使用 TikZ 创建更多图形的并集

Question

今天早上我用 Geogebra 创建了这个图形

有两个功能：

f(x)=-2/3 π G ρ (3a² - x²) （绿色抛物线）

g(x)=-4/3 π G ρ (1/x) a³ （蓝色函数）

其中 ρ 是球体的密度，a 是球体的半径，0<=x=r<=a 或 r>=a。r 是一般点的距离。我已经使用 TikZ 导出了代码，但图形不太漂亮。由于tikz更精确，我如何用 TikZ 重新创建以下两个图形（(1) 和 (2)），就像我用 Adob​​e Illustrator 创建的一样？

图 1

图2

问候。

Answer 1

这当然不是一个答案（也是因为我不理解这个问题）。我所做的是，按照 Torbjørn T. 的建议，限制第一个图中的域，并替换 Ti钾Zplot命令\addplot。（Ti 没有问题钾Zplot命令，但由于您无论如何都要加载 pgfplots，因此使用可能更合适\addplot。）我还沿着第二个图的线条画了一些东西，相信您在第一个图中得到的斜率是正确的。

\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.16}
% \usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{ffqqqq}{rgb}{1.,0.,0.}
\definecolor{qqqqff}{rgb}{0.,0.,1.}
\definecolor{qqwuqq}{rgb}{0.,0.39215686274509803,0.}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\begin{axis}[
x=1.0cm,y=1.0cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-2.118707736780596,
xmax=5.255760268305019,
ymin=-4.168187134916317,
ymax=0.14792878906557064,
xtick={-2.0,-1.0,...,5.0},
ytick={-4.0,-3.0,...,0.0},]
\clip(-2.118707736780596,-4.168187134916317) rectangle (5.255760268305019,0.14792878906557064);
% \draw[line width=4.pt] (7.811006812257485,-1.2289916284010438) -- (10.458930692000973,-1.2289916284010438);
% \draw[line width=4.pt] (7.78452757346005,-2.261681941501005) -- (10.432451453203537,-2.261681941501005);
% \draw[line width=4.pt] (7.7977671928587675,-1.7453367849510244) -- (10.445691072602255,-1.7453367849510244);
\addplot[line width=2.pt,color=qqwuqq,smooth,samples=100,domain=-2.118707736780596:1] 
{0-2.0/3.0*3.141592653589793*0.05*10.2*(3.0*1.0^(2.0)-(x)^(2.0))};
\addplot[line width=2.pt,color=qqqqff,smooth,samples=100,domain=1:5.255760268305019] 
{0-4.0/3.0*3.141592653589793*0.05*10.2*1.0/(\x)*1.0^(3.0)};
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt] (1.,-4.168187134916317) -- (1.,0.14792878906557064);
\addplot[line width=2.pt,color=ffqqqq,domain=-2.118707736780596:5.255760268305019] 
{(-4.272566012175239--2.1362830077341797*\x)/1.};
\begin{scriptsize}
\draw[color=black] (9.187927229724098,-0.9178605725311839) node {$a = 1$};
\draw[color=black] (8.062559580833117,-1.9505508856311446) node {$G = 0.05$};
\draw[color=black] (8.76425940896514,-1.4342057290811645) node {$\rho = 10.2$};
\draw[color=qqwuqq] (-1.8539153488062472,-0.7589851397465746) node {$f$};
\draw[color=qqqqff] (0.5027369041654571,-6.518219578188664) node {$g$};
\draw[color=black] (1.2044367322974814,-1.9902697438272972) node {$A$};
\draw[color=ffqqqq] (1.9061365604295057,-0.6001097069619652) node {$i$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}


\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\begin{axis}[
x=1.0cm,y=1.0cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-2.118707736780596,
xmax=5.255760268305019,
ymin=-4.168187134916317,
ymax=0.14792878906557064,
xtick={-2.0,-1.0,...,5.0},
ytick={-4.0,-3.0,...,0.0},]
\clip(-2.118707736780596,-4.168187134916317) rectangle (5.255760268305019,0.14792878906557064);
% \draw[line width=4.pt] (7.811006812257485,-1.2289916284010438) -- (10.458930692000973,-1.2289916284010438);
% \draw[line width=4.pt] (7.78452757346005,-2.261681941501005) -- (10.432451453203537,-2.261681941501005);
% \draw[line width=4.pt] (7.7977671928587675,-1.7453367849510244) -- (10.445691072602255,-1.7453367849510244);
\addplot[line width=2.pt,color=qqqqff,smooth,samples=100,domain=1:5.255760268305019] 
{0-4.0/3.0*3.141592653589793*0.05*10.2*1.0/(\x)*1.0^(3.0)};
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt] (1.,-4.168187134916317) -- (1.,0.14792878906557064);
\addplot[line width=2.pt,color=qqwuqq,domain=-2.118707736780596:1] 
{(-4.272566012175239-2.1362830077341797*(\x-2))/1.};
\begin{scriptsize}
\draw[color=black] (9.187927229724098,-0.9178605725311839) node {$a = 1$};
\draw[color=black] (8.062559580833117,-1.9505508856311446) node {$G = 0.05$};
\draw[color=black] (8.76425940896514,-1.4342057290811645) node {$\rho = 10.2$};
\draw[color=qqwuqq] (-1.8539153488062472,-0.7589851397465746) node {$f$};
\draw[color=qqqqff] (0.5027369041654571,-6.518219578188664) node {$g$};
\draw[color=black] (1.2044367322974814,-1.9902697438272972) node {$A$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}
\end{document}