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pgfplots 中的表面加填充投影

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pgfplots 中的表面加填充投影

可以用 pgfplots 做这样的事吗？

在此处输入图片描述

它是使用以下 gnuplot 脚本生成的：

set view equal xy
set view 72,32
set xyplane relative 0.2
unset key
unset colorbox
set samples 21
set isosamples 21,21

set multiplot

unset border
unset tics
set contour
splot [-1:1][-1:1] sqrt(x**2+y**2) w pm3d at b

set border 4095
set ztics out
unset contour
set palette gray
splot [-1:1][-1:1] x**2+y**2 w pm3d

unset multiplot

重要的特征是表面，我知道如何单独获取它，以及底部的彩色投影以及轮廓线，我可以在 2D 平面中获取它，但在 3D 中作为平面获取它被证明是困难的。

附加功能是底部平面移动，并且 z 轴只在最左侧轴上刻度（如果它们是水平的就更好了，就像在 gnuplot 中一样）

编辑：快到了：

在此处输入图片描述

\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{width=10cm,compat=1.10}

\begin{document}
\begin{tikzpicture}
\pgfplotsset{set layers}
\begin{axis}[
  domain=-1:1, y domain=-1:1,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  3d box=complete,
  3d box foreground style={major tick length=0pt},
  xtick=\empty, ytick=\empty,
  ztick pos=left, ztick align=outside,
  samples=21, samples y=21,
  shader=flat, z buffer=sort,
]
\addplot3[surf,colormap/blackwhite] {x^2+y^2};
\end{axis}

\begin{axis}[
  domain=-1:1, y domain=-1:1,
  xmin=-1, xmax=1,
  ymin=-1, ymax=1,
  zmin=0, zmax=1,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  axis lines=none,
  samples=21, samples y=21,
  clip=false,
]

% color-mapped plane
\addplot3[surf,
mesh/color input=colormap,
colormap/hot,
point meta={sqrt(x^2+y^2)},
point meta rel=per plot,
point meta min=0, point meta max=1.5,
shader=interp, patch type=bilinear,
update limits=false,
on layer=axis background,
] {-0.2};

% contours (needs --shell-escape)
\addplot3[contour gnuplot={levels={0.01,0,02,0,05,0.1,0.2,0.5,1},labels=false},
contour/draw color=black,
samples=51, samples y=51,
z buffer=default,
z filter/.code={\def\pgfmathresult{-0.2}},
update limits=false,
on layer=axis background,
] {sqrt(x^2+y^2)};

\end{axis}
\end{tikzpicture}
\end{document}

我在一个单独的轴上添加了底部平面，以便能够将其移动一段相对距离（相对于主图的大小）。前景轴上的刻度可以禁用，但后轴上的刻度不能禁用，它们被表面隐藏（顶角除外），但在不同的表面上可见。我还想删除 3D 框中的底线...

答案1

您可以完全移除 3D 框，然后自己绘制它的各个部分。

\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{width=10cm,compat=1.10}

\begin{document}
\begin{tikzpicture}
\pgfplotsset{set layers}
\begin{axis}[
  domain=-1:1, y domain=-1:1,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  axis lines=right,
  %3d box=complete,
  %3d box foreground style={major tick length=0pt},
  xtick=\empty, ytick=\empty,
  ztick pos=left, ztick align=outside,
  samples=21, samples y=21,
  shader=flat, z buffer=sort,
]
\pgfplotsextra{\draw (rel axis cs: 0,1,1) -- (rel axis cs: 0,1,0);}%hidden
\addplot3[surf,colormap/blackwhite] {x^2+y^2};
\pgfplotsextra{\draw (rel axis cs: 1,1,0) -- (rel axis cs: 1,1,1)
  -- (rel axis cs: 1,0,1) -- (rel axis cs: 0,0,1)
  (rel axis cs: 1,0,1) -- (rel axis cs: 1,0,0);}
\end{axis}

\begin{axis}[
  domain=-1:1, y domain=-1:1,
  xmin=-1, xmax=1,
  ymin=-1, ymax=1,
  zmin=0, zmax=1,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  axis lines=none,
  samples=21, samples y=21,
  clip=false,
]

% color-mapped plane
\addplot3[surf,
mesh/color input=colormap,
colormap/hot,
point meta={sqrt(x^2+y^2)},
point meta rel=per plot,
point meta min=0, point meta max=1.5,
shader=interp, patch type=bilinear,
update limits=false,
on layer=axis background,
] {-0.2};

% contours (needs --shell-escape)
\addplot3[contour gnuplot={levels={0.01,0,02,0,05,0.1,0.2,0.5,1},labels=false},
contour/draw color=black,
samples=51, samples y=51,
z buffer=default,
z filter/.code={\def\pgfmathresult{-0.2}},
update limits=false,
on layer=axis background,
] {sqrt(x^2+y^2)};

