\pgfmathparse/\pgfmathsetmacro 产生一个奇怪的不完整的 \iffalse;

Question

我正在尝试计算\newcommand

\documentclass[tikz]{standalone}

\usepackage{tikz}

\def\spradius{1}
\newcommand*{\projectToSphere}[2]{%
        % calculate a reverse projection point of (#1, #2, 0) on the sphere centered at (0,0,\spradius) of \spradius (radius)
        \pgfmathsetmacro{\XYTwo}{(#1)^2 + (#2)^2}
        \pgfmathsetmacro{\zvalue}{(2 * \XYTwo) / (\XYTwo / \spradius + 4 * \spradius)}
        \pgfmathsetmacro{\xvalue}{(2 * \spradius - \zvalue) / (2 * \spradius) * #1}
        \pgfmathsetmacro{\yvalue}{(2 * \spradius - \zvalue) / (2 * \spradius) * #2}
        {\xvalue}, {\yvalue}, {\zvalue}
}%

\begin{document}

    \begin{tikzpicture}

        \draw[fill=green] (\projectToSphere{3}{4}) circle (0.5pt);
    \end{tikzpicture}
\end{document}

我不断得到! Incomplete \iffalse;

我已尝试过：

• 移至\newcommand​ tikzpicture
• 移出\newcommand文档
• 添加*到\newcommand
• 直接计算是可行的，但是我的实际计算更复杂，因此很难在里面进行直接计算。

有可能制作\pgfmathsetmacro或\pgfmathparse在里面工作吗\newcommand？

编辑：我想实现什么

Answer 1

\pgfmathparse并\pgfmathsetmacro在 中工作\newcommand，只是以tikz一种在大多数情况下都很好但在这里却不行的方式解析坐标。您可以定义一个函数，但不幸的是，您需要逐个组件地插入它。

\documentclass[tikz]{standalone}
\def\spradius{1} %<- maybe not a good practice

\pgfmathdeclarefunction{projectToSphereX}{2}{%
\begingroup%
\pgfmathparse{{projectToSphere(#1,#2)}[0]}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}%
\pgfmathdeclarefunction{projectToSphereY}{2}{%
\begingroup%
\pgfmathparse{{projectToSphere(#1,#2)}[1]}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}%
\pgfmathdeclarefunction{projectToSphereZ}{2}{%
\begingroup%
\pgfmathparse{{projectToSphere(#1,#2)}[2]}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}%


\pgfmathdeclarefunction{projectToSphere}{2}{%
\begingroup%
\pgfmathsetmacro{\XYTwo}{(#1)^2 + (#2)^2}%
\pgfmathsetmacro{\zvalue}{(2 * \XYTwo) / (\XYTwo / \spradius + 4 * \spradius)}%
\pgfmathsetmacro{\xvalue}{(2 * \spradius - \zvalue) / (2 * \spradius) * #1}%
\pgfmathsetmacro{\yvalue}{(2 * \spradius - \zvalue) / (2 * \spradius) * #2}%
\edef\pgfmathresult{\xvalue,\yvalue,\zvalue}%
\pgfmathsmuggle\pgfmathresult\endgroup%
}%


\begin{document}
    \pgfmathparse{projectToSphere(3,4)}
        \begin{tikzpicture}
    \draw[fill=green] 
        ({projectToSphereX(3,4)},{projectToSphereY(3,4)},{projectToSphereZ(3,4)}) 
        circle[radius=0.5pt];
    \end{tikzpicture}
\end{document}

在我看来，您可能正在寻找非线性变换。

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usepgflibrary{fpu}
\usepgfmodule{nonlineartransformations} 
\newcommand{\PgfmathsetmacroFPU}[2]{\begingroup% https://tex.stackexchange.com/a/503835
\pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
\pgfmathsetmacro{#1}{#2}%
\pgfmathsmuggle#1\endgroup}%
\makeatletter
\def\fancyspheretransformation{% similar to the pgfmanual section 103.4.2
\PgfmathsetmacroFPU{\XYTwo}{\pgf@x*\pgf@x+\pgf@y*\pgf@y}%
\PgfmathsetmacroFPU{\zvalue}{-(2*\XYTwo)/(\XYTwo/\spradius+4*\spradius)}%
\PgfmathsetmacroFPU{\xvalue}{(2*\spradius-\zvalue)/(2*\spradius)*\pgf@x}%
\PgfmathsetmacroFPU{\yvalue}{(2*\spradius-\zvalue)/(2*\spradius)*\pgf@y}%
\PgfmathsetmacroFPU{\myx}{cos(\tdplotmainphi)*\xvalue+sin(\tdplotmainphi)*\yvalue}%
\PgfmathsetmacroFPU{\myy}{-cos(\tdplotmaintheta)*sin(\tdplotmainphi)*\xvalue+cos(\tdplotmaintheta)*cos(\tdplotmainphi)*\yvalue-sin(\tdplotmaintheta)*\zvalue}%
\pgf@y=\myy pt% \typeout{z=\zvalue,x=\xvalue,y=\yvalue}%
\pgf@x=\myx pt%
} 
\makeatother
\begin{document}
\begin{tikzpicture}
 \def\spradius{4cm} %<- maybe not a good practice
 \tdplotsetmaincoords{70}{110}
 \begin{scope}[tdplot_main_coords,canvas is xy plane at z=-2]
  \foreach \Color [count=\X starting from -3] in {blue,cyan,green,yellow,orange,red}
   {\foreach \Y in {-3,...,2}
   {\draw[fill=\Color] (\X,\Y) rectangle (\X+1,\Y+1);}}
 \end{scope}
 \begin{scope}[transform shape nonlinear=true,]
  \pgftransformnonlinear{\fancyspheretransformation}
  \foreach \Color [count=\X starting from -3] in {blue,cyan,green,yellow,orange,red}
   {\foreach \Y in {-3,...,2}
   {\draw[fill=\Color] (\X,\Y) rectangle (\X+1,\Y+1);}}
 \end{scope}
\end{tikzpicture}
\end{document}