我有两张类似的图像，其中绘制了抛物面及其轮廓。
我曾经尝试过的是下面的代码，与图中有很大不同。
\documentclass{standalone}
\usepackage{tikz, tikz-3dplot}
\usetikzlibrary{arrows.meta}
\tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
\begin{document}
\tdplotsetmaincoords{120}{-25}
\begin{tikzpicture}[tdplot_main_coords]
\draw [thick] (0,0,0) -- (4,0,0) node {y} (0,0,0) -- (0,4,0) node {x} (0,0,0) -- (0,0,10) node {z};
\tdplotsetrotatedcoords{0}{0}{-25}
\draw [red, thick, tdplot_rotated_coords] (0,0,0) -- (4,0,0) node {y} (0,0,0) -- (0,4,0) node {x} (0,0,0) -- (0,0,10) node {z};
\fill [cyan, tdplot_rotated_coords, canvas is xy plane at z=0, opacity=0.67] (0,0) circle [radius=3];
\fill [cyan, tdplot_rotated_coords, canvas is xz plane at y=0, opacity=0.67] plot [variable=\x, domain=-3:3, samples=50] ({\x},{9-\x*\x});
\foreach \r in {1,2,3}
\draw [red, very thick, canvas is xy plane at z=0] (0,0) circle [radius=\r];
\node [below] at (0,3,0) {10};
\node [below] at (3,0,0) {10};
\node [left] at (0,0,9) {100};
\begin{scope}
\clip [canvas is xy plane at z=6] (0,0) circle [radius={sqrt(3)}] [reverseclip];
\fill [orange, canvas is xy plane at z=6] (-4,-4) rectangle (4,4);
\end{scope}
\end{tikzpicture}
\end{document}
怎样画出比较逼真的人物？
答案1
为什么不使用pgfplots; 类似的东西：
\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel=$x$, ylabel=$y$, zlabel=$z$,
xmin=-19, xmax=19,
ymin=-19, ymax=19,
zmin=-1, zmax=110,
x={(-0.125cm,-0.05cm)}, y={(0.125cm,-0.05cm)}, z={(0cm,0.05cm)},
axis lines=middle,
every axis x label/.style={ at={(ticklabel* cs:1.05)}, },
every axis y label/.style={ at={(ticklabel* cs:1.05)}, },
every axis z label/.style={ at={(ticklabel* cs:1.05)}, },
]
% Paraboloid
\addplot3[surf,
shader=flat, draw=lightgray, fill=green, ultra thin,
left color=green, right color=green, middle color=green!25,
opacity=0.5, fill opacity=0.5,
data cs=polar, domain=0:360,
y domain=0:10,
restrict z to domain=0:101,
](x, y, 100-y^2);
% Plane
\addplot3[surf, shader=faceted,
color=orange,
opacity=0.01, fill opacity=0.4,
domain=-10:10,
](x,y,75);
% Circle at plane
\addplot3[red, smooth,
domain=0:360, variable=\t
]({5*cos(\t)},{5*sin(\t)},{75});
% Circles at xy-plane
\pgfplotsinvokeforeach{10, 7, 2.5}{%%
\pgfmathsetmacro\Radius{#1}
\addplot3[red, smooth,
%no markers,
%samples=55,% samples y=0,
domain=0:360, variable=\t
]({\Radius*cos(\t)},{\Radius*sin(\t)},{0});
}%%
% Annotations 1/2
\coordinate[label=](A) at ({7*cos(135)},{7*sin(135)},{0});
\coordinate[label=](B) at (8, -8, 75);
\coordinate[label=](C) at (-4, 5, 40);
\coordinate[label=](D) at({5*cos(300)},{5*sin(300)},{75});
\end{axis}
% Annotations 2/2
\draw[semithick] (A) -- +(45:2) node[right, align=left]{
$f(x,y)=51$\\ (a typical\\ level curve in\\ the function's\\ domain)};
\draw[semithick] (B) -- +(135:0.75) node[above, align=left]{
Plane $z=75$};
