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如何绘制圆柱形棋盘？

tag-icon • tag-icon tikz-pgf
如何绘制圆柱形棋盘？

我可以画出圆柱体：

\documentclass[border=5pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

\begin{document}
\begin{center}
\begin{tikzpicture}
  \node [cylinder, black, rotate=180, draw,
    minimum height=5cm, minimum width=2cm] (c) {};  
\end{tikzpicture}
\end{center}
\end{document}

但是，我甚至无法在圆柱体的侧面区域画出棋盘，如下图所示 在此处输入图片描述

答案1

以下解决方案使用plot命令绘制曲线。通过在水平和垂直方向上绘制每个第二个条纹并进行even odd rule填充来创建棋盘状区域。

\documentclass{article}
\usepackage{tikz}

\begin{document}
  \begin{tikzpicture}[
    x=10mm,
    y=10mm,
    z={(2.5mm, 0)},
  ]
    \newcommand*{\CylinderLength}{5}
    \newcommand*{\CylinderRadius}{1}
    \newcommand*{\HorizontalStripes}{5}
    \newcommand*{\VerticalStripes}{10}
    \pgfmathsetmacro{\HorizontalStripeAngle}{180/\HorizontalStripes}
    \draw
      (\CylinderLength, \CylinderRadius) 
      -- plot[domain=90:270, smooth, variable=\t]
         (0, {\CylinderRadius*sin(\t)}, {\CylinderRadius*cos(\t)})
      -- ++(\CylinderLength, 0) 
      plot[domain=0:360, smooth cycle, variable=\t]
      (\CylinderLength, {\CylinderRadius*sin(\t)}, {\CylinderRadius*cos(\t)})
    ;
    \fill[black, even odd rule]
      % Vertical stripes
      \foreach \x in {2, 4, ..., \VerticalStripes} { 
        plot[domain=90:270, smooth, variable=\t] 
        ({(\x-1)*\CylinderLength/\VerticalStripes},
          {\CylinderRadius*sin(\t)}, {\CylinderRadius*cos(\t)})  
        -- ++(\CylinderLength/\VerticalStripes, 0)
        -- plot[domain=90:270, smooth, variable=\t]  
           (\x*\CylinderLength/\VerticalStripes,
             {\CylinderRadius*sin(-\t)}, {\CylinderRadius*cos(-\t)})
        -- cycle
      }
      % Horizontal stripes
      \foreach \y in {2, 4, ..., \HorizontalStripes} {
        plot[domain=90+(\y-1)*\HorizontalStripeAngle:
                    90+\y*\HorizontalStripeAngle,
             smooth, variable=\t]
        (0, {\CylinderRadius*sin(\t)}, {\CylinderRadius*cos(\t)})
        -- ++(\CylinderLength, 0)
        -- plot[domain=-90-\y*\HorizontalStripeAngle:
                       -90-(\y-1)*\HorizontalStripeAngle,
                smooth, variable=\t]
           (\CylinderLength, {\CylinderRadius*sin(-\t)},
             {\CylinderRadius*cos(-\t)})
        -- cycle
      }
    ;  
  \end{tikzpicture}
\end{document}

结果

对评论的备注，缺少分号。我无法使用下面发布的版本重现此错误消息。\fill命令包含二 \foreach循环，用于水平和垂直条纹，否则使用 的技巧even odd rule将不起作用。因此，\fill命令的分号位于第 49 行，就在结束 之前\end{tikzpicture}。

