这需要在原点 (A) = (0,0) 且尺寸为 2 厘米的红色参考系中制作一个金字塔（四面体，SABCD），然后在面上描绘一个绿色三角形 ((S), (B), (C))，为此，毫无疑问需要暂时确定原点 (B) 的参考点（蓝色），其横坐标与半线 [BC] 重合，因此与主横坐标轴平行，纵坐标与半右 [BS] 重合。
必须使用路径 绘制绿色三角形(start) -- ++(60:2) -- ++(-60:2) -- cycle。我无法确定计算 参数的代码行\tdplotsetrotatedcoords{\alpha}{\beta}{\gamma}。下面的代码可以编译，只需更正计算。注意：BC 的首项系数（因此是蓝色标记中的横坐标）与原始红色标记 (A) 中的线 AD 的首项系数相同。我们可以在模型上引入其他焦点线\node at (0,0, -5) {alpha: \alpha, beta: \beta gamma; \gamma}
\input{preambule-utf8.ltx}
\begin{document}
\newcommand{\DefinePoints}[1]{%
\foreach \x/\y/\z/\name in {#1} {
\coordinate (\name) at (\x, \y, \z);
}
}
\tdplotsetmaincoords{70}{120} % Si absent, « tdplot_main_coords » sera inconnu
\begin{tikzpicture}[tdplot_main_coords,
line cap=round,line join=round,>=triangle 45,scale=2]
\tdplotsetmaincoords{70}{120}
\draw[line width=1pt, red] (0,0,0) -- (3,0,0) node[below right]{$X$};
\draw[line width=1pt, red] (0,0,0) -- (0,3,0) node[below right]{$Y$};
\draw[line width=1pt, red] (0,0,0) -- (0,0,2.5) node[below right]{$Z$};
\def\cote{2}
\DefinePoints{
0/ 0/ 0/A,
\cote/ 0/ 0/B,
\cote/ \cote/ 0/C,
0/ \cote/ 0/D,
0.5*\cote/ 0.5*\cote/ \cote /S,
0/ 0/ \cote /Z%
}
\draw (A) -- (B) -- (C) -- (D) -- cycle;
\foreach \point in {A, B, C, D} {
\draw (S) -- (\point);
}
\draw (A) -- (S) -- (B);
\draw (B) -- (S) -- (C);
% Calcul des angles pour le changemnt de repère momentané
\tdplotsetrotatedcoordsorigin{(A)}
% Calcul des vecteurs BC, BS et AD
\coordinate (BC) at ($(C)-(B)$);
\coordinate (BS) at ($(S)-(B)$);
\coordinate (AD) at ($(D)-(A)$);
% Calcul des vecteurs BC, BS et AD
\coordinate (BC) at ($(C)-(B)$);
\coordinate (BS) at ($(S)-(B)$);
\coordinate (AD) at ($(D)-(A)$);
% Calcul de l'angle α entre BC et l'axe x
\pgfmathanglebetweenpoints
{\pgfpoint{1cm}{0cm}}
{\pgfpointanchor{BC}{center}}
\let\alpha\pgfmathresult
% Calcul de l'angle β entre BS et l'axe y
\pgfmathanglebetweenpoints
{\pgfpoint{0cm}{1cm}}
{\pgfpointanchor{BS}{center}}
\let\beta\pgfmathresult
% Calcul de l'angle γ entre AD et l'axe z
\pgfmathanglebetweenpoints
{\pgfpoint{1cm}{0cm}}
{\pgfpointanchor{AD}{center}}
\let\gamma\pgfmathresult
% Utiliser ces angles pour définir le repère bleu
\tdplotsetrotatedcoords{\alpha}{\beta}{\gamma}
\tdplotsetrotatedcoordsorigin{(B)}
\node at (0,0, -5) {alpha : \alpha, beta : \beta gamma ; \gamma} ;
\begin{scope}[tdplot_rotated_coords]
% Draw blue axes
\draw[blue, thick,->](0,0)--(3,0,0)node[below right]{$X'$};
\draw[blue, thick,->](0,0)--(0,3,0)node[below left]{$Y'$};
\draw[blue, thick,->](0,0)--(0,0,3)node[above]{$Z'$};
\draw[-, green, line width=2pt] (B) -- ++(60:2) -- ++(-60:2) ; % -- cycle ;
\end{scope}
\foreach \n/\pos in {S/above, A/{above left}, B/{above left}, C/below, D/{above right}, Z/right}{
\tkzDrawPoint (\n)
\tkzLabelPoints[\pos](\n)
}
\node at (0,0, -5) {alpha : \alpha, beta : \beta gamma ; \gamma} ;
\end{tikzpicture}
\end{document}
谢谢你帮助我摆脱因无法解决这个问题而导致的强迫症 80）
考虑到我对“tikz-3dplot_documentation.pdf”的阅读，我试图在我的代码注释中更加明确地说明，一定是有些东西我忘记了，因为结果是：
使用以下代码。
\newcommand{\DefinePoints}[1]{%
\foreach \x/\y/\z/\name in {#1} {
\coordinate (\name) at (\x, \y, \z);
}
}
\tdplotsetmaincoords{70}{120}%
\begin{tikzpicture} [
tdplot_main_coords,
cube/.style={very thick,black},