\draw[semithick] (C) -- +(45:3) node[above]{$z=100-x^2-y^2$};
\draw[semithick] (D) -- +(122:2.5) node[above, align=left, xshift=2cm]{The contour curve $f(x,y)=100-x^2-y^2=75$ \\ is the circle $x^2+y^2=25$ in the plane $z=75$.};
\end{tikzpicture}
\end{document}
答案2
我能够借助adipro 的回答：如何在 TikZ 中绘制抛物面？。
第一个代码：
\documentclass[border=3mm]{standalone}
\usepackage{tikz,amsmath}
\usetikzlibrary{calc, shapes.geometric, arrows.meta}
\begin{document}
\begin{tikzpicture}[xscale=1, yscale=0.50, font=\Large]
\def\a{4};
\draw [red, very thick] (\a,0) circle [radius=\a];
\draw [red, very thick] (\a,0) circle [radius=0.7*\a];
\draw [red, very thick] (\a,0) circle [radius=0.5*\a];
\fill [red] (\a,0) circle [radius=3pt, yscale=2];
\shadedraw [draw=black, thick, left color=green, right color=green, middle color=green!25, opacity=0.33] ({\a-sqrt(\a*\a-1/(\a*\a))},{1/\a}) parabola bend (\a,{\a*\a+1/(\a*\a)}) ({\a+sqrt(\a*\a-1/(\a*\a))},{1/\a}) arc ({asin(1/\a/\a)}:{-180-asin(1/\a/\a)}:\a);
\draw [thick] ($(\a,0)+(4.2,4.2)$) -- ($(\a,0)+(3.57,3.57)$);
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(3.45,3.45)$) -- ($(\a,0)+(-2.80,-2.80)$);
\draw [thick, -Stealth] ($(\a,0)+(-2.85,-2.85)$) -- ($(\a,0)+(-4.5,-4.5)$) node [left=-0.5mm] {$x$};
\draw [thick] ($(\a,0)+(-4.5,4.5)$) -- ($(\a,0)+(-3.575,3.575)$);
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(-3.45,3.45)$) -- ($(\a,0)+(2.8,-2.8)$);
\draw [thick, -Stealth] ($(\a,0)+(2.85,-2.85)$) -- ($(\a,0)+(4,-4)$) node [right=-0.5mm] {$y$};
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(0,-1.5)$) -- ($(\a,0)+(0,\a*\a-1/2)$);
\draw [thick, -Stealth] ($(\a,0)+(0,\a*\a-1/3)$) -- ($(\a,0)+(0,18)$) node [left=-0.5mm] {$z$};
\fill [cyan]($(\a,0)+(0,\a*\a-1/3)$) circle [radius=3pt, yscale=2];
\draw [thick] ($(\a,0)+(-2.85,-2.85)$) -- ++(0pt,15pt);
\node [below=2.5pt] at ($(\a,0)+(-2.85,-2.85)$) {10};
\draw [thick] ($(\a,0)+(2.85,-2.85)$) -- ++(0pt,15pt);
\node [below=2.5pt] at ($(\a,0)+(2.85,-2.85)$) {10};
\draw [semithick] (3.7,-4.1) -- ++(-60:2) node [below] {$f(x,y)=0$};
\draw [semithick] (3.2,1.95) -- ++(109:9) node [above] {$f(x,y)=75$};
\draw [semithick] (6.85,0.4) -- ++(45:2.5) node [right, align=left] {$f(x,y)=51$\\ (a typical\\ level curve in\\ the function's\\ domain)};
\draw [semithick] (5.75,10) -- ++(58:2.5) node [right, align=left] {The surface\\ $z=f(x,y)$\\ \phantom{$-$}$=100-x^2-y^2$\\ is the graph of $f$.};
\draw [semithick] ($(\a,0)+(0,\a*\a-1/3)+(45:4pt)$) -- ++(45:1) node [right] {100};
\end{tikzpicture}
\end{document}
第一个图：
第二段代码：
\documentclass[border=3mm]{standalone}
\usepackage{tikz,amsmath}
\usetikzlibrary{calc,shapes.geometric, arrows.meta}
\begin{document}
\begin{tikzpicture}[xscale=1, yscale=0.50, font=\Large]
\def\a{4};
\pgfmathsetmacro{\b}{0.75*\a*\a}
