3 个平面的交点

Question 1

更新：由于这是一个重复的问题，我试图改进这一点。到目前为止，人们必须手动对绘图元素进行排序。这种类型的示例可以在本答案的下半部分找到。人们可能想知道是否有可能让 Ti钾Z 决定以什么顺序绘制事物。答案是肯定的。这可以被认为是原理证明。

绘制顺序取决于物体的距离。该距离可以定义为物体重心在屏幕法线上的投影。
为了计算这些预测，我们需要一些工具。我在这里使用的工具来自实验图书馆3dtools，可以找到这里。您需要将库另存为，tikzlibrary3dtools.code.tex并将其放在 TeX 可以找到的地方，例如与下面文档相同的文件夹。
给定投影，我们可以建立一个顺序并在相应的层中绘制内容。

此时，您仍然需要手动找出交集部分。正如我所说，这是一个原理证明。pgfplots 提供了非常类似的功能patchplots。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
\begin{document}
% define a command for the projections (to become a part of the library)
\newcommand\GetProj[2]{\begingroup
\foreach \Coord [count=\nCoord] in #1
  {\ifnum\nCoord=1
  \xdef\temp{\Coord}
  \else
  \xdef\temp{\temp+\Coord}
  \fi}
  \edef\ntemp{\noexpand\path[overlay,3d coordinate={(tmp)=\temp}];}
  \ntemp
  \pgfmathsetmacro{#2}{TD("(n)o(tmp)")}
  \pgfmathsmuggle#2\endgroup}
% counter for 3d ordering  
\newcounter{tdorder}
% set a sufficient number of layers (for more complex scenarios you need more)
\foreach \X in {1,...,20}
{\pgfdeclarelayer{layer\X}
\ifnum\X=1
\xdef\LstLayers{layer\X}
\else
\xdef\LstLayers{\LstLayers,layer\X}
\fi}
\pgfsetlayers\LstLayers
\tikzset{closed polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
 {\ifnum\nCoord=1
  \Coord
 \else
  -- \Coord
 \fi} -- cycle}},polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
 {\ifnum\nCoord=1
  \Coord
 \else
  -- \Coord
 \fi}}}}
% main code
\foreach \X in {5,15,...,355}
{\tdplotsetmaincoords{90+30*sin(\X)}{\X}
\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,fill opacity=1]
  \path[tdplot_screen_coords,use as bounding box] (-5,-5) rectangle (5,5);
  % define the vertices (there are certainly superior naming conventions)
  \path (-3,-3,0)  coordinate (m1) (-3,0,-3) coordinate (m2)
   (-3,0,0)  coordinate (m3) (-3,0,3) coordinate (m4) (-3,3,0)  coordinate (m5)
   (-2,-3,3) coordinate (m6) (-2,0,3)  coordinate (m7) (-2,3,3) coordinate (m8)
   (0,-3,0) coordinate (m9) (0,0,0) coordinate (O) (0,3,0) coordinate (p1)
   (2,-3,-3) coordinate (p2) (2,0,-3) coordinate (p3) (2,3,-3) coordinate (p4)
   (3,-3,0) coordinate (p5) (3,0,-3) coordinate (p6) (3,0,0) coordinate (p7)
   (3,0,3) coordinate (p8) (3,3,0) coordinate (p9);
  % define the plane data as a list of <drawing options>/<shape>/<vertices> 
  \def\PlaneData{%
  {draw,fill=red}/closed polygon/{(m2),(p3),(O),(m3)},%
  {draw,fill=red}/closed polygon/{(p6),(p3),(O),(p7)},%
  {draw,fill=red}/closed polygon/{(m4),(m7),(O),(m3)},%
  {draw,fill=red}/closed polygon/{(p8),(m7),(O),(p7)},%
  {draw,fill=blue}/closed polygon/{(m1),(m3),(O),(m9)},%
  {draw,fill=blue}/closed polygon/{(m5),(m3),(O),(p1)},%
  {draw,fill=blue}/closed polygon/{(p5),(p7),(O),(m9)},%
  {draw,fill=blue}/closed polygon/{(p9),(p7),(O),(p1)},%
  {draw,fill=green}/closed polygon/{(m6),(m9),(O),(m7)},%
  {draw,fill=green}/closed polygon/{(m8),(p1),(O),(m7)},%
  {draw,fill=green}/closed polygon/{(p2),(m9),(O),(p3)},%
  {draw,fill=green}/closed polygon/{(p4),(p1),(O),(p3)},%
  {draw,thick}/polygon/{(m3),(O)},%
  {draw,thick}/polygon/{(O),(p7)}}
  % normal of screen (last row of the rotation matrix)
  \path[overlay] ({sin(\tdplotmaintheta)*sin(\tdplotmainphi)},
       {-1*sin(\tdplotmaintheta)*cos(\tdplotmainphi)},
       {cos(\tdplotmaintheta)}) coordinate (n); 
  % build up the list of projections       
  \foreach \Style/\Poly/\CoordLst [count=\nC] in \PlaneData
  {%
  \GetProj{\CoordLst}{\currproj}
  \ifnum\nC=1
    \xdef\LstProj{\currproj}
  \else
    \xdef\LstProj{\LstProj,\currproj}
  \fi}
  % draw the planes in appropriate layers
  \foreach \Style/\Poly/\CoordLst [count=\nC] in \PlaneData
  {%
  \GetProj{\CoordLst}{\currproj}
  \setcounter{tdorder}{1}
  \foreach \Proj in \LstProj
  {\pgfmathtruncatemacro{\itest}{ifthenelse(\Proj<\currproj,1,0)}
  \ifnum\itest=1
  \stepcounter{tdorder}
  \fi}
  \begin{pgfonlayer}{layer\number\value{tdorder}}
  \edef\temp{\noexpand\path[\Style,\Poly={\CoordLst}];}
  \temp
  \end{pgfonlayer}
  }
%   
\end{tikzpicture}}
\end{document}

