沿曲面变形/投影 TikZ（-cd）中的文本

Question

主要思想是将text along path图书馆decorations.text与canvas is plane图书馆结合起来3d。在我的最后答案，我已经展示了如何通过设置将节点放置在指定的平面上x 单位向量和y 单位向量. 装饰text along path将每个字符放在一个中\qboxsynced，这意味着在插入文本之前，将当前坐标变换矩阵应用于当前画布变换矩阵。

我定义了一个新的装饰3d text along path。它的主要代码来自装饰text along path，我添加了一些来自的\tikz@canvas@is@plane 代码tikzlibrary3d.code.tex

\def\tikz@canvas@is@plane{
  \pgf@process{\tikz@plane@x}%
  \pgf@xa=\pgf@x%
  \pgf@ya=\pgf@y%
  \pgf@process{\tikz@plane@y}%
  \pgf@xb=\pgf@x%
  \pgf@yb=\pgf@y%
  \pgf@process{\tikz@plane@origin}%
  \edef\pgf@marshal{\noexpand\tikz@addtransform{%
      \noexpand\pgftransformtriangle
      {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}
      {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}
      {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}
      \noexpand\pgftransformscale{0.035146}%
      \noexpand\pgfsetxvec{\noexpand\pgfpoint{1cm}{0cm}}%
      \noexpand\pgfsetyvec{\noexpand\pgfpoint{0cm}{1cm}}%
      \noexpand\pgfsetzvec{\noexpand\pgfpoint{0cm}{0cm}}%
    }}%
  \pgf@marshal%
}%

接下来是应用正确的画布变换\pgfqboxsynced\pgf@hbox。代码如下

  \pgftransformtriangle%
  {\pgfpointxy{0}{0}}%
  {\pgfpointxy{1}{0}}%
  {\pgfpointpolarxy{<some angle>}{1}}%
  \pgftransformscale{0.035146}%
  \pgfsetxvec{\pgfpointxy{1}{0}}%
  \pgfsetyvec{\pgfpointxy{0}{1}}%
  \pgfsetzvec{\pgfpointxy{0}{0}}%

看起来几乎没有什么变化。请注意，在这段代码之前，所有变换都已应用，这意味着\pgfpoingxy{1}{0}指向路径的方向。

关键点是y 单位向量，如上所述，如果<some angle>，90则 y 单位向量垂直于 x 单位向量，这是默认行为。

经过设置 y 单位向量中，有两种方法可以使文本看起来像是放置在曲面上：

将 y 单位向量设置为常数单位向量
将 y 单位向量设置为从线段指向某个点的矢量

第一种方法很容易实现，只需设置<some angle>为<angle of constant y unit vector> - \pgfdecoratedangle（减号\pgfdecoratedangle来反转段旋转）。

第二种方式需要在装饰段装饰之前计算不同 y 单位向量的角度。这项工作可以在persistent precomputation状态下完成typeset

  persistent precomputation={
     \pgfmathanglebetweenpoints%
     {\pgfpointlineatdistance{\pgfdecoratedinputsegmentcompleteddistance}{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@last}}%
     {\pgf@decorate@rel@point}
     \xdef\pgf@decorate@yvec@angle{\pgfmathresult}
  }

最后，定义用户界面

\pgfkeys{%
  /pgf/decoration/.cd,
  3d raise/.store in=\tikz@lib@dec@te@threedimraisevar,
  3d raise=0pt,
  yvec/.code={\tikz@handle@vec{\tikz@lib@dec@te@yvec@point}{\tikz@lib@dec@te@yvec@angle}#1\relax}
  yvec/.initial=90,
}

\tikzset{
  mytext/.style={
    postaction=decorate,
    decoration={
      3d text along path,
      3d raise=.8ex,
      text align={align=center},#1
    }
  }
}

然后您可以使用mytext={...}来指定一段曲面上的文本，/pgf/decoration支持的所有原有键，并添加了两个新键，您可以通过将 y 单位向量设置为常数向量，yvec=<angle>或通过将其设置为指向某个点的向量yvec={<point>}。此外，使用3d raise=<dimen>可获得 y 单位向量的正确移位。

以下是一些示例和完整的代码：

main.tex

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{decorations,decorations.text}
\input{text.tex}

