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Añade ángulos al dron 3D

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Añade ángulos al dron 3D

¿Cómo puedo agregar ángulos de Euler y ángulos XYZ al código como en la imagen?ingrese la descripción de la imagen aquí

\documentclass[tikz]{standalone}
%\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{3d, arrows.meta, calc, quotes}
\begin{document}
\begin{tikzpicture}[
  x = ( 20:-2cm), y = (-30: 2cm), z = ( 80: 1.6cm),
  > = Triangle]
\draw coordinate (O) (0,0,-.05) ellipse [radius=.2];

\foreach \xy/\yx in {x/y, y/x} {
  \fill[white] (xyz cs: \xy = -1, \yx = -.05) -- (xyz cs: \xy =  1, \yx=-.05)
            -- (xyz cs: \xy =  1, \yx =  .05) -- (xyz cs: \xy = -1, \yx= .05) -- cycle;
  \foreach \lmr in {-.05, 0, .05}
    \draw[gray] (xyz cs: \xy=-1, \yx = \lmr) -- (xyz cs: \xy=1, \yx=\lmr);
  \draw[fill=white, radius=.15] (xyz cs: \xy = -1) ellipse[]
                                (xyz cs: \xy =  1) ellipse[];
}
\draw[fill=white] (O) ellipse [radius=.2];

\foreach \xyz/\Label/\Ang in {% \Ang needs to start with a ,
  x/left/ {, longitude = 70},
  y/right/{, longitude =-20},
  z/above/{, longitude = 70, latitude=70}%
} {
  \draw[->, densely dashed, red] (0, 0, 0) -- ++(xyz cs: \xyz= 1.5)
    coordinate (ax-\xyz) node[\Label] {$\xyz$};
  \draw[blue, ->]
     (0, 0, 0) -- (xyz spherical cs: radius = 1.5,/tikz/style/.expanded=\Ang)
      coordinate (ax-\xyz') node[\Label] {$\xyz$};
}

\draw[canvas is xy plane at z=0]
  (0, 1) arc[start angle=90, delta angle=20, radius=1]
  node[midway, below right] {$\varphi$};
\end{tikzpicture}
\end{document}

Respuesta1

Yo recomendaría usar eltikz-3dplot paquete. Dentro del paquete, ya existe una transformación de coordenadas definida utilizando ángulos de Euler. Puede encontrar una pregunta similar con algunas respuestas útiles.aquí. Básicamente, puede definir un sistema de coordenadas principal cuya orientación puede establecerse con dos ángulos (p. ej. \tdplotsetmaincoords{50}{115}). Luego, este sistema de coordenadas se puede rotar mediante el comando \tdplotsetrotatedcoords{<angle1>}{<angle2>}{<angle3>}. Dentro del paquete, este comando se implementa para realizar una rotación del sistema de coordenadas utilizando los ángulos de Euler en la secuencia zyz.

Para obtener otra secuencia, se puede redefinir el comando de transformación como ya se explicó enesteyesta respuestahaciapregunta antes mencionada. De esta manera, en última instancia, puede agregar todas las secuencias posibles y alternar entre ellas. En el código siguiente, utilicé la secuencia zyx (que se llama ángulos de Tait-Bryan o Cardan (verWikipedia para los ángulos de Euler)), ya que es el más cercano a la imagen dada y también el más común para los ángulos de Tait-Byran y también una secuencia zxz como los ángulos clásicos de Euler más comunes.

Luego puede dibujar en el sistema de coordenadas principal o rotado. De esta manera, es fácil añadir cualquier dibujo en 3D, por ejemplo, tu dron, y también los arcos para marcar los ángulos. El tikz-3dplotpaquete incluye un \tdplotdrawarc[coordinates_frame,->,colo]{origin}{radius}{start angle}{end angle}{node info}{label}comando, pero encontré que es más intuitivo simplemente dibujar el arco manualmente en los planos de los sistemas de coordenadas rotados con la opción canvas is xy plane at z=0que ya ha usado.

