自定义颜色混合的表面图：n 维色彩图

Question

常规的 pgfplots-colormap 是一维的。它需要一个元值并推断相应的颜色。但是，我有三个元值，而不是一个元值，每个元值都与一个值相关联。

为了简单起见，我们假设三个元值（，，n1）始终为正数且总和为 1，则颜色混合规则很简单：。n2n3color = n1 * color1 + n2 * color2 + n3 * color3

给定这个元数据（来自表格），我想用适当混合的颜色为网格着色。

基于这个问题我已经弄清楚可以明确提供 RGB 值。但我无法正确得出公式。特别是，我不知道如何访问已定义颜色的 RBG 值。

下面的代码说明了这个问题：

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7}

\begin{document}

\definecolor{color1}{red}
\definecolor{color2}{cyan}
\definecolor{color3}{yellow}

\begin{tikzpicture}
  \begin{axis}
  \addplot3[surf, mesh/color input=explicit mathparse,
            point meta/symbolic={\thisrow{n1}, \thisrow{n2}, \thisrow{n3} } % problematic line
            % how do I mix the colors here so that color = n1 * color1 + n2 * color2 + n3 * color3?
           ] table[] {data.csv};
  \end{axis}
\end{tikzpicture}

\end{document}

数据文件data.csv包含如下内容：

x,y,z,n1,n2,n3
-1.0,-1.0,0,0.243910357114819,0.2666555209251139,0.4894341219600671
-0.5,-1.0,0,0.3013791690628364,0.2152633649632925,0.48335746597387114
0.0,-1.0,0,0.5021192190297844,0.16757485484227622,0.3303059261279394
0.5,-1.0,0,0.5979647407883067,0.14009437103777442,0.2619408881739188

-1.0,-0.5,0,0.164292920913273,0.2655366172800358,0.5701704618066912
-0.5,-0.5,0,0.1355599513531367,0.2040615139888475,0.6603785346580158
0.0,-0.5,0,0.4083574985065873,0.2049743531246625,0.3866681483687502
0.5,-0.5,0,0.4880958726415202,0.2436859445670927,0.2682181827913871

-1.0,0.0,0,0.13994145285914186,0.26041474337409753,0.5996438037667606
-0.5,0.0,0,0.08883801351075463,0.19202791600642005,0.7191340704828253
0.0,0.0,0,0.1290235911491401,0.22620482004695425,0.6447715888039056
0.5,0.0,0,0.1901399752789048,0.49178772678672855,0.31807229793436664

-1.0,0.5,0,0.15879820629696065,0.2619254086260544,0.579276385076985
-0.5,0.5,0,0.11257406503995221,0.18855240164294096,0.6988735333171068
0.0,0.5,0,0.09915126016628552,0.243518553933322,0.6573301859003925
0.5,0.5,0,0.0914288508897056,0.5882997108532986,0.3202714382569958

Answer 1

欢迎来到 TeX.SE！这是我对这个有趣问题的解决方案：

\begin{filecontents*}{my-data.csv}
x   y   z   n1  n2  n3
0.0 0.0 0.0 0.0 0.0 0.0
1.0 0.0 0.0 1.0 0.0 0.0

0.0 1.0 0.0 0.0 1.0 0.0
1.0 1.0 1.0 0.0 0.0 1.0
\end{filecontents*}

\documentclass[tikz, border=2mm]{standalone}
\usepackage{xparse}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat=1.16}

% Each point of the plot will be assigned a color which is a mix of these
% three colors according to the weights given by columns n1, n2 and n3 of the
% data point, respectively.
\definecolor{color1}{rgb}{0.1,1.0,0.5}
\definecolor{color2}{rgb}{0.6,0.2,1.0}
\definecolor{color3}{rgb}{1.0,0.6,0.3}

% Extract the color components into 9 macros so that accessing each component
% when drawing the plot is as fast as possible. The target control sequences
% are \color<num>r, \color<num>g and \color<num>b where <num> is I, II or III
% (corresponding to the three colors 'color1', 'color2' and 'color3').
\ExplSyntaxOn
\int_new:N \l__minze_color_index_int
\seq_new:N \l__minze_color_components_seq