\tikzset{
  mytext/.style={
    postaction=decorate,
    decoration={
      3d text along path,
      3d raise=.8ex,
      text align={align=center},#1
    }
  }
}

\begin{document}
\begin{tikzpicture}
\draw [mytext={text along path, text={Do you know $x + y = z$? You don't know, what a pity!}}] (0, 0) arc (90:90+360:4cm and 1cm);
\draw [yshift=2.5cm, mytext={text={Do you know $x + y = z$? You don't know, what a pity!}, yvec={(0,12)}}] (0, 0) arc (90:90+360:4cm and 1cm);
\draw [yshift=5cm, mytext={text={Do you know $x + y = z$? You don't know, what a pity!}, yvec=90}] (0, 0) arc (90:90+360:4cm and 1cm);
\draw [yshift=6cm, mytext={text={Do you know $x + y = z$? You don't know, what a pity!}, yvec=120}] (0, 0) to[relative, out=80, in=-80, distance=7cm] (0, 4);
\node at (0, -1) {ellipse plane};
\node at (0, 1.5) {point to curve plane};
\node at (0, 4) {shifted curve plane};
\end{tikzpicture}
\end{document}

text.tex

\makeatletter
\newif\iftikz@lib@dec@te@yvecispoint
\let\tikz@lib@dec@te@yvecendpoint=\pgfutil@empty
\def\tikz@lib@dec@te@yvecangle{90}
\let\tikz@lib@dec@te@threedimraisevar=\pgfutil@empty
% keys for 3d text
\pgfkeys{%
  /pgf/decoration/.cd,
  3d raise/.store in=\tikz@lib@dec@te@threedimraisevar,
  3d raise=0pt,
  yvec/.code={\tikz@handle@vec{\tikz@lib@dec@te@yvec@point}{\tikz@lib@dec@te@yvec@angle}#1\relax}
}

% Parse yvec
% If #1 is an angle, save the angle as the direction of yvec
% If #1 is a point, parse the point and save it in
% `\tikz@lib@dec@te@yvecendpoint'
\def\tikz@lib@dec@te@yvec@angle#1{%
  \tikz@lib@dec@te@yvecispointfalse%
  \def\tikz@lib@dec@te@yvecangle{#1}%
}%
\def\tikz@lib@dec@te@yvec@point#1{%
  \tikz@lib@dec@te@yvecispointtrue%
  \def\tikz@lib@dec@te@yvecendpoint{#1}%
}%


