☰

在 3D 图表中对齐文本

tag-icon • tag-icon tikz-pgf graphics luatex inkscape
在 3D 图表中对齐文本

这个问题导致了 TikZ 中出现了一个新库：
perspective（PGF 手册，第 63 章）

我有一个 3d 对象，inkscape如下所示：

在此处输入图片描述

现在我尝试将文本放置在与浅蓝色区域相同的方向。但是，我想使用 插入文本，而latex不是直接将其嵌入（因此，我使用中的选项pdf保存它）。pdf+Latexinkscape

但是当我尝试在 3d 区域插入文本时，我得到：

![在此处输入图片描述

我怎样才能OMEAG与浅蓝色区域平行对齐。

我无法附加它的 pdf，但是MWE如下所示：

%&lualatex
% !TeX program = lualatex
\documentclass[11pt,a4paper]{article}
%\usepackage[latin1]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{xcolor}
\usepackage{pgfplots}
\usepackage{pstricks}    %for embedding pspicture.
\pgfplotsset{compat=newest}
\usepackage{tikz}
\begin{document}
    \begin{figure}[h]
    \centering{
        \input{drawing4.pdf_tex}
        \caption{Top view.}
        \label{fig:aktomnpView}
    }
\end{figure}
\end{document}

如下\input{drawing4.pdf_tex}：

\begingroup%
  \makeatletter%
  \providecommand\color[2][]{%
    \errmessage{(Inkscape) Color is used for the text in Inkscape, but the package 'color.sty' is not loaded}%
    \renewcommand\color[2][]{}%
  }%
  \providecommand\transparent[1]{%
    \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}%
    \renewcommand\transparent[1]{}%
  }%
  \providecommand\rotatebox[2]{#2}%
  \newcommand*\fsize{\dimexpr\f@size pt\relax}%
  \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}%
  \ifx\svgwidth\undefined%
    \setlength{\unitlength}{303.69978591bp}%
    \ifx\svgscale\undefined%
      \relax%
    \else%
      \setlength{\unitlength}{\unitlength * \real{\svgscale}}%
    \fi%
  \else%
    \setlength{\unitlength}{\svgwidth}%
  \fi%
  \global\let\svgwidth\undefined%
  \global\let\svgscale\undefined%
  \makeatother%
  \begin{picture}(1,1.35089637)%
    \lineheight{1}%
    \setlength\tabcolsep{0pt}%
    \put(0,0){\includegraphics[width=\unitlength,page=1]{drawing4.pdf}}%
    \put(0.54334545,0.71256022){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}OMEAG\end{tabular}}}}%
  \end{picture}%
\endgroup%

答案1

编辑3

我很高兴地宣布，这个答案的部分代码现在作为perspective库包含在 Tikz 包（v3.1.2）中。

编辑2

使用这个很棒的答案结合我的tpp坐标系，我设法对块的侧面进行了非线性映射的近似。

在此处输入图片描述

或者没有帮助热线：

在此处输入图片描述

静止图像：

在此处输入图片描述

梅威瑟：

\documentclass[tikz]{standalone}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\usepgfmodule{nonlineartransformations}

\usepackage{mathtools}

\makeatletter

\def\tikz@scan@transform@one@point#1{%
  \tikz@scan@one@point\pgf@process#1%
  \pgf@pos@transform{\pgf@x}{\pgf@y}}
\tikzset{%
  grid source opposite corners/.code args={#1and#2}{%
   \pgfextract@process\tikz@transform@source@southwest{%
     \tikz@scan@transform@one@point{#1}}%
   \pgfextract@process\tikz@transform@source@northeast{%
     \tikz@scan@transform@one@point{#2}}%
  },
  grid target corners/.code args={#1--#2--#3--#4}{%
   \pgfextract@process\tikz@transform@target@southwest{%
     \tikz@scan@transform@one@point{#1}}%
   \pgfextract@process\tikz@transform@target@southeast{%
     \tikz@scan@transform@one@point{#2}}%
   \pgfextract@process\tikz@transform@target@northeast{%
     \tikz@scan@transform@one@point{#3}}%
   \pgfextract@process\tikz@transform@target@northwest{%
     \tikz@scan@transform@one@point{#4}}%
  }
}

\def\tikzgridtransform{%
  \pgfextract@process\tikz@current@point{}%
  \pgf@process{%
    \pgfpointdiff{\tikz@transform@source@southwest}%
      {\tikz@transform@source@northeast}%
  }%
  \pgf@xc=\pgf@x\pgf@yc=\pgf@y%
  \pgf@process{%
    \pgfpointdiff{\tikz@transform@source@southwest}{\tikz@current@point}%
  }%
  \pgfmathparse{\pgf@x/\pgf@xc}\let\tikz@tx=\pgfmathresult%
  \pgfmathparse{\pgf@y/\pgf@yc}\let\tikz@ty=\pgfmathresult%
  %
  \pgfpointlineattime{\tikz@ty}{%
    \pgfpointlineattime{\tikz@tx}{\tikz@transform@target@southwest}%
      {\tikz@transform@target@southeast}}{%
    \pgfpointlineattime{\tikz@tx}{\tikz@transform@target@northwest}%
      {\tikz@transform@target@northeast}}%
}

