如果没有John Kormylo 制作的超酷宏和Torbjørn T. 的回答非常有帮助。我不可能走到这一步。我的最终目标是让使用 Ti 伪造 3D 球体变得更容易钾Z. 这已经很好了,但我想尝试一种不同的、可以说是更直接的方法来绘制相关对象。这是我的 MWE。
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shadings}
% parametrizations from https://tex.stackexchange.com/a/410379/121799
\newcommand{\latitudearc}[4]{% #1=label (optional), #2=latitude
%#3 start angle #4 end angle
\pgfextra{\pgfmathsetmacro{\RX}{\RadiusSphere*cos(#2)} % from https://tex.stackexchange.com/a/410567/121799
\global\let\RX=\RX % from https://tex.stackexchange.com/a/352269/121799
\pgfmathsetmacro{\RY}{\RX*sin(\Clat)}%
\global\let\RY=\RY
\pgfmathsetmacro{\CY}{\RadiusSphere*sin(#2)*cos(\Clat)}
\global\let\CY=\CY
\pgfmathsetmacro{\Xend}{\RX*cos(#4)}
\global\let\Xend=\Xend
\pgfmathsetmacro{\Yend}{\CY+\RY*sin(#4)}
\global\let\Yend=\Yend}%
plot [domain=#3:#4,smooth,#1] ({\RX*cos(\noexpand\x)},{\CY+\RY*sin(\noexpand\x)})
}
% compute ellipse rotation=\ROT, xradius=\RX, arc angle at equator=\LAT
\newcommand{\longitudearc}[4]{% #1=label (optional), #2=longitude
%#3 start angle #4 end angle
\pgfextra{\pgfmathsetmacro{\ROT}{atan2(sin(\Clat)*sin(#2-\Clong),cos(#2-\Clong))}% alpha
\global\let\ROT=\ROT
\pgfmathsetmacro{\LAT}{asin(cos(\Clat)*cos(\ROT))}% north pole theta_n
\global\let\LAT=\LAT
\pgfmathsetmacro{\RX}{\RadiusSphere*tan(\LAT)*tan(\ROT)}% r_x
\global\let\RX=\RX
\pgfmathsetmacro{\DELTAX}{-90+\LAT}
\global\let\DELTAX=\DELTAX
\pgfmathsetmacro{\Xend}{\RX*cos(\ROT)*cos(#4+\DELTAX)-\RadiusSphere*sin(\ROT)*sin(#4+\DELTAX)}
\global\let\Xend=\Xend
\pgfmathsetmacro{\Yend}{\RadiusSphere*cos(\ROT)*sin(#4+\DELTAX)+\RX*sin(\ROT)*cos(#4+\DELTAX)}
\global\let\Yend=\Yend
}
plot[domain=#3:#4,smooth,#1]({\RX*cos(\ROT)*cos(\noexpand\x+\DELTAX)-\RadiusSphere*sin(\ROT)*sin(\noexpand\x+\DELTAX)},
{\RadiusSphere*cos(\ROT)*sin(\noexpand\x+\DELTAX)+\RX*sin(\ROT)*cos(\noexpand\x+\DELTAX)})
}
\newcommand{\hotspot}[3]{% #1=label (optional), #3=latitude, #2=longitude
\pgfextra{\pgfmathsetmacro{\RX}{\RadiusSphere*cos(#3)} % from https://tex.stackexchange.com/a/410567/121799
\global\let\RX=\RX % from https://tex.stackexchange.com/a/352269/121799
\pgfmathsetmacro{\RY}{\RX*sin(\Clat)}%
\global\let\RY=\RY
\pgfmathsetmacro{\CY}{\RadiusSphere*sin(#3)*cos(\Clat)}
\global\let\CY=\CY
\pgfmathsetmacro{\Xloc}{\RX*cos(#2)}
\global\let\Xloc=\Xloc
\pgfmathsetmacro{\Yloc}{\CY+\RY*sin(#2)}
\global\let\Yloc=\Yloc}%
}
\begin{document}
\begin{tikzpicture}
\def\RadiusSphere{4}% sphere radius
\def\Clat{20}% point of view latitude
\def\Clong{-90}% point of view longitude
\shade[ball color = gray!40, opacity = 0.5] (0,0) circle (\RadiusSphere);
\hotspot{0}{-120}{-40}
\filldraw (\Xloc,\Yloc) circle (0.2);
\hotspot{0}{-120}{30}
\filldraw (\Xloc,\Yloc) circle (0.2);
\hotspot{0}{-50}{-40}
\filldraw (\Xloc,\Yloc) circle (0.2);
\hotspot{0}{-50}{30}
\filldraw (\Xloc,\Yloc) circle (0.2);
\begin{scope}
\clip[variable=\x] \longitudearc{blue}{-120}{-40}{30}
%\pgfextra{\hotspot{0}{-50}{-40}} to (\Xloc,\Yloc) % <-NEEDED?