\clist_map_inline:nn { color1, color2, color3 }
  {
    \int_incr:N \l__minze_color_index_int
    \extractcolorspecs {#1} { \l_tmpa_tl } { \l_tmpb_tl }
    \seq_set_split:NnV \l__minze_color_components_seq { , } \l_tmpb_tl

    \clist_map_inline:nn { r, g, b }
      {
        \seq_pop_left:NN \l__minze_color_components_seq \l_tmpa_tl
        \cs_new_nopar:cpx
          { color \int_to_Roman:n { \l__minze_color_index_int } ##1 }
          { \tl_use:N \l_tmpa_tl }
      }
  }
\ExplSyntaxOff

\begin{document}

\begin{tikzpicture}[font=\scriptsize]
\begin{axis}[xlabel=$x$, ylabel=$y$, zlabel=$z$, z label style={rotate=-90}]
  \addplot3 [
    surf, mesh/color input=explicit mathparse,
    patch type=bilinear, shader=interp,
    point meta/symbolic={
      (\thisrow{n1}*\colorIr + \thisrow{n2}*\colorIIr + \thisrow{n3}*\colorIIIr)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3}),
      (\thisrow{n1}*\colorIg + \thisrow{n2}*\colorIIg + \thisrow{n3}*\colorIIIg)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3}),
      (\thisrow{n1}*\colorIb + \thisrow{n2}*\colorIIb + \thisrow{n3}*\colorIIIb)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3})
    },
    ] table[x=x, y=y, z=z] {my-data.csv};

  % Color legend
  \begin{scope}[nodes={minimum width=0.5cm, minimum height=0.25cm,
                       inner sep=0, draw=black, right, label distance=2mm}]
    \coordinate (p) at (rel axis cs:0.3,0.5,1.1);
    \path (p)
      node[fill=color1, label=right:{color 1}] (node 1) {}
      ++(axis direction cs:0,0,-0.15)
      node[fill=color2, label=right:{color 2}] (node 2) {}
      ++(axis direction cs:0,0,-0.15)
      node[fill=color3, label=right:{color 3}] (node 3) {};
  \end{scope}
\end{axis}
\end{tikzpicture}

\end{document}

这符合来自文件的输入数据my-data.csv：

• (0,0,0) 处的点有 (n ₁ , n ₂ , n ₃ ) = (0,0,0) → 黑色；

• (1,0,0) 处的点具有 (n ₁ , n ₂ , n ₃ ) = (1,0,0) → 自定义颜色color1；

• (0,1,0) 处的点有 (n ₁ , n ₂ , n ₃ ) = (0,1,0) → 自定义颜色color2；

• 位于 (1,1,1) 处的点具有 (n ₁ , n ₂ , n ₃ ) = (0,0,1) → 自定义颜色color3。

网格的每个点都被分配一种颜色，该颜色是颜色的混合color1，color2和根据数据点color3分别由n1、n2和列给出的权重。n3

不需要确保 n1 + n2 + n3 = 1，因为我的代码在适当的地方除以 n1 + n2 + n3。

如果我们获取经过修改的您的数据文件是坐标（你们的坐标都是相等的），在调用的选项col sep=comma中使用，并在选项中（因为这次，我在轴外绘制了图例，我不希望它被剪掉），我们得到：table\addplot3 [...] table[...]clip=falseaxis

\begin{filecontents*}{data.csv}
x,y,z,n1,n2,n3
-1.0,-1.0,0,0.243910357114819,0.2666555209251139,0.4894341219600671
-0.5,-1.0,0,0.3013791690628364,0.2152633649632925,0.48335746597387114
0.0,-1.0,0,0.5021192190297844,0.16757485484227622,0.3303059261279394
0.5,-1.0,0,0.5979647407883067,0.14009437103777442,0.2619408881739188

-1.0,-0.5,0.2,0.164292920913273,0.2655366172800358,0.5701704618066912
-0.5,-0.5,0.2,0.1355599513531367,0.2040615139888475,0.6603785346580158
0.0,-0.5,0.2,0.4083574985065873,0.2049743531246625,0.3866681483687502
0.5,-0.5,0.2,0.4880958726415202,0.2436859445670927,0.2682181827913871

