如何使用其他颜色创建色轮阴影？

Question

在 pgf 手册中，可以使用 jet-colormap 色轮阴影获得一个圆圈，其内容如下：

\tikz \shade[shading=color wheel] (0,0) circle (1.5);

我怎样才能用另一个颜色图获得相同的效果？这个“其他”颜色图可能需要循环（第一个颜色需要等于最后一个颜色）才能在色轮中工作。但其他解决方案也会受到赞赏。谢谢！

Answer 1

不确定这是否严格回答了问题，但展示了 2、3、4 和 5 色轮的原理。以这种方式扩展到任意数量的颜色有点麻烦，因此可以使用一些（相当曲折的）LaTeX 宏魔法PGF从颜色列表中生成阴影。

的定义\pgfdeclarecolorwheelshading如下所示，但首先是单独的阴影：

\documentclass[tikz,border=5]{standalone}
\begin{document}

\colorlet{col1}{red}
\colorlet{col2}{green}
\colorlet{col3}{blue}
\colorlet{col4}{yellow}
\colorlet{col5}{cyan}

\pgfdeclarefunctionalshading[col1,col2]{2-color-wheel}
{\pgfpoint{-50bp}{-50bp}}{\pgfpoint{50bp}{50bp}}
{
\pgfshadecolortorgb{col1}{\first}\pgfshadecolortorgb{col2}{\second}
}{
  2 copy 
  abs exch abs add 0.0001 ge 
  { atan }                   
  { pop } 
  ifelse
  360 2 div div dup floor dup 3 1 roll neg add dup neg 1 add exch
  2 copy 2 copy 7 -1 roll 
  0 eq
  { 
    \firstred mul exch \secondred mul add
    5 1 roll
    \firstgreen mul exch \secondgreen mul add
    3 1 roll
    \firstblue mul exch \secondblue mul add
  }
  { 
    \secondred mul exch \firstred mul add
    5 1 roll
    \secondgreen mul exch \firstgreen mul add
    3 1 roll
    \secondblue mul exch \firstblue mul add
  }
  ifelse
}


\pgfdeclarefunctionalshading[col1,col2,col3]{3-color-wheel}
{\pgfpoint{-50bp}{-50bp}}{\pgfpoint{50bp}{50bp}}
{
\pgfshadecolortorgb{col1}{\first}\pgfshadecolortorgb{col2}{\second}
\pgfshadecolortorgb{col3}{\third}
}{
  2 copy 
  abs exch abs add 0.0001 ge 
  { atan }                   
  { pop } 
  ifelse
  360 3 div div dup floor dup 3 1 roll neg add dup neg 1 add exch
  2 copy 2 copy 7 -1 roll 
  dup 
  0 eq
  { 
    pop
    \firstred mul exch \thirdred mul add
    5 1 roll
    \firstgreen mul exch \thirdgreen mul add
    3 1 roll
    \firstblue mul exch \thirdblue mul add
  } 
  {
    1 eq
    {
      \secondred mul exch \firstred mul add
      5 1 roll
      \secondgreen mul exch \firstgreen mul add
      3 1 roll
      \secondblue mul exch \firstblue mul add
    }
    {
      \thirdred mul exch \secondred mul add
      5 1 roll
      \thirdgreen mul exch \secondgreen mul add
      3 1 roll
      \thirdblue mul exch \secondblue mul add
    }
    ifelse
  }
  ifelse
}