\documentclass[tikz]{standalone}
%\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, quotes}
%\usetikzlibrary{3d, arrows.meta, calc, quotes}

\usepackage{tikz-3dplot}

% Define new arc command
% Syntax: [draw options] (center) (initial angle:final angle:radius)
% https://tex.stackexchange.com/a/66220
\def\centerarc[#1](#2)(#3:#4:#5){%
    \draw [#1] ($(#2)+({#5*cos(#3)}, {#5*sin(#3)})$) arc (#3:#4:#5)%
}
 
% Redefine the rotation sequence for the tikz3d-plot to Euler-Angles:
% z-x-z with alpha-beta-gamma (psi-theta-phi)
% https://tex.stackexchange.com/q/118069/98906
\newcommand{\tdseteulerzxz}{%
    \renewcommand{\tdplotcalctransformrotmain}{%
        %
        % Determine the sin and cos of the specified angle in degrees
        % \tdplotsinandcos{sin}{cos}{theta}
        % - #1: Returns sin(#3)
        % - #2: Returns cos(#3)
        % - #3: User-specified angle theta
        \tdplotsinandcos{\sinalpha}{\cosalpha}{\tdplotalpha} 
        \tdplotsinandcos{\sinbeta}{\cosbeta}{\tdplotbeta}
        \tdplotsinandcos{\singamma}{\cosgamma}{\tdplotgamma}
        %
        % Define trigonometric abbreviations
        %
        \tdplotmult{\sasb}{\sinalpha}{\sinbeta}
        \tdplotmult{\sacb}{\sinalpha}{\cosbeta}
        \tdplotmult{\sacbsg}{\sacb}{\singamma}
        \tdplotmult{\sacbcg}{\sacb}{\cosgamma}
        \tdplotmult{\sasg}{\sinalpha}{\singamma}
        \tdplotmult{\sacg}{\sinalpha}{\cosgamma}
        %
        \tdplotmult{\sbsg}{\sinbeta}{\singamma}
        \tdplotmult{\sbcg}{\sinbeta}{\cosgamma}
        %
        \tdplotmult{\casb}{\cosalpha}{\sinbeta}
        \tdplotmult{\cacb}{\cosalpha}{\cosbeta}
        \tdplotmult{\cacbsg}{\cacb}{\singamma}
        \tdplotmult{\cacbcg}{\cacb}{\cosgamma}
        \tdplotmult{\casg}{\cosalpha}{\singamma}
        \tdplotmult{\cacg}{\cosalpha}{\cosgamma}
        %
        % Define the entries for the rotation matrix from the B-System to the I-System
        % This is A_IB = (A_BI)^T
        %
        \pgfmathsetmacro{\raaeul}{+\cacg - \sacbsg}
        \pgfmathsetmacro{\rabeul}{-\casg - \sacbcg}
        \pgfmathsetmacro{\raceul}{+\sasb}
        %
        \pgfmathsetmacro{\rbaeul}{+\sacg + \cacbsg}
        \pgfmathsetmacro{\rbbeul}{-\sasg + \cacbcg}
        \pgfmathsetmacro{\rbceul}{-\casb}
        %
        \pgfmathsetmacro{\rcaeul}{+\sbsg}
        \pgfmathsetmacro{\rcbeul}{+\sbcg}
        \pgfmathsetmacro{\rcceul}{+\cosbeta}
        %
    }
}
 
% Redefine the rotation sequence for the tikz3d-plot to Cardan-Angles:
% z-y-x with alpha-beta-gamma
% https://tex.stackexchange.com/q/118069/98906
\newcommand{\tdsetcardanzyx}{%
    \renewcommand{\tdplotcalctransformrotmain}{%
        %
        % Determine the sin and cos of the specified angle in degrees
        % \tdplotsinandcos{sin}{cos}{theta}
        % - #1: Returns sin(#3)
        % - #2: Returns cos(#3)
        % - #3: User-specified angle theta
        \tdplotsinandcos{\sinalpha}{\cosalpha}{\tdplotalpha} 
        \tdplotsinandcos{\sinbeta}{\cosbeta}{\tdplotbeta}
        \tdplotsinandcos{\singamma}{\cosgamma}{\tdplotgamma}
        %
        % Define trigonometric abbreviations
        %
        \tdplotmult{\sasb}{\sinalpha}{\sinbeta}
        \tdplotmult{\sasbsg}{\sasb}{\singamma}
        \tdplotmult{\sasbcg}{\sasb}{\cosgamma}
        %
        \tdplotmult{\sacb}{\sinalpha}{\cosbeta}
        \tdplotmult{\sasg}{\sinalpha}{\singamma}
        \tdplotmult{\sacg}{\sinalpha}{\cosgamma}
        %
        \tdplotmult{\casb}{\cosalpha}{\sinbeta}
        \tdplotmult{\casbsg}{\casb}{\singamma}
        \tdplotmult{\casbcg}{\casb}{\cosgamma}
        %
        \tdplotmult{\cacb}{\cosalpha}{\cosbeta}
        \tdplotmult{\casg}{\cosalpha}{\singamma}
        \tdplotmult{\cacg}{\cosalpha}{\cosgamma}
        \tdplotmult{\cbsg}{\cosbeta}{\singamma}
        \tdplotmult{\cbcg}{\cosbeta}{\cosgamma}
        %
        % Define the entries for the rotation matrix from the B-System to the I-System
        % This is A_IB = (A_BI)^T
        %
        \pgfmathsetmacro{\raaeul}{+\cacb}
        \pgfmathsetmacro{\rabeul}{+\casbsg - \sacg}
        \pgfmathsetmacro{\raceul}{+\sasg+\casbcg}
        %
        \pgfmathsetmacro{\rbaeul}{+\sacb}
        \pgfmathsetmacro{\rbbeul}{+\cacg + \sasbsg}
        \pgfmathsetmacro{\rbceul}{\sasbcg-\casg}
        %
        \pgfmathsetmacro{\rcaeul}{-\sinbeta}
        \pgfmathsetmacro{\rcbeul}{+\cbsg}
        \pgfmathsetmacro{\rcceul}{+\cbcg}
        %
    }
}
 