 *File List*
 article.cls    2007/10/19 v1.4h Standard LaTeX document class
  size10.clo    2007/10/19 v1.4h Standard LaTeX file (size option)
    tikz.sty    2013/12/13 v3.0.0 (rcs-revision 1.142)
     pgf.sty    2013/12/18 v3.0.0 (rcs-revision 1.14) 
  pgfrcs.sty    2013/12/20 v3.0.0 (rcs-revision 1.28) 
everyshi.sty    2001/05/15 v3.00 EveryShipout Package (MS)
  pgfrcs.code.tex
 pgfcore.sty    2010/04/11 v3.0.0 (rcs-revision 1.7)
graphicx.sty    2014/04/25 v1.0g Enhanced LaTeX Graphics (DPC,SPQR)
  keyval.sty    2014/05/08 v1.15 key=value parser (DPC)
graphics.sty    2009/02/05 v1.0o Standard LaTeX Graphics (DPC,SPQR)
    trig.sty    1999/03/16 v1.09 sin cos tan (DPC)
graphics.cfg    2010/04/23 v1.9 graphics configuration of TeX Live
  pdftex.def    2011/05/27 v0.06d Graphics/color for pdfTeX
infwarerr.sty    2010/04/08 v1.3 Providing info/warning/error messages (HO)
 ltxcmds.sty    2011/11/09 v1.22 LaTeX kernel commands for general use (HO)
  pgfsys.sty    2013/11/30 v3.0.0 (rcs-revision 1.47)
  pgfsys.code.tex
pgfsyssoftpath.code.tex    2013/09/09  (rcs-revision 1.9)
pgfsysprotocol.code.tex    2006/10/16  (rcs-revision 1.4)
  xcolor.sty    2007/01/21 v2.11 LaTeX color extensions (UK)
   color.cfg    2007/01/18 v1.5 color configuration of teTeX/TeXLive
 pgfcore.code.tex
pgfcomp-version-0-65.sty    2007/07/03 v3.0.0 (rcs-revision 1.7)
pgfcomp-version-1-18.sty    2007/07/23 v3.0.0 (rcs-revision 1.1)
  pgffor.sty    2013/12/13 v3.0.0 (rcs-revision 1.25)
 pgfkeys.sty    
 pgfkeys.code.tex
 pgfmath.sty     
 pgfmath.code.tex
  pgffor.code.tex
    tikz.code.tex
supp-pdf.mkii
pdftexcmds.sty    2011/11/29 v0.20 Utility functions of pdfTeX for LuaTeX (HO)
ifluatex.sty    2010/03/01 v1.3 Provides the ifluatex switch (HO)
   ifpdf.sty    2011/01/30 v2.3 Provides the ifpdf switch (HO)   
epstopdf-base.sty    2010/02/09 v2.5 Base part for package epstopdf
  grfext.sty    2010/08/19 v1.1 Manage graphics extensions (HO)
kvdefinekeys.sty    2011/04/07 v1.3 Define keys (HO)
kvoptions.sty    2011/06/30 v3.11 Key value format for package options (HO)
kvsetkeys.sty    2012/04/25 v1.16 Key value parser (HO)
etexcmds.sty    2011/02/16 v1.5 Avoid name clashes with e-TeX commands (HO)
epstopdf-sys.cfg    2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live
 ***********

答案2

使用xelatex或latex-> dvips->运行ps2pdf

\documentclass[pstricks,border=5pt]{standalone}
\usepackage{pst-solides3d}

\begin{document}
\psset{Decran=15,viewpoint=20 -60 0 rtp2xyz}
\begin{pspicture}(-1,-2)(5,2)
\pstVerb{ /ELEMENT 0 store }
\psSolid[object=cylindrecreux,h=5,r=1.5,RotY=90,ngrid=11 15,
  fcol= 0 2 165 { (black) } for ]% for loop with step 2
\end{pspicture}
\end{document}

在此处输入图片描述

对于 8x8 棋盘来说也是一样：

\documentclass[pstricks,border=5pt]{standalone}
\usepackage{pst-solides3d}

\begin{document}
\psset{Decran=15,viewpoint=20 -60 0 rtp2xyz}
\begin{pspicture}(-1,-2)(7,2)
\pstVerb{ /Element 0 store }
\psSolid[object=cylindrecreux,h=8,r=1.5,RotY=90,ngrid=8 8,
  fcol= 32 {
    Element (black) /Element Element 2 add store    
    Element 8 mod 0 eq 
      { /Element Element 1 add store } 
      { Element 8 mod 1 eq { /Element Element 1 sub store } if } ifelse } repeat
]
\end{pspicture}
\end{document}

在此处输入图片描述

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