnuplot smooth
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
1
With pleasure! No problem!
– Thanos
Feb 24 at 21:00
add a comment |
3
3
3
1
I am drawing a surf 3d plot in Tikz/Pgf using gnuplot. This surface need to be projected on a plane, which can be achieved by adding another surf plot.
The thing is that the transition between colors, in both surf plots actually is not very smooth, despite using
shader=interp
One possibility is to increase the number of samples however building becomes slow and I cannot exceed 75 samples.
An example code can be found right next
documentclass{standalone}
usepackage{pgfplots}
usepackage{tikz}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf,
samples=51,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(x**2+y**2)};
end{axis}
end{tikzpicture}
end{document}
and the result of this code is the following image
Any idea on how to make a smoother transition from color to color?
tikz-pgf pgfplots 3d gnuplot smooth
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
I am drawing a surf 3d plot in Tikz/Pgf using gnuplot. This surface need to be projected on a plane, which can be achieved by adding another surf plot.
The thing is that the transition between colors, in both surf plots actually is not very smooth, despite using
shader=interp
One possibility is to increase the number of samples however building becomes slow and I cannot exceed 75 samples.
An example code can be found right next
documentclass{standalone}
usepackage{pgfplots}
usepackage{tikz}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf,
samples=51,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(x**2+y**2)};
end{axis}
end{tikzpicture}
end{document}
and the result of this code is the following image
Any idea on how to make a smoother transition from color to color?
tikz-pgf pgfplots 3d gnuplot smooth
tikz-pgf pgfplots 3d gnuplot smooth
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
edited Feb 24 at 21:00
Thanos
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
asked Feb 24 at 16:32
ThanosThanos
6,0801454107
6,0801454107
1
With pleasure! No problem!
– Thanos
Feb 24 at 21:00
add a comment |
1
With pleasure! No problem!
– Thanos
Feb 24 at 21:00
1
1
With pleasure! No problem!
– Thanos
Feb 24 at 21:00
With pleasure! No problem!
– Thanos
Feb 24 at 21:00
add a comment |
1 Answer
1
active
oldest
votes
4
If your main concern is the color transitions, then you may want to use a polar plot because the function only depends on the radius and not on the angle. Then you could increase the samples in radial direction while leaving the samples in angular direction comparatively small.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
data cs=polar,
]
addplot3[surf, samples=37,samples y=101,
shader=interp,
z buffer=sort,
%mesh/ordering=y varies,
domain=0:360,
y domain=3.1:0,
]
gnuplot {besj0(y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
As a "side-effect" the wiggles will also disappear as they result from plotting a rotationally symmetric function in cartesian coordinates.
And here is a combination of a cartesian and a polar plot.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf, samples=75,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
data cs=polar,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
answered Feb 24 at 18:44
marmotmarmot
105k4126241
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
|
show 3 more comments
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
If your main concern is the color transitions, then you may want to use a polar plot because the function only depends on the radius and not on the angle. Then you could increase the samples in radial direction while leaving the samples in angular direction comparatively small.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
data cs=polar,
]
addplot3[surf, samples=37,samples y=101,
shader=interp,
z buffer=sort,
%mesh/ordering=y varies,
domain=0:360,
y domain=3.1:0,
]
gnuplot {besj0(y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
As a "side-effect" the wiggles will also disappear as they result from plotting a rotationally symmetric function in cartesian coordinates.
And here is a combination of a cartesian and a polar plot.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf, samples=75,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
data cs=polar,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
answered Feb 24 at 18:44
marmotmarmot
105k4126241
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
|
show 3 more comments
4
If your main concern is the color transitions, then you may want to use a polar plot because the function only depends on the radius and not on the angle. Then you could increase the samples in radial direction while leaving the samples in angular direction comparatively small.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
data cs=polar,
]
addplot3[surf, samples=37,samples y=101,
shader=interp,
z buffer=sort,
%mesh/ordering=y varies,
domain=0:360,
y domain=3.1:0,
]
gnuplot {besj0(y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
As a "side-effect" the wiggles will also disappear as they result from plotting a rotationally symmetric function in cartesian coordinates.