% Initialize H matrix for perspective view
\pgfmathsetmacro\H@tpp@aa{1}\pgfmathsetmacro\H@tpp@ab{0}\pgfmathsetmacro\H@tpp@ac{0}%\pgfmathsetmacro\H@tpp@ad{0}
\pgfmathsetmacro\H@tpp@ba{0}\pgfmathsetmacro\H@tpp@bb{1}\pgfmathsetmacro\H@tpp@bc{0}%\pgfmathsetmacro\H@tpp@bd{0}
\pgfmathsetmacro\H@tpp@ca{0}\pgfmathsetmacro\H@tpp@cb{0}\pgfmathsetmacro\H@tpp@cc{1}%\pgfmathsetmacro\H@tpp@cd{0}
\pgfmathsetmacro\H@tpp@da{0}\pgfmathsetmacro\H@tpp@db{0}\pgfmathsetmacro\H@tpp@dc{0}%\pgfmathsetmacro\H@tpp@dd{1}

%Initialize H matrix for main rotation
\pgfmathsetmacro\H@rot@aa{1}\pgfmathsetmacro\H@rot@ab{0}\pgfmathsetmacro\H@rot@ac{0}%\pgfmathsetmacro\H@rot@ad{0}
\pgfmathsetmacro\H@rot@ba{0}\pgfmathsetmacro\H@rot@bb{1}\pgfmathsetmacro\H@rot@bc{0}%\pgfmathsetmacro\H@rot@bd{0}
\pgfmathsetmacro\H@rot@ca{0}\pgfmathsetmacro\H@rot@cb{0}\pgfmathsetmacro\H@rot@cc{1}%\pgfmathsetmacro\H@rot@cd{0}
%\pgfmathsetmacro\H@rot@da{0}\pgfmathsetmacro\H@rot@db{0}\pgfmathsetmacro\H@rot@dc{0}\pgfmathsetmacro\H@rot@dd{1}

\pgfkeys{
    /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#1))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ba{#2/#1}
                \pgfmathsetmacro\H@tpp@ca{#3/#1}
                \pgfmathsetmacro\H@tpp@da{ 1/#1}
                \coordinate (vp-p) at (#1,#2,#3);
            \fi
        },
        q/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#2))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ab{#1/#2}
                \pgfmathsetmacro\H@tpp@cb{#3/#2}
                \pgfmathsetmacro\H@tpp@db{ 1/#2}
                \coordinate (vp-q) at (#1,#2,#3);
            \fi
        },
        r/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#3))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ac{#1/#3}
                \pgfmathsetmacro\H@tpp@bc{#2/#3}
                \pgfmathsetmacro\H@tpp@dc{ 1/#3}
                \coordinate (vp-r) at (#1,#2,#3);
            \fi
        },
        coordinate/.code args={#1,#2,#3}{
            \def\tpp@x{#1}
            \def\tpp@y{#2}
            \def\tpp@z{#3}
        },
}

\tikzset{
    view/.code 2 args={
        \pgfmathsetmacro\rot@main@theta{#1}
        \pgfmathsetmacro\rot@main@phi{#2}
        % Row 1
        \pgfmathsetmacro\H@rot@aa{cos(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ab{sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ac{0}
        % Row 2
        \pgfmathsetmacro\H@rot@ba{-cos(\rot@main@theta)*sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@bb{cos(\rot@main@phi)*cos(\rot@main@theta)}
        \pgfmathsetmacro\H@rot@bc{sin(\rot@main@theta)}
        % Row 3
        \pgfmathsetmacro\H@m@ca{sin(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cb{-cos(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cc{cos(\rot@main@theta)}
        % Set vector values
        \pgfmathsetmacro\vec@x@x{\H@rot@aa}
        \pgfmathsetmacro\vec@y@x{\H@rot@ab}
        \pgfmathsetmacro\vec@z@x{\H@rot@ac}
        \pgfmathsetmacro\vec@x@y{\H@rot@ba}
        \pgfmathsetmacro\vec@y@y{\H@rot@bb}
        \pgfmathsetmacro\vec@z@y{\H@rot@bc}
        % Set pgf vectors
        \pgfsetxvec{\pgfpoint{\vec@x@x cm}{\vec@x@y cm}}
        \pgfsetyvec{\pgfpoint{\vec@y@x cm}{\vec@y@y cm}}
        \pgfsetzvec{\pgfpoint{\vec@z@x cm}{\vec@z@y cm}}
    },
}

\tikzset{
    perspective/.code={\pgfkeys{/three point perspective/.cd,#1}},
    perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
}

\tikzdeclarecoordinatesystem{three point perspective}{
    \pgfkeys{/three point perspective/.cd,coordinate={#1}}
    \pgfmathsetmacro\temp@p@w{\H@tpp@da*\tpp@x + \H@tpp@db*\tpp@y + \H@tpp@dc*\tpp@z + 1}
    \pgfmathsetmacro\temp@p@x{(\H@tpp@aa*\tpp@x + \H@tpp@ab*\tpp@y + \H@tpp@ac*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@y{(\H@tpp@ba*\tpp@x + \H@tpp@bb*\tpp@y + \H@tpp@bc*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@z{(\H@tpp@ca*\tpp@x + \H@tpp@cb*\tpp@y + \H@tpp@cc*\tpp@z)/\temp@p@w}
    \pgfpointxyz{\temp@p@x}{\temp@p@y}{\temp@p@z}
}
\tikzaliascoordinatesystem{tpp}{three point perspective}