% Plot display orientation
\tdplotsetmaincoords{50}{115}

\begin{document}


% z-y-x Tait-Bryan angles
\begin{tikzpicture}[scale=2,tdplot_main_coords,> = Triangle]
    % change ratation to z-y-x Tait-Bryan / Cardan angles
    \tdsetcardanzyx
    
    \pgfmathsetmacro{\angpsi}{-20}  % or alpha
    \pgfmathsetmacro{\angtheta}{-10}    % or beta
    \pgfmathsetmacro{\angphi}{-5}   % or gamma

    \pgfmathsetmacro{\r}{2} % unit length radius      
    
    \coordinate (O) at (0,0,0);     
    
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{\angphi}    
    \begin{scope}[tdplot_rotated_coords,scale=1.2]
        \draw coordinate (O) (0,0,-.05) ellipse [radius=.2];
        \foreach \xy/\yx in {x/y, y/x} {
          \fill[white] (xyz cs: \xy = -1, \yx = -.05) -- (xyz cs: \xy =  1, \yx=-.05)
                    -- (xyz cs: \xy =  1, \yx =  .05) -- (xyz cs: \xy = -1, \yx= .05) -- cycle;
          \foreach \lmr in {-.05, 0, .05}
            \draw[gray] (xyz cs: \xy=-1, \yx = \lmr) -- (xyz cs: \xy=1, \yx=\lmr);
          \draw[fill=white, radius=.15] (xyz cs: \xy = -1) ellipse[]
                                        (xyz cs: \xy =  1) ellipse[];
        }
        \draw[fill=white] (0,0,0) ellipse [radius=.2];
        
    \end{scope}     
    
    
    % original coordinate system
    \foreach \xyz/\Label in {x/left,y/right,z/above}
        \draw[->,blue] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz$};
    
    % angle of first rotation around z-axis
    \draw[canvas is xy plane at z=0,->] (1.5,0) arc (0:\angpsi:1.5);
    \node at ({1.7*cos(\angpsi/2)},{1.7*sin(\angpsi/2)},0){$\psi$};
    \draw[canvas is xy plane at z=0,->] (0,1.5) arc (90:90+\angpsi:1.5);
    \node at ({-1.7*sin(\angpsi/2)},{1.7*cos(\angpsi/2)},0){$\psi$};    
    \tdplotsetrotatedcoords{\angpsi}{0}{0}
    
    % new coordinate system
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {x/left,y/right}
            \draw[->,green] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz'$};
        
        % angle of second rotation around new y-axis
        \draw[canvas is xz plane at y=0,->] (1.5,0) arc (0:-\angtheta:1.5);
        \node at ({1.7*cos(\angtheta/2)},0,{-1.7*sin(\angtheta/2)}){$\theta$};
        \draw[canvas is xz plane at y=0,->] (0,1.5) arc (90:90-\angtheta:1.5);
        \node at ({1.7*sin(\angtheta/2)},0,{1.7*cos(\angtheta/2)}){$\theta$};
    \end{scope} 
    
        
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{0}  
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {z/above}
            \draw[->,magenta] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz''$};
        
        % angle of third rotation around new x-axis
        \draw[canvas is yz plane at x=0,->] (1.5,0) arc (0:\angphi:1.5);
        \node at (0,{1.7*cos(\angphi/2)},{1.7*sin(\angphi/2)}){$\varphi$};
        \draw[canvas is yz plane at x=0,->] (0,1.5) arc (90:90+\angphi:1.5);
        \node at (0,{-1.7*sin(\angphi/2)},{1.7*cos(\angphi/2)}){$\varphi$};
    \end{scope}     
    