-1.0,0.0,0.9,0.13994145285914186,0.26041474337409753,0.5996438037667606
-0.5,0.0,0.9,0.08883801351075463,0.19202791600642005,0.7191340704828253
0.0,0.0,0.9,0.1290235911491401,0.22620482004695425,0.6447715888039056
0.5,0.0,0.9,0.1901399752789048,0.49178772678672855,0.31807229793436664

-1.0,0.5,1.2,0.15879820629696065,0.2619254086260544,0.579276385076985
-0.5,0.5,1.6,0.11257406503995221,0.18855240164294096,0.6988735333171068
0.0,0.5,1.6,0.09915126016628552,0.243518553933322,0.6573301859003925
0.5,0.5,1.4,0.0914288508897056,0.5882997108532986,0.3202714382569958
\end{filecontents*}

\documentclass[tikz, border=2mm]{standalone}
\usepackage{xparse}
\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat=1.16}

% Each point of the plot will be assigned a color which is a mix of these
% three colors according to the weights given by columns n1, n2 and n3 of the
% data point, respectively.
\definecolor{color1}{rgb}{0.1,1.0,0.5}
\definecolor{color2}{rgb}{0.6,0.2,1.0}
\definecolor{color3}{rgb}{1.0,0.6,0.3}

% Extract the color components into 9 macros so that accessing each component
% when drawing the plot is as fast as possible. The target control sequences
% are \color<num>r, \color<num>g and \color<num>b where <num> is I, II or III
% (corresponding to the three colors 'color1', 'color2' and 'color3').
\ExplSyntaxOn
\int_new:N \l__minze_color_index_int
\seq_new:N \l__minze_color_components_seq

\clist_map_inline:nn { color1, color2, color3 }
  {
    \int_incr:N \l__minze_color_index_int
    \extractcolorspecs {#1} { \l_tmpa_tl } { \l_tmpb_tl }
    \seq_set_split:NnV \l__minze_color_components_seq { , } \l_tmpb_tl

    \clist_map_inline:nn { r, g, b }
      {
        \seq_pop_left:NN \l__minze_color_components_seq \l_tmpa_tl
        \cs_new_nopar:cpx
          { color \int_to_Roman:n { \l__minze_color_index_int } ##1 }
          { \tl_use:N \l_tmpa_tl }
      }
  }
\ExplSyntaxOff

\begin{document}

\begin{tikzpicture}[font=\scriptsize]
\begin{axis}[xlabel=$x$, ylabel=$y$, zlabel=$z$, z label style={rotate=-90},
             clip=false]
  \addplot3 [
    surf, mesh/color input=explicit mathparse,
    patch type=bilinear, shader=interp,
    point meta/symbolic={
      (\thisrow{n1}*\colorIr + \thisrow{n2}*\colorIIr + \thisrow{n3}*\colorIIIr)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3}),
      (\thisrow{n1}*\colorIg + \thisrow{n2}*\colorIIg + \thisrow{n3}*\colorIIIg)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3}),
      (\thisrow{n1}*\colorIb + \thisrow{n2}*\colorIIb + \thisrow{n3}*\colorIIIb)
        / (\thisrow{n1} + \thisrow{n2} + \thisrow{n3})
    },
    ] table[x=x, y=y, z=z, col sep=comma] {data.csv};

  % Color legend
  \begin{scope}[nodes={minimum width=0.5cm, minimum height=0.25cm,
                       inner sep=0, draw=black, right, label distance=2mm}]
    \coordinate (p) at (rel axis cs:-0.4,0.5,1.1);
    \path (p)
      node[fill=color1, label=right:{color 1}] (node 1) {}
      ++(axis direction cs:0,0,-0.15)
      node[fill=color2, label=right:{color 2}] (node 2) {}
      ++(axis direction cs:0,0,-0.15)
      node[fill=color3, label=right:{color 3}] (node 3) {};
  \end{scope}
\end{axis}
\end{tikzpicture}

\end{document}