Drawing six hemispheres

Question

I am trying to draw the following six hemispheres next to each other with their centers aligned on a horizontal line. I am using Alenanno's answer to the question.

I have done this just for the hemisphere with z > 0 using the following code taken from the question.

\documentclass[12pt]{report}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{60}{110}
\pgfmathsetmacro{\radius}{1}
\pgfmathsetmacro{\thetavec}{0}
\pgfmathsetmacro{\phivec}{0}
\begin{tikzpicture}[scale=1,tdplot_main_coords]
\tdplotsetthetaplanecoords{\phivec}
\draw[dashed] (\radius,0,0) arc (0:360:\radius);
\shade[ball color=blue!10!white,opacity=0.2] (1cm,0) arc (0:-180:1cm and 5mm)
arc(180:0:1cm and 1cm);
\shade[ball color=blue!10!white,opacity=0.2] (1cm,0) arc (180::1cm and 5mm)
arc(360:0:1cm and 1cm);
\end{tikzpicture}
\end{document}

@anis Hi. I want to draw the remaining five hemispheres as I explained in above question. — Math learner, May 12 '23 at 08:36
first, there is a compiling error with this (180::1cm and 5mm) — anis, May 12 '23 at 08:44

Juan Castaño · Accepted Answer · 2023-05-12T19:32:22.937

Welcome to TeX.SE!!

This is another approach, using an isometric view (from perspective TikZ library) and a \foreach loop. This way you only need tho draw two hemispheres and rotate them.

For example:

\documentclass[tikz,border=1.618mm]{standalone}
\usetikzlibrary{perspective}
\tikzset{sphere/.style={shading=ball,ball color=gray!30,fill opacity=0.8}}
\begin{document}
\begin{tikzpicture}[isometric view,rotate around z=180]
\foreach\i in {0,1,2}
{
  \begin{scope}[shift={(135:4.5\i)},rotate=-120\i]
    \draw (0,0) circle (1);
    \draw[sphere] (-45:1) arc (180:0:1cm) arc (135:-45:1);
  \end{scope}
  \begin{scope}[shift={(135:4.5\i+2.25)},rotate=-120\i]
    \draw[sphere] (0,0) circle (1);
    \draw[sphere] (-45:1) arc (-180:0:1cm) arc (135:-45:1);
  \end{scope}
}

\end{tikzpicture}
\end{document}

Update: Almost the same, but using a \pic. Now it's more customizable, but also requires more code:

\documentclass[tikz,border=1.618mm]{standalone}
\tikzset
{
  sphere/.style={ball color=#1,fill opacity=0.6},
  pics/hemisphere/.style={code=%
  {
     \ifnum#1=0
       \draw (0,0) ellipse (1 and {sqrt(1/3)});
     \fi
     \begin{scope}
       \clip (-1,0) arc (180:0:1cm) arc (0:-180:1 and {(1-2#1)sqrt(1/3)});
       \fill[pic actions] (0,0) circle (1);
     \end{scope}
     \draw (-1,0) arc (180:0:1cm) arc (0:-180:1 and {(1-2#1)sqrt(1/3)});
     \ifnum#1=1
       \begin{scope}
         \clip (0,0) ellipse (1 and {sqrt(1/3)});
         \fill[pic actions] (0.25,-0.25) circle (2);
       \end{scope}
       \draw (0,0) ellipse (1 and {sqrt(1/3)});
     \fi
   }},
}
\begin{document}
\begin{tikzpicture}
\pic[sphere=red!70]             at (0,0)    {hemisphere=0}; % 0 = interior not visible
\pic[sphere=red!70,rotate=180]  at (2.25,0) {hemisphere=1}; % 1 = interior visible
\pic[sphere=blue!50,rotate=60]  at (5,0)    {hemisphere=1};
\pic[sphere=blue!50,rotate=240] at (6.5,0)  {hemisphere=0};
\pic[sphere=green,rotate=120]   at (9.5,0)  {hemisphere=0};
\pic[sphere=green,rotate=300]   at (11,0)   {hemisphere=1};
\end{tikzpicture}
\end{document}

Thanks for your very helpful answer. – Math learner May 12 '23 at 08:57 — Math learner, May 12 '23 at 08:57

Black Mild · Answer 2 · 2023-05-22T01:44:20.223

For this situation, Asymptote with the 3D module three gives a kind of code simplification.