\makeatother

\definecolor{mydarkbluishgray}{RGB}{134 134 191}
\definecolor{mylightbluishgray}{RGB}{215 215 255}

\begin{document}
    \foreach \vp in {10,12.5,...,50}{
%    \foreach \vp in {10}{
    \begin{tikzpicture}[line join=round]

        \clip (-12,0) rectangle (12,10);

        \begin{scope}[
            view={85}{-40},
            perspective={
                p = {(\vp,0,5.5)},
                q = {(0,\vp,5.5)},
            }
        ]
            \fill[mydarkbluishgray]  (tpp cs:0,0,0) -- (tpp cs:0,0,10) -- (tpp cs:0,5,10) -- (tpp cs:0,5,0) -- cycle;
            \fill[mylightbluishgray] (tpp cs:0,0,0) -- (tpp cs:0,0,10) -- (tpp cs:15,0,10) -- (tpp cs:15,0,0) -- cycle;

            \begin{scope}[
                grid source opposite corners={(0cm,0cm) and (15cm,10cm)},
                grid target corners={(tpp cs:0,0,0)--(tpp cs:15,0,0)--(tpp cs:15,0,10)--(tpp cs:0,0,10)}
            ]
                \pgftransformnonlinear\tikzgridtransform

%                \draw[dotted] (0cm,4.75cm) -- (15cm,4.75cm);
%                \draw[red]    (0cm,5.00cm) -- (15cm,5.00cm);
%                \draw[dotted] (0cm,5.25cm) -- (15cm,5.25cm);
%                
%                \draw[dotted] (6.1cm,0cm) -- (6.1cm,10cm);
%                \draw[red]    (7.5cm,0cm) -- (7.5cm,10cm);
%                \draw[dotted] (8.9cm,0cm) -- (8.9cm,10cm);

                \foreach \char [count=\i from -2] in {O,M,E,A,G}{
                    \pgftransformshift{\pgfpointadd{\pgfpoint{7.5cm}{5cm}}{\pgfpoint{\i *0.6cm}{0cm}}}
                    \pgftransformscale{2}
                    \pgfnode{rectangle}{center}{\char}{}{}
                }
            \end{scope}

%            \begin{scope}[dotted,line width=0.2pt]
%                \node[label=right:p,fill,circle,inner sep = 2pt] (p) at (vp-p){};
%
%                \draw (tpp cs:0,0,10) -- (p.center);
%                \draw (tpp cs:0,0,0) -- (p.center);
%                \draw (tpp cs:0,5,10) -- (p.center);
%                \draw (tpp cs:0,5,0) -- (p.center);
%
%                \node[label=left:q,fill,circle,inner sep = 2pt] (q) at (vp-q){};
%
%                \draw (tpp cs:0,0,10) -- (q.center);
%                \draw (tpp cs:0,0,0) -- (q.center);
%                \draw (tpp cs:15,0,10) -- (q.center);
%                \draw (tpp cs:15,0,0) -- (q.center);
%            \end{scope}
        \end{scope}
    \end{tikzpicture}
    }
\end{document}

编辑请参阅我之前的回答的先前编辑

我定义了一个新的坐标系three point perspective。它可以用作

\draw (three point perspective cs:0,0,0) -- (three point perspective cs:5,5,5);

或者稍微方便一点

\draw (tpp cs:0,0,0) -- (tpp cs:5,5,5);

要打开透视视图，您可以调用perspective={<options>}Tikz 键。选项包括：

  • p={(p_x,p_y,p_z)}设置消失点的x方向，将其设置p_x为 0。
  • q={(q_x,q_y,q_z)}设置消失点的y方向，将其设置q_y为 0。
  • r={(r_x,r_y,r_z)}设置消失点的z方向，将其设置r_z为 0。

默认视角设置为p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}。

为了改变视角，我还添加了一个view={<rotate about x>}{<rotate about z>}键。后者确保我不再需要它tikz-3dplot。

在此处输入图片描述

结果类似，但更易于使用。

\documentclass[tikz]{standalone}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\usepackage{mathtools}

\makeatletter

% Initialize H matrix for perspective view
\pgfmathsetmacro\H@tpp@aa{1}\pgfmathsetmacro\H@tpp@ab{0}\pgfmathsetmacro\H@tpp@ac{0}%\pgfmathsetmacro\H@tpp@ad{0}
\pgfmathsetmacro\H@tpp@ba{0}\pgfmathsetmacro\H@tpp@bb{1}\pgfmathsetmacro\H@tpp@bc{0}%\pgfmathsetmacro\H@tpp@bd{0}
\pgfmathsetmacro\H@tpp@ca{0}\pgfmathsetmacro\H@tpp@cb{0}\pgfmathsetmacro\H@tpp@cc{1}%\pgfmathsetmacro\H@tpp@cd{0}
\pgfmathsetmacro\H@tpp@da{0}\pgfmathsetmacro\H@tpp@db{0}\pgfmathsetmacro\H@tpp@dc{0}%\pgfmathsetmacro\H@tpp@dd{1}