\draw [red, very thick, dashed, dash pattern=on 5.6pt off 5.6pt] (\a,0) circle [radius=0.5*\a];
\shadedraw [draw=black, thick, left color=green, right color=green, middle color=green!25, opacity=0.33] ({\a-sqrt(\a*\a-1/(\a*\a))},{1/\a}) parabola bend (\a,{\a*\a+1/(\a*\a)}) ({\a+sqrt(\a*\a-1/(\a*\a))},{1/\a}) arc ({asin(1/\a/\a)}:{-180-asin(1/\a/\a)}:\a);
\draw [thick] ($(\a,0)+(4.2,4.2)$) -- ($(\a,0)+(3.57,3.57)$);
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(3.45,3.45)$) -- ($(\a,0)+(-2.80,-2.80)$);
\draw [thick, -Stealth] ($(\a,0)+(-2.85,-2.85)$) -- ($(\a,0)+(-4.5,-4.5)$) node [left=-0.5mm] {$x$};
\draw [thick] ($(\a,0)+(-4.5,4.5)$) -- ($(\a,0)+(-3.575,3.575)$);
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(-3.45,3.45)$) -- ($(\a,0)+(2.8,-2.8)$);
\draw [thick, -Stealth] ($(\a,0)+(2.85,-2.85)$) -- ($(\a,0)+(4,-4)$) node [right=-0.5mm] {$y$};
\draw [thick, dashed, dash pattern=on 5.6pt off 5.6pt] ($(\a,0)+(0,-1.5)$) -- ($(\a,0)+(0,7)$) ($(\a,0)+(0,10.2)$) -- ($(\a,0)+(0,\a*\a-1/2)$);
\draw [thick, -Stealth] ($(\a,0)+(0,\a*\a-1/3)$) -- ($(\a,0)+(0,18)$) node [left=-0.5mm] {$z$};
\draw [thick] ($(\a,0)+(-2.85,-2.85)$) -- ++(0pt,15pt);
\node [below=2.5pt] at ($(\a,0)+(-2.85,-2.85)$) {10};
\draw [thick] ($(\a,0)+(2.85,-2.85)$) -- ++(0pt,15pt);
\node [below=2.5pt] at ($(\a,0)+(2.85,-2.85)$) {10};
\draw [dashed, dash pattern=on 6pt off 6pt] ({\a-sqrt(\a*\a-1/(\a*\a))},{1/\a}) arc ({180-asin(1/\a/\a)}:{asin(1/\a/\a)}:\a);
\fill [orange, opacity=0.50] (-1,11.8) -- ++(5,-5) -- ++(4.7,4.7) -- ++(-5,5) -- cycle;
\draw [red, very thick, dashed, dash pattern=on 5.6pt off 5.6pt] (1.50*\a,0.75*\a*\a) arc [start angle=0, end angle=180, radius=0.50*\a];
\shadedraw [draw=black, thick, left color=green, right color=green, middle color=green!25, opacity=0.10] (1.50*\a,0.75*\a*\a) parabola bend (\a,{\a*\a+1/(\a*\a)}) (0.50*\a,0.75*\a*\a) arc [start angle=180, end angle=360, radius=0.5*\a];
\draw [red, very thick] (0.50*\a,0.75*\a*\a) arc [start angle=180, end angle=360, radius=0.50*\a];
\draw [thick] ($(\a,0)+(0,\a*\a-1/3)$) node [left] {100} -- ++(8pt,0pt);
\draw [thick] ($(\a,0)+(0,\b)$) node [left] {75} -- ++(8pt,0pt);
\draw [semithick] (3.90,-2.2) -- ++(-70:3.4) node [below, align=left] {The level curve $f(x,y)=100-x^2-y^2=75$ \\ is the circle $x^2+y^2=25$ in the $xy$-plane.};
\draw [semithick] (0.8,11.8) -- ++(110:2.75) node [above] {Plane $z=75$};
\draw [semithick] (6.5,6.5) -- ++(75:8) node [above] {$z=100-x^2-y^2$};
\draw [semithick] (3.2,10.3) -- ++(110:9) node [above, align=left] {The contour curve $f(x,y)=100-x^2-y^2=75$ \\ is the circle $x^2+y^2=25$ in the plane $z=75$.};
\end{tikzpicture}
\end{document}
第二幅图：
答案3
画出来inkscape然后导入到LaTeX，可以另存为pstricks图片或者tikz图片代码，Pstricks需要xelatex编译，下面是代码示例tikz。
\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\begin{document}
