弗拉姆的抛物面图

Question

如何绘制 弗拉姆抛物面？

tikz、pstricks、metapost、渐近线

\documentclass[12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{pgfplots}
\pgfplotsset{compat=newest,width=8cm}

\begin{document}

The spatial curvature of the Schwarzschild solution for $r > r_s$ .....

$w=2\sqrt{r_s(r-r_w)}$

For this exemple: w=z, r_s=y and r=x.

\begin{tikzpicture}
\begin{axis}
\addplot3{2*sqrt(y*(x-y))}; 
\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

我对这个表面，即弗拉姆抛物面不太熟悉，但我会想到类似这样的东西，假设该方程使用圆柱极坐标：

\documentclass[12pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest,width=8cm}

\begin{document}
The spatial curvature of the Schwarzschild solution for $r>r_s\ldots$
\[w=2\sqrt{r_s(r-r_s)}.\]

For this example: $w=z$ and $r_s=1$.
\begin{figure}[ht]\centering
\begin{tikzpicture}
\begin{axis}
\addplot3[surf,domain=1:10,domain y=0:2*pi,samples=31] ({\x*cos(\y r)},{\x*sin(\y r)},{2*sqrt(\x-1)});
\end{axis}
\end{tikzpicture}
\caption{Flamm's paraboloid.}
\end{figure}
\end{document}