\pgfdeclarefunctionalshading[col1,col2,col3,col4]{4-color-wheel}
{\pgfpoint{-50bp}{-50bp}}{\pgfpoint{50bp}{50bp}}
{
\pgfshadecolortorgb{col1}{\first}\pgfshadecolortorgb{col2}{\second}
\pgfshadecolortorgb{col3}{\third}\pgfshadecolortorgb{col4}{\fourth}
}{
  2 copy 
  abs exch abs add 0.0001 ge 
  { atan }                   
  { pop } 
  ifelse
  360 4 div div dup floor dup 3 1 roll neg add dup neg 1 add exch
  2 copy 2 copy 7 -1 roll
  dup 
  dup 
  0 eq
  {
    pop pop
    \firstred mul exch \fourthred mul add
      5 1 roll
      \firstgreen mul exch \fourthgreen mul add
      3 1 roll
      \firstblue mul exch \fourthblue mul add
  }
  {
    1 eq
    {
      pop
      \secondred mul exch \firstred mul add
      5 1 roll
      \secondgreen mul exch \firstgreen mul add
      3 1 roll
      \secondblue mul exch \firstblue mul add
    }
    {
      2 eq
      {
        \thirdred mul exch \secondred mul add
      5 1 roll
      \thirdgreen mul exch \secondgreen mul add
      3 1 roll
      \thirdblue mul exch \secondblue mul add
      }
      {
       \fourthred mul exch \thirdred mul add
      5 1 roll
      \fourthgreen mul exch \thirdgreen mul add
      3 1 roll
      \fourthblue mul exch \thirdblue mul add
      } ifelse
    } 
    ifelse
  } 
  ifelse
}



\pgfdeclarefunctionalshading[col1,col2,col3,col4,col5]{5-color-wheel}
{\pgfpoint{-50bp}{-50bp}}{\pgfpoint{50bp}{50bp}}
{
\pgfshadecolortorgb{col1}{\first}\pgfshadecolortorgb{col2}{\second}
\pgfshadecolortorgb{col3}{\third}\pgfshadecolortorgb{col4}{\fourth}
\pgfshadecolortorgb{col5}{\fifth}
}{
  2 copy 
  abs exch abs add 0.0001 ge 
  { atan }                   
  { pop } 
  ifelse
  360 5 div div dup floor dup 3 1 roll neg add dup neg 1 add exch
  2 copy 2 copy 7 -1 roll
  dup 
  dup 
  dup
  0 eq 
  {
    pop pop pop
    \firstred mul exch \fifthred mul add
    5 1 roll
    \firstgreen mul exch \fifthgreen mul add
    3 1 roll
    \firstblue mul exch \fifthblue mul add
  }
  {
    1 eq 
    {
      pop pop
      \secondred mul exch \firstred mul add
      5 1 roll
      \secondgreen mul exch \firstgreen mul add
      3 1 roll
      \secondblue mul exch \firstblue mul add
    }
    {
      2 eq 
      {
        pop
        \thirdred mul exch \secondred mul add
        5 1 roll
        \thirdgreen mul exch \secondgreen mul add
        3 1 roll
        \thirdblue mul exch \secondblue mul add
      }
      {
        3 eq 
        {
          \fourthred mul exch \thirdred mul add
          5 1 roll
          \fourthgreen mul exch \thirdgreen mul add
          3 1 roll
          \fourthblue mul exch \thirdblue mul add
        }
        {
          \fifthred mul exch \fourthred mul add
          5 1 roll
          \fifthgreen mul exch \fourthgreen mul add
          3 1 roll
          \fifthblue mul exch \fourthblue mul add
        }
        ifelse
      }
      ifelse
    }
    ifelse
  }
  ifelse
}




\begin{tikzpicture}[even odd rule]
 \path [shading=2-color-wheel] 
   ( 45:1.5) circle [radius=1] circle [radius=0.5];
 \path [shading=3-color-wheel] 
   (135:1.5) circle [radius=1] circle [radius=0.5];
 \path [shading=4-color-wheel] 
   (225:1.5) circle [radius=1] circle [radius=0.5];
 \path [shading=5-color-wheel] 
   (315:1.5) circle [radius=1] circle [radius=0.5];
\end{tikzpicture}
\end{document}

其次，一个\pgfdeclarecolorwheelshading宏。这个宏有三个参数：阴影的名称、阴影的旋转（颜色列表中的第一个颜色在角度 0）和颜色列表。我思考它运行正常。

\documentclass[tikz,border=5]{standalone}

\makeatletter
\newtoks\pgf@ps@toks
\newcount\c@pgf@ps

\def\pgf@ps@sp{ }

\def\pgf@ps@esettoks#1{\edef\pgf@ps@tmp{#1}\pgf@ps@toks\expandafter{\pgf@ps@tmp}}

