在我研究期间，我偶然发现了两个参考系的图示。我认为这个图示不够完整，因为没有画出坐标系。这使得人们很难理解，例如，如何测量赤经和赤纬，见下文。
（Seidelmann 等人）
为了澄清这一点，我试图补充显示坐标系并测量 alpha0 和 delta0 的绘图。这是我得出的结论：
请注意，两个框架的方向略有不同，以便于绘制。
我的主要问题是我无法绘制偏角 delta0。（在 ICRF 框架中，从 alpha0 的弧到身体的北极进行测量。）我正在尝试使用伟大的 tikz3dplot 包来实现这一点，请参阅下面的代码！
\documentclass{article}
\usepackage{wasysym}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage{pgfplots}
% Workaround for making use of externalization possible
% -> remove hardcoded pdflatex and replace by lualatex
\usepgfplotslibrary{external}
\tikzset{external/system call={lualatex \tikzexternalcheckshellescape%
-halt-on-error -interaction=batchmode -jobname "\image" "\texsource"}}
% Redefine rotation sequence for tikz3d-plot to z-y-x
\newcommand{\tdseteulerxyz}{
\renewcommand{\tdplotcalctransformrotmain}{%
%perform some trig for the Euler transformation
\tdplotsinandcos{\sinalpha}{\cosalpha}{\tdplotalpha}
\tdplotsinandcos{\sinbeta}{\cosbeta}{\tdplotbeta}
\tdplotsinandcos{\singamma}{\cosgamma}{\tdplotgamma}
%
\tdplotmult{\sasb}{\sinalpha}{\sinbeta}
\tdplotmult{\sasg}{\sinalpha}{\singamma}
\tdplotmult{\sasbsg}{\sasb}{\singamma}
%
\tdplotmult{\sacb}{\sinalpha}{\cosbeta}
\tdplotmult{\sacg}{\sinalpha}{\cosgamma}
\tdplotmult{\sasbcg}{\sasb}{\cosgamma}
%
\tdplotmult{\casb}{\cosalpha}{\sinbeta}
\tdplotmult{\cacb}{\cosalpha}{\cosbeta}
\tdplotmult{\cacg}{\cosalpha}{\cosgamma}
\tdplotmult{\casg}{\cosalpha}{\singamma}
%
\tdplotmult{\cbsg}{\cosbeta}{\singamma}
\tdplotmult{\cbcg}{\cosbeta}{\cosgamma}
%
\tdplotmult{\casbsg}{\casb}{\singamma}
\tdplotmult{\casbcg}{\casb}{\cosgamma}
%
%determine rotation matrix elements for Euler transformation
\pgfmathsetmacro{\raaeul}{\cacb}
\pgfmathsetmacro{\rabeul}{\casbsg - \sacg}
\pgfmathsetmacro{\raceul}{\sasg + \casbcg}
\pgfmathsetmacro{\rbaeul}{\sacb}
\pgfmathsetmacro{\rbbeul}{\sasbsg + \cacg}
\pgfmathsetmacro{\rbceul}{\sasbcg - \casg}
\pgfmathsetmacro{\rcaeul}{-\sinbeta}
\pgfmathsetmacro{\rcbeul}{\cbsg}
\pgfmathsetmacro{\rcceul}{\cbcg}
}
}
\tdseteulerxyz
\usepackage{siunitx}
\begin{document}
% Set the plot display orientation
% Syntax: \tdplotsetdisplay{\theta_d}{\phi_d}
\tdplotsetmaincoords{60}{110}
% Start tikz picture, and use the tdplot_main_coords style to implement the display
% coordinate transformation provided by 3dplot.
\begin{tikzpicture}[scale=5,tdplot_main_coords]
% Set origin of main (body) coordinate system
\coordinate (O) at (0,0,0);
% Draw main coordinate system
\draw[red, thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{};
\draw[red, thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{};
\draw[red, thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{Body's north pole ($\alpha_0$, $\delta_0$)};
% Draw body's equator
\tdplotdrawarc[red,]{(O)}{1}{0}{360}{anchor=east}{}
% Manually fine-tune position of label
\node[tdplot_main_coords,anchor=south] at (-0.1,1.3,0){\color{red} Body's equator};
% Draw the prime meridian
\tdplotsetthetaplanecoords{60}
\tdplotdrawarc[densely dashed, tdplot_rotated_coords]{(O)}{1}{0}{90}{anchor=north west}{}
% Fine-tune position of label
\node[tdplot_main_coords, rotate=-65] at (0,0.5,0.3){Prime meridian};
% Rotate coordinate system to create ICRF
% Use and angles in z-y-x rotation sequence
% Syntax: \tdplotsetrotatedcoords{\alpha}{\beta}{\gamma}
\tdplotsetrotatedcoords{-60}{-25}{-15}
% Translate the rotated coordinate system (NOT NEEDED HERE)
% Syntax: \tdplotsetrotatedcoordsorigin{point}
\tdplotsetrotatedcoordsorigin{(O)}
% Use the tdplot_rotated_coords style to work in the rotated, translated coordinate frame
% Draw the coordinate axes
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (1,0,0) node[anchor=south west]{\vernal};
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (0,1,0) node[anchor=west]{};
\draw[thick,tdplot_rotated_coords,->, blue] (0,0,0) -- (0,0,1) node[anchor=west]{ICRF north pole};
% Draw the ICRF Equator
