使用 PGF/TikZ 进行圆柱着色

Question 1

为了创建独立圆柱体，而不使用预定义的 TikZ 形状，您可以执行以下操作：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}    
   \coordinate (ll) at (-3,-2);
   \coordinate (lr) at (3,-2);
   \coordinate (ul) at (-3,2);
   \coordinate (ur) at (3,2);
   \shade [shading angle=90] (ll) arc (-180:-60:3cm and .75cm) -- +(0,4) arc (-60:-180:3cm and .75cm) -- cycle;
   \shade [shading angle=270] (lr) arc (0:-60:3cm and .75cm) -- +(0,4) arc (-60:0:3cm and .75cm) -- cycle;
   \draw [thick] (ll) arc (-180:0:3cm and .75cm) -- (ur) arc (0:-180:3cm and .75cm) -- cycle;
   \draw [thick, shade, shading angle=30] (ul) arc (-180:180:3cm and .75cm);
   \node at (0,-.75){\Huge A};
\end{tikzpicture}
\end{document}

Answer

为了创建独立圆柱体，而不使用预定义的 TikZ 形状，您可以执行以下操作：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}    
   \coordinate (ll) at (-3,-2);
   \coordinate (lr) at (3,-2);
   \coordinate (ul) at (-3,2);
   \coordinate (ur) at (3,2);
   \shade [shading angle=90] (ll) arc (-180:-60:3cm and .75cm) -- +(0,4) arc (-60:-180:3cm and .75cm) -- cycle;
   \shade [shading angle=270] (lr) arc (0:-60:3cm and .75cm) -- +(0,4) arc (-60:0:3cm and .75cm) -- cycle;
   \draw [thick] (ll) arc (-180:0:3cm and .75cm) -- (ur) arc (0:-180:3cm and .75cm) -- cycle;
   \draw [thick, shade, shading angle=30] (ul) arc (-180:180:3cm and .75cm);
   \node at (0,-.75){\Huge A};
\end{tikzpicture}
\end{document}

Question 2

您可以使用预定义的圆柱形状，然后绘制一个顶部有实心填充的椭圆。使用以下代码，您可以cylinder像以前一样为形状提供所有选项，let椭圆中的代码负责处理椭圆的位置、大小和旋转。您只需调整颜色。

let \p<number> = (<coordinate>) in ... pgf 手册第 150 页（第 14.15 节）描述了该操作：它将由描述的点分配(<coordinate>)给局部变量\p<number>，其中<number>可以任意选择。变量\x<number>和\y<number>然后包含该点的 x 和 y 值。寄存器\n<number>可用于存储数学运算的结果。

该构造在手册的第 135 页（第 13.5.5 节）中描述：它描述从到的<coordinate>!<number>!<second coordinate>线上的一点，其中 0 表示第一点，1 表示第二点，0.5 表示中间的一点。<first coordinate><second coordinate>

点(cyl.before top)、(cyl.after top)和(cyl.top)由圆柱形状定义（参见 pgf 手册第 434 页第 48.3 节）。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,calc}
\begin{document}
\begin{tikzpicture}

\node [draw,
  shape=cylinder,
  name=nodename, % Can be defined arbitrarily
  alias=cyl, % Will be used by the ellipse to reference the cylinder
  aspect=1.5,
  minimum height=3cm,
  minimum width=2cm,
  left color=blue!30,
  right color=blue!60,
  middle color=red!20, % Has to be called after left color and middle color
  outer sep=-0.5\pgflinewidth, % to make sure the ellipse does not draw over the lines
  shape border rotate=90
] at (1,2) {A};

\fill [red!20] let
  \p1 = ($(cyl.before top)!0.5!(cyl.after top)$),
  \p2 = (cyl.top),
  \p3 = (cyl.before top),
  \n1={veclen(\x3-\x1,\y3-\y1)},
  \n2={veclen(\x2-\x1,\y2-\y1)},
  \n3={atan2((\y2-\y1),(\x2-\x1))}
 in 
  (\p1) ellipse [x radius=\n1, y radius = \n2, rotate=\n3];

\end{tikzpicture}
\end{document}

在此处输入图片描述

PGF 2.0 版本

对于 PGF 2.0，代码需要稍微进行调整，因为atan2旧版本中缺少数学函数并且椭圆的语法不同。

该操作let \p = () in ...在 pgf 2.0 手册（“Let 操作”）第 127 页（第 13.14 节）中进行了描述。

该构造<coordinate>!<number>!<coordinate>在 pgf 2.0 手册第 116 页第 12.4.3 节中进行了描述。

点 (cyl.before top)、(cyl.after top) 和 (cyl.top) 由圆柱形状定义（参见 pgf 2.0 手册第 326 页第 39.3 节（“几何形状”））。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,calc}
\begin{document}
\begin{tikzpicture}

\node [draw,
  shape=cylinder,
  name=nodename, % Can be defined arbitrarily
  alias=cyl, % Will be used by the ellipse to reference the cylinder
  aspect=1.5,
  minimum height=3cm,
  minimum width=2cm,
  left color=blue!30,
  right color=blue!60,
  middle color=red!20, % Has to be called after left color and middle color
  outer sep=-0.5\pgflinewidth, % to make sure the ellipse does not draw over the lines
  shape border rotate=90
] at (1,2) {A};

\fill [red!20] let
  \p1 = ($(cyl.before top)!0.5!(cyl.after top)$),
  \p2 = (cyl.top),
  \p3 = (cyl.before top),
  \n1={veclen(\x3-\x1,\y3-\y1)},
  \n2={veclen(\x2-\x1,\y2-\y1)}
 in 
  (\p1) ellipse (\n1 and \n2);

\end{tikzpicture}
\end{document}

Answer