\def\pgf@ps@repop#1#2{%
  \c@pgf@countb=#2\relax%
  \def\pgf@ps@op{#1}%
  \def\pgf@ps@ops{}\pgf@ps@@repop}
\def\pgf@ps@@repop{%
  \ifnum\c@pgf@countb<1\relax%
  \else%
    \edef\pgf@ps@ops{\pgf@ps@op\pgf@ps@ops}%
    \advance\c@pgf@countb by-1\relax%
    \expandafter\pgf@ps@@repop%
  \fi%
}

\def\pgf@ps@generate@ps{%
  \c@pgf@counta=\pgf@ps@ncol\relax%
  \c@pgf@countb=\c@pgf@counta%
  \advance\c@pgf@countb by-1\relax%
  \pgf@ps@esettoks{ \noexpand\pgf@ps@interp{col@\the\c@pgf@counta}{col@\the\c@pgf@countb} }%
  \pgfmathloop
  \ifnum\c@pgf@counta<2\relax%
  \else%
    \c@pgf@countb=-\c@pgf@counta%
    \advance\c@pgf@countb by\pgf@ps@ncol\relax%
    \advance\c@pgf@counta by-1\relax%
    \pgf@ps@repop{pop\pgf@ps@sp}{\c@pgf@countb}%
    \c@pgf@countb=\c@pgf@counta%
    \advance\c@pgf@countb by-1\relax%
    \ifnum\c@pgf@countb=0\relax%
      \c@pgf@countb=\pgf@ps@ncol\relax%
    \fi%
    \pgf@ps@esettoks{ \the\c@pgf@counta\pgf@ps@sp eq { \pgf@ps@ops \noexpand\pgf@ps@interp{col@\the\c@pgf@counta}{col@\the\c@pgf@countb} }{ \the\pgf@ps@toks } ifelse}%
  \repeatpgfmathloop%
  \c@pgf@counta=\pgf@ps@ncol\relax%
  \advance\c@pgf@counta by-2\relax%
  \pgf@ps@repop{dup\pgf@ps@sp}{\c@pgf@counta}%
  \pgf@ps@esettoks{ \pgf@ps@ops \the\pgf@ps@toks }%
}

\def\pgf@ps@colorstorgb#1{%
  \c@pgf@ps=1\relax%
  \pgfutil@for\pgf@ps@:={#1}\do{%
     \pgf@ps@coltorgb{\pgf@ps@}{col@\the\c@pgf@ps}%
     \advance\c@pgf@ps by1\relax}%
}

\def\pgf@ps@coltorgb#1#2{%
 \edef\pgf@ps@marshal{\noexpand\pgfshadecolortorgb{#1}}%
 \expandafter\pgf@ps@marshal\expandafter{\csname#2\endcsname}%
}

\def\pgf@ps@rgb#1{\csname#1\endcsname}
\def\pgf@ps@interp#1#2{%
  \pgf@ps@rgb{#1red} mul exch \pgf@ps@rgb{#2red} mul add
    5 1 roll
  \pgf@ps@rgb{#1green} mul exch \pgf@ps@rgb{#2green} mul add
    3 1 roll
  \pgf@ps@rgb{#1blue} mul exch \pgf@ps@rgb{#2blue} mul add
}




\def\pgfdeclarecolorwheelshading#1#2#3{%
  \pgf@ps@getcols{#3}%
  \pgfmathparse{mod(#2+360/\pgf@ps@ncol-90,360)}%
  \pgf@x=\pgfmathresult pt\relax%
  \ifdim\pgf@x<0pt\relax%
    \advance\pgf@x by360pt\relax%
  \fi%
  \edef\pgf@ps@rot{\pgfmath@tonumber{\pgf@x}}%
  \pgf@ps@generate@ps%
  \pgf@ps@esettoks{%
    \noexpand\pgfdeclarefunctionalshading[#3]{#1}%
    {\noexpand\pgfpoint{-50bp}{-50bp}}{\noexpand\pgfpoint{50bp}{50bp}}%
    {\noexpand\pgf@ps@colorstorgb{#3}}%
    {%
      2 copy abs exch abs add 0.0001 ge { atan } { pop } ifelse
      \pgf@ps@rot\pgf@ps@sp add dup 360 ge { -360 add } { } ifelse
      360 \pgf@ps@ncol\pgf@ps@sp 
      div div dup floor dup 3 1 roll neg add dup neg 1 add exch
      2 copy 2 copy 7 -1 roll 1 add
      \the\pgf@ps@toks}}%
  \edef\pgf@ps@marshal{\the\pgf@ps@toks}%
  \pgf@ps@marshal}

