我想要复制下图。
我不想使用 addplot3 并尝试了以下方法
\begin{tikzpicture}[font=\sffamily,declare function={%
f(\x,\y)=3+0.075*cos(\x*100)*cos(\y*100)-0.035*(\y-5)^2-0.01*(\x-5)^2; % f(x,y) = 3 + 0.075*cos(x*100)*cos(y*100) - 0.035*(y-5)^2 - 0.01*(x-5)^2
\tdplotsetmaincoords{70}{110}
\begin{scope}[tdplot_main_coords]
\draw[-latex] (0,0,0) -- (8,0,0) node[anchor=north] {$x$};
\draw[-latex] (0,0,0) -- (0,8,0) node[anchor=west] {$y$};
\draw[-latex] (0,0,0) -- (0,0,4) node[anchor=south] {$z$};
% draw 2 x Grid
\foreach \a in {3,...,7}
{
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\a},{\b},0);
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\b},{\a},0);
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\a},{\b},{f(\a,\b)});
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\b},{\a},{f(\b,\a)});
}
\fill[black,name path=x0] (5,5,0) circle (1pt) node[anchor=north] {\footnotesize $x_0$};
\coordinate (x0) at (5,5,0);
\draw[densely dashed,red,name path=circle_2D] (x0) circle (1);
\coordinate (z0) at (5,5,{f(5,5)});
\coordinate (z1) at (4,5,{f(4,5)});
\coordinate (z2) at (5,6,{f(5,6)});
\coordinate (z3) at (6,5,{f(6,5)});
\coordinate (z4) at (4,5,{f(4,5)});
\end{scope}
\end{tikzpicture}
使用 XeLatex 编译
但我无法在表面上画圆，有人能帮我吗？提前谢谢了。
答案1
您可以借助f定义表面的函数来实现。投影圆的参数方程为
x=5+cos(x),
y=5+sin(x),
函数 f 将给出z坐标
z=f(x,y)=f(5+cos(x),5+sin(x))
因此，完整的代码可能是：
\documentclass[tikz,border=2mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[font=\sffamily,declare function={%
f(\x,\y)=3+0.075*cos(\x*100)*cos(\y*100)-0.035*(\y-5)^2-0.01*(\x-5)^2; % f(x,y) = 3 + 0.075*cos(x*100)*cos(y*100) - 0.035*(y-5)^2 - 0.01*(x-5)^2
g(\x) = 0.075*(\x-4)^2+4;
h(\x) = 0.02*(\x-4)^3-.2*(\x-4)+4;
t(\x,\y)=f(4,4)-0.05*(\x-4) 0.02*(\y-4);}]
\tdplotsetmaincoords{70}{110}
\begin{scope}[tdplot_main_coords]
\draw[-latex] (0,0,0) -- (8,0,0) node[anchor=north] {$x$};
\draw[-latex] (0,0,0) -- (0,8,0) node[anchor=west] {$y$};
\draw[-latex] (0,0,0) -- (0,0,4) node[anchor=south] {$z$};
% draw 2 x Grid
\foreach \a in {3,...,7}
{
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\a},{\b},0);
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\b},{\a},0);
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\a},{\b},{f(\a,\b)});
\draw[thin,gray] plot[variable=\b,samples=60,smooth,domain=3:7] ({\b},{\a},{f(\b,\a)});
}
% Circle on the surface
\draw[red] plot[samples=60,smooth,domain=0:360] ({5+cos(\x)},{5+sin(\x)},{f(5+cos(\x),5+sin(\x)});
% Points
\fill[black,name path=x0] (5,5,0) circle (1pt) node[anchor=north] {\footnotesize $x_0$};
% \node[circle,fill=myorange,minimum size=6pt,inner sep=0pt] (P) at (2,2){};
\coordinate (x0) at (5,5,0);
\draw[densely dashed,red,name path=circle_2D] (x0) circle (1);
% \fill[red] (5,5,{f(5,5)}) circle (1pt) node[anchor=north east] {};
\coordinate (z0) at (5,5,{f(5,5)});
\coordinate (z1) at (4,5,{f(4,5)});
\coordinate (z2) at (5,6,{f(5,6)});
\coordinate (z3) at (6,5,{f(6,5)});
\coordinate (z4) at (4,5,{f(4,5)});
\end{scope}
\end{tikzpicture}
\end{document}
输出结果如下：
编辑：正如评论中所建议的，我正在向表面添加一些填充。“圆圈”很容易，但网格需要关闭四个plots。
\documentclass[tikz,border=2mm]{standalone}
\usepackage{tikz-3dplot}
\tdplotsetmaincoords{70}{110}
\tikzset{my plot/.style={samples=61,smooth}}
\begin{document}
\begin{tikzpicture}[font=\sffamily,tdplot_main_coords,declare function={%
f(\x,\y)=3+0.075*cos(\x*100)*cos(\y*100)-0.035*(\y-5)^2-0.01*(\x-5)^2;}]
% axes
\draw[-latex] (0,0,0) -- (8,0,0) node[anchor=north] {$x$};
\draw[-latex] (0,0,0) -- (0,8,0) node[anchor=west] {$y$};
\draw[-latex] (0,0,0) -- (0,0,4) node[anchor=south] {$z$};
% grids
\foreach \a in {3,...,7}
{
\draw[thin,gray] plot[my plot,variable=\b,domain=3:7] ({\a},{\b},0);
\draw[thin,gray] plot[my plot,variable=\b,domain=3:7] ({\b},{\a},0);
\draw[thin,gray] plot[my plot,variable=\b,domain=3:7] ({\a},{\b},{f(\a,\b)});
\draw[thin,gray] plot[my plot,variable=\b,domain=3:7] ({\b},{\a},{f(\b,\a)});
}
\fill[gray,fill opacity=0.2] plot[my plot,variable=\b,domain=3:7] (3,{\b},{f(3,\b)}) --
plot[my plot,variable=\a,domain=3:7] ({\a},7,{f(\a,7)}) --
plot[my plot,variable=\b,domain=7:3] (7,{\b},{f(7,\b)}) --
plot[my plot,variable=\a,domain=7:3] ({\a},3,{f(\a,3)});
% Circle on the surface
\draw[red,fill=red,fill opacity=0.2] plot[my plot,domain=0:360] ({5+cos(\x)},{5+sin(\x)},{f(5+cos(\x),5+sin(\x)});
% Point and other circle
\coordinate (x0) at (5,5,0);
\fill (x0) circle (1pt) node[anchor=north] {\footnotesize $x_0$};
\draw[densely dashed,red] (x0) circle (1);
\end{tikzpicture}
\end{document}