\latitudearc{blue}{30}{-120}{-50} %to ({\Xend},{\Yend})
%\pgfextra{\hotspot{0}{-120}{-40}} to (\Xloc,\Yloc) % <-NEEDED?
\longitudearc{blue}{-50}{30}{-40} %to ({\Xend},{\Yend})
%\pgfextra{\hotspot{0}{-120}{30}} to (\Xloc,\Yloc) % <-NEEDED?
\latitudearc{blue}{-40}{-50}{-120} %to ({\Xend},{\Yend})
%\pgfextra{\hotspot{0}{-50}{30}} to (\Xloc,\Yloc) % <-NEEDED?
-- cycle;
\shade[ball color = blue!40, opacity = 0.5] (0,0) circle (\RadiusSphere);
\end{scope}
\end{tikzpicture}
\end{document}
这不是我想要的。但是,如果我取消注释底部\pgfextra
的命令scope
,即使用scope
\begin{scope}
\clip[variable=\x] \longitudearc{blue}{-120}{-40}{30}
\pgfextra{\hotspot{0}{-50}{-40}} to (\Xloc,\Yloc) % <-NEEDED?
\latitudearc{blue}{30}{-120}{-50} %to ({\Xend},{\Yend})
\pgfextra{\hotspot{0}{-120}{-40}} to (\Xloc,\Yloc) % <-NEEDED?
\longitudearc{blue}{-50}{30}{-40} %to ({\Xend},{\Yend})
\pgfextra{\hotspot{0}{-120}{30}} to (\Xloc,\Yloc) % <-NEEDED?
\latitudearc{blue}{-40}{-50}{-120} %to ({\Xend},{\Yend})
\pgfextra{\hotspot{0}{-50}{30}} to (\Xloc,\Yloc) % <-NEEDED?
-- cycle;
\shade[ball color = blue!40, opacity = 0.5] (0,0) circle (\RadiusSphere);
\end{scope}
相反,我得到:
这几乎就是我想要的。(上下边界不正确。)也就是说,通过人为地将点插入路径,我可以得到由图限定的形状。在上图中,Ti钾出于某种原因,Z 总是通过返回起点来“完成”各个情节。现在我的问题是,是否有办法关闭它。
编辑:这是一个非常简单的例子。
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}
\node[text width=3.5cm] at (1,5){with cycle};
\path[draw,blue,variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)}) -- cycle;
\clip[variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)}) -- cycle;
\fill (0,0) circle (1);
\end{scope}
\begin{scope}[transform canvas={xshift=4cm}]
\node[text width=3.5cm] at (1,5){path closed by hand};
\path[draw,blue,variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)}) -- (0,0);
\clip[variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)}) -- (0,0);
\fill (0,0) circle (1);
\end{scope}
\begin{scope}[transform canvas={xshift=10cm}]
\node[text width=3.5cm] at (1,5){a somewhat more complex example};
\path[draw,blue,variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)})
plot ({-\x},{-4+\x*\x})-- (0,0);
\clip[variable=\x,domain=0:2] (0,0) -- plot ({\x},{\x*\x})
plot ({1*(2-\x)},{4*(1-\x)})
plot ({-\x},{-4+\x*\x})-- (0,0);
\fill (0,0) circle (1);
\draw [red,dashed] (0,0) -- (2,4);
\draw [red,dashed] (0,0) -- (0,-4);
\end{scope}
\end{tikzpicture}
\end{document}
可以看出,只有在我手动关闭路径的中间图中,剪辑才是正确的(或者至少我认为应该是正确的)。在右边的图中,即使我手动关闭路径,我认为剪辑也不是应该的。我还添加了红色虚线,似乎表明每个图都形成一条闭合路径。但中间的例子表明情况并非总是如此。有没有办法总是有中间例子中的行为没有手动添加坐标?