\definecolor{cb9d9c0}{RGB}{185,217,192}
\definecolor{c8cd9c0}{RGB}{140,217,192}
\definecolor{cfce0a8}{RGB}{252,224,168}
\definecolor{cfce3ab}{RGB}{252,227,171}
\definecolor{cff0000}{RGB}{255,0,0}
\begin{tikzpicture}[y=0.80pt, x=0.80pt, yscale=-1.000000, xscale=1.000000, inner sep=0pt, outer sep=0pt]
\begin{scope}[shift={(-32.01988,-26.65196)},opacity=0.288,transparency group]
\end{scope}
\begin{scope}[shift={(-32.01988,-26.65196)}]
\path[fill=cb9d9c0,line join=miter,line cap=butt,miter limit=4.00,line
width=0.161pt] (104.3783,44.9346) -- (49.2649,138.9067) -- (159.4916,138.9067)
-- cycle;
\path[draw=c8cd9c0,fill=cb9d9c0,line join=miter,line cap=butt,miter
limit=4.00,line width=0.161pt] (49.2649,138.9067) .. controls
(55.2911,98.6213) and (76.9704,67.0133) .. (91.2895,52.2007) .. controls
(96.6722,46.6325) and (102.2947,45.1596) .. (104.3783,44.9346);
\path[draw=c8cd9c0,fill=cb9d9c0,line join=miter,line cap=butt,miter
limit=4.00,line width=0.161pt] (49.2649,138.9067) .. controls
(58.7199,168.1684) and (152.3115,167.5824) .. (159.4916,138.9067);
\path[draw=c8cd9c0,fill=cb9d9c0,line join=miter,line cap=butt,miter
limit=4.00,draw opacity=0.995,line width=0.161pt] (159.4916,138.9067) ..
controls (153.4654,98.6213) and (131.7862,67.0133) .. (117.4670,52.2007) ..
controls (112.0843,46.6325) and (106.4618,45.1596) .. (104.3783,44.9346);
\path[draw=cfce0a8,fill=cfce3ab,line join=miter,line cap=butt,miter
limit=4.00,line width=0.161pt] (36.7438,83.6156) -- (92.7460,38.6360) --
(172.5715,58.7257) -- (124.3918,108.5056) -- cycle;
\path[draw=cff0000,dash pattern=on 0.16pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (76.0343,71.7930) .. controls
(86.5965,56.6895) and (120.4663,55.4382) .. (133.1032,71.6210);
\path[draw=cff0000,line join=miter,line cap=butt,miter limit=4.00,line
width=0.161pt] (76.0343,71.7930) .. controls (86.5965,86.8966) and
(124.1064,87.3077) .. (133.1032,71.9650);
\path[draw=black,dash pattern=on 0.16pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (49.2649,138.9067) .. controls
(72.2488,103.0780) and (141.8639,108.1076) .. (159.4916,138.9067);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,line
width=0.161pt] (32.1214,118.6394) -- (51.3222,123.9728);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,line
width=0.161pt] (152.1262,150.2850) -- (180.5718,157.5742);
\path[draw=black,dash pattern=on 0.32pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (53.1718,124.5209) --
(149.6879,149.5062);
\path[draw=black,dash pattern=on 0.32pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (126.3474,117.5727) --
(85.0569,157.9742);
\path[draw=black,line join=miter,line cap=butt,miter limit=4.00,line
width=0.161pt] (83.5944,159.4376) -- (66.6117,176.7750);
\path[draw=black,dash pattern=on 0.32pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (104.8398,137.5323) --
