我希望在美学上达到与以下效果最接近的效果：
到目前为止我仅能获得：
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
align =center,
title = {\textbf{Six-hump camel back function}\\ ${\scriptsize f(x,y)=\left(4-2.1 x_1^2+\frac{x_1^4}{3}\right) x_1^2+x_1 x_2+\left(-4+4 x_2^2\right) x_2^2}$},
view={310}{30},
xtick = {2,1,...,-2},
ytick = {1,0.5,...,-1},
ztick = {6,5,...,-2},
xmin=-2,
xmax=2,
ymin=-1,
ymax=1,
zmin=-2,
zmax=6,
ticklabel style = {font = \scriptsize},
grid=major,
xlabel=$x$,
ylabel=$y$,
zlabel=$z$
]
%some miminum points
\addplot3[mark=*,red,point meta=explicit symbolic,nodes near coords]
coordinates {(0,0.75,-2)[{\scriptsize A minimum}]};
\addplot3[mark=*,red,point meta=explicit symbolic,nodes near coords]
coordinates {(0,-0.75,-2)[{\scriptsize A minimum}]};
\addplot3 [
surf,
colormap/jet,
shader=faceted,
fill opacity=0.75,
samples=50,
domain=-2:2,
y domain=-1:1
] {(4-2.1*x^2+x^4/3)*x^2+x*y+(-4+4*y^2)*y^2};
\end{axis}
\end{tikzpicture}
\end{document}
得出：
感谢您的帮助
PS：我在 Microsoft Windows 机器上运行 LaTeX
答案1
受到以下答案的启发这个问题，你可以尝试gnuplot：
\documentclass[border=10pt]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
align = center,
title = {
\textbf{Six-hump camel back function} \\
$\scriptsize f(x,y) =
\left(4 - 2.1 x_1^2 + \frac{x_1^4}{3}\right) x_1^2 + x_1
x_2 + \left(-4 + 4 x_2^2\right) x_2^2$
},
view = {310}{30},
xtick = {2,1,...,-2},
ytick = {1,0.5,...,-1},
ztick = {6,5,...,-2},
xmin = -2, xmax = 2,
ymin = -1, ymax = 1,
zmin = -2, zmax = 6,
ticklabel style = {
font = \scriptsize
},
grid = major,
xlabel = $x$,
ylabel = $y$,
zlabel = $z$
]
\addplot3[
mark=*,
red,
draw = none,
point meta = explicit symbolic,
nodes near coords
] coordinates {
(0,0.75,-2) [{\scriptsize A minimum}]
(0,-0.75,-2) [{\scriptsize A minimum}]
};
\addplot3+[
no markers,
raw gnuplot,
z filter/.code={\def\pgfmathresult{-2}},
] gnuplot {
unset surface;
set contour base;
set cntrparam levels 20;
set isosamples 200;
set samples 51;
splot [-2:2][-1:1][-2:6]
(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2;
};
\addplot3[
surf,
colormap/jet,
shader = faceted,
fill opacity = 0.75,
samples = 51,
domain = -2:2,
y domain = -1:1
] {(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2};
\end{axis}
\end{tikzpicture}
\end{document}
着色可以通过以下方式完成contour prepared：
\documentclass[border=10pt]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
align = center,
title = {
\textbf{Six-hump camel back function} \\
$\scriptsize f(x,y) =
\left(4 - 2.1 x_1^2 + \frac{x_1^4}{3}\right) x_1^2 + x_1
x_2 + \left(-4 + 4 x_2^2\right) x_2^2$
},
view = {310}{30},
xtick = {2,1,...,-2},
ytick = {1,0.5,...,-1},
ztick = {6,5,...,-2},
xmin = -2, xmax = 2,
ymin = -1, ymax = 1,
zmin = -2, zmax = 6,
ticklabel style = {
font = \scriptsize
},
grid = major,
xlabel = $x$,
ylabel = $y$,
zlabel = $z$
]
\addplot3[
mark=*,
red,
draw = none,
point meta = explicit symbolic,
nodes near coords
] coordinates {
(0,0.75,-2) [{\scriptsize A minimum}]
(0,-0.75,-2) [{\scriptsize A minimum}]
};
\addplot3+[
contour prepared,
contour/labels = false,
colormap/jet,
point meta = rawz,
no markers,
raw gnuplot,
z filter/.code={\def\pgfmathresult{-2}},
] gnuplot {
unset surface;
set contour base;
set cntrparam levels 20;
set isosamples 200;
splot [-2:2][-1:1][-2:6]
(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2;
};
\addplot3[
surf,
colormap/jet,
shader = faceted,
fill opacity = 0.75,
samples = 51,
domain = -2:2,
y domain = -1:1
] {(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2};
\end{axis}
\end{tikzpicture}
\end{document}
通过添加一些选项，您将获得非常接近原始版本的效果：
\documentclass[border=10pt]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
align = center,
title = {
\textbf{Six-hump camel back function} \\
$\scriptsize f(x,y) =
\left(4 - 2.1 x_1^2 + \frac{x_1^4}{3}\right) x_1^2 + x_1
x_2 + \left(-4 + 4 x_2^2\right) x_2^2$
},
view = {310}{30},
xtick = {2,1,...,-2},
ytick = {1,0.5,...,-1},
ztick = {6,5,...,-2},
xmin = -2, xmax = 2,
ymin = -1, ymax = 1,
zmin = -2, zmax = 6,
ticklabel style = {
font = \scriptsize
},
grid = major,
xlabel = {$x_1$},
ylabel = {$x_2$},
zlabel = {$f(x_1,x_2)$},
axis lines*=left,
tick align=outside,
major grid style={
dotted, gray
}
]
\addplot3[
mark=*,
red,
draw = none,
point meta = explicit symbolic,
nodes near coords
] coordinates {
(0,0.75,-2) [{\scriptsize A minimum}]
(0,-0.75,-2) [{\scriptsize A minimum}]
};
\addplot3+[
contour prepared,
contour/labels = false,
colormap/jet,
point meta = rawz,
no markers,
raw gnuplot,
z filter/.code={\def\pgfmathresult{-2}},
] gnuplot {
unset surface;
set contour base;
set cntrparam levels 20;
set isosamples 200;
splot [-2:2][-1:1][-2:6]
(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2;
};
\addplot3[
surf,
colormap/jet,
shader = flat,
draw = black,
samples = 51,
domain = -2:2,
y domain = -1:1
] {(4 - 2.1*x^2 + x^4/3)*x^2 + x*y + (-4 + 4*y^2)*y^2};
\end{axis}
\end{tikzpicture}
\end{document}
