4
Overall this looks pretty decent to me. Here is what you can do in order to avoid repetition, and improve the appearance.
Instead of adding several statements of the form \draw[fill = black] (V1one, P1one) circle (2pt);, just add \addplot[only marks,mark=*] coordinates{ <list of coordinates>};.
Instead of three almost identical plots use \...
2
Welcome! You can work with \uncover. As I do not have your images, I replaced them with some generic graphics that comes with most of the installations.
\documentclass{beamer}
\usepackage{subcaption}
\begin{document}
\begin{frame}
\frametitle{Foo}
Some sentence:
\begin{itemize}
\item<1,2,3>
Text1
\item<2,3>
Text2
\item&...
2
Here is a way with polar coordinates and arcs that derive from intersections.
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,intersections}
\begin{document}
\begin{tikzpicture}[Dotted/.style={% https://tex.stackexchange.com/a/52856/194703
line width=1.5pt,
dash pattern=on 0.001\pgflinewidth off #1,line cap=round,
shorten <=#...
2
Use simple node position like this.
\documentclass[margin=3mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node[shape=circle,draw=black] (a1) at (0,0) {1};
\node[shape=circle,draw=black] (a2) at (5,0) {2};
\node[shape=circle,draw=black] (a3) at (2,2) {3};
\node[shape=circle,draw=black] (a4) at (2,-2) {4};
...
1
\picdims[...]{<x-dim>}{<ydim>}{<image-file>} is provided, where the user can specify the x and y dimensions of the cropped image. Cropping is done symmetrically.
\documentclass{article}
\usepackage{graphicx,trimclip}
\newcommand\picdims[4][]{%
\setbox0=\hbox{\includegraphics[#1]{#4}}%
\clipbox{.5\dimexpr\wd0-#2\relax{} %
.5\...
1
Let mi convert my comment to an answer:
the case when images have the same heights
\documentclass{article}
\usepackage{mathtools}
\usepackage[font=small]{caption, subcaption}
\usepackage[demo]{graphicx}
\begin{document}
\begin{figure}[htb!]
\centering
\begin{subfigure}[t]{0.45\textwidth}
\centering
\includegraphics[width=\textwidth]...
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