Starting with the unithemisphere, we can take reflection with respect to the XY-plane, suitable rotations and shifts. That's it!

// http://asymptote.ualberta.ca/
unitsize(2cm);
import three;
currentprojection=orthographic(X+.3Z,zoom=.9);
picture uhsN;                    // the north hemisphere
draw(uhsN,unithemisphere,yellow+opacity(.7));
draw(uhsN,unitcircle3,gray);
picture uhsS=zscale3(-1)*uhsN;   // the south hemisphere
real a=.3,b=.6;
add(uhsN);
add(shift(0,2+a,0)uhsS);
add(shift(0,4+a+b,0)rotate(60,X)uhsN);
add(shift(0,4.5+2a+b,0)rotate(60,X)uhsS);
add(shift(0,7+a+b,0)rotate(-60,X)uhsN);
add(shift(0,9+2a+b,0)rotate(-60,X)*uhsS);

Jasper Habicht · Answer 3 · 2023-05-12T10:31:23.130

Three cuts without any 3D-related packages (to provide a simple solution which admittedly might not work everywhere):

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\begin{scope}[shift={(-2.25,0)}]
    \draw[dashed] (1,0) 
        arc[start angle=0, end angle=360, x radius=1, y radius=1];
    \shade[ball color=blue!10!white, opacity=0.2] (1,0) 
        arc[start angle=0, end angle=360, x radius=1, y radius=1];
\end{scope}
\begin{scope}[shift={(-2.25,-2.25)}]
    \draw[dashed, opacity=0.25] (1,0) 
        arc[start angle=0, end angle=360, x radius=1, y radius=1];
    \shade[ball color=blue!10!white, opacity=0.2] (1,0) 
        arc[start angle=0, end angle=360, x radius=1, y radius=1];
\end{scope}
\begin{scope}[shift={(0,0)}]
    \draw[dashed] (1,0) 
        arc[start angle=0, end angle=-180, x radius=1, y radius=.5];
    \draw[dashed, opacity=0.25] (1,0) 
        arc[start angle=0, end angle=180, x radius=1, y radius=.5];
    \shade[ball color=blue!10!white, opacity=0.2] (1,0) 
        arc[start angle=0, end angle=-180, x radius=1, y radius=.5]
        arc[start angle=180, end angle=0, x radius=1, y radius=1];
\end{scope}
\begin{scope}[shift={(0,-2.25)}]
    \draw[dashed] (1,0) 
        arc[start angle=0, end angle=360, x radius=1, y radius=.5];
    \shade[ball color=blue!10!white, opacity=0.2] (1,0) 
        arc[start angle=0, end angle=180, x radius=1, y radius=.5]
        arc[start angle=180, end angle=360, x radius=1, y radius=1];
\end{scope}
\begin{scope}[shift={(2.25,0)}]
    \draw[dashed] (0,1) 
        arc[start angle=90, end angle=450, x radius=.5, y radius=1];
    \shade[ball color=blue!10!white, opacity=0.2] (0,1) 
        arc[start angle=90, end angle=-90, x radius=.5, y radius=1]
        arc[start angle=270, end angle=90, x radius=1, y radius=1];
\end{scope}
\begin{scope}[shift={(2.25,-2.25)}]
    \draw[dashed] (0,1) 
        arc[start angle=90, end angle=270, x radius=.5, y radius=1];
    \draw[dashed, opacity=0.25] (0,1) 
        arc[start angle=90, end angle=-90, x radius=.5, y radius=1];
    \shade[ball color=blue!10!white, opacity=0.2] (0,1) 
        arc[start angle=90, end angle=270, x radius=.5, y radius=1]
        arc[start angle=-90, end angle=90, x radius=1, y radius=1];
\end{scope}
\end{tikzpicture}
\end{document}

Thanks for your answer. I will try to see if can rotate the first and forth hemispheres to get them look sitting inside three dimensions. — Math learner, May 12 '23 at 09:00
@Ali With the above code, you can't rotate the single parts in a 3D manner, because I did not make use of such libraries. The hemispheres in the first column are just plain circles really. I just thought that this could be a simple solution in certain cases. — Jasper Habicht, May 12 '23 at 09:02
The above follows a coordinate system where the x axis is horizontal, the y axis is vertical and the z axis is at 45 degrees (and scaled to 50%). — Jasper Habicht, May 12 '23 at 09:14

Drawing six hemispheres

3 Answers3