    % rotated coordinate system
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{\angphi}    
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {x/left,y/right,z/above}
            \draw[->,densely dashed,red] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\tilde\xyz$};
    \end{scope}
\end{tikzpicture}

% z-x-z Euler angles
\begin{tikzpicture}[scale=2,tdplot_main_coords,> = Triangle]
    % change ratation to z-y-x Tait-Bryan / Cardan angles
    \tdseteulerzxz
    
    \pgfmathsetmacro{\angpsi}{-10}  % or alpha
    \pgfmathsetmacro{\angtheta}{-20}    % or beta
    \pgfmathsetmacro{\angphi}{-10}  % or gamma

    \pgfmathsetmacro{\r}{2} % unit length radius      
    
    \coordinate (O) at (0,0,0);     
    
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{\angphi}    
    \begin{scope}[tdplot_rotated_coords,scale=1.2]
        \draw coordinate (O) (0,0,-.05) ellipse [radius=.2];
        \foreach \xy/\yx in {x/y, y/x} {
          \fill[white] (xyz cs: \xy = -1, \yx = -.05) -- (xyz cs: \xy =  1, \yx=-.05)
                    -- (xyz cs: \xy =  1, \yx =  .05) -- (xyz cs: \xy = -1, \yx= .05) -- cycle;
          \foreach \lmr in {-.05, 0, .05}
            \draw[gray] (xyz cs: \xy=-1, \yx = \lmr) -- (xyz cs: \xy=1, \yx=\lmr);
          \draw[fill=white, radius=.15] (xyz cs: \xy = -1) ellipse[]
                                        (xyz cs: \xy =  1) ellipse[];
        }
        \draw[fill=white] (0,0,0) ellipse [radius=.2];
        
    \end{scope}     
    
    
    % original coordinate system
    \foreach \xyz/\Label in {x/left,y/right,z/above}
        \draw[->,blue] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz$};
    
    % angle of first rotation around z-axis
    \draw[canvas is xy plane at z=0,->] (1.5,0) arc (0:\angpsi:1.5);
    \node at ({1.7*cos(\angpsi/2)},{1.7*sin(\angpsi/2)},0){$\psi$};
    \draw[canvas is xy plane at z=0,->] (0,1.5) arc (90:90+\angpsi:1.5);
    \node at ({-1.7*sin(\angpsi/2)},{1.7*cos(\angpsi/2)},0){$\psi$};    
    \tdplotsetrotatedcoords{\angpsi}{0}{0}
    
    % new coordinate system
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {x/left,y/right}
            \draw[->,green] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz'$};
        
        % angle of second rotation around new x-axis
        \draw[canvas is yz plane at x=0,->] (1.5,0) arc (0:\angtheta:1.5);
        \node at (0,{1.7*cos(\angtheta/2)},{1.7*sin(\angtheta/2)}){$\theta$};
        \draw[canvas is yz plane at x=0,->] (0,1.5) arc (90:90+\angtheta:1.5);
        \node at (0,{-1.7*sin(\angtheta/2)},{1.7*cos(\angtheta/2)}){$\theta$};
    \end{scope} 
    
        
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{0}  
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {y/right}
            \draw[->,magenta] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\xyz''$};
        
        % angle of third rotation around new z-axis
        \draw[canvas is xy plane at z=0,->] (1.5,0) arc (0:\angphi:1.5);
        \node at ({1.7*cos(\angphi/2)},{1.7*sin(\angphi/2)},0){$\varphi$};
        \draw[canvas is xy plane at z=0,->] (0,1.5) arc (90:90+\angphi:1.5);
        \node at ({-1.7*sin(\angphi/2)},{1.7*cos(\angphi/2)},0){$\varphi$};
    \end{scope}     
    
    % rotated coordinate system
    \tdplotsetrotatedcoords{\angpsi}{\angtheta}{\angphi}    
    \begin{scope}[tdplot_rotated_coords]
        \foreach \xyz/\Label in {x/left,y/right,z/above}
            \draw[->,densely dashed,red] (O) -- (xyz cs: \xyz=\r) node[\Label]{$\tilde\xyz$};
    \end{scope}
\end{tikzpicture}


\end{document}

Resultados:

Tait-Bryann zyx Tait-Bryan_zyx euler zxz Euler_zxz

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