grid/.style={very thin,gray},
axis/.style={->,blue,thick},
rotated axis/.style={->,purple,thick},
line cap=round,
line join=round,
>=triangle 45,
scale=3]
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (4,0,0) node[anchor=south]{$x$};
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (0,3,0) node[anchor=north west]{$y$};
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (0,0,3) node[anchor=west]{$z$};
\def\cote{2}
\pgfmathsetmacro{\hauteur}{sqrt(3) }
\DefinePoints{
0/ 0/ 0/A,
\cote/ 0/ 0/B,
\cote/ \cote/ 0/C,
0/ \cote/ 0/D,
0.5*\cote/ 0.5*\cote/ \hauteur /S,
0/ 0/ \cote /Z%
}
\draw[ ] (A) -- (B) -- (C) -- (D) -- cycle;
\foreach \point in {A, B, C, D} {
\draw (S) -- (\point);
}
\draw[ ] (A) -- (S) -- (B);
\draw[ ] (B) -- (S) -- (C);
% --------------------------------------------
% Calculate the rotation angles
% α (alpha) : Rotation z of α degrees to align the z' axis with the global Z axis
\pgfmathanglebetweenpoints
{\pgfpointanchor{B}{center}}
{\pgfpointanchor{Z}{center}}
\let\alpha\pgfmathresult
% β (beta) : Rotation y of β degrees with respect to the system resulting from the first rotation
\pgfmathanglebetweenpoints
{\pgfpointanchor{B}{center}}
{\pgfpointanchor{D}{center}} % Use the point corresponding to the Y axis in the system resulting from the first rotation
\let\beta\pgfmathresult
% γ (gamma) : Rotation z of γ degrees with respect to the system resulting from the first two rotations
\pgfmathanglebetweenpoints
{\pgfpointanchor{B}{center}}
{\pgfpointanchor{B}{center}} % Use the point corresponding to the X axis in the system resulting from the first two rotations
\let\gamma\pgfmathresult
\tdplotsetrotatedcoords{60}{90}{0}
\tdplotsetrotatedcoordsorigin{(B)}
% ---------------------------------------------------
\begin{scope}[tdplot_rotated_coords]
% draw the rotated coordinate frame axes
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (3,0,0) node[anchor=west]{$x'$};
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (0,4,0) node[anchor=south west]{$y'$};
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (0,0,3) node[anchor=west]{$z'$};
\draw (0,0,0) -- (1.5*\cote,0,0) -- (1.5*\cote, 1.5*\cote, 0) -- (0,1.5*\cote,0) -- cycle ;
% Tracer le triangle vert avec un chemin relatif dans le plan (SBC)
\draw[-, green, line width=2pt] (B) -- ++(60:2) -- ++(-60:2) ; % -- cycle ;
\end{scope}
\node at (1,-1, -2) {alpha : \alpha } ;
\node at (1,-1, -2.5) {beta : \beta} ;
\node at (1,-1, -3) {gamma : \gamma} ;
\foreach \n/\pos in {S/above, A/{above left}, B/{above left}, C/below, D/{above right}, Z/right}{
\tkzDrawPoint (\n)
\tkzLabelPoints[\pos](\n)
}
\end{tikzpicture}
我失眠了！
答案1
我又睡着了
\documentclass[12pt]{standalone}
\usepackage{tkz-base}
\usepackage{tikz-3dplot}
%
% Jj Dhénin: 2023/10/11
% Uncomment if necessary
% \newcommand{\MainAxes}{} % main_coords,
% \newcommand{\RotatedAxes}{} % rotated axis,
% \newcommand{\FacilitateFocus}{}
\tikzset{
axis/.style={->, blue, thick},
rotated axis/.style={->, purple, thick},
base/.style={gray!60},
line cap=round,
line join=round,
>=triangle 45,
base/.style={gray!50}
}
\begin{document}
% Following the tkz-euclide model, "\definePoints"
\newcommand{\DefinePoints}[1]{%