\tdplotdrawarc[tdplot_rotated_coords,color=blue]{(O)}{1}{0}{360}{anchor=south
west,color=black}{}
% Manually fine-tune label
\node[tdplot_main_coords,anchor=south] at (0.3,1.33,0){\color{blue} ICRF equator};
% Draw alpha (right ascension), delta (declination) in ICRF
% Get coordinates of body's north-pole in ICRF frame
\tdplottransformmainrot{0}{0}{1}
% This returns
% \tdplotresx
% \tdplotresy
% \tdplotresz
% Get polar coordinates of this vector
\tdplotgetpolarcoords{\tdplotresx}{\tdplotresy}{\tdplotresz}
% This returns
% \tdplotrestheta
% \tdplotresphi
% Draw the right ascension
\tdplotdrawarc[tdplot_rotated_coords, color=magenta, line
width=2pt]{(O)}{1}{0}{\tdplotresphi}{anchor=west}{$\alpha_0$}
% Draw the declination
% THIS GOES WRONG AND DOES NOT WORK
% Should go from end of alpha0 arc to the body's north pole in the ICRF frame
% \tdplotsetrotatedthetaplanecoords{\tdplotresphi}
% \tdplotdrawarc[tdplot_rotated_coords, color=red]{(O)}{1}{0}{90-\tdplotrestheta}{anchor=south
% west,color=black}{\textcolor{blue}{x}}
% Coordinate output for debugging
\node[tdplot_main_coords,anchor=south] at (1,1,2){Main coords: \tdplotrestheta,
\tdplotresphi, \tdplotresx, \tdplotresy, \tdplotresz};
\end{tikzpicture}
\end{document}
（奖励）
我也很难制作如图所示的 90+alpha0 这样的弧线，或者让文本“本初子午线”遵循曲率。任何文体上的帮助也将不胜感激。
Seidelmann、P.Kenneth 等人。IAU/IAG 制图坐标和旋转元素工作组报告：2006 年.Celestial Mech Dyn Astr（2007）98：155–180
答案1
您可能指的是下面这张图所示的内容吗？
一旦你理解了弧线的基本限制，这就会变得非常简单：它只适用于二维平面。这意味着，如果你简单地定义一个与第二个坐标系垂直的第三个坐标系，并且以 x'+alpha0 和 z' 的点与平面重合的方式对齐，你就能够用弧线连接这两个点。
请原谅我对此的快速而粗略的处理，我只是偶然发现了你的问题并且没有对此进行过多思考，我自己正在编写出版物。:p 如果你进行三角学计算，你会很容易找出正确的坐标，而不是我使用的近似坐标。
我希望我也能够回答您有关 90+alpha0 的问题。
无论如何，不用多说，以下是代码：
\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{2mm}
\begin{document}
\tdplotsetmaincoords{60}{110}
\pgfmathsetmacro{\rvec}{0}
\pgfmathsetmacro{\thetavec}{30}
\pgfmathsetmacro{\phivec}{110}
\begin{tikzpicture}[scale=5,tdplot_main_coords]
\coordinate (O) at (0,0,0);
\tdplotsetcoord{P}{\rvec}{\thetavec}{\phivec}
\draw[red,thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[red,thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
\draw[red,thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
\tdplotsetthetaplanecoords{\phivec}
\tdplotdrawarc[tdplot_rotated_coords]{(0,0,0)}{1}{0}{\thetavec}{anchor=south west}{$\gamma_{0}$}
\draw[dashed,red] (1,0,0) arc (0:360:1);
\tdplotsetrotatedcoords{\phivec}{\thetavec}{30}
\tdplotsetrotatedcoordsorigin{(P)}
\draw[blue,thick,tdplot_rotated_coords,->] (0,0,0) -- (-1,0,0) node[anchor=south west]{$x'$};
\draw[blue,thick,tdplot_rotated_coords,->] (0,0,0) -- (0,-1,0) node[anchor=south west]{$y'$};
\draw[blue,thick,tdplot_rotated_coords,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z'$};
\draw[dashed,blue,tdplot_rotated_coords] (1,0,0) arc (0:360:1);
\tdplotdrawarc[black,line width=1pt,tdplot_rotated_coords]{(0,0,0)}{1}{270}{180}{anchor=west}{$90+\alpha_{0}$}
\tdplotdrawarc[green,line width=2pt,dashed,tdplot_rotated_coords]{(0,0,0)}{1}{210}{180}{anchor=east}{$\alpha_{0}$}
\pgfmathsetmacro{\rveca}{0}
\pgfmathsetmacro{\thetaveca}{131}
\pgfmathsetmacro{\phiveca}{101}
\tdplotsetcoord{Q}{\rveca}{\thetaveca}{\phiveca}
\tdplotsetrotatedcoords{\phiveca}{\thetaveca}{35}
\tdplotsetrotatedcoordsorigin{(Q)}
\tdplotdrawarc[black,dashed,tdplot_rotated_coords]{(0,0,0)}{1}{0}{90}{anchor=east}{$\delta_{0}$}
\pgfmathsetmacro{\rvecb}{0}
\pgfmathsetmacro{\thetavecb}{-90}
\pgfmathsetmacro{\phivecb}{-30}
\tdplotsetcoord{R}{\rvecb}{\thetavecb}{\phivecb}
\tdplotsetrotatedcoords{\phivecb}{\thetavecb}{0}
\tdplotsetrotatedcoordsorigin{(R)}
\tdplotdrawarc[black,tdplot_rotated_coords]{(0,0,0)}{1}{0}{90}{anchor=west}{Prime Meridian}
\end{tikzpicture}
\end{document}
哦，是的！最后一件事：您可以将任意变换矩阵应用于坐标系，请参阅 tikz 手册第 2.18 章。如果您想弯曲文本，请查看该章节。这取决于您的三角学有多好，这是一种方法！就我个人而言，我认为这需要付出很多努力，只是为了让图表变得漂亮。但如果你想让你的大脑活跃起来，那就去做吧！;)