我想创建一个 tikz 图片来将平面图从球体映射到平面。虽然已经有人出于类似目的这样做过，但我没有找到任何包含图形边缘的图片。
我已经使用了一些模板这里（代码在那里，注释得很好，因此包括 MWE）。但我对 tikz 还不太熟悉，无法添加我想要的东西。
我“仅”需要对 MWE 进行微小的更改，确切地说，我添加了这个小小的自绘修改，以便您看到差异。点和边缘的确切位置并不重要，但球体上的边缘应该是圆的。事实上，它已经帮助我在图形中获得一些线条。
% Source: http://www.texample.net/tikz/examples/map-projections/
\documentclass[varwidth=true, border=2pt]{standalone}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\begin{document}
%% helper macros
\begin{tikzpicture} % CENT
\newcommand\pgfmathsinandcos[3]{%
\pgfmathsetmacro#1{sin(#3)}%
\pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % azimuth
\tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
\pgfmathsinandcos\sint\cost{#3} % latitude
\pgfmathsetmacro\yshift{\cosEl*\sint}
\tikzset{#1/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][1]{
\LongitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
% angle of "visibility"
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
\draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
\draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][1]{
\LatitudePlane{\angEl}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
% angle of "visibility"
\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
\draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
\draw[current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}
\tikzset{%
>=latex, % option for nice arrows
inner sep=0pt,%
outer sep=2pt,%
mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
fill=black,circle}%
}
%% some definitions
\def\R{2.5} % sphere radius
\def\angEl{35} % elevation angle
\def\angAz{-105} % azimuth angle
\def\angPhi{-40} % longitude of point P
\def\angBeta{19} % latitude of point P
%% working planes
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\tikzset{xyplane/.estyle={cm={cos(\angAz),sin(\angAz)*sin(\angEl),-sin(\angAz),
cos(\angAz)*sin(\angEl),(0,-\H)}}}
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhi}
\LatitudePlane[equator]{\angEl}{0}
%% draw xyplane and sphere
\draw[xyplane] (-2*\R,-2*\R) rectangle (2.2*\R,2.8*\R);
\fill[ball color=white] (0,0) circle (\R); % 3D lighting effect
\draw (0,0) circle (\R);
%% characteristic points
\coordinate (O) at (0,0);
\coordinate[mark coordinate] (N) at (0,\H);
\coordinate[mark coordinate] (S) at (0,-\H);
\path[pzplane] (\angBeta:\R) coordinate[mark coordinate] (P);
\path[pzplane] (\R,0) coordinate (PE);
\path[xzplane] (\R,0) coordinate (XE);
\path (PE) ++(0,-\H) coordinate (Paux); % to aid Phat calculation
\coordinate[mark coordinate] (Phat) at (intersection cs: first line={(N)--(P)},
second line={(S)--(Paux)});
%% draw meridians and latitude circles
\DrawLatitudeCircle[\R]{0} % equator
\DrawLongitudeCircle[\R]{\angAz} % xzplane
\DrawLongitudeCircle[\R]{\angAz+90} % yzplane
\DrawLongitudeCircle[\R]{\angPhi} % pzplane
%% draw xyz coordinate system
\draw[xyplane,<->] (1.8*\R,0) node[below] {$x,\xi$} -- (0,0) -- (0,2.4*\R)
node[right] {$y$};
\draw[->] (0,-\H) -- (0,1.6*\R) node[above] {$z$};
%% draw lines and put labels
\draw[blue,dashed] (P) -- (N) +(0.3ex,0.6ex) node[above left,black] {$\mathbf{N}$};
\draw[blue] (P) -- (Phat) node[above right,black] {$\mathbf{\hat{P}}$};
\path (S) +(0.4ex,-0.4ex) node[below] {$\mathbf{0}$};
\draw (P) node[above right] {$\mathbf{P}$};
\end{tikzpicture}
\end{document}
虽然我知道我不是第一个问这个一般性问题的人，但我的问题应该是独一无二的。我很感激任何提示！