(104.8807,102.9054);
\path[draw=black,dash pattern=on 0.32pt off 0.16pt,line join=miter,line
cap=butt,miter limit=4.00,line width=0.161pt] (104.8398,82.5955) --
(104.7882,50.4248);
\path[draw=c8cd9c0,line join=miter,line cap=butt,miter limit=4.00,draw
opacity=0.996,line width=0.161pt] (76.0343,71.7930) .. controls
(83.3359,60.7691) and (96.9122,44.7693) .. (104.3783,44.9346) .. controls
(113.5053,44.7411) and (123.7077,57.8811) .. (133.1032,71.6210);
\path[draw=c8cd9c0,fill=cb9d9c0,line join=round,line cap=rect,miter
limit=4.00,line width=0.003pt] (102.3095,82.7912) .. controls
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(77.2516,70.8308) .. (77.4326,70.6418) .. controls (77.6135,70.4523) and
(77.7432,70.2498) .. (77.7205,70.1912) .. controls (77.6636,70.0433) and
(78.0237,69.6065) .. (78.1597,69.6587) .. controls (78.2211,69.6815) and
(78.3855,69.5819) .. (78.5255,69.4357) .. controls (78.7348,69.2172) and
(78.7604,69.1467) .. (78.6700,69.0375) .. controls (78.5573,68.9015) and
(78.5898,68.7928) .. (78.8259,68.5180) .. controls (78.9544,68.3684) and
(78.9698,68.3696) .. (79.1513,68.5408) -- (79.3419,68.7200) --
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(111.5148,47.1648) .. (114.7327,49.8270) .. controls (118.7826,53.1774) and
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(109.0192,82.7643) .. controls (107.8932,82.8457) and (103.5189,82.8645) ..
(102.3078,82.7928) -- cycle(105.2430,81.8750) -- (105.2430,81.0749) --
(104.8430,81.0749) -- (104.4431,81.0749) -- (104.4431,81.8750) --
(104.4431,82.6750) -- (104.8430,82.6750) -- (105.2430,82.6750) --
cycle(105.2430,79.5638) -- (105.2430,78.7637) -- (104.8430,78.7637) --
(104.4431,78.7637) -- (104.4431,79.5638) -- (104.4431,80.3638) --
(104.8430,80.3638) -- (105.2430,80.3638) -- cycle(105.2430,77.2526) --
(105.2430,76.4525) -- (104.8430,76.4525) -- (104.4431,76.4525) --
(104.4431,77.2526) -- (104.4431,78.0526) -- (104.8430,78.0526) --
(105.2430,78.0526) -- cycle(105.2430,75.0303) -- (105.2430,74.2303) --
(104.8430,74.2303) -- (104.4431,74.2303) -- (104.4431,75.0303) --
(104.4431,75.8303) -- (104.8430,75.8303) -- (105.2430,75.8303) --
cycle(105.2430,72.7191) -- (105.2430,71.9191) -- (104.8430,71.9191) --
(104.4431,71.9191) -- (104.4431,72.7191) -- (104.4431,73.5191) --
(104.8430,73.5191) -- (105.2430,73.5191) -- cycle(105.2259,70.4745) --
(105.2543,69.6967) -- (104.8509,69.6967) -- (104.4476,69.6967) --
(104.4476,70.5018) -- (104.4476,71.3070) -- (104.8253,71.2786) --
(105.2031,71.2501) -- cycle(105.2430,68.1807) -- (105.2430,67.3758) --
(104.8209,67.4042) -- (104.3987,67.4327) -- (104.3703,68.0911) .. controls
(104.3532,68.4529) and (104.3643,68.8032) .. (104.3874,68.8689) .. controls
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