不用说，这可以应用于与 D 膜相交的其他场景。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}
\begin{document}
\newcommand\GetProj[2]{\begingroup
\foreach \Coord [count=\nCoord] in #1
  {\ifnum\nCoord=1
  \xdef\temp{\Coord}
  \else
  \xdef\temp{\temp+\Coord}
  \fi}
  \edef\ntemp{\noexpand\path[overlay,3d coordinate={(tmp)=\temp}];}
  \ntemp
  \pgfmathsetmacro{#2}{TD("(n)o(tmp)")}
  \pgfmathsmuggle#2\endgroup}
\newcounter{tdorder}
\foreach \X in {1,...,20}
{\pgfdeclarelayer{layer\X}
\ifnum\X=1
\xdef\LstLayers{layer\X}
\else
\xdef\LstLayers{\LstLayers,layer\X}
\fi}
\pgfsetlayers\LstLayers
\tikzset{closed polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
 {\ifnum\nCoord=1
  \Coord
 \else
  -- \Coord
 \fi} -- cycle}},polygon/.style={insert path={foreach \Coord [count=\nCoord] in {#1}
 {\ifnum\nCoord=1
  \Coord
 \else
  -- \Coord
 \fi}}}}
%
\foreach \X in {5,15,...,355}
{\tdplotsetmaincoords{90-30*cos(\X)}{\X}
\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,fill opacity=1]
  \path[tdplot_screen_coords,use as bounding box] (-5,-5) rectangle (5,5);
  \path foreach \X [count=\cX] in {A,B}
   {foreach \Y [count=\cY] in {A,B}
   {foreach \Z [count=\cZ] in {A,B}
   {(4.5-3*\cX,4.5-3*\cY,4.5-3*\cZ) coordinate(\X\Y\Z)}}}
   (0,0,4.5) coordinate (T);
  \def\PlaneData{%
  {draw,fill=red}/closed polygon/{(AAA),(ABA),(ABB),(AAB)},%
  {draw,fill=red!80}/closed polygon/{(ABA),(BBA),(BBB),(ABB)},%
  {draw,fill=red!50}/closed polygon/{(BBA),(BAA),(BAB),(BBB)},%
  {draw,fill=red!70}/closed polygon/{(BAA),(AAA),(AAB),(BAB)},%
  {draw,fill=blue}/closed polygon/{(AAA),(ABA),(T)},%
  {draw,fill=blue!80}/closed polygon/{(ABA),(BBA),(T)},%
  {draw,fill=blue!50}/closed polygon/{(BBA),(BAA),(T)},%
  {draw,fill=blue!70}/closed polygon/{(BAA),(AAA),(T)},%
  {draw,fill=gray}/closed polygon/{(AAB),(ABB),(BBB),(BAB)},%
  {draw,thick}/polygon/{(AAA),(AAB)}}
  % normal of screen 
  \path[overlay] ({sin(\tdplotmaintheta)*sin(\tdplotmainphi)},
       {-1*sin(\tdplotmaintheta)*cos(\tdplotmainphi)},
       {cos(\tdplotmaintheta)}) coordinate (n); 
  % build up the list of projections       
  \foreach \Style/\Poly/\CoordLst [count=\nC] in \PlaneData
  {%
  \GetProj{\CoordLst}{\currproj}
  \ifnum\nC=1
    \xdef\LstProj{\currproj}
  \else
    \xdef\LstProj{\LstProj,\currproj}
  \fi}
  % draw the planes in appropriate layers
  \foreach \Style/\Poly/\CoordLst [count=\nC] in \PlaneData
  {%
  \GetProj{\CoordLst}{\currproj}
  \setcounter{tdorder}{1}
  \foreach \Proj in \LstProj
  {\pgfmathtruncatemacro{\itest}{ifthenelse(\Proj<\currproj,1,0)}
  \ifnum\itest=1
  \stepcounter{tdorder}
  \fi}
  \begin{pgfonlayer}{layer\number\value{tdorder}}
  \edef\temp{\noexpand\path[\Style,\Poly={\CoordLst}];}
  \temp
  \end{pgfonlayer}
  }
%   
\end{tikzpicture}}
\end{document}

