How to draw intersect of line sphere?

Question

How to draw intersect of line sphere?

Answer 1

One way is to use spherical coordinates to define the two points A and B on the sphere, and then draw a dashed line between them and to use calc to extend the line beyond the sphere.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{backgrounds,calc,positioning}
\makeatletter
%from https://tex.stackexchange.com/a/375604/121799
% spherical coordinates 
\define@key{z sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{z sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{z sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
    \setkeys{z sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}{\myradius*cos(\mytheta)}}
\makeatother
\begin{document}
\tdplotsetmaincoords{110}{00} 
\begin{tikzpicture}[font=\sffamily]
\node[circle,fill,inner sep=1.5pt,label=below right:O] (O) at (0,0,0){};
\shade[ball color=blue,opacity=0.3] (O) circle (4);
\begin{scope}[tdplot_main_coords]
\begin{scope}[on background layer]
\draw[thick,dashed] (z spherical cs:radius=4,theta=120,phi=140) 
coordinate (p1) -- (z spherical cs:radius=4,theta=50,phi=240) coordinate (p2);
\draw[thick,dashed] plot[variable=\x,domain=\tdplotmainphi+180:\tdplotmainphi+360,smooth,samples=60]  (z spherical cs:radius=4,theta=90,phi=\x);
\end{scope}
\draw[thick] plot[variable=\x,domain=\tdplotmainphi:\tdplotmainphi+180,smooth,samples=60]  (z spherical cs:radius=4,theta=90,phi=\x);
\end{scope}
\node[circle,fill,inner sep=1.5pt,label=below right:B] at (p2){};
\node[circle,fill,inner sep=1.5pt,label=below right:A] at (p1){};
\draw[thick] let \p1=($(p2)-(p1)$),\n1={atan2(\y1,\x1)} in (p2) -- ++(\n1:2.5)
(p1) -- ++(\n1+180:2.5);
\end{tikzpicture}
\end{document}

Almost forgot the animation.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{backgrounds,calc,positioning}
\makeatletter
%from https://tex.stackexchange.com/a/375604/121799
% spherical coordinates 
\define@key{z sphericalkeys}{radius}{\def\myradius{#1}}
\define@key{z sphericalkeys}{theta}{\def\mytheta{#1}}
\define@key{z sphericalkeys}{phi}{\def\myphi{#1}}
\tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x
    \setkeys{z sphericalkeys}{#1}%
    \pgfpointxyz{\myradius*sin(\mytheta)*cos(\myphi)}{\myradius*sin(\mytheta)*sin(\myphi)}{\myradius*cos(\mytheta)}}
\makeatother
\begin{document}
\foreach \X in {0,9,...,354}
{\tdplotsetmaincoords{120}{0} 
\begin{tikzpicture}[font=\sffamily]
\path (-5,-6) rectangle (5,7);
\node[circle,fill,inner sep=1.5pt,label=below right:O] (O) at (0,0,0){};
\shade[ball color=blue,opacity=0.3] (O) circle (4);
\begin{scope}[tdplot_main_coords]
\begin{scope}[on background layer]
\draw[thick,dashed] (z spherical cs:radius=4,theta=120,phi=140) 
coordinate (p1) -- (z spherical cs:radius=4,theta=20,phi=240+\X) coordinate (p2);
\draw[thick,dashed] plot[variable=\x,domain=\tdplotmainphi+180:\tdplotmainphi+360,smooth,samples=60] 
(z spherical cs:radius=4,theta=90,phi=\x);
\end{scope}
\draw[thick] plot[variable=\x,domain=\tdplotmainphi:\tdplotmainphi+180,smooth,samples=60] 
(z spherical cs:radius=4,theta=90,phi=\x);
\draw[thin,gray] plot[variable=\x,domain=0:360,smooth,samples=60] 
(z spherical cs:radius=4,theta=20,phi=\x);
\end{scope}
\node[circle,fill,inner sep=1.5pt,label=below right:B] at (p2){};
\node[circle,fill,inner sep=1.5pt,label=below right:A] at (p1){};
\draw[thick] let \p1=($(p2)-(p1)$),\n1={atan2(\y1,\x1)} in (p2) -- ++(\n1:2.5)
(p1) -- ++(\n1+180:2.5);
\end{tikzpicture}}
\end{document}

(Note that the spurious lines are not there on the pdf, they come only after the conversion to gif, and I do not know why nor how to get rid of them.)

Addendum

Spurious lines into animated gif above come from ghostscript (a bug with shadings?).

By using pdftopnm then convert, spurious lines disappear:

• pdftoppm -r 100 tikz-3d-sphere.pdf temp -png

• convert -delay 4 temp-* tikz-3d-sphere.gif

• rm temp-*

Answer 2

Consider the sphere center at O(0,0,0) and radius R = 5. We know that two points A(0,-4,-3) and B(-3,0,4) on the sphere. I copied some lines at here How can I draw this cylinder with 3D?

 \documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{backgrounds,calc,positioning}
\begin{document}
    \def\myr{5}
\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords]
\coordinate (O) at (0,0,0);
\coordinate (A) at (0,-4,-3);
\coordinate (B) at (-3,0,4);
\coordinate (C) at ($(B)!1.3!(A)$); 
\coordinate (D) at ($(A)!1.3!(B)$); 
\begin{scope}[canvas is xy plane at z=0]

    \draw[dashed] (\tdplotmainphi:\myr) arc(\tdplotmainphi:\tdplotmainphi+180:\myr);

    \draw[thick] (\tdplotmainphi:\myr) coordinate(BR) arc(\tdplotmainphi:\tdplotmainphi-180:\myr)
    coordinate(BL);
\end{scope}

\begin{scope}[tdplot_screen_coords, on background layer] 
\fill[ball color=orange,opacity=1] (O) circle (\myr); 
\end{scope}

\draw[dashed] (A) -- (B);
\draw[thick] (A) -- (C) (B) -- (D);

 \foreach \point/\position in {A/below,B/left,O/below} {\fill (\point) circle (1.5pt); \node[\position=1pt] at (\point) {$\point$};
}
\end{tikzpicture}
\end{document}