126 lines
4.4 KiB
TeX
126 lines
4.4 KiB
TeX
\documentclass{standalone}
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\usepackage{pgfplots} % TikZ (TeX ist kein Zeichenprogramm)
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\usetikzlibrary{calc} % for vector arithmetics
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\usepackage{amssymb, bm}
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\renewcommand{\t}[1]{{#1}^{T}}
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\newcommand{\mat}[1]{\boldsymbol{#1}}
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\newcommand{\manifold}[1]{\mathfrak{#1}}
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% PGF-Plot / TikZ config
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\usetikzlibrary{%
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calc, through, intersections, patterns, patterns.meta, pgfplots.colormaps
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}
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\pgfplotsset{
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compat = newest,
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colormap = {grayscale}{color=(lightgray) color=(white) color=(lightgray)},
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colormap = {blackscale}{color=(black!70) color=(black!50) color=(black!70)},
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colormap = {redscale}{color=(black!70!red) color=(black!50!red) color=(black!70!red)},
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colormap = {bluescale}{color=(black!70!blue) color=(black!50!blue) color=(black!70!blue)},
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}
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\begin{document}
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\begin{tikzpicture}[
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>=latex,
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scale = 1,
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declare function = { % Note: NO spaces in function argument list!
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X(\u,\v) = (2 + cos(\u)) * cos(\v);
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Y(\u,\v) = (2 + cos(\u)) * sin(\v);
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Z(\u,\v) = sin(\u);
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tx(\u,\v,\x,\y) = - sin(\u) * cos(\u) * \x - (2 + cos(\u)) * sin(\v) * \y;
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ty(\u,\v,\x,\y) = - sin(\u) * cos(\u) * \x + (2 + cos(\u)) * cos(\v) * \y;
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tz(\u,\v,\x,\y) = + cos(\u) * \x;
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}
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]
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\begin{axis}[
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axis equal image,
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hide axis,
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view = {120}{30},
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scale = 2
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]
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\addplot3[
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surf,
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shader = faceted interp,
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samples = 20,
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samples y = 40,
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domain = 0:360,
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domain y = 0:360,
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z buffer = sort,
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colormap name = grayscale,
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thin
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]
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({X(\x, \y)}, {Y(\x, \y)}, {Z(\x, \y)});
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% at = (1.433013, 2.482051, 0.5) // \u, \v = (30, 60)
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% into = (-0.4330127, -0.4330127, 0.8660254)
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% and = (-2.482051, 1.433013, 0)
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% X <- c(1.433013, 2.482051, 0.5)
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% dx <- c(-0.4330127, -0.4330127, 0.8660254)
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% dy <- c(-2.482051, 1.433013, 0)
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\addplot3[
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mesh,
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shader = interp,
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patch type = line,
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variable = t,
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domain = -44:210.5,
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samples = 64,
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samples y = 1,
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colormap name = redscale
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]
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({X(\t, \t + 30)}, {Y(\t, \t + 30)}, {Z(\t, \t + 30)});
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\addplot3[
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mesh,
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shader = interp,
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patch type = line,
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variable = t,
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domain = -50:119,
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samples = 64,
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samples y = 1,
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colormap name = bluescale
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]
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({X(\t, -0.3 * \t + 69)}, {Y(\t, -0.3 * \t + 69)}, {Z(\t, -0.3 * \t + 69)});
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\coordinate (x) at ({X(30, 60)}, {Y(30, 60)}, {Z(30, 60)});
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\draw[dashed, fill = gray, opacity = 0.4] (
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{X(30, 60) + tx(30, 60, 0.4 + 0.8, 0.4 - 0.24)},
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{Y(30, 60) + ty(30, 60, 0.4 + 0.8, 0.4 - 0.24)},
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{Z(30, 60) + tz(30, 60, 0.4 + 0.8, 0.4 - 0.24)}
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) -- (
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{X(30, 60) + tx(30, 60, -0.4 + 0.8, -0.4 - 0.24)},
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{Y(30, 60) + ty(30, 60, -0.4 + 0.8, -0.4 - 0.24)},
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{Z(30, 60) + tz(30, 60, -0.4 + 0.8, -0.4 - 0.24)}
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) node[anchor = west, opacity = 1, outer sep=0.5em] {$T_{\mat{x}}\manifold{A}$} -- (
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{X(30, 60) + tx(30, 60, -0.4 - 0.8, -0.4 + 0.24)},
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{Y(30, 60) + ty(30, 60, -0.4 - 0.8, -0.4 + 0.24)},
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{Z(30, 60) + tz(30, 60, -0.4 - 0.8, -0.4 + 0.24)}
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) -- (
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{X(30, 60) + tx(30, 60, 0.4 - 0.8, 0.4 + 0.24)},
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{Y(30, 60) + ty(30, 60, 0.4 - 0.8, 0.4 + 0.24)},
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{Z(30, 60) + tz(30, 60, 0.4 - 0.8, 0.4 + 0.24)}
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) -- cycle;
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\draw[->, black!50!red] (x) -- (
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{X(30, 60) + tx(30, 60, 0.4, 0.4)},
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{Y(30, 60) + ty(30, 60, 0.4, 0.4)},
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{Z(30, 60) + tz(30, 60, 0.4, 0.4)}
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) node[pos = 0.7, anchor = north west, inner sep = 0pt] {$\t{\nabla\gamma_1(0)}$};
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\draw[->, black!50!blue] (x) -- (
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{X(30, 60) + tx(30, 60, 0.8, -0.24)}, % -0.24 = 0.8 * -0.3
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{Y(30, 60) + ty(30, 60, 0.8, -0.24)},
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{Z(30, 60) + tz(30, 60, 0.8, -0.24)}
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) node[pos = 0.7, anchor = south west, inner sep = 0pt] {$\t{\nabla\gamma_2(0)}$};
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\node[anchor = north] at (x) {$\mat{x}$};
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\node[circle, inner sep={1pt}, outer sep={0pt}, fill=black] at (x) {};
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\end{axis}
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\end{tikzpicture}
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\end{document}
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