# latex-pictures

A collection of TikZ drawings and other images 🖌️

## smooth-manifold.tikz (1745B)

 1 % This picture represents the definition of a smooth manifold
2 % Copyright Pablo (C) 2021
3 \begin{tikzpicture}
4   % The manifold
5   \begin{scope}[shift={(-0.5, 0)}]
6     % The frontire
7     \draw (-4, 2) to[relative, out=20, in=160]
8           ( 2, 0) to[relative, out=20, in=160]
9           ( 4, 3) to[relative, out=-20, in=-160]
10           cycle;
11     \draw (-4, 2) node[below]{$M$};
12
13     % The open sets of the manifold and their intersection
14     \begin{scope}[shift={(1, 2.2)}]
15       \draw (-0.5, 0) ellipse (0.7 and 0.5);
16       \draw (-1.2, 0) node[right]{$U$};
17       \draw (0.5, 0) ellipse (0.7 and 0.5);
18       \draw (1.2, 0) node[left]{$V$};
19       \clip (-0.5, 0) ellipse (0.7 and 0.5);
20       \draw[pattern=north west lines] (0.5, 0) ellipse (0.7 and 0.5);
21     \end{scope}
22   \end{scope}
23
24   % The cards
25   \draw[->] (-0.7, 1.7) to[relative, out=-20, in=-160]
26             node[left]{$\varphi_U$} (-2, -0.7);
27   \draw[->] (1.7, 1.7) to[relative, out=20, in=160]
28             node[right]{$\varphi_V$} (2, -0.7);
29
30   % The corresponding open sets in euclidian space
31   \begin{scope}[shift={(0, -1.5)}]
32     % The open sets
33     \draw (-2, 0) ellipse (1 and 0.6) (2, 0) ellipse (1 and 0.6);
34     \draw (-3, 0.5) node[above]{$\varphi_U(U)$};
35     \draw (3, 0.5) node[above]{$\varphi_V(V)$};
36
37     % The intersections
38     \begin{scope}
39       \clip (-2, 0) ellipse (1 and 0.6);
40       \draw[pattern=north west lines] (-0.5, 0) ellipse (1 and 0.6);
41     \end{scope}
42     \begin{scope}
43       \clip (2, 0) ellipse (1 and 0.6);
44       \draw[pattern=north west lines] (0.5, 0) ellipse (1 and 0.6);
45     \end{scope}
46
47     % The diffeomorphism
48     \draw[->] (-0.9, 0) --
49               node[above]{$\varphi_V \circ \varphi_U^{-1}$} (0.9, 0);
50   \end{scope}
51 \end{tikzpicture}
52