为什么设置点元数据会破坏轮廓lua中的数据？

Question

问题

contour lua我正在尝试通过设置 来更改轮廓图 ( ) 的颜色point meta。但是，我不想使用图中的信息，而是想使用另一个函数来为它们着色。在我的例子中，我使用一条线来定义颜色，这样一边应该是一种颜色，另一边应该是另一种颜色。

但是，当我设置时，point meta={y>discriminant?.5:-.5}轮廓图被破坏了。我通过强制颜色的阶跃函数来解决这个问题，但在中间出现了一些错误，因为它最终没有定义（参见白色轮廓）。

问题

• 为什么当我设置时轮廓图被破坏了point meta？那不应该只改变颜色吗？
• 有没有更好的方法来使用函数（如本surf例所示）来为轮廓图着色，而不是改变colormap？（见下面的例子）。

平均能量损失

高斯数据的原始问题

% !TeX program=lualatex
\documentclass{standalone}
\usepackage[dvipsnames]{xcolor}
\usepackage{pgfplots}

\begin{document}
  
\pgfplotsset{
  compat=1.18,
  colormap={bluewhiteorange}{color(0cm)=(NavyBlue); color(0.5cm)=(white); color(1cm)=(BurntOrange)},
  colormap={stepblueorange}{color(0cm)=(NavyBlue); color(.4999cm)=(NavyBlue); color(0.5cm)=(white); color(0.5001cm)=(BurntOrange); color(1cm)=(BurntOrange)},
}

\begin{tikzpicture}[
  declare function={
    mu11=.2;
    mu12=.25;
    sigma11=.35;
    sigma12=.35;
    mu21=-.1;
    mu22=-.1;
    sigma21=.35;
    sigma22=.35;
    rho1=0.0;
    rho2=0.0;
    % functions
    bivar(\ma,\sa,\mb,\sb,\rho)=1/(2*pi*\sa*\sb*sqrt(1-\rho*\rho)) * exp(-((x-\ma)^2/\sa^2 + (y-\mb)^2/\sb^2 - (2*\rho*(x-\ma)*(y-\mb))/(\sa*\sb)))/(2*(1-\rho*\rho));
    twogauss=max(bivar(mu11,sigma11,mu12,sigma12,rho1), bivar(mu21,sigma21,mu22,sigma22,rho2));
    % hyperplane
    line(\m,\b)=\m*x + \b;
    slope=-(mu21-mu11)/(mu22-mu12);
    intercept=(mu12+mu22)/2-slope*(mu11+mu21)/2;
    discriminant=line(slope, intercept);
  },
]
  \begin{axis}[
    width=15cm,
    view={60}{45},
    enlargelimits=false,
    grid=major,
    domain=-1:1,
    y domain=-1:1,
    samples=50,
    xlabel=$x_1$,
    ylabel=$x_2$,
    zlabel={$P$},
  ]
    \addplot3 [
      surf,
      colormap name={bluewhiteorange},
      point meta={(
        bivar(mu11,sigma11,mu12,sigma12,rho1)>
        bivar(mu21,sigma21,mu22,sigma22,rho2)?
        bivar(mu11,sigma11,mu12,sigma12,rho1):
        -bivar(mu21,sigma21,mu22,sigma22,rho2)
        )},
      % this works on the surf, but not on the contours
      % point meta={y>discriminant?.5:-.5},
    ] {twogauss};
    
    % work around with a semi step function (but it inserts spurious white contours at the middle)
    \addplot3 [
      contour lua={
        number=15,
        labels=false,
      },
      colormap name={stepblueorange},
      point meta={(
          bivar(mu11,sigma11,mu12,sigma12,rho1)>
          bivar(mu21,sigma21,mu22,sigma22,rho2)?
          bivar(mu11,sigma11,mu12,sigma12,rho1):
          -bivar(mu21,sigma21,mu22,sigma22,rho2)
      )},
      z filter/.code={\def\pgfmathresult{.8}},
    ] {twogauss};
    