\foreach \x/\y/\z/\name in {#1} {
\coordinate (\name) at (\x, \y, \z);
}
}
% The small base triangle
% #1: Initial position, e.g., (X)
% #2: Length of the triangle's side
% #3: Color and other style arguments
\newcommand\faisUn[3] {\fill[#3] #1 -- ++(-60:#2) -- ++(-#2,0) -- cycle;
}
% Three "solid" triangles around an empty triangle
% #1: Initial position, e.g., (X)
% #2: Length of the triangle's side
% #3: Color and other style arguments
\newcommand{\faisTrois}[3]{
\coordinate (X) at (#1) ;
\coordinate (tmpA) at (X) ;
\def\coteA{#2}
\faisUn{(X)} {\coteA}{#3}
\coordinate (X) at ([shift={(-120:\coteA)}]X);
\faisUn{(X)} {\coteA} {#3}
\coordinate (X) at ([shift={(\coteA,0)}]X);
\faisUn{(X)} {\coteA} {#3}
\coordinate (X) at (tmpA) ;
}
% Three times three "solid" triangles around an empty triangle
% #1: Initial position, e.g., (X)
% #2: Length of the triangle's side
% #3: Color and other style arguments
\newcommand{\faisNeuf}[3]{
\coordinate (X) at (#1) ;
\coordinate (tmpB) at (X) ;
\def\coteB{#2}
\faisTrois{X}{\coteB}{#3}
\coordinate (X) at ([shift={(-120:2*\coteB)}]X);
\faisTrois{X}{\coteB}{#3}
\coordinate (X) at ([shift={(2*\coteB,0)}]X);
\faisTrois{X}{\coteB}{#3}
\coordinate (X) at (tmpB) ;
}
% 3 x three times 3 "solid" triangles around an empty triangle
% #1: Initial position, e.g., (X)
% #2: Length of the triangle's side
% #3: Color and other style arguments
\newcommand{\faisTroisNeuf}[3]{
\coordinate (X) at (#1) ;
\coordinate (tmpC) at (X) ;
\def\coteC{#2}
\faisNeuf{X}{\coteC}{#3}
\coordinate (X) at ([shift={(-120:4*\coteB)}]X);
\faisNeuf{X}{\coteC}{#3}
\coordinate (X) at ([shift={(4*\coteB,0)}]X);
\faisNeuf{X}{\coteC}{#3}
}
% ------------
% Create a face based on
% #1: Orientation of the abscissas according to the face
% #2: Bottom-left vertex of the face (A or B or C or D)
% #3: Color and other style of the face
% #4: Step (level of division)
\newcommand\faireFace[4]{
\def\alpha{#1}
% \beta has been calculated once and for all during initialization
\def\gamma{90}
% Origin at the bottom right of the triangle
\tdplotsetrotatedcoordsorigin{#2}
\tdplotsetrotatedcoords{\alpha}{\beta}{\gamma}
\begin{scope}[tdplot_rotated_coords]
\ifdefined\RotatedAxes
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (5,0,0) node[anchor=west]{$x'$};
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (0,4,0) node[anchor=south west]{$y'$};
\draw[rotated axis, blue, line width=1pt] (0,0,0) -- (0,0,3) node[anchor=west]{$z'$};
\fi
% Use the top of the triangle to position it, regardless of its size
\coordinate (X) at (S) ;
\ifnum #4=4
\def\cote{4} % Length of the edge
\def\coteDeco{0.25} % Length of the side of the small triangle
\faisTroisNeuf{X} {\coteDeco}{#3}
\coordinate (X) at ([shift={(-0.25*\cote,0)}]X);
\coordinate (X) at ([shift={(-120:0.25*\cote)}]X);
\faisTroisNeuf{X} {\coteDeco}{#3}
\coordinate (X) at ([shift={(0.25*\cote,0)}]X);
\coordinate (X) at ([shift={(60:0.25*\cote)}]X);
\faisTroisNeuf{X} {\coteDeco}{#3}
\fi
\ifnum #4=3
\def\cote{4} % Length of the edge
\def\coteDeco{0.5} % Length of the side of the small triangle
\faisNeuf{X}{\coteDeco}{#3}
\coordinate (X) at ([shift={(-120:0.5*\cote)}]X);
\faisNeuf{X}{\coteDeco}{#3}