%Initialize H matrix for main rotation
\pgfmathsetmacro\H@rot@aa{1}\pgfmathsetmacro\H@rot@ab{0}\pgfmathsetmacro\H@rot@ac{0}%\pgfmathsetmacro\H@rot@ad{0}
\pgfmathsetmacro\H@rot@ba{0}\pgfmathsetmacro\H@rot@bb{1}\pgfmathsetmacro\H@rot@bc{0}%\pgfmathsetmacro\H@rot@bd{0}
\pgfmathsetmacro\H@rot@ca{0}\pgfmathsetmacro\H@rot@cb{0}\pgfmathsetmacro\H@rot@cc{1}%\pgfmathsetmacro\H@rot@cd{0}
%\pgfmathsetmacro\H@rot@da{0}\pgfmathsetmacro\H@rot@db{0}\pgfmathsetmacro\H@rot@dc{0}\pgfmathsetmacro\H@rot@dd{1}

\pgfkeys{
    /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#1))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ba{#2/#1}
                \pgfmathsetmacro\H@tpp@ca{#3/#1}
                \pgfmathsetmacro\H@tpp@da{ 1/#1}
                \coordinate (vp-p) at (#1,#2,#3);
            \fi
        },
        q/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#2))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ab{#1/#2}
                \pgfmathsetmacro\H@tpp@cb{#3/#2}
                \pgfmathsetmacro\H@tpp@db{ 1/#2}
                \coordinate (vp-q) at (#1,#2,#3);
            \fi
        },
        r/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#3))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ac{#1/#3}
                \pgfmathsetmacro\H@tpp@bc{#2/#3}
                \pgfmathsetmacro\H@tpp@dc{ 1/#3}
                \coordinate (vp-r) at (#1,#2,#3);
            \fi
        },
        coordinate/.code args={#1,#2,#3}{
            \def\tpp@x{#1}
            \def\tpp@y{#2}
            \def\tpp@z{#3}
        },
}

\tikzset{
    view/.code 2 args={
        \pgfmathsetmacro\rot@main@theta{#1}
        \pgfmathsetmacro\rot@main@phi{#2}
        % Row 1
        \pgfmathsetmacro\H@rot@aa{cos(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ab{sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ac{0}
        % Row 2
        \pgfmathsetmacro\H@rot@ba{-cos(\rot@main@theta)*sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@bb{cos(\rot@main@phi)*cos(\rot@main@theta)}
        \pgfmathsetmacro\H@rot@bc{sin(\rot@main@theta)}
        % Row 3
        \pgfmathsetmacro\H@m@ca{sin(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cb{-cos(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cc{cos(\rot@main@theta)}

        \pgfmathsetmacro\vec@x@x{\H@rot@aa}
        \pgfmathsetmacro\vec@y@x{\H@rot@ab}
        \pgfmathsetmacro\vec@z@x{\H@rot@ac}
        \pgfmathsetmacro\vec@x@y{\H@rot@ba}
        \pgfmathsetmacro\vec@y@y{\H@rot@bb}
        \pgfmathsetmacro\vec@z@y{\H@rot@bc}

        \pgfsetxvec{\pgfpoint{\vec@x@x cm}{\vec@x@y cm}}
        \pgfsetyvec{\pgfpoint{\vec@y@x cm}{\vec@y@y cm}}
        \pgfsetzvec{\pgfpoint{\vec@z@x cm}{\vec@z@y cm}}
    },
}

\tikzset{
    perspective/.code={\pgfkeys{/three point perspective/.cd,#1}},
    perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
}

\tikzdeclarecoordinatesystem{three point perspective}{
    \pgfkeys{/three point perspective/.cd,coordinate={#1}}
    \pgfmathsetmacro\temp@p@w{\H@tpp@da*\tpp@x + \H@tpp@db*\tpp@y + \H@tpp@dc*\tpp@z + 1}
    \pgfmathsetmacro\temp@p@x{(\H@tpp@aa*\tpp@x + \H@tpp@ab*\tpp@y + \H@tpp@ac*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@y{(\H@tpp@ba*\tpp@x + \H@tpp@bb*\tpp@y + \H@tpp@bc*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@z{(\H@tpp@ca*\tpp@x + \H@tpp@cb*\tpp@y + \H@tpp@cc*\tpp@z)/\temp@p@w}
    \pgfpointxyz{\temp@p@x}{\temp@p@y}{\temp@p@z}
}
\tikzaliascoordinatesystem{tpp}{three point perspective}

