如何改变矩形区域外表面的不透明度？

Question

我做了以下简单的 MWE 来解释约束函数：

\begin{tikzpicture}‎‎[scale=1]
‎\begin{axis}[xlabel=$x$‎, ‎ylabel=$y$‎, ‎zlabel={$z$}]‎‎
 \addplot3 ‎[‎‎surf‎, ‎samples=20‎, ‎domain=-4:4 ‎,‎‎color=gray!20,z buffer=auto] {4-x^2-y^2‎};‎‎
  \addplot3 [variable=t,domain=-2:2,black‎, ‎very thick‎, ‎samples y=0‎, ‎smooth]    ({t},{2},{-t^2});‎‎
  ‎\addplot3 [variable=t,domain=-2:2,black‎, ‎very thick‎, ‎samples y=0‎, ‎smooth] ({t},{-2},{-t^2});‎‎
  ‎\addplot3 [variable=t,domain=-2:2,black‎, ‎very thick‎, ‎samples y=0‎, ‎smooth] ({2},{t},{-t^2});‎‎
\addplot3 [variable=t,domain=-2:2,black‎, ‎very thick‎, ‎samples y=0‎, ‎smooth] ({-2},{t},{-t^2});‎
\end{axis}‎
‎\end{tikzpicture}‎‎‏‎‏‎

我的问题是：我们能否改变表面上矩形外区域的透明度，使其稍微淡化，以便我们可以通过集中矩形区域来解释约束函数？我不想删除整个形状。谢谢。

Answer 1

答案是肯定的。如果你将样本从 20 增加到 21，这很简单。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[scale=1]
\begin{axis}[xlabel=$x$, ylabel=$y$, zlabel={$z$}]
 \addplot3 [surf, samples=21, domain=-4:4 ,color=gray!20,z
 buffer=auto,opacity=0.3] {4-x^2-y^2};
 \addplot3 [surf, samples=20, domain=-2:2 ,color=gray!20,z buffer=auto,
 samples=11,samples y=11] {4-x^2-y^2};
%   \addplot3 [variable=t,domain=-2:2,black, very thick, samples y=0, smooth]    ({t},{2},{-t^2});
%   \addplot3 [variable=t,domain=-2:2,black, very thick, samples y=0, smooth] ({t},{-2},{-t^2});
%   \addplot3 [variable=t,domain=-2:2,black, very thick, samples y=0, smooth] ({2},{t},{-t^2});
%   \addplot3 [variable=t,domain=-2:2,black, very thick, samples y=0, smooth] ({-2},{t},{-t^2});
\end{axis}
\end{tikzpicture}
\end{document}