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% Dominik Gothe
% Based on Marco Miani's work on "Spherical and cartesian grids"
\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{amsmath}
\pgfplotsset{compat=1.9}
%\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\tikzset{ >=latex } % Prettier Arrows
%% helper macros
\def\R{5} % Radius of Sphere
\def\D{5} % Distance to Project outside of Sphere
\def\tilt{10} % Tilt of Sphere
\def\zeroAz{-100} % Zero Azimuth Reference Line
\def\leftLong{-25} % Longitude of point P
\def\midLong{-40}
\def\rightLong{-55} % longitude of point Q
\def\lowLat{30} % Low Latitude of FOV
\def\midLat{45} % Center Latitude
\def\highLat{60} % High Latitude of FOV
\newcommand\pgfmathsinandcos[3]{%
\pgfmathsetmacro#1{sin(#3)}%
\pgfmathsetmacro#2{cos(#3)}%
}
% Macro to define Longitudenal Planes
\newcommand\LongitudePlane[3][current plane]{
\pgfmathsinandcos\sinEl\cosEl{#2}
\pgfmathsinandcos\sint\cost{#3}
\tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
% Macro to define Latitudenal Planes
\newcommand\LatitudePlane[3][current plane]{
\pgfmathsinandcos\sinEl\cosEl{#2}
\pgfmathsinandcos\sint\cost{#3}
\pgfmathsetmacro\yshift{\cosEl*\sint}
\tikzset{#1/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}}
}
% Drawing Longitudenal Circles (all Great-Circles)
\newcommand\DrawLongitudeCircle[2][1]{
\LongitudePlane{\tilt}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\tilt)/sin(\tilt))}
\draw[current plane, thin, solid, black] (\angVis:1) arc (\angVis:\angVis+180:1);
\draw[current plane, thin, dashed, black] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
% Drawing Latitudenal Circles (not Great-Circles, except Horizon)
\newcommand\DrawLatitudeCircle[2][1]{
\LatitudePlane{\tilt}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\tilt)/cos(\tilt)}
\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);
}
% Draw Green Latitutdenal Planes (used to draw Horizon plane)
\newcommand\DrawLatPlane[2][\R]{
\LatitudePlane{\tilt}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\tilt)/cos(\tilt)}
\fill[current plane,green!60!black, opacity=.2] (0:1) arc (0:360:1);
}
% Used to draw spherical coordinate grids
% Draw a Longitudenal Line from leftLon to rightLon @ given angle
\newcommand\DrawLonGrid[2][1]{
\LongitudePlane{\tilt}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\draw[current plane,thick,red] (180-\highLat:1) arc (180-\highLat:180-\lowLat:1);
}
% Draw a Latitudenal Line from lowLat to highLat @ given angle
\newcommand\DrawLatGrid[2][1]{
\LatitudePlane{\tilt}{#2}
\tikzset{current plane/.prefix style={scale=#1}}
\draw[current plane,red,thick] (\rightLong:1) arc (\rightLong:\leftLong:1);
}
\pagestyle{empty}
\begin{document}
\begin{figure}[ht!]