\def\pgf@ps@getcols#1{%
  \c@pgf@ps=0\relax%
  \pgfutil@for\pgf@ps@:={#1}\do{\advance\c@pgf@ps by1}%
  \edef\pgf@ps@ncol{\the\c@pgf@ps}%
}

\pgfdeclarecolorwheelshading{rgb}{0}{red,green,blue}
\pgfdeclarecolorwheelshading{rgb-90}{90}{red,green,blue}
\pgfdeclarecolorwheelshading{rainbow}{-45}{red,yellow,pink,green,orange,purple,blue}
\begin{document}

\begin{tikzpicture}

\path [shading=rgb]     (30:1.5)  circle [radius=1];
\path [shading=rgb-90]  (150:1.5) circle [radius=1];
\path [shading=rainbow] (270:1.5) circle [radius=1];

\end{tikzpicture}

\end{document}

Answer 2

请参阅第 110.2.3 节“一般（功能）阴影”，第 1087 页，手册。

以下是一个例子（原始的color wheel，略有修改）：

\documentclass[tikz]{standalone}

\pgfdeclarefunctionalshading{my color wheel}
{\pgfpoint{-50bp}{-50bp}}
{\pgfpoint{50bp}{50bp}}
{}
{ % x y
  2 copy abs exch abs add 0.0001 ge 
  {atan 360.0 div} % ... x y heading;  heading being in
                   %the interval [0, 1.0]
  { pop } % silently deal with error: return
                  % arbitrary heading of zero for origin
  ifelse  % because we will use it for 'Hue'
  1 copy .5 gt {0.5 sub 0.5 exch sub} {} ifelse
  1 1.0 % ... H S V 
  % C version to use as model:
  % H' = H * 6
  % i = floor(H')
  % f = H' - i
  % P = V * (1.0 - S)
  % Q = V * (1.0 - (S*f))
  % T = V * (1.0 - (S * (1.0 - f)))
  3 2 roll 6.0 mul dup 4 1 roll % H' S V H'
  floor cvr  % H' S V i
  dup 5 1 roll % i H' S V i
  3 index sub neg % i H' S V f
  1.0 3 index sub % i H' S V f (1.0 - S )
  2 index mul % i H' S V f P
  6 1 roll % P i H' S V f
  dup 3 index mul neg 1.0 add % P i H' S V f ( 1.0 - (f*S))
  2 index mul % P i H' S V f Q
  7 1 roll % Q P i H' S V f
  neg 1.0 add % Q P i H' S V (1.0 - f)
  2 index mul neg 1.0  add % Q P i H' S V (1.0 - S * (1.0 - f))
  1 index mul % Q P i H' S V T
  7 2 roll % V T Q P i H' S
  pop pop % V T Q P i
  %%% 
  % end of BLOCK B. The rest is just stack manipulation
  dup 0.5 le % TEST II [ i == 0 ]
  { % BLOCK C [ take stack to V T P ]
    pop exch pop
  }
  { dup 1.5 le % TEST III [ i == 1 ]
    { % BLOCK D [ take stack to Q V P ]
      pop exch 4 1 roll exch pop
    }
    { dup 2.5 le % TEST IV [ i == 2 ]
      { % BLOCK E [ take stack to P V T ]
        pop 4 1 roll pop
      }
      { dup 3.5 le % TEST V [ i == 3 ]
        { % BLOCK F [ take stack to P Q V ]
          pop exch 4 2 roll pop
        }
        { dup 4.5 le % TEST VI [ i == 4 ]
          { % BLOCK G [ take stack to T P V ]
            pop exch pop 3 -1 roll
          }
          { % BLOCK H [ take stack to V P Q ]
            pop 3 1 roll exch pop
          }
          ifelse
        }
        ifelse % for V
      }
      ifelse % for IV
    }
    ifelse % for III
  }
  ifelse % for II
}

\begin{document}
\begin{tikzpicture}
  \shade[shading=my color wheel] (0,0) circle (2);
\end{tikzpicture}
\end{document}