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spherical coordinates
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Martin Thoma
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31
tikz/spherical-coordinates/Makefile
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31
tikz/spherical-coordinates/Makefile
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SOURCE = spherical-coordinates
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DELAY = 80
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DENSITY = 300
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WIDTH = 512
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make:
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pdflatex $(SOURCE).tex -output-format=pdf
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make clean
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clean:
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rm -rf $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
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gif:
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pdfcrop $(SOURCE).pdf
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convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
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make clean
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png:
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make
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make svg
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inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
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transparentGif:
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convert $(SOURCE).pdf -transparent white result.gif
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make clean
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svg:
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#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
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pdf2svg $(SOURCE).pdf $(SOURCE).svg
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# Necessary, as pdf2svg does not always create valid svgs:
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inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg
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3
tikz/spherical-coordinates/Readme.md
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3
tikz/spherical-coordinates/Readme.md
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Compiled example
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----------------
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BIN
tikz/spherical-coordinates/spherical-coordinates.png
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BIN
tikz/spherical-coordinates/spherical-coordinates.png
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After Width: | Height: | Size: 70 KiB |
159
tikz/spherical-coordinates/spherical-coordinates.tex
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159
tikz/spherical-coordinates/spherical-coordinates.tex
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% Author: Marco Miani
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\documentclass[varwidth=true, border=2pt]{standalone}
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\usepackage{tikz}
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\usetikzlibrary{positioning}
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%% helper macros
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% The 3D code is based on The drawing is based on Tomas M. Trzeciak's
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% `Stereographic and cylindrical map projections example`:
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% http://www.texample.net/tikz/examples/map-projections/
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\newcommand\pgfmathsinandcos[3]{%
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\pgfmathsetmacro#1{sin(#3)}%
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\pgfmathsetmacro#2{cos(#3)}%
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}
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\newcommand\LongitudePlane[3][current plane]{%
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\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
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\pgfmathsinandcos\sint\cost{#3} % azimuth
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\tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
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}
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\newcommand\LatitudePlane[3][current plane]{%
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\pgfmathsinandcos\sinEl\cosEl{#2} % elevation
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\pgfmathsinandcos\sint\cost{#3} % latitude
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\pgfmathsetmacro\yshift{\cosEl*\sint}
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\tikzset{#1/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
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}
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\newcommand\DrawLongitudeCircle[2][1]{
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\LongitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
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\draw[current plane,thin,black] (\angVis:1) arc (\angVis:\angVis+180:1);
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\draw[current plane,thin,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
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}%this is fake: for drawing the grid
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\newcommand\DrawLongitudeCirclered[2][1]{
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\LongitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
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\draw[current plane,red,thick] (150:1) arc (150:180:1);
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}%for drawing the grid
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\newcommand\DLongredd[2][1]{
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\LongitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
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\draw[current plane,black,dashed, ultra thick] (150:1) arc (150:180:1);
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}
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\newcommand\DLatred[2][1]{
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\LatitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
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\draw[current plane,dashed,black,ultra thick] (-50:1) arc (-50:-35:1);
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}
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\newcommand\fillred[2][1]{
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\LongitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
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\draw[current plane,red,thin] (\angVis:1) arc (\angVis:\angVis+180:1);
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}
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\newcommand\DrawLatitudeCircle[2][1]{
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\LatitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
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\draw[current plane,thin,black] (\angVis:1) arc (\angVis:-\angVis-180:1);
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\draw[current plane,thin,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
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}%Defining functions to draw limited latitude circles (for the red mesh)
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\newcommand\DrawLatitudeCirclered[2][1]{
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\LatitudePlane{\angEl}{#2}
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\tikzset{current plane/.prefix style={scale=#1}}
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\pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
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% angle of "visibility"
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\pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
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%\draw[current plane,red,thick] (-\angVis-50:1) arc (-\angVis-50:-\angVis-20:1);
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\draw[current plane,red,thick] (-50:1) arc (-50:-35:1);
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}
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\tikzset{%
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>=latex,
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inner sep=0pt,%
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outer sep=2pt,%
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mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
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fill=black,circle}%
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}
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\usepackage{amsmath}
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\usetikzlibrary{arrows}
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\pagestyle{empty}
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\usepackage{pgfplots}
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\usetikzlibrary{calc,fadings,decorations.pathreplacing}
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\begin{document}
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\begin{tikzpicture}[scale=1,every node/.style={minimum size=1cm}]
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%% some definitions
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\def\R{4} % sphere radius
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\def\angEl{25} % elevation angle
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\def\angAz{-100} % azimuth angle
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\def\angPhiOne{-50} % longitude of point P
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\def\angPhiTwo{-35} % longitude of point Q
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\def\angBeta{30} % latitude of point P and Q
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%% working planes
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\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
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\LongitudePlane[xzplane]{\angEl}{\angAz}
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\LongitudePlane[pzplane]{\angEl}{\angPhiOne}
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\LongitudePlane[qzplane]{\angEl}{\angPhiTwo}
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\LatitudePlane[equator]{\angEl}{0}
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\fill[ball color=white!10] (0,0) circle (\R); % 3D lighting effect
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\coordinate (O) at (0,0);
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\coordinate[mark coordinate] (N) at (0,\H);
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\coordinate[mark coordinate] (S) at (0,-\H);
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\path[xzplane] (\R,0) coordinate (XE);
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%defining points outsided the area bounded by the sphere
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\path[qzplane] (\angBeta:\R+5.2376) coordinate (XEd);
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\path[pzplane] (\angBeta:\R) coordinate (P);%fino alla sfera
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\path[pzplane] (\angBeta:\R+5.2376) coordinate (Pd);%sfora di una quantità pari a 10 dopo la sfera
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\path[pzplane] (\angBeta:\R+5.2376) coordinate (Td);%sfora di una quantità pari a 10 dopo la sfera
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\path[pzplane] (\R,0) coordinate (PE);
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\path[pzplane] (\R+4,0) coordinate (PEd);
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\path[qzplane] (\angBeta:\R) coordinate (Q);
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\path[qzplane] (\angBeta:\R) coordinate (Qd);%sfora di una quantità pari a 10 dopo la sfera
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\path[qzplane] (\R,0) coordinate (QE);
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\path[qzplane] (\R+4,0) coordinate (QEd);%sfora di una quantità 10 dalla sfera sul piano equat.
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\DrawLongitudeCircle[\R]{\angPhiOne} % pzplane
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\DrawLongitudeCircle[\R]{\angPhiTwo} % qzplane
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\DrawLatitudeCircle[\R]{\angBeta}
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\DrawLatitudeCircle[\R]{0} % equator
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%labelling north and south
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\node[above=8pt] at (N) {$\mathbf{N}$};
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\node[below=8pt] at (S) {$\mathbf{S}$};
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\draw[-,dashed, thick] (N) -- (S);
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\draw[->] (O) -- (P);
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\draw[dashed] (XE) -- (O) -- (PE);
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\draw[dashed] (O) -- (QE);
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\draw[pzplane,->,thin] (0:0.5*\R) to[bend right=15]
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node[midway,right] {$v$} (\angBeta:0.5*\R);
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\path[pzplane] (0.5*\angBeta:\R) node[right] {$$};
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\path[qzplane] (0.5*\angBeta:\R) node[right] {$$};
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\draw[equator,->,thin] (\angAz:0.5*\R) to[bend right=30]
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node[pos=0.4,above] {$u$} (\angPhiOne:0.5*\R);
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\end{tikzpicture}
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\end{document}
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