旧答案：您需要按正确的顺序绘制飞机的各个部分。对于您案例中给定的视图，这是

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{110}
\foreach \X in {0.1,0.2,...,1,0.9,0.8,...,0.2}
{\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,fill opacity=\X]
  \draw[fill=red] (-3,0,-3)  -- (2,0,-3) -- (0,0,0) -- (-3,0,0) -- cycle;
   \draw[thick](-3,0,0) -- (0,0,0);
  \draw[fill=blue] (-3,-3,0) -- (-3,3,0) -- (0,3,0) -- (0,-3,0) -- cycle;
  \draw[fill=red] (-3,0,0) -- (0,0,0) --  (-2,0,3) -- (-3,0,3) -- cycle;
  \draw[fill=green] (2,-3,-3) -- (2,3,-3) -- (-2,3,3) -- (-2,-3,3) -- cycle;
  \draw[fill=red] (3,0,-3)  -- (2,0,-3) -- (0,0,0) -- (3,0,0) -- cycle;
  \draw[fill=blue] (3,-3,0) -- (3,3,0) -- (0,3,0) -- (0,-3,0) -- cycle;% %\draw (0,-3,0) -- (0,3,0);
  \draw[fill=red] (3,0,0) -- (0,0,0) --  (-2,0,3) -- (3,0,3) -- cycle;
  \draw[thick](0,0,0)--(3,0,0);
  \fill[red] (0,0,0) circle (3pt);
  \node[anchor=south west,align=center] (line) at (4,6,3.5) 
   {Solution\\ intersection};
  \draw[-latex] (line) to[out=180,in=75] (0.05,0.05,0.1);
\end{tikzpicture}}
\end{document}

您需要fill opacity从循环中选择您最喜欢的。

这里是使相交平面完全可旋转的另一种方法。

您“仅”需要区分足够多的情况。

附录：至于您在评论中提出的要求：该策略与上述完全相同。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{110}
\foreach \X in {0.1,0.2,...,1,0.9,0.8,...,0.2}
{\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,fill opacity=\X]
 \draw[fill=red] (-3,0,-3) -- (-3,0,0) -- (3,0,0) -- (3,0,-3) --  cycle;
 \draw[fill=green] (-3,2,-3) -- (-3,0,0) -- (3,0,0) -- (3,2,-3)  -- cycle;
 \draw[fill=blue] (-3,-3,0) -- (-3,3,0) -- (3,3,0) -- (3,-3,0) --  cycle;
 \draw[fill=green] (-3,-2,3) -- (-3,0,0) -- (3,0,0) -- (3,-2,3)  -- cycle;
 \draw[fill=red] (-3,0,3) -- (-3,0,0) -- (3,0,0) -- (3,0,3) --  cycle;
 \draw[thick](-3,0,0)--(3,0,0);
 \fill[red] (0,0,0) circle (3pt);
 \node[anchor=south west,align=center,text opacity=1] (line) at (4,6,3.5) {Solution\\ 
    intersection};
 \draw[-latex] (line) to[out=180,in=75] (0.05,0.05,0.1);
\end{tikzpicture}}
\end{document}

Answer