And here is a combination of a cartesian and a polar plot.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf, samples=75,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
data cs=polar,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
answered Feb 24 at 18:44
marmotmarmot
105k4126241
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
|
show 3 more comments
4
4
4
If your main concern is the color transitions, then you may want to use a polar plot because the function only depends on the radius and not on the angle. Then you could increase the samples in radial direction while leaving the samples in angular direction comparatively small.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
data cs=polar,
]
addplot3[surf, samples=37,samples y=101,
shader=interp,
z buffer=sort,
%mesh/ordering=y varies,
domain=0:360,
y domain=3.1:0,
]
gnuplot {besj0(y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
As a "side-effect" the wiggles will also disappear as they result from plotting a rotationally symmetric function in cartesian coordinates.
And here is a combination of a cartesian and a polar plot.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf, samples=75,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
data cs=polar,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
answered Feb 24 at 18:44
marmotmarmot
105k4126241
If your main concern is the color transitions, then you may want to use a polar plot because the function only depends on the radius and not on the angle. Then you could increase the samples in radial direction while leaving the samples in angular direction comparatively small.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
data cs=polar,
]
addplot3[surf, samples=37,samples y=101,
shader=interp,
z buffer=sort,
%mesh/ordering=y varies,
domain=0:360,
y domain=3.1:0,
]
gnuplot {besj0(y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
As a "side-effect" the wiggles will also disappear as they result from plotting a rotationally symmetric function in cartesian coordinates.
And here is a combination of a cartesian and a polar plot.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.16}
usepgfplotslibrary{patchplots}
begin{document}
begin{tikzpicture}
begin{axis} [width=textwidth,
height=textwidth,
ultra thick,
colorbar,
colorbar style={yticklabel style={text width=2.5em,
align=right,
/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1,
},
},
xlabel={$rho_x=k_xr_x$},
ylabel={$rho_y=k_yr_y$},
zlabel={$j_l(rho)$},
3d box,
zmax=2.5,
xmin=-3, xmax=3,
ymin=-3.1, ymax=3.1,
ytick={-3, -2, ..., 3},
grid=major,
grid style={line width=.1pt, draw=gray!30, dashed},
x tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
y tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
z tick label style={/pgf/number format/.cd,
fixed,
fixed zerofill,
precision=1
},
]
addplot3[surf, samples=75,
shader=interp,
mesh/ordering=y varies,
domain=-3:3,
y domain=-3.1:3.1,
]
gnuplot {besj0(x**2+y**2)};
addplot3[surf, samples=36, samples y=101,
shader=interp,
%mesh/ordering=y varies,
domain=0:360,
y domain=0:3.1,
point meta=rawz,
data cs=polar,
z filter/.code={defpgfmathresult{2.5}},
]
gnuplot {besj0(y**2)};
end{axis}
end{tikzpicture}
end{document}
answered Feb 24 at 18:44
marmotmarmot
105k4126241
edited Feb 24 at 19:37
answered Feb 24 at 18:44
marmotmarmot
105k4126241
answered Feb 24 at 18:44
marmotmarmot
105k4126241
answered Feb 24 at 18:44
marmotmarmot
105k4126241
105k4126241
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
|
show 3 more comments
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
Thank you very much for your answer! The point is that in the 3d surface the folding of the function is more prominent, therefore the wiggles are indeed needed! I could however use a polar plot on the projection. Is this possible?
– Thanos
Feb 24 at 18:58
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
@Thanos Yes, but I do not understand what you mean by "folding".
– marmot
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
I mean the wiggles you mentioned in the side-effect.
– Thanos
Feb 24 at 19:00
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@Thanos But aren't the wiggles "unphysical", meaning that the true Bessel function doesn't have them (since they imply an angular dependence, which J0 does not have)?
– marmot
Feb 24 at 19:02
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
@ marmot You are perfectly right. However, I believe that for illustration reasons, someone can better observe the oscillating behaviour.
– Thanos
Feb 24 at 19:07
|
show 3 more comments
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With pleasure! No problem!
– Thanos
Feb 24 at 21:00