将乳胶填充到气缸中

Question

我想填充下面的圆柱体，就像图片一样

我的代码

\begin{tikzpicture}
  \def\a{1} % bán trục lớn = bán kính trụ
  \def\b{0.3} % bán trục nhỏ
  \def\h{3} % chiều cao trụ
  \shadedraw[left color=gray,right color=white, draw=none]
  (-\a,1) -- (-\a,0) arc [x radius=\a, y radius=\b, start angle=180, end angle=360] (\a,0)--(\a,1)arc [x radius=\a, y radius=\b, start angle=0, end angle=180];
  \draw (\a,0)--(\a,\h) (-\a,0)--(-\a,\h);
  \draw[dashed] (\a,0) arc [x radius=\a, y radius=\b, start angle=0, end angle=180];
  \draw (-\a,0) arc [x radius=\a, y radius=\b, start angle=180, end angle=360];
  \draw[dashed] (\a,1) arc [x radius=\a, y radius=\b, start angle=0, end angle=180];
  \draw (-\a,1) arc [x radius=\a, y radius=\b, start angle=180, end angle=360];
  \draw (0,\h) ellipse (\a cm and \b cm);
 \end{tikzpicture}


 \begin{tikzpicture}[rotate=-70]
  \def\a{1} % bán trục lớn = bán kính trụ
  \def\b{0.3} % bán trục nhỏ
  \def\h{3} % chiều cao trụ
  \draw (\a,0)--(\a,\h) (-\a,0)--(-\a,\h);
  \tkzDefPoints{-\a/0/A,\a/0/B,-\a/\h/a}
  \tkzDefMidPoint(A,B)\tkzGetPoint{O}
  \coordinate(M) at ([shift={(O)}]-70:\a cm and \b cm);
  \draw[draw=none,name path=elip] (O) ellipse (\a cm and \b cm);
  \tkzDefPointBy[rotation=center O angle 180](M)\tkzGetPoint{N}
  \coordinate(C) at ([shift={(O)}]0:\a cm and \b cm);
  \tkzDefPointBy[translation=from A to a](C)\tkzGetPoint{C'}
  \fill[color=gray!50, draw=none]
  (O) -- (M) .. controls (0.8,1.6) and (1,2.8) .. (C');
  \fill[color=gray!50, draw=none]
  (O) -- (N) .. controls (0.6,2.6) and (0.8,3.3) .. (C');
  \tkzFindAngle(B,O,M)\tkzGetAngle{angBOM}
  \fill[color=gray!40, draw=none]
  (M) .. controls (0.8,1.5) and (1,2.6) .. (C')--(B);
  \fill[color=gray!40, draw=none]
  (M) arc [x radius=\a, y radius=\b, start angle=0, end angle=\angBOM]--(B);
  \draw[dashed](M)--(N) (O)--(C');
  \draw[name path=elip1] (M) .. controls (0.8,1.6) and (1,2.8) .. (C');
  \draw[dashed,name path=elip2] (N) .. controls (0.6,2.6) and (0.8,3.3) .. (C');
  \draw[dashed] (\a,0) arc [x radius=\a, y radius=\b, start angle=0, end angle=180];
  \draw (-\a,0) arc [x radius=\a, y radius=\b, start angle=180, end angle=360];
  \draw (0,\h) ellipse (\a cm and \b cm);
 \end{tikzpicture}

请帮助我！非常感谢！

Answer 1

这绘制了部分填充的旋转圆柱体。水面的顶部表面是椭圆形，可能会被圆柱体的顶部和/或底部截断。如果查看合适的投影，相关角度的计算相当简单。我要感谢 minhthien_2016 提醒我这个好问题。