\coordinate (X) at ([shift={(0.5*\cote,0)}]X);
\faisNeuf{X}{\coteDeco}{#3}
\fi
\ifnum #4=2
\def\cote{4} % Length of the edge
\def\coteDeco{1} % Length of the side of the small triangle
\faisTrois{X}{\coteDeco}{#3}
\coordinate (X) at ([shift={(-120:0.5*\cote)}]X);
\faisTrois{X}{\coteDeco}{#3}
\coordinate (X) at ([shift={(0.5*\cote,0)}]X);
\faisTrois{X}{\coteDeco}{#3}
\fi
\ifnum #4=1
\def\cote{4} % Length of the edge
\def\coteDeco{2} % Length of the side of the small triangle
\faisUn{(X)} {\coteDeco} {#3}
\coordinate (X) at ([shift={(-120:0.5*\cote)}]X);
\faisUn{(X)} {\coteDeco} {#3}
\coordinate (X) at ([shift={(0.5*\cote,0)}]X);
\faisUn{(X)} {\coteDeco} {#3}
\fi
\ifnum #4=0
\def\cote{4} % Length of the edge
\def\coteDeco{4} % Length of the side of the small triangle
\faisUn{(X)} {\coteDeco} {#3}
\fi
\end{scope}
} % End of command faireFace
\tdplotsetmaincoords{70}{120}%
% We need five different pyramids
% #1: Step number
% #2: Measurement of the pyramid
% #3: Measurement of the triangle's side (according to the step)
\newcommand\faisLaPyramide[1]{
\setbox1\hbox{
\begin{tikzpicture} [
tdplot_main_coords,
scale=0.35 % Set the scale here!
]
% Draw the main axes
\ifdefined\MainAxes
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (5,0,0) node[anchor=south]{$x$};
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (0,5,0) node[anchor=north west]{$y$};
\draw[axis, tdplot_main_coords, red] (0,0,0) -- (0,0,3) node[anchor=west]{$z$};
\fi
% Initialization of characteristics
\def\cote{4} % Length of the edge
\def\coteDeco{0.25} % Length of the side of the small triangle
% Measurement of the height of the main face
\pgfmathsetmacro{\SMbc} {sqrt( (\cote)^2 - (0.5*\cote)^2 }
% Measurement of the height of the pyramid
\pgfmathsetmacro{\hauteur} {sqrt( (\SMbc)^2 - (0.5*\cote)^2 }
% Angle of a face with the base
\pgfmathsetmacro{\beta}{atan2(\hauteur, 0.5*\cote}
% Vertices and useful points
\DefinePoints{
0/ 0/ 0/A,
\cote/ 0/ 0/B,
\cote/ \cote/ 0/C,
0/ \cote/ 0/D,
0.5*\cote/ 0.5*\cote/ \hauteur /S,
\cote/ 0.5*\cote/ 0/Mbc
}
% Shaded base
\fill [base] (A) -- (B) -- (C) -- (D) -- cycle;
\ifdefined\FacilitateFocus
% Pyramid's contour
\foreach \point in {A, B, C, D} {
\draw (S) -- (\point);
}
\draw[ ] (A) -- (S) -- (B);
\draw[ ] (B) -- (S) -- (C);
\fi
% Face on the right (DSA)
% Starting with a face hidden by the front
\faireFace{180} {(D)} {red!40} {#1} % Perspective distorts and deceives
% Front face on the right (DSA)
\faireFace{270} {(A)} {red!50} {#1} % Perspective distorts and deceives
% Front face on the left (BSC)
\faireFace{0} {(B)} {red!60} {#1}
% Front face on the right (CSD)
\faireFace{90} {(C)} {red!70} {#1}
\ifdefined\FacilitateFocus
\foreach \n/\pos in {S/above, A/{above left}, B/{above left}, C/below, D/{above right}, Mbc/below}{
\tkzDrawPoint (\n)
\tkzLabelPoints[\pos](\n)
}
\fi
\end{tikzpicture}
} % End of setbox1\hbox
} % End of command\faisLaPyramide
\begin{tikzpicture}
\faisLaPyramide{0}
\node at (0,0) {\box1};
\faisLaPyramide{1}
\node at (2,0) {\box1};
\faisLaPyramide{2}
\node at (4,0) {\box1};
\faisLaPyramide{3}
\node at (6,0) {\box1};
\faisLaPyramide{4}
\node at (8,0) {\box1};
\end{tikzpicture}
\end{document}
很诚挚