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Adicione ângulos ao drone 3D

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Adicione ângulos ao drone 3D

Como posso adicionar ângulos de Euler e ângulos XYZ ao código como na imagem?insira a descrição da imagem aqui

\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}

Responder1

Eu recomendaria usar o tikz-3dplotpacote. Dentro do pacote, já existe uma transformação de coordenadas definida usando ângulos de Euler. Você pode encontrar uma pergunta semelhante com algumas respostas úteisaqui. Basicamente, você pode definir um sistema de coordenadas principal do qual pode definir a orientação com dois ângulos (por exemplo, \tdplotsetmaincoords{50}{115}). Então, este sistema de coordenadas pode ser girado através do comando \tdplotsetrotatedcoords{<angle1>}{<angle2>}{<angle3>}. Dentro do pacote, este comando é implementado para realizar uma rotação do sistema de coordenadas usando os ângulos de Euler na sequência zyz.

Para obter outra sequência, pode-se redefinir o comando de transformação conforme já discutido emesseeesta respostapara opergunta antes mencionada. Dessa forma, você pode adicionar todas as sequências possíveis e alternar entre elas. No código abaixo, usei a sequência zyx (que são chamados de ângulos Tait-Bryan ou Cardan (vejaWikipedia sobre ângulos de Euler)), uma vez que é o mais próximo da imagem dada e também o mais comum para ângulos de Tait-Byran e também uma sequência zxz como os ângulos de Euler clássicos mais comuns.

Você pode então desenhar no sistema de coordenadas principal ou girado. Desta forma, é fácil adicionar qualquer desenho 3D, por exemplo, o seu drone e também os arcos para marcar os ângulos. O tikz-3dplotpacote inclui um \tdplotdrawarc[coordinates_frame,->,colo]{origin}{radius}{start angle}{end angle}{node info}{label}comando, mas achei mais intuitivo apenas desenhar o arco manualmente nos planos dos sistemas de coordenadas girados com a opção que canvas is xy plane at z=0você já usou.

\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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