\documentclass[a4paper,10pt]{article}
% Use UTF8 since the laptop is configured so and use ngerman for word breaking.
% If you encounter an encoding problem, remove the line with utf8.
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage[pdftex]{graphicx}
% TikZ für schöne Grafiken und so.
\usepackage{tikz}
\usetikzlibrary{positioning,calc,fadings,decorations.pathreplacing,arrows}
\usepackage{pgfplots}
% \usepackage{hyperref}
\usepackage{colortbl}
\usepackage{tabularx}
\usepackage{color}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{listings}
\usepackage{multirow}
\usepackage{fancyhdr}
\usepackage{multicol}
\usepackage{pdfpages}
\usepackage[colorlinks=true,
linkcolor=black,
citecolor=black,
filecolor=black,
pagecolor=black,
urlcolor=black,
bookmarks=true,
bookmarksopen=true,
bookmarksopenlevel=3,
plainpages=false,
pdfpagelabels=true]{hyperref}
% Hack for german umlaute
\lstset{
literate={ö}{{\"o}}1
{ä}{{\"a}}1
{ü}{{\"u}}1
}
% I set here a different sidemargin because the original margin looks not so
% good for normal documents. Additionally I have to enlarge the textwidth.
\setlength{\oddsidemargin}{0cm}
\setlength{\evensidemargin}{0cm}
\addtolength{\textwidth}{4cm}
\newcolumntype{C}[1]{>{\centering\arraybackslash}m{#1}}
\begin{document}
% Here I use the up-to-date font encoding T1 and the font familly Computer Modern
% Sans Serif (since I don't like the standard font) medium and normal (non-italic or so).
\usefont{T1}{cmss}{m}{n}
\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,thin,black] (\angVis:1) arc (\angVis:\angVis+180:1);
\draw[current plane,thin,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}%this is fake: for drawing the grid
\newcommand\DrawLongitudeCirclered[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,red,thick] (150:1) arc (150:180:1);
%\draw[current plane,dashed] (-50:1) arc (-50:-35:1);
}%for drawing the grid
\newcommand\DLongredd[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,black,dashed, ultra thick] (150:1) arc (150:180:1);
}
\newcommand\DLatred[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,dashed,black,ultra thick] (-50:1) arc (-50:-35:1);
}
\newcommand\fillred[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,red,thin] (\angVis:1) arc (\angVis:\angVis+180:1);
}
\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,thin,black] (\angVis:1) arc (\angVis:-\angVis-180:1);
\draw[current plane,thin,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}%Defining functions to draw limited latitude circles (for the red mesh)
\newcommand\DrawLatitudeCirclered[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,red,thick] (-\angVis-50:1) arc (-\angVis-50:-\angVis-20:1);
\draw[current plane,red,thick] (-50:1) arc (-50:-35:1);
}
\tikzset{
>=latex,
inner sep=0pt,
outer sep=2pt,
mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt, fill=black,circle}
}
\begin{tikzpicture}[scale=1,every node/.style={minimum size=1cm}]
%% some definitions
\def\R{4} % sphere radius
\def\angEl{25} % elevation angle
\def\angAz{-100} % azimuth angle
\def\angPhiOne{-110} % longitude of point P
\def\angPhiTwo{-45} % longitude of point Q
\def\angBeta{30} % latitude of point P and Q
%% working planes
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhiOne}
\LongitudePlane[qzplane]{\angEl}{\angPhiTwo}
\LongitudePlane[nzplane]{\angEl}{-86}
\LatitudePlane[equator]{\angEl}{0}
\fill[ball color=white!10] (0,0) circle (\R); % 3D lighting effect
\coordinate (O) at (0,0);
\coordinate[mark coordinate] (N) at (0,\H);
\coordinate[mark coordinate] (S) at (0,-\H);
\DrawLongitudeCircle[\R]{\angPhiOne} % pzplane
\DrawLongitudeCircle[\R]{\angPhiTwo} % qzplane
\DrawLatitudeCircle[\R]{\angBeta}
\DrawLatitudeCircle[\R]{0} % equator
%labelling north and south
\node[above=8pt] at (N) {$\mathbf{N}$};
\node[below=8pt] at (S) {$\mathbf{S}$};
\draw[-,dashed, thick] (N) -- (S);
%setup coordinates P and Q
\path[pzplane] (0:\R) coordinate (P);
\draw[->] (O) -- node[above=4pt] {$\overrightarrow{P}$} (P);
\path[qzplane] (\angBeta:\R) coordinate (Q);
\draw[->] (O) -- node[above=2pt] {$\overrightarrow{Q}$} (Q);
\path[nzplane] (153:\R) coordinate (N);
\draw[->,color=red] (O) -- node[right=2pt] {$\overrightarrow{N}$} (N);
\draw (P) arc (-110:-45:\R) (Q);
\end{tikzpicture}
\end{document}