AngleSD
Author:
ImJaviPerez@gmail.com
Last Updated:
4 years ago
License:
Creative Commons CC BY 4.0
Abstract:
Angle measurement standard deviation
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[compress,9pt]{beamer}
\usepackage{tikz} %TikZ is required for this to work. Make sure this exists before the next line
\begin{document}
\begin{frame}[fragile]{}
\begin{figure}[H]
%\centering
%\resizebox{0.5\textwidth}{!}{}
\begin{tikzpicture}
\def \accX {3}
\def \accY {2}
\def \sigmaAccX {1}
\def \sigmaAccY {1}
\def \Xaxis {\accX+\sigmaAccX+0.7}
\def \Yaxis {\accY+\sigmaAccY+0.7}
%
% Define angles
% It is very important to get redundant parenthesis
\pgfmathsetmacro{\bottomAngle}{atan(((\accY-\sigmaAccY)) / ((\accX+\sigmaAccX)))}
\pgfmathsetmacro{\mediumAngle}{atan(((\accY)) / ((\accX)))}
\pgfmathsetmacro{\upperAngle}{atan(((\accY+\sigmaAccY)) / ((\accX-\sigmaAccX)))}
%
% Draw coordinate system
\draw[thick,->](0,0) -- (\Xaxis,0) node[right]{$X$};
\draw[thick,->](0,0) -- (0,\Yaxis) node[above]{$Y$};
%
% Draw arrow medium position
\draw[thick,-stealth](0,0) -- (\accX,\accY) node[right]{$\theta$};
% Draw medium point
\draw[dashed] (\accX,\accY) -- (\accX,0) node[below] {$x_k$};
\draw[dashed] (\accX,\accY) -- (0,\accY) node[left] {$y_k$};
% Draw angle
\def \radiusMediumAngle {1.5}
\draw[thick,black] ([shift=(0:\radiusMediumAngle)]0,0) arc (0:\mediumAngle:\radiusMediumAngle)node[below right]{$\theta$};
\pause
% Draw horizontal SD
\draw[dotted] (\accX+\sigmaAccX,\accY-\sigmaAccY) -- (\accX+\sigmaAccX,0) node[rotate=90,left]{$(x_k+\sigma_x)$};
\node[rotate=90,left] at (\accX-\sigmaAccX,0) {$(x_k-\sigma_x)$};
\pause
% Draw vertical SD
\node[left] at (0,\accY-\sigmaAccY) {$(y_k-\sigma_y)$};
\draw[dotted] (\accX-\sigmaAccX,\accY+\sigmaAccY) -- (0,\accY+\sigmaAccY) node[left]{$(y_k+\sigma_y)$};
\pause
% Draw arrow bottom position
\draw[-stealth,blue](0,0) -- (\accX+\sigmaAccX, \accY-\sigmaAccY) node[right]{$(\theta-\sigma_{\theta -})$};
% Angle. Syntax: (startingPointX,startingPointY) arc (startAngle:stopAngle:radius)
% ([shift=(t:r)] x, y) is the proper starting point, where (x,y) is the center and (t:r) is the polar coordinate of starting point.
\def \radiusBottomAngle {2.5}
\draw[thick,blue] ([shift=(\bottomAngle:\radiusBottomAngle)]0,0) arc (\bottomAngle:\mediumAngle:\radiusBottomAngle)node[below right]{$\sigma_{\theta -}$};
\pause
% Draw arrow upper position
\draw[-stealth,red](0,0) -- (\accX-\sigmaAccX, \accY+\sigmaAccY) node[right]{$(\theta+\sigma_{\theta +})$};
% Angle
\def \radiusUpperAngle {2.6}
\draw[thick,red] ([shift=(\mediumAngle:\radiusUpperAngle)]0,0) arc (\mediumAngle:\upperAngle:\radiusUpperAngle)node[right]{$\sigma_{\theta +}$};
\end{tikzpicture}
\end{figure}
\onslide<6->{
\begin{equation}
(\theta_z - \sigma_{\theta -}) = \arctan \frac{y_k-\sigma_y}{x_k+\sigma_x}
,\quad
(\theta_z + \sigma_{\theta +}) = \arctan \frac{y_k+\sigma_y}{x_k-\sigma_x}
\end{equation}}
\onslide<7->{
\begin{equation}\label{eq:sigmaPlusMinus}
\sigma_k =(\sigma_{\theta +} + \sigma_{\theta -}) = \arctan \frac{y_k+\sigma_y}{x_k-\sigma_x} - \arctan \frac{y_k-\sigma_y}{x_k+\sigma_x}
\end{equation}
}
\end{frame}
\end{document}