\makeatother

\definecolor{mydarkbluishgray}{RGB}{134 134 191}
\definecolor{mylightbluishgray}{RGB}{215 215 255}

\begin{document}
    \begin{tikzpicture}[line join=round]

        \begin{scope}[
            scale=10,
            view={85}{-40},
            perspective={
                p = {(1,0,0.55)},
                q = {(0,1,0.55)},
            }
        ]
            \fill[mydarkbluishgray]  (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:0,0.5,1) -- (tpp cs:0,0.5,0) -- cycle;
            \fill[mylightbluishgray] (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:1.5,0,1) -- (tpp cs:1.5,0,0) -- cycle;

            \path (tpp cs:0,0,0.5) -- node[sloped]{OMEAG} (tpp cs:1.5,0,0.5);

            \begin{scope}[dotted,line width=0.2pt]
                \node[label=right:p,fill,circle,inner sep = 2pt] (p) at (vp-p){};

                \draw (tpp cs:0,0,1) -- (p.center);
                \draw (tpp cs:0,0,0) -- (p.center);
                \draw (tpp cs:0,0.5,1) -- (p.center);
                \draw (tpp cs:0,0.5,0) -- (p.center);

                \node[label=left:q,fill,circle,inner sep = 2pt] (q) at (vp-q){};

                \draw (tpp cs:0,0,1) -- (q.center);
                \draw (tpp cs:0,0,0) -- (q.center);
                \draw (tpp cs:1.5,0,1) -- (q.center);
                \draw (tpp cs:1.5,0,0) -- (q.center);
            \end{scope}
        \end{scope}
    \end{tikzpicture}
\end{document}

当然我必须制作一个动画来显示不同的消失点距离：

在此处输入图片描述

MWE动画：

\documentclass[tikz]{standalone}

\usepackage{tikz}
\usepackage{tikz-3dplot}

\usepackage{mathtools}

\makeatletter

% Initialize H matrix for perspective view
\pgfmathsetmacro\H@tpp@aa{1}\pgfmathsetmacro\H@tpp@ab{0}\pgfmathsetmacro\H@tpp@ac{0}%\pgfmathsetmacro\H@tpp@ad{0}
\pgfmathsetmacro\H@tpp@ba{0}\pgfmathsetmacro\H@tpp@bb{1}\pgfmathsetmacro\H@tpp@bc{0}%\pgfmathsetmacro\H@tpp@bd{0}
\pgfmathsetmacro\H@tpp@ca{0}\pgfmathsetmacro\H@tpp@cb{0}\pgfmathsetmacro\H@tpp@cc{1}%\pgfmathsetmacro\H@tpp@cd{0}
\pgfmathsetmacro\H@tpp@da{0}\pgfmathsetmacro\H@tpp@db{0}\pgfmathsetmacro\H@tpp@dc{0}%\pgfmathsetmacro\H@tpp@dd{1}

%Initialize H matrix for main rotation
\pgfmathsetmacro\H@rot@aa{1}\pgfmathsetmacro\H@rot@ab{0}\pgfmathsetmacro\H@rot@ac{0}%\pgfmathsetmacro\H@rot@ad{0}
\pgfmathsetmacro\H@rot@ba{0}\pgfmathsetmacro\H@rot@bb{1}\pgfmathsetmacro\H@rot@bc{0}%\pgfmathsetmacro\H@rot@bd{0}
\pgfmathsetmacro\H@rot@ca{0}\pgfmathsetmacro\H@rot@cb{0}\pgfmathsetmacro\H@rot@cc{1}%\pgfmathsetmacro\H@rot@cd{0}
%\pgfmathsetmacro\H@rot@da{0}\pgfmathsetmacro\H@rot@db{0}\pgfmathsetmacro\H@rot@dc{0}\pgfmathsetmacro\H@rot@dd{1}

\pgfkeys{
    /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#1))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ba{#2/#1}
                \pgfmathsetmacro\H@tpp@ca{#3/#1}
                \pgfmathsetmacro\H@tpp@da{ 1/#1}
                \coordinate (vp-p) at (#1,#2,#3);
            \fi
        },
        q/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#2))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ab{#1/#2}
                \pgfmathsetmacro\H@tpp@cb{#3/#2}
                \pgfmathsetmacro\H@tpp@db{ 1/#2}
                \coordinate (vp-q) at (#1,#2,#3);
            \fi
        },
        r/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#3))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ac{#1/#3}
                \pgfmathsetmacro\H@tpp@bc{#2/#3}
                \pgfmathsetmacro\H@tpp@dc{ 1/#3}
                \coordinate (vp-r) at (#1,#2,#3);
            \fi
        },
        coordinate/.code args={#1,#2,#3}{
            \def\tpp@x{#1}
            \def\tpp@y{#2}
            \def\tpp@z{#3}
        },
}