\documentclass[tikz,border=3.14mm]{standalone} 
\usepackage{tikz-3dplot} 
\tikzset{pics/filled cylinder/.style={code={\tikzset{filled cylinder/.cd,#1}
 \newcommand*{\pv}[1]{\pgfkeysvalueof{/tikz/filled cylinder/##1}}
 \pgfmathsetmacro\angVis{atan(sin(\pv{rot})*cos(\tdplotmaintheta)/sin(\tdplotmaintheta))}% see tex.stackexchange.com/a/49589/ 
 \draw[dashed] plot[variable=\t,domain=\angVis:\angVis-180,smooth] ({\pv{radius}*cos(\pv{rot})*cos(\t)}, 
 {\pv{radius}*sin(\t)}, 
 {\pv{radius}*sin(\pv{rot})*cos(\t)}); 
 \pgfmathtruncatemacro{\itestU}{sign(\pv{radius}-(\pv{height}-\pv{level})*cos(\pv{rot})/cos(90-\pv{rot})}
 \pgfmathsetmacro{\alphaU}{acos(min(1,abs(((\pv{height}-\pv{level})*cos(\pv{rot})/cos(90-\pv{rot}))/\pv{radius})))}     
 \pgfmathsetmacro{\angU}{ifthenelse(\alphaU>0,\alphaU,\angVis)}     
 \pgfmathsetmacro{\alphaL}{acos(min(1,abs(((\pv{level})*cos(\pv{rot})/cos(90-\pv{rot}))/\pv{radius})))}     
 \pgfmathsetmacro{\angL}{ifthenelse(\alphaL>0,180-\alphaL,\angVis+180)}     
 \ifdim\alphaU pt>0pt % distinguish between cut at top end and not
  \path[fill=blue!50,fill opacity=0.5]  
   plot[variable=\t,domain=\angVis:-1*\angU,smooth]
   ({\pv{radius}*cos(\pv{rot})*cos(\t)  -sin(\pv{rot})*\pv{height}}, 
    {\pv{radius}*sin(\t)}, 
    {\pv{radius}*sin(\pv{rot})*cos(\t) +cos(\pv{rot})*\pv{height}}) --
   plot[variable=\t,domain=\angU:\angL,smooth]
    ({-\pv{level}*sin(\pv{rot})+\pv{radius}*cos(\t)/cos(\pv{rot})},{\pv{radius}*sin(\t)},{zprime(0,\pv{level},-1*\pv{rot})})
     -- plot[variable=\t,domain=\angL:\angVis,smooth] ({\pv{radius}*cos(\pv{rot})*cos(\t)}, 
    {\pv{radius}*sin(\t)},{\pv{radius}*sin(\pv{rot})*cos(\t)}) 
    -- cycle;   
 \else  
  \path[fill=blue!50,fill opacity=0.5]  
   plot[variable=\t,domain=\angU:\angL,smooth]
    ({-\pv{level}*sin(\pv{rot})+\pv{radius}*cos(\t)/cos(\pv{rot})},{\pv{radius}*sin(\t)},{zprime(0,\pv{level},-1*\pv{rot})})
     -- plot[variable=\t,domain=\angL:\angVis,smooth] ({\pv{radius}*cos(\pv{rot})*cos(\t)}, 
    {\pv{radius}*sin(\t)},{\pv{radius}*sin(\pv{rot})*cos(\t)}) 
    -- cycle;   
 \fi
 \draw[fill=blue,fill opacity=0.5] 
   plot[variable=\t,domain=\alphaU:180-\alphaL,smooth]
     ({-\pv{level}*sin(\pv{rot})+\pv{radius}*cos(\t)/cos(\pv{rot})},{\pv{radius}*sin(\t)},{zprime(0,\pv{level},-1*\pv{rot})})
   -- plot[variable=\t,domain=180+\alphaL:360-\alphaU,smooth]
     ({-\pv{level}*sin(\pv{rot})+\pv{radius}*cos(\t)/cos(\pv{rot})},{\pv{radius}*sin(\t)},{zprime(0,\pv{level},-1*\pv{rot})})
    -- cycle;
 \draw plot[variable=\t,domain=\angVis:\angVis+180,smooth] ({\pv{radius}*cos(\pv{rot})*cos(\t)}, 
 {\pv{radius}*sin(\t)}, 
 {\pv{radius}*sin(\pv{rot})*cos(\t)}) 
 -- plot[variable=\t,domain=\angVis+180:\angVis-360,smooth] ({\pv{radius}*cos(\pv{rot})*cos(\t) 
 -sin(\pv{rot})*\pv{height}}, 
 {\pv{radius}*sin(\t)}, 
 {\pv{radius}*sin(\pv{rot})*cos(\t) 
 +cos(\pv{rot})*\pv{height}}) -- cycle; 
}}}
\begin{document} 
\tdplotsetmaincoords{110}{0} 
\foreach \Angle in {-5,-10,...,-80,-75,-70,...,-10}
{\begin{tikzpicture}[tdplot_main_coords,
 declare function={zprime(\x,\z,\a)=\z*cos(\a)-\x*sin(\a);
 xprime(\x,\z,\a)=\x*cos(\a)+\z*sin(\a);}, 
 filled cylinder/.cd,radius/.initial=1,height/.initial=4,
 level/.initial=1.5,rot/.initial=-50] 
 \path[tdplot_screen_coords,use as bounding box]  (-1.5,-1) rectangle (4.5,5);
 \path pic{filled cylinder={rot=\Angle}};
\end{tikzpicture}} 
\end{document}