diff options
Diffstat (limited to 'buch/papers')
-rw-r--r-- | buch/papers/kugel/figures/tikz/Makefile | 2 | ||||
-rw-r--r-- | buch/papers/kugel/figures/tikz/legendre-substitution.pdf | bin | 0 -> 44247 bytes | |||
-rw-r--r-- | buch/papers/kugel/figures/tikz/legendre-substitution.tex | 69 |
3 files changed, 70 insertions, 1 deletions
diff --git a/buch/papers/kugel/figures/tikz/Makefile b/buch/papers/kugel/figures/tikz/Makefile index 4ec4e5a..3b2df59 100644 --- a/buch/papers/kugel/figures/tikz/Makefile +++ b/buch/papers/kugel/figures/tikz/Makefile @@ -1,4 +1,4 @@ -FIGURES := spherical-coordinates.pdf curvature-1d.pdf +FIGURES := spherical-coordinates.pdf curvature-1d.pdf legendre-substitution.pdf all: $(FIGURES) diff --git a/buch/papers/kugel/figures/tikz/legendre-substitution.pdf b/buch/papers/kugel/figures/tikz/legendre-substitution.pdf Binary files differnew file mode 100644 index 0000000..f77b6cb --- /dev/null +++ b/buch/papers/kugel/figures/tikz/legendre-substitution.pdf diff --git a/buch/papers/kugel/figures/tikz/legendre-substitution.tex b/buch/papers/kugel/figures/tikz/legendre-substitution.tex new file mode 100644 index 0000000..3a699b8 --- /dev/null +++ b/buch/papers/kugel/figures/tikz/legendre-substitution.tex @@ -0,0 +1,69 @@ + +% vim: ts=2 sw=2 et : +\documentclass[tikz, border=2mm]{standalone} + +\usepackage{amsmath} +\usepackage{bm} + +\usepackage{times} +\usepackage{txfonts} + +\usepackage{tikz-3dplot} + +\tdplotsetmaincoords{60}{130} +\pgfmathsetmacro{\l}{2} + +\begin{document} + \begin{tikzpicture}[ + >=latex, + tdplot_main_coords, + ] + + % origin and poles + \coordinate (O) at (0,0,0); + \coordinate (NP) at (0,0,\l); + \coordinate (SP) at (0,0,-\l); + + % gray unit circle + \tdplotdrawarc[lightgray, dashed]{(O)}{\l}{0}{360}{}{}; + \draw[lightgray, dashed] (-\l, 0, 0) to (\l, 0, 0); + \draw[lightgray, dashed] (0, -\l, 0) to (0, \l, 0); + + % axis + \draw[->] (O) -- ++(0,0,1.25*\l) node[above] {\(\mathbf{\hat{z}}\)}; + + % meridians + \foreach \phi in {0, 30, 60, ..., 150}{ + \tdplotsetrotatedcoords{\phi}{90}{0}; + \tdplotdrawarc[lightgray, densely dotted, tdplot_rotated_coords]{(O)}{\l}{0}{360}{}{}; + } + + % dot above and its projection + \pgfmathsetmacro{\phi}{120} + \pgfmathsetmacro{\theta}{40} + + \pgfmathsetmacro{\px}{cos(\phi)*sin(\theta)*\l} + \pgfmathsetmacro{\py}{sin(\phi)*sin(\theta)*\l} + \pgfmathsetmacro{\pz}{cos(\theta)*\l}) + + % Special meridian + \tdplotsetrotatedcoords{\phi-90}{90}{0}; + \tdplotdrawarc[gray, tdplot_rotated_coords]{(O)}{\l}{0}{360}{}{}; + + % point A + \coordinate (A) at (\px,\py,\pz); + \coordinate (Ap) at (\px,\py, 0); + + % lines + \draw[red!80!black, thick, ->] (O) -- (A); + \draw[red!80!black] + (O) -- node[midway, below, font=\small, sloped, fill=white] {$\sqrt{1 - z^2}$} + (Ap) -- node[midway, right, font=\small, sloped, fill=white, anchor=north] {$z = \cos \vartheta$} + (A) node[above right, fill=white] {$r = 1$}; + + % theta arc + \tdplotsetrotatedcoords{\phi-90}{-90}{0}; + \tdplotdrawarc[blue!80!black, ->, tdplot_rotated_coords]{(O)}{.95\l}{0}{\theta}{}{}; + \node[above right = 1mm, blue!80!black] at (0,0,.8\l) {\(\bm{\hat{\vartheta}}\)}; + \end{tikzpicture} +\end{document} |