\tikzset{
    view/.code 2 args={
        \pgfmathsetmacro\rot@main@theta{#1}
        \pgfmathsetmacro\rot@main@phi{#2}
        % Row 1
        \pgfmathsetmacro\H@rot@aa{cos(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ab{sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ac{0}
        % Row 2
        \pgfmathsetmacro\H@rot@ba{-cos(\rot@main@theta)*sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@bb{cos(\rot@main@phi)*cos(\rot@main@theta)}
        \pgfmathsetmacro\H@rot@bc{sin(\rot@main@theta)}
        % Row 3
        \pgfmathsetmacro\H@m@ca{sin(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cb{-cos(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cc{cos(\rot@main@theta)}
        % Set vector values
        \pgfmathsetmacro\vec@x@x{\H@rot@aa}
        \pgfmathsetmacro\vec@y@x{\H@rot@ab}
        \pgfmathsetmacro\vec@z@x{\H@rot@ac}
        \pgfmathsetmacro\vec@x@y{\H@rot@ba}
        \pgfmathsetmacro\vec@y@y{\H@rot@bb}
        \pgfmathsetmacro\vec@z@y{\H@rot@bc}
        % Set pgf vectors
        \pgfsetxvec{\pgfpoint{\vec@x@x cm}{\vec@x@y cm}}
        \pgfsetyvec{\pgfpoint{\vec@y@x cm}{\vec@y@y cm}}
        \pgfsetzvec{\pgfpoint{\vec@z@x cm}{\vec@z@y cm}}
    },
}

\tikzset{
    perspective/.code={\pgfkeys{/three point perspective/.cd,#1}},
    perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
}

\tikzdeclarecoordinatesystem{three point perspective}{
    \pgfkeys{/three point perspective/.cd,coordinate={#1}}
    \pgfmathsetmacro\temp@p@w{\H@tpp@da*\tpp@x + \H@tpp@db*\tpp@y + \H@tpp@dc*\tpp@z + 1}
    \pgfmathsetmacro\temp@p@x{(\H@tpp@aa*\tpp@x + \H@tpp@ab*\tpp@y + \H@tpp@ac*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@y{(\H@tpp@ba*\tpp@x + \H@tpp@bb*\tpp@y + \H@tpp@bc*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@z{(\H@tpp@ca*\tpp@x + \H@tpp@cb*\tpp@y + \H@tpp@cc*\tpp@z)/\temp@p@w}
    \pgfpointxyz{\temp@p@x}{\temp@p@y}{\temp@p@z}
}
\tikzaliascoordinatesystem{tpp}{three point perspective}

\makeatother

\definecolor{mydarkbluishgray}{RGB}{134 134 191}
\definecolor{mylightbluishgray}{RGB}{215 215 255}

\begin{document}
    \foreach \vp in {1,1.1,...,5}{
%    \foreach \vp in {1}{
    \begin{tikzpicture}[line join=round]

        \clip (-12,0) rectangle (12,10);

        \begin{scope}[
            scale=10,
            view={85}{-40},
            perspective={
                p = {(\vp,0,0.55)},
                q = {(0,\vp,0.55)},
            }
        ]
            \fill[mydarkbluishgray]  (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:0,0.5,1) -- (tpp cs:0,0.5,0) -- cycle;
            \fill[mylightbluishgray] (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:1.5,0,1) -- (tpp cs:1.5,0,0) -- cycle;

            \path[dotted] (tpp cs:0,0,0.5) -- node[sloped]{OMEAG} (tpp cs:1.5,0,0.5);

            \begin{scope}[dotted,line width=0.2pt]
                \node[label=right:p,fill,circle,inner sep = 2pt] (p) at (vp-p){};

                \draw (tpp cs:0,0,1) -- (p.center);
                \draw (tpp cs:0,0,0) -- (p.center);
                \draw (tpp cs:0,0.5,1) -- (p.center);
                \draw (tpp cs:0,0.5,0) -- (p.center);

                \node[label=left:q,fill,circle,inner sep = 2pt] (q) at (vp-q){};

                \draw (tpp cs:0,0,1) -- (q.center);
                \draw (tpp cs:0,0,0) -- (q.center);
                \draw (tpp cs:1.5,0,1) -- (q.center);
                \draw (tpp cs:1.5,0,0) -- (q.center);
            \end{scope}
        \end{scope}
    \end{tikzpicture}
    }
\end{document}

附录：二点透视理论

p_x <> 0具有两个消失点的透视变换可以用四乘四的变换矩阵 H 来描述，该矩阵 H 是两个消失点 p 和以及 和 的 r的函数r_y <> 0。

在此处输入图片描述

您可以按如下方式构建 H

在此处输入图片描述

为了能够用 H 变换三维表示的点 x，必须在投影空间中表示它，可以写成

在此处输入图片描述

投影空间中的向量与非零标量 alpha 的任何乘积（四维向量的延伸）仍会映射到三维空间中的同一点。例如，以下两点映射到三维空间中的同一点：

在此处输入图片描述

因此，要获得 3D 点的三个坐标，您可以将所有条目除以第四个条目（我们需要将其与变换矩阵 H 相乘后得到）。

答案2

当我看到Max 的回答很棒我忍不住要添加一些decorations.text效果。@Max：如果你想把这个添加到你的答案中，我很乐意删除它。结果也不是很完美，因为单个角色确实被重新缩放了，但角色的不同侧面没有。

编辑：虽然在我之前的版本中高度的重新缩放是可以的（我认为），但我没有正确拉伸字符的宽度。因此，效果比应有的要弱。非常感谢 AndreC 让我走上正确的轨道！

\documentclass[tikz]{standalone}

\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{decorations.text,calc,math}