答案1
如果前面没有--
(p.326, pgfmanual, v3.0.1a),则每个绘图都以隐式移动到操作开始。即使当前点与绘图的第一个坐标相同,也会包含隐式移动到操作。
要获得单个闭合路径,您必须通过 链接您的绘图操作--
。但 TikZ 不允许在 之后调用宏--
:您不能\latitudearc
在 之后使用您的宏--
。
这是一个更符合 TikZ 精神的解决方案。此解决方案不再使用宏,而是使用键来定义坐标(hot spot
)或构建弧(latitude arc
和longitude arc
)。
\documentclass[tikz]{standalone}
\usetikzlibrary{shadings}
\tikzset{
hot spot/.style n args={2}{% #1=longitude, #2=latitude
/utils/exec={
\pgfmathsetmacro{\RX}{\RadiusSphere*cos(#2)} % from https://tex.stackexchange.com/a/410567/121799
\pgfmathsetmacro{\RY}{\RX*sin(\Clat)}%
\pgfmathsetmacro{\CY}{\RadiusSphere*sin(#2)*cos(\Clat)}
\pgfmathsetmacro{\Xloc}{\RX*cos(#1)}
\pgfmathsetmacro{\Yloc}{\CY+\RY*sin(#1)}
},
at={(\Xloc,\Yloc)},
},
latitude arc/.style n args={4}{% #1=additional keys for plot, #2=latitude, #3 start longitude, #4 end longitude
to path={
\pgfextra{
\pgfmathsetmacro{\RX}{\RadiusSphere*cos(#2)} % from https://tex.stackexchange.com/a/410567/121799
\pgfmathsetmacro{\RY}{\RX*sin(\Clat)}%
\pgfmathsetmacro{\CY}{\RadiusSphere*sin(#2)*cos(\Clat)}
\pgfmathsetmacro{\Xend}{\RX*cos(#4)}
\pgfmathsetmacro{\Yend}{\CY+\RY*sin(#4)}
}%
-- plot [domain=#3:#4,#1] ({\RX*cos(\x)},{\CY+\RY*sin(\x)}) -- (\tikztotarget)
},
},
longitude arc/.style n args={4}{% #1=additional keys for plot, #2=longitude, #3 start latitude, #4 end latitude
to path={
\pgfextra{
\pgfmathsetmacro{\ROT}{atan2(sin(\Clat)*sin(#2-\Clong),cos(#2-\Clong))}% alpha
\pgfmathsetmacro{\LAT}{asin(cos(\Clat)*cos(\ROT))}% north pole theta_n
\pgfmathsetmacro{\RX}{\RadiusSphere*tan(\LAT)*tan(\ROT)}% r_x
\pgfmathsetmacro{\DELTAX}{-90+\LAT}
\pgfmathsetmacro{\Xend}{\RX*cos(\ROT)*cos(#4+\DELTAX)-\RadiusSphere*sin(\ROT)*sin(#4+\DELTAX)}
\pgfmathsetmacro{\Yend}{\RadiusSphere*cos(\ROT)*sin(#4+\DELTAX)+\RX*sin(\ROT)*cos(#4+\DELTAX)}
}
--
plot[domain=#3:#4,variable=\x,#1]({\RX*cos(\ROT)*cos(\x+\DELTAX)-\RadiusSphere*sin(\ROT)*sin(\x+\DELTAX)},
{\RadiusSphere*cos(\ROT)*sin(\x+\DELTAX)+\RX*sin(\ROT)*cos(\x+\DELTAX)})
-- (\tikztotarget)
},
},
}
\begin{document}
\begin{tikzpicture}
\def\RadiusSphere{4}% sphere radius
\def\Clat{20}% point of view latitude
\def\Clong{-90}% point of view longitude
\shade[ball color = gray!40, opacity = 0.5] (0,0) circle (\RadiusSphere);
\coordinate[hot spot={-120}{-40}] (p1);
\coordinate[hot spot={-120}{30}] (p2);
\coordinate[hot spot={-50}{-40}] (p3);
\coordinate[hot spot={-50}{30}] (p4);
\begin{scope}
\clip
(p2) to[latitude arc={}{30}{-120}{-50}]
(p4) to[longitude arc={}{-50}{30}{-40}]
(p3) to[latitude arc={}{-40}{-50}{-120}]
(p1) to[longitude arc={}{-120}{-40}{30}]
cycle;
\shade[ball color=blue!40,opacity=.5] (0,0) circle (\RadiusSphere);
\end{scope}
\path \foreach \num in {1,...,4}{(p\num) node{p\num}};
\end{tikzpicture}
\end{document}