\begin{tikzpicture}[scale=1,every node/.estyle={minimum size=1cm}]
% Do some on-the-fly math
\pgfmathsetmacro\H{\R*cos(\tilt)} % Distance to the North Pole
\pgfmathsetmacro\DR{(\R+\D)*(2-cos(15))} % Extra distance to elevate Rectilinear plane
% Setup the Sphere and Horizon Plane
\fill[ball color=white!10] (0,0) circle (\R); % 3D Lighting Effect
\DrawLatPlane[\R]{0} % Draw the Horizon-plane
% Define Working Planes
\LongitudePlane[zeroAzPlane] {\tilt}{\zeroAz} % Zero Azimuth Plane
\LongitudePlane[leftLongPlane] {\tilt}{\leftLong} % Left Longitudenal Plane
\LongitudePlane[centerLongPlane]{\tilt}{\midLong} % Center Longitudenal Plane
\LongitudePlane[rightLongPlane] {\tilt}{\rightLong} % Right Longitudenal Plane
\LatitudePlane[horizonPlane] {\tilt}{0} % Horizon Plane (Latitudenal)
% Define Working Coordinates
\coordinate (O) at (0,0); % Origin of Sphere
\coordinate (N) at (0,\H); % North-Pole of Sphere
\coordinate (S) at (0,-\H); % South-Pole of Sphere
\path[zeroAzPlane] (\R,0) coordinate (ZA); % Zero Azimuth point on Horizon Plane
\path[centerLongPlane] (\R,0) coordinate (AZ); % Point on the Horizon corrosponding to the azimuth
% Define Points Project outside of SPhere
\path[rightLongPlane] (\highLat:\DR) coordinate (TRO); % Top Right of FocalPlane projected onto Rectilinear
\path[leftLongPlane] (\highLat:\DR) coordinate (TLO); % Top Left of FocalPlane projected onto Rectilinear
\path[centerLongPlane] (\midLat:\R+\D) coordinate (CO); % Center of FocalPlane projected onto Rectilinear
\path[leftLongPlane] (\lowLat:\DR) coordinate (BLO); % Bottom Left of FocalPlane projected onto Rectilinear
\path[rightLongPlane] (\lowLat:\DR) coordinate (BRO); % Bottom Right of FocalPlane projected onto Rectilinear
% Draw some reference lines
\draw[dashed] (N) -- (S); % Connect the North and South Pole
\draw[dashed] (O) -- (ZA); % Draw a reference line to show where azimuth = 0 falls
% \draw[dashed, thick] (O) -- (AZ); % Draw a reference line corrosponding to the azimuth
\draw[centerLongPlane, ->, very thick, red!30!blue] (0:0.5*\R)
to [bend right=30] node[midway, right, black] {$\mathbf{Elevation}$} (\midLat:0.5*\R);
\draw[horizonPlane, ->, very thick, red!30!blue] (\zeroAz:0.5*\R)
to [bend right=40] node[midway, below, black] {$\mathbf{Azimuth}$} (\midLong:0.5*\R);
% Longitudenal bounds of the FOV
\DrawLongitudeCircle[\R]{\leftLong} % Left Longitude Circle (great circle)
\DrawLongitudeCircle[\R]{\rightLong} % Right Longitude Circle (great circle)
% Latitudenal bounds of the FOV
\DrawLatitudeCircle[\R]{\highLat} % High Latitude Circle (not great circle)
\DrawLatitudeCircle[\R]{\lowLat} % Low Latitude Circle (not great circle)
\DrawLatitudeCircle[\R]{0} % Horizon Circle
% Project FocalPlane Defining Beams
\draw[-, dashed, black, thick] (O) -- (TLO); % Top-Left corner
\draw[-, dashed, black, thick] (O) -- (BLO); % Bottom-Left corner
\draw[-, dashed, black, thick] (O) -- (BRO); % Bottom-Right corner
\draw[-, dashed, black, thick] (O) -- (TRO); % Top-Right corner
\draw[->, thick, red!30!blue] (O) -- (CO); % Actuall pointing
% Grid on Sphere
\foreach \t in {30,35,...,60} { \DrawLatGrid[\R]{\t} }
\foreach \t in {125,130,...,155} { \DrawLonGrid[\R]{\t} }
% Grid Outside Sphere
\foreach \t in {30,35,...,60} { \DrawLatGrid[\R+\D]{\t} }
\foreach \t in {125,130,...,155} { \DrawLonGrid[\R+\D]{\t} }
% Rectilinear Grid Outside
\fill[thick, red!30!blue, opacity=.1] (TLO) -- (BLO) -- (BRO) -- (TRO) -- (TLO);
\draw[thick, black, opacity=1] (TLO) -- (BLO) -- (BRO) -- (TRO) -- (TLO);
% Some Labels
\node[above=8pt] at (N) {$\mathbf{Zenith}$}; % Label the Zenith
\draw[-latex,thick](4,-5.5)node[left]{$\mathsf{Grid(s)\ in\ Fig. \ (\ref{fig:Grid})}$} to[out=0,in=270] (5.8,-2.3);
\draw[thick](3.6,-6)node[left]{$[\mathsf{Rectilinear}]$};
\end{tikzpicture}
\caption[cap]
{WUts dis.}
\label{fig:Grid}
\end{figure}
\end{document} https://www.writelatex.com/1728124nbzskd#/4317742/
Several questions:
1. Can someone reproduce this with MikTex?
2. Does this happen in Tex Live as well?
3. Why does WriteLatex render it correctly but my computer does not?
4. How do I fix it so that I can render it locally on my PC.
Thank You
Dominik Gothe