\usepackage{mathtools}

\makeatletter

% Initialize H matrix for perspective view
\pgfmathsetmacro\H@tpp@aa{1}\pgfmathsetmacro\H@tpp@ab{0}\pgfmathsetmacro\H@tpp@ac{0}%\pgfmathsetmacro\H@tpp@ad{0}
\pgfmathsetmacro\H@tpp@ba{0}\pgfmathsetmacro\H@tpp@bb{1}\pgfmathsetmacro\H@tpp@bc{0}%\pgfmathsetmacro\H@tpp@bd{0}
\pgfmathsetmacro\H@tpp@ca{0}\pgfmathsetmacro\H@tpp@cb{0}\pgfmathsetmacro\H@tpp@cc{1}%\pgfmathsetmacro\H@tpp@cd{0}
\pgfmathsetmacro\H@tpp@da{0}\pgfmathsetmacro\H@tpp@db{0}\pgfmathsetmacro\H@tpp@dc{0}%\pgfmathsetmacro\H@tpp@dd{1}

%Initialize H matrix for main rotation
\pgfmathsetmacro\H@rot@aa{1}\pgfmathsetmacro\H@rot@ab{0}\pgfmathsetmacro\H@rot@ac{0}%\pgfmathsetmacro\H@rot@ad{0}
\pgfmathsetmacro\H@rot@ba{0}\pgfmathsetmacro\H@rot@bb{1}\pgfmathsetmacro\H@rot@bc{0}%\pgfmathsetmacro\H@rot@bd{0}
\pgfmathsetmacro\H@rot@ca{0}\pgfmathsetmacro\H@rot@cb{0}\pgfmathsetmacro\H@rot@cc{1}%\pgfmathsetmacro\H@rot@cd{0}
%\pgfmathsetmacro\H@rot@da{0}\pgfmathsetmacro\H@rot@db{0}\pgfmathsetmacro\H@rot@dc{0}\pgfmathsetmacro\H@rot@dd{1}

\pgfkeys{
    /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#1))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ba{#2/#1}
                \pgfmathsetmacro\H@tpp@ca{#3/#1}
                \pgfmathsetmacro\H@tpp@da{ 1/#1}
                \coordinate (vp-p) at (#1,#2,#3);
            \fi
        },
        q/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#2))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ab{#1/#2}
                \pgfmathsetmacro\H@tpp@cb{#3/#2}
                \pgfmathsetmacro\H@tpp@db{ 1/#2}
                \coordinate (vp-q) at (#1,#2,#3);
            \fi
        },
        r/.code args={(#1,#2,#3)}{
            \pgfmathparse{int(round(#3))}
            \ifnum\pgfmathresult=0\else
                \pgfmathsetmacro\H@tpp@ac{#1/#3}
                \pgfmathsetmacro\H@tpp@bc{#2/#3}
                \pgfmathsetmacro\H@tpp@dc{ 1/#3}
                \coordinate (vp-r) at (#1,#2,#3);
            \fi
        },
        coordinate/.code args={#1,#2,#3}{
            \def\tpp@x{#1}
            \def\tpp@y{#2}
            \def\tpp@z{#3}
        },
}

\tikzset{
    view/.code 2 args={
        \pgfmathsetmacro\rot@main@theta{#1}
        \pgfmathsetmacro\rot@main@phi{#2}
        % Row 1
        \pgfmathsetmacro\H@rot@aa{cos(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ab{sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@ac{0}
        % Row 2
        \pgfmathsetmacro\H@rot@ba{-cos(\rot@main@theta)*sin(\rot@main@phi)}
        \pgfmathsetmacro\H@rot@bb{cos(\rot@main@phi)*cos(\rot@main@theta)}
        \pgfmathsetmacro\H@rot@bc{sin(\rot@main@theta)}
        % Row 3
        \pgfmathsetmacro\H@m@ca{sin(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cb{-cos(\rot@main@phi)*sin(\rot@main@theta)}
        \pgfmathsetmacro\H@m@cc{cos(\rot@main@theta)}
        % Set vector values
        \pgfmathsetmacro\vec@x@x{\H@rot@aa}
        \pgfmathsetmacro\vec@y@x{\H@rot@ab}
        \pgfmathsetmacro\vec@z@x{\H@rot@ac}
        \pgfmathsetmacro\vec@x@y{\H@rot@ba}
        \pgfmathsetmacro\vec@y@y{\H@rot@bb}
        \pgfmathsetmacro\vec@z@y{\H@rot@bc}
        % Set pgf vectors
        \pgfsetxvec{\pgfpoint{\vec@x@x cm}{\vec@x@y cm}}
        \pgfsetyvec{\pgfpoint{\vec@y@x cm}{\vec@y@y cm}}
        \pgfsetzvec{\pgfpoint{\vec@z@x cm}{\vec@z@y cm}}
    },
}

\tikzset{
    perspective/.code={\pgfkeys{/three point perspective/.cd,#1}},
    perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
}