% 3d text along path
\pgfdeclaredecoration{3d text along path}{initial}{%
    \state{initial}[
        width=+0pt, next state=left indent,
        persistent precomputation={%
            \edef\pgf@lib@dec@text@indent@left{\pgfkeysvalueof{/pgf/decoration/text align/left indent}}%
            \edef\pgf@lib@dec@text@indent@right{\pgfkeysvalueof{/pgf/decoration/text align/right indent}}%
            \edef\pgf@lib@dec@text@align{\pgfkeysvalueof{/pgf/decoration/text align/align}}%
            \pgfdecoratedremainingdistance=\pgfdecoratedpathlength%
        \advance\pgfdecoratedremainingdistance by-\pgf@lib@dec@text@indent@right\relax%
        \edef\pgfdecoratedpathlength{\the\pgfdecoratedremainingdistance}%
        \pgf@lib@dec@text@getwidth%
        \pgf@x=\pgf@lib@dec@text@width\relax%
        \pgf@y=\pgfdecoratedremainingdistance%
        \ifpgf@lib@dec@text@fit%
            \advance\pgf@y by-\pgf@lib@dec@text@indent@left\relax%
            \advance\pgf@y by-\pgf@x%
            \ifpgf@lib@dec@text@stretch@spaces%
                \def\pgf@lib@dec@text@character@shift{0pt}%
                \divide\pgf@y by\pgf@lib@dec@space@count\relax%
                \edef\pgf@lib@dec@text@space@shift{\the\pgf@y}%
            \else%
                \c@pgf@counta=\pgf@lib@dec@character@count\relax%
                \advance\c@pgf@counta by-1\relax%
                \divide\pgf@y by\c@pgf@counta\relax%
                \edef\pgf@lib@dec@text@character@shift{\the\pgf@y}%
                \def\pgf@lib@dec@text@space@shift{0pt}%
            \fi%
            \ifdim\pgf@y<0pt\relax%
                \pgf@lib@dec@text@fitfalse%
                \pgf@lib@dec@text@stretch@spacesfalse%
                \def\pgf@lib@dec@text@character@shift{0pt}%
                \def\pgf@lib@dec@text@space@shift{0pt}%
            \fi%
        \else%
            \def\pgf@lib@dec@text@character@shift{0pt}%
            \def\pgf@lib@dec@text@space@shift{0pt}%
                \ifx\pgf@lib@dec@text@align\pgf@lib@dec@text@left@text%
                \else%
                    \ifx\pgf@lib@dec@text@align\pgf@lib@dec@text@right@text%
                        \advance\pgf@y by-\pgf@x%
                        \edef\pgf@lib@dec@text@indent@left{\the\pgf@y}%
                    \else%
                        \advance\pgf@y by-\pgf@x%
                        \advance\pgf@y by-\pgf@lib@dec@text@indent@left\relax%
                        \pgf@y=0.5\pgf@y%
                        \advance\pgf@y by\pgf@lib@dec@text@indent@left\relax%
                        \edef\pgf@lib@dec@text@indent@left{\the\pgf@y}%
                    \fi%
                \fi%
        \fi%
        \let\pgfdecorationrestoftext=\pgfdecorationtext%
    }]{}%
\state{left indent}[width=+\pgf@lib@dec@text@indent@left, next state=scan]{}%
%
\state{scan}[
    width=+0pt,
    next state=before typeset,
    persistent precomputation={
        \pgf@lib@dec@text@scanchar%
        \ifvoid\pgf@lib@dec@text@box%
            \setbox\pgf@lib@dec@text@box\hbox{}%
            \wd\pgf@lib@dec@text@box16383pt\relax%
        \fi%
}]{}%
%
\state{before typeset}[width=+.5\wd\pgf@lib@dec@text@box, next state=typeset]{}%
%
\state{typeset}[width=+0pt, next state=after typeset,
  persistent precomputation={
    \iftikz@lib@dec@te@yvecispoint
      \pgfmathanglebetweenpoints%
      {\pgfpointlineatdistance{\pgfdecoratedinputsegmentcompleteddistance}{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@last}}%
      {\tikz@lib@dec@te@yvecendpoint}%
      \edef\tikz@lib@dec@te@yvecangle{\pgfmathresult}
    \fi
  }
]
{%
  \pgftransformxshift{+-.5\wd\pgf@lib@dec@text@box}%
  \setbox\pgf@hbox\hbox{\copy\pgf@lib@dec@text@box}%
  \pgftransformtriangle%
  {\pgfpointxy{0}{0}}%
  {\pgfpointxy{1}{0}}%
  {\pgfpointpolarxy{\tikz@lib@dec@te@yvecangle-\pgfdecoratedangle}{1}}%
%   {\pgfpointpolarxy{\tikz@lib@dec@te@yvecangle-\pgfdecoratedangle}{1}}%
  \pgftransformscale{0.035146}%
  \pgfsetxvec{\pgfpointxy{1}{0}}%
  \pgfsetyvec{\pgfpointxy{0}{1}}%
  \pgfsetzvec{\pgfpointxy{0}{0}}%
  \pgftransformshift{\pgfpoint{0pt}{\tikz@lib@dec@te@threedimraisevar}}
  \pgfqboxsynced\pgf@hbox%
}%
\state{after typeset}[width=+.5\wd\pgf@lib@dec@text@box, next state=shift,
    persistent precomputation={%
    \ifpgf@lib@dec@text@fit%
        \ifpgf@lib@dec@text@stretch@spaces%
            \ifpgf@lib@dec@text@scan@space%
                \let\pgf@lib@dec@text@shift=\pgf@lib@dec@text@space@shift%
            \else%
                \def\pgf@lib@dec@text@shift{0pt}%
            \fi%
        \else%
            \let\pgf@lib@dec@text@shift=\pgf@lib@dec@text@character@shift%
          \fi%
        \else%
            \def\pgf@lib@dec@text@shift{0pt}%
      \fi%
  }]{}%
\state{shift}[width=+\pgf@lib@dec@text@shift, next state=scan]{}%
\state{final}{}%
}%
\makeatother

Answer 1