spherical coordinates

tikz/spherical-coordinates/Makefile

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+SOURCE = spherical-coordinates
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/spherical-coordinates/Readme.md

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+Compiled example
+----------------
+![Example](spherical-coordinates.png)

tikz/spherical-coordinates/spherical-coordinates.tex

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+% Author: Marco Miani
+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{positioning}
+%% helper macros
+
+% The 3D code is based on The drawing is based on Tomas M. Trzeciak's 
+% `Stereographic and cylindrical map projections example`: 
+% http://www.texample.net/tikz/examples/map-projections/
+\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);
+}%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}%
+}
+\usepackage{amsmath}
+\usetikzlibrary{arrows}
+\pagestyle{empty}
+\usepackage{pgfplots}
+\usetikzlibrary{calc,fadings,decorations.pathreplacing}
+
+\begin{document}
+\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{-50} % longitude of point P
+\def\angPhiTwo{-35} % 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}
+\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);
+\path[xzplane] (\R,0) coordinate (XE);
+
+%defining points outsided the area bounded by the sphere
+\path[qzplane] (\angBeta:\R+5.2376) coordinate (XEd);
+\path[pzplane] (\angBeta:\R) coordinate (P);%fino alla sfera
+\path[pzplane] (\angBeta:\R+5.2376) coordinate (Pd);%sfora di una quantità pari a 10 dopo la sfera
+\path[pzplane] (\angBeta:\R+5.2376) coordinate (Td);%sfora di una quantità pari a 10 dopo la sfera
+\path[pzplane] (\R,0) coordinate (PE);
+\path[pzplane] (\R+4,0) coordinate (PEd);
+\path[qzplane] (\angBeta:\R) coordinate (Q);
+\path[qzplane] (\angBeta:\R) coordinate (Qd);%sfora di una quantità pari a 10 dopo la sfera
+
+\path[qzplane] (\R,0) coordinate (QE);
+\path[qzplane] (\R+4,0) coordinate (QEd);%sfora di una quantità 10 dalla sfera sul piano equat.
+
+
+\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);
+\draw[->] (O) -- (P);
+\draw[dashed] (XE) -- (O) -- (PE);
+\draw[dashed] (O) -- (QE);
+		
+\draw[pzplane,->,thin] (0:0.5*\R) to[bend right=15]
+    node[midway,right] {$v$} (\angBeta:0.5*\R);
+\path[pzplane] (0.5*\angBeta:\R) node[right] {$$};
+\path[qzplane] (0.5*\angBeta:\R) node[right] {$$};
+\draw[equator,->,thin] (\angAz:0.5*\R) to[bend right=30]
+    node[pos=0.4,above] {$u$} (\angPhiOne:0.5*\R);
+	
+\end{tikzpicture}
+\end{document}