\tikzdeclarecoordinatesystem{three point perspective}{
    \pgfkeys{/three point perspective/.cd,coordinate={#1}}
    \pgfmathsetmacro\temp@p@w{\H@tpp@da*\tpp@x + \H@tpp@db*\tpp@y + \H@tpp@dc*\tpp@z + 1}
    \pgfmathsetmacro\temp@p@x{(\H@tpp@aa*\tpp@x + \H@tpp@ab*\tpp@y + \H@tpp@ac*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@y{(\H@tpp@ba*\tpp@x + \H@tpp@bb*\tpp@y + \H@tpp@bc*\tpp@z)/\temp@p@w}
    \pgfmathsetmacro\temp@p@z{(\H@tpp@ca*\tpp@x + \H@tpp@cb*\tpp@y + \H@tpp@cc*\tpp@z)/\temp@p@w}
    \pgfpointxyz{\temp@p@x}{\temp@p@y}{\temp@p@z}
}
\tikzaliascoordinatesystem{tpp}{three point perspective}

\makeatother

\definecolor{mydarkbluishgray}{RGB}{134 134 191}
\definecolor{mylightbluishgray}{RGB}{215 215 255}

\begin{document}
    \foreach \vp in {1,1.1,...,5}{
%    \foreach \vp in {1}{
    \begin{tikzpicture}[line join=round]

        \clip (-12,0) rectangle (12,10);

        \begin{scope}[
            scale=10,
            view={85}{-40},
            perspective={
                p = {(\vp,0,0.55)},
                q = {(0,\vp,0.55)},
            }
        ]
            \fill[mydarkbluishgray]  (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:0,0.5,1) -- (tpp cs:0,0.5,0) -- cycle;
            \fill[mylightbluishgray] (tpp cs:0,0,0) -- (tpp cs:0,0,1) -- (tpp cs:1.5,0,1) -- (tpp cs:1.5,0,0) -- cycle;

            \path[dotted] (tpp cs:0,0,0.5) -- (tpp cs:1.5,0,0.5)
            node[sloped,midway,opacity=0](TEXT){~~Ducks, marmots and koala bears!~} ;
            % text effects1
            \draw let \p1=($(tpp cs:1.5,0,0.5)-(tpp cs:0,0,0.5)$), % x
            \p2=($(tpp cs:0,0,1)-(tpp cs:0,0,0)$), % z @ x=0
            \p3=($(tpp cs:1.5,0,1)-(tpp cs:1.5,0,0)$), % z @ x=1.5
            \n1={\y3/\y2},\n2={\x1/\y2} % n1 : decrease in z
            in
            \pgfextra{\pgfmathsetmacro{\RatioOne}{\n1}\xdef\RatioOne{\RatioOne}
            \pgfmathsetmacro{\RatioTwo}{\n2}\xdef\RatioTwo{\RatioTwo}
            \typeout{\RatioOne,\RatioTwo}}
            [decorate,decoration={text effects along path, text={Ducks, marmots and koala bears!},raise=-3pt,
            text effects/.cd,
                character count=\i, character total=\n,
                characters={text along path, 
            xscale=\RatioOne*1.15,
            yscale=1.15*((1.5-0.5*\RatioTwo)-(\i/\n)*(1-\RatioTwo))}}] 
            (tpp cs:0.2,0,0.5) -- (tpp cs:1.5,0,0.5);
            \draw (tpp cs:1,0,1) -- (tpp cs:1,0,0);
            %
            \begin{scope}[dotted,line width=0.2pt]
                \node[label=right:p,fill,circle,inner sep = 2pt] (p) at (vp-p){};

                \draw (tpp cs:0,0,1) -- (p.center);
                \draw (tpp cs:0,0,0) -- (p.center);
                \draw (tpp cs:0,0.5,1) -- (p.center);
                \draw (tpp cs:0,0.5,0) -- (p.center);

                \node[label=left:q,fill,circle,inner sep = 2pt] (q) at (vp-q){};

                \draw (tpp cs:0,0,1) -- (q.center);
                \draw (tpp cs:0,0,0) -- (q.center);
                \draw (tpp cs:1.5,0,1) -- (q.center);
                \draw (tpp cs:1.5,0,0) -- (q.center);
            \end{scope}
        \end{scope}
    \end{tikzpicture}
    }
\end{document}

在此处输入图片描述

答案3

\documentclass{article}
\usepackage{pst-solides3d}

\begin{document}
\psset{viewpoint=50 20 30 rtp2xyz,Decran=50}
\begin{pspicture}(-4,-4)(4,5)
\psset{unit=0.5,solidmemory,lightsrc=viewpoint}
\psSolid[object=cube,a=8,action=draw**,name=A,linecolor=red]%
\psset{fontsize=80}
\psSolid[object=plan,action=none, definition=solidface,args=A 0,name=P0]
\psProjection[object=texte,linecolor=red,text=Side A,plan=P0]%
\psSolid[object=plan,action=none,definition=solidface,args=A 1,name=P1]
\psProjection[object=texte,linecolor=red,text=Side B,plan=P1]%
\psSolid[object=plan,action=none,definition=solidface,args=A 4,name=P4]
\psProjection[object=texte,linecolor=red,text=Side E,plan=P4]%
\axesIIID(4,4,4)(6,6,6)
\end{pspicture}
\end{document}

在此处输入图片描述

相关内容