    % this collapses the contour into the boundary
    \addplot3 [
      contour lua={
        number=15,
        labels=false,
      },
      colormap name={bluewhiteorange},
      point meta={y>discriminant?.5:-.5},
      z filter/.code={\def\pgfmathresult{1}},
    ] {twogauss};
  
  \end{axis}
\end{tikzpicture}
\end{document}

使用更简单的抛物面并仅编译轮廓的示例。

% !TeX program=lualatex
\documentclass{standalone}
\usepackage[dvipsnames]{xcolor}
\usepackage{pgfplots}
 \pgfplotsset{
  compat=1.18,
  colormap={bluewhiteorange}{color(0cm)=(NavyBlue); color(0.5cm)=(white); color(1cm)=(BurntOrange)},
  colormap={stepblueorange}{color(0cm)=(NavyBlue); color(.4999cm)=(NavyBlue); color(0.5cm)=(white); color(0.5001cm)=(BurntOrange); color(1cm)=(BurntOrange)},
}

\begin{document}
  \begin{tikzpicture}[
    declare function={
      % center
      pc11=1;
      pc12=1;
      % center
      pc21=-2;
      pc22=-2;
      % functions
      parb(\cx,\cy)=-(x-\cx)^2-(y-\cy)^2;
      twoparb=max(parb(pc11,pc12), parb(pc21,pc22));
      % hyperplane
      line(\m,\b)=\m*x + \b;
      slope=-(pc21-pc11)/(pc22-pc12);
      intercept=(pc12+pc22)/2-slope*(pc11+pc21)/2;
      discriminant=line(slope, intercept);
    },
    ]
    \begin{axis}[
      width=15cm,
      view={60}{45},
      domain=-5:5,
    ]

    % This one plots the 3D surfaces
%    \addplot3 [
%      surf,
%      samples=10,
%      colormap name={bluewhiteorange},
%      point meta={y>discriminant?.5:-.5},
%    ] {twoparb};
      
    \addplot3 [
      contour lua={
        number=6,
        labels=false,
      },
      colormap name={stepblueorange},
      % this shows the contours with the spurious boundaries in the middle
%      point meta={(
%        parb(pc11,pc12)>
%        parb(pc21,pc22)?
%        parb(pc11,pc12):
%        -parb(pc21,pc22)
%      )},
      % this colors the contours based on the line, but destroyes them
      point meta={y>discriminant?.5:-.5},
      z filter/.code={\def\pgfmathresult{1}},
    ] {twoparb};
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 1

当您更改时point meta，您会更改轮廓所基于的值。就 PGFPlots 而言，轮廓是具有单一样式和颜色的线。

以下是对您要实现的目标的猜测：

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{fadings}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\pgfplotsset{colormap={bluewhiteorange}{color=(blue); color=(white); color=(orange)}}
\tikzset{
declare function={
gauss(\x,\y)=exp(-6*(\x^2+\y^2));
f(\x,\y)=max( gauss(\x-0.3,\y-0.3) , gauss(\x+0.3,\y+0.3) )-1;
}}
\begin{tikzfadingfrompicture}[name=myfading]
\begin{axis}[
axis lines=none,
view={60}{45},
zmin=-1, zmax=1,
]
\addplot3[
contour lua={number=8, labels=false, draw color=transparent!0},
domain=-1:1, samples=50,
z filter/.code={\def\pgfmathresult{.8}},
] {f(x,y)};
\end{axis}
\path (0,0) circle[radius=10]; %encompassing circle for alignment
\end{tikzfadingfrompicture}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
name=graph,
view={60}{45},
zmin=-1, zmax=1,
xlabel=x, ylabel=y, zlabel=z,
]
\addplot3[
surf,
domain=-1:1, samples=50,
point meta={x+y<0?-z-1:z+1},
] {f(x,y)};
\coordinate (a) at (1,-1,0.8);
\coordinate (b) at (-1,1,0.8);
\end{axis}
\fill[path fading=myfading, fit fading=false, blue] (graph.south west) -- (graph.north west) -- (b) -- (a) -- cycle;
\fill[path fading=myfading, fit fading=false, orange] (graph.north east) -- (graph.south east) -- (a) -- (b) -- cycle;
\end{tikzpicture}
\end{document}