\end{axis}
\end{tikzpicture}
\end{document}

移除了 3d 框的底部

答案2

我可以称之为决赛：

在此处输入图片描述

由于我是手动绘制方框的，因此我也可以手动绘制刻度（使用一些低级技巧），并避免使用十字。我认为内部颜色很不错，我决定不使用纯基于 z 的颜色作为表面，因为它看起来太“假”（渐变太水平）。

\documentclass{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{width=10cm,compat=1.10}

\newcommand\dist{0.2}
\newcommand\asym{-0.5}

\begin{document}
\begin{tikzpicture}

\begin{axis}[
  domain=-1:1, y domain=-1:1,
  xmin=-1, xmax=1,
  ymin=-1, ymax=1,
  zmin=0, zmax=1,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  axis lines=none,
  axis line style=gray,
  samples=21, samples y=21,
  clip=false,
]

% color-mapped plane
\addplot3[surf,
mesh/color input=colormap,
colormap/hot,
point meta={2*sqrt(x^2+y^2+(\asym*(x^2-y^2)))},
point meta rel=per plot,
point meta min=0, point meta max=3,
shader=interp, patch type=bilinear,
update limits=false,
] {-\dist};

% contours (needs --shell-escape)
\addplot3[contour gnuplot={levels={0.1,0.2,0.5,1,2,5},labels=false},
contour/draw color=black,
% high samples for smoother contours
samples=100, samples y=100,
z buffer=default,
z filter/.code={\def\pgfmathresult{-\dist}},
update limits=false,
] {2*sqrt(x^2+y^2+(\asym*(x^2-y^2)))};

\pgfplotsextra{
\draw[/pgfplots/every outer z axis line]
  (axis cs:-1,-1,-\dist)--(axis cs:1,-1,-\dist)--(axis cs:1,1,-\dist)--(axis cs:-1,1,-\dist)--cycle;
}

\end{axis}

\begin{axis}[
  % x is radius, y is angle
  % with -1<x<1 we plot both surfaces at once,
  % with even samples on x we ensure 0 is skipped,
  % and avoid problems with wrongly-oriented triangles
  domain=-1:1, y domain=0:360,
  samples=30, samples y=37,
  enlargelimits=false,
  view={32}{22},
  z post scale=1.5,
  xtick=\empty, ytick=\empty,
  axis x line=none, axis y line=none,
  ztick pos=left, ztick align=outside,
  major tick length=0pt,
  z tick label style={left=0.15cm,/pgf/number format/.cd,fixed,fixed zerofill,precision=2},
  axis z line*=right,
  axis line style=gray,
  z buffer=sort,
  shader=faceted, faceted color=black,
  % patch sampling for nice curved surface lines (slow)
  patch type=biquadratic, patch type sampling,
  point meta={sqrt(x^2+y^2)},
  colormap={graywhite}{color(0cm)=(black!80) color(1cm)=(white)},
  mesh/interior colormap={bluewhite}{color(0cm)=(blue!50!black!70) color(1cm)=(white)},
  line join=round,
  clip=false,
]

% Manual side and back axes
\pgfplotsextra{
\draw[/pgfplots/every outer z axis line]
  (rel axis cs:0,0,0)--(rel axis cs:0,0,1)--(rel axis cs:0,1,1)--(rel axis cs:1,1,1)--(rel axis cs:1,1,0)
  (rel axis cs:0,1,1)--(rel axis cs:0,1,0);
}

\addplot3[surf,fill opacity=0.9] ({x*cos(y)},{x*sin(y)},{x*sqrt(1+(\asym*cos(2*y)))});

% Manual front axes
\pgfplotsextra{
\draw[/pgfplots/every outer z axis line]
  (rel axis cs:0,0,1)--(rel axis cs:1,0,1)--(rel axis cs:1,1,1)
  (rel axis cs:1,0,1)--(rel axis cs:1,0,0);
}

% Manual tick marks
\makeatletter
\pgfplotsextra{
  \pgfplotslistforeach\pgfplots@prepared@tick@positions@major@z\as\pgfplots@curtickpos{
    \expandafter\pgfplots@prepared@tick@pos@unpack\pgfplots@curtickpos
    % \pgfplots@tick is given in absolute units, luckily we want the ticks at (0,0,z)
    \draw[/pgfplots/every outer z axis line] (0,0,\pgfplots@tick) -- +(180:0.15cm);
  }
}
\makeatother

\end{axis}

\end{tikzpicture}
\end{document}

仅有几个问题：

  • fill opacity不适用于shader=faceted interp。如果可能的话，我甚至会尝试对外部和内部颜色使用不同的不透明度。

  • 我找不到获得平滑轮廓线的方法（除非将采样量增加到合理范围之外）：

    在此处输入图片描述

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