Roll, Pitch and Yaw
Author:
Javi Pérez
Last Updated:
4 years ago
License:
Creative Commons CC BY 4.0
Abstract:
Roll, Pitch and Yaw angles rotation around X, Y, Z axes
\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{pgfpages}
\usepackage{tikz} %TikZ is required for this to work. Make sure this exists before the next line
\usepackage{tikz-3dplot} %requires 3dplot.sty to be in same directory, or in your LaTeX installation
\begin{document}
\section{Magnetic Roll, Pitch and Yaw}
\begin{frame}[fragile]
\begin{figure}[H]
\centering
% Select a perspective
%\tdplotsetmaincoords{65}{105}
%\tdplotsetmaincoords{65}{235}
\tdplotsetmaincoords{65}{205}
\begin{tikzpicture}[scale=1,tdplot_main_coords,>=latex,line join=bevel]
% Parameters ---------------------
% Coordinates parameters
\pgfmathsetmacro{\sizeCoordX}{4.2}
\pgfmathsetmacro{\sizeCoordY}{4.2}
\pgfmathsetmacro{\sizeCoordZ}{4.2}
\coordinate (O) at (0,0,0);
% Figures ---------------------
% Coordinates
\draw[->] (O) -- (\sizeCoordX,0,0) node[anchor=east]{$X$};
\draw[->] (O) -- (0,\sizeCoordY,0) node[anchor=north]{$Y$};
\draw[->] (O) -- (0,0,\sizeCoordZ) node[anchor=south]{$Z$};
% \draw[dashed] (O) -- (-0.7*\sizeCoordX,0,0);
% \draw[dashed] (O) -- (0,-0.7*\sizeCoordY,0);
% \draw[dashed] (O) -- (0,0,-\sizeCoordZ);
\pause
% Create a new rotated system in the center
%\tdplotsetrotatedcoords{45}{-60}{-30}
\tdplotsetrotatedcoords{65}{-40}{-30}
\draw[thick,tdplot_rotated_coords,->, color=darkgray] (0,0,0) -- (\sizeCoordX,0,0) node[anchor=north east]{$\mathbf{e_E}$};
\draw[very thick,tdplot_rotated_coords,->, color=darkgray] (0,0,0) -- (0,\sizeCoordY,0) node[anchor=north]{$\mathbf{e_N}$};
\draw[thick,tdplot_rotated_coords,->, color=darkgray] (0,0,0) -- (0,0,\sizeCoordZ) node[anchor=south east]{$\mathbf{e_Z}$};
\pause
% Draw a box around East direction
\tdplottransformrotmain{\sizeCoordX}{0}{0}
% Draw box
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (\tdplotresx,\tdplotresy,0);
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (\tdplotresx,0,\tdplotresz);
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (0,\tdplotresy,\tdplotresz);
\draw[dotted] (\tdplotresx,\tdplotresy,0) -- (\tdplotresx,0,0);
\draw[dotted] (\tdplotresx,\tdplotresy,0) -- (0,\tdplotresy,0);
\draw[dotted] (\tdplotresx,0,\tdplotresz) -- (0,0,\tdplotresz);
\draw[dotted] (\tdplotresx,0,\tdplotresz) -- (\tdplotresx,0,0);
\draw[dotted] (0,\tdplotresy,\tdplotresz) -- (0,0,\tdplotresz);
\draw[dotted] (0,\tdplotresy,\tdplotresz) -- (0,\tdplotresy,0);
\draw[dotted] (0,0,0) -- (\tdplotresx,0,0);
% Transforms a coordinate from the rotated coordinate frame to the main coordinate frame. Results at (\tdplotresx,\tdplotresy,\tdplotresz)
\tdplottransformrotmain{0}{\sizeCoordY}{0}
% Draw North box
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (\tdplotresx,\tdplotresy,0);
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (\tdplotresx,0,\tdplotresz);
\draw[dotted] (\tdplotresx,\tdplotresy,\tdplotresz) -- (0,\tdplotresy,\tdplotresz);
\draw[dotted] (\tdplotresx,\tdplotresy,0) -- (\tdplotresx,0,0);
\draw[dotted] (\tdplotresx,\tdplotresy,0) -- (0,\tdplotresy,0);
\draw[dotted] (\tdplotresx,0,\tdplotresz) -- (0,0,\tdplotresz);
\draw[dotted] (\tdplotresx,0,\tdplotresz) -- (\tdplotresx,0,0) node[anchor= north west]{$x_N$};
\draw[dotted] (0,\tdplotresy,\tdplotresz) -- (0,0,\tdplotresz) node[anchor= south west]{$z_N$};
\draw[dotted] (0,\tdplotresy,\tdplotresz) -- (0,\tdplotresy,0) node[anchor= south east]{$y_N$};
\draw[dotted] (0,0,0) -- (\tdplotresx,0,0);
% Draw arcs ---------------------------------
%
\pause
\draw[dashed] (0,0,0) -- (0,\tdplotresy,\tdplotresz);
% Calculate (0,y,z) polar coordinates
\tdplotgetpolarcoords{0.001}{\tdplotresy}{\tdplotresz}
\pgfmathsetmacro{\radius}{sqrt{((\tdplotresy)^2 + (\tdplotresz)^2)}}
%syntax: \tdplotdrawarc[coordinate frame, draw options]{center point}{r}{angle start}{angle end}{label options}{label}
\tdplotsetthetaplanecoords{90}
\tdplotdrawarc[thick,tdplot_rotated_coords,thick,-stealth,blue]{(0,0,0)}{\radius}{0}{\tdplotrestheta}{anchor=north west}{$\theta_{x}$}
%
\pause
\draw[dashed] (0,0,0) -- (\tdplotresx,0,\tdplotresz);
% Calculate (x,0,z) polar coordinates
\tdplotgetpolarcoords{\tdplotresx}{0}{\tdplotresz}
\pgfmathsetmacro{\radius}{sqrt{((\tdplotresx)^2 + (\tdplotresz)^2)}}
%syntax: \tdplotdrawarc[coordinate frame, draw options]{center point}{r}{angle start}{angle end}{label options}{label}
\tdplotsetthetaplanecoords{180}
\tdplotdrawarc[thick,tdplot_rotated_coords,thick,-stealth,blue]{(0,0,0)}{\radius}{90}{\tdplotrestheta}{anchor=north west}{$\theta_{y}$}
%
\pause
\draw[dashed] (0,0,0) -- (\tdplotresx,\tdplotresy,0);
% Calculate (x,y,0) polar coordinates
\tdplotgetpolarcoords{\tdplotresx}{\tdplotresy}{0}
\pgfmathsetmacro{\radius}{sqrt{((\tdplotresx)^2 + (\tdplotresy)^2)}}
%%%% %syntax: \tdplotdrawarc[coordinate frame, draw options]{center point}{r}{angle start}{angle end}{label options}{label}
\tdplotsetthetaplanecoords{0}
\tdplotdrawarc[thick,thick,-stealth,blue]{(0,0,0)}{\radius}{90}{\tdplotresphi}{anchor=north west}{$\theta_{z}$}
\end{tikzpicture}
\end{figure}
\end{frame}
\end{document}