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cómo: imagen de 5 coordenadas en 3d

tag-icon • tag-icon tikz-pgf tikz-graphdrawing
cómo: imagen de 5 coordenadas en 3d

He estado intentando hacer una imagen tikz que ilustre 5 puntos en 3d donde desde un punto son 4 vectores que salen a los otros 4 puntos. Me pregunto si hay alguna manera de hacer que esta imagen parezca más 3D.

\documentclass[landscape]{article}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{10pt}%
\usetikzlibrary{calc}


\begin{document}
\begin{tikzpicture}
[
scale=3,
>=stealth,
point/.style = {draw, circle,  fill = black, inner sep = 1pt},
dot/.style   = {draw, circle,  fill = black, inner sep = .2pt},
]

%% Vanishing points for perspective handling
\coordinate (P1) at (-9cm,1.5cm); % left vanishing point (To pick)
\coordinate (P2) at (9cm,1.5cm); % right vanishing point (To pick)

%% (A1) and (A2) defines the 2 central points of the cuboid
\coordinate (A1) at (0em,3cm); % central top point (To pick)
\coordinate (A2) at (0em,-3cm); % central bottom point (To pick)

%% (A3) to (A8) are computed given a unique parameter (or 2) .8
% You can vary .8 from 0 to 1 to change perspective on left side
\coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective 
\coordinate (A4) at ($(P1)!.8!(A1)$);

% You can vary .8 from 0 to 1 to change perspective on right side
\coordinate (A7) at ($(P2)!.7!(A2)$);
\coordinate (A8) at ($(P2)!.7!(A1)$);

%% Automatically compute the last 2 points with intersections
\coordinate (A5) at
  (intersection cs: first line={(A8) -- (P1)},
            second line={(A4) -- (P2)});
\coordinate (A6) at
  (intersection cs: first line={(A7) -- (P1)}, 
            second line={(A3) -- (P2)});



%% Possibly draw back faces
\fill[gray!90] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
\node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
\fill[gray!50] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
\node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
\fill[gray!30] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
\node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };

\draw[thick] (A5) -- (A6);
\draw[thick] (A3) -- (A6);
\draw[thick] (A7) -- (A6);

\node (n0) at (0,0) [point, label = left:$S$] {};
\node (n1) at (1.2,1.7) [point, label = left:$R_{1}$] {};
\node (n2) at (-0.5, 1.2) [point, label = left:$R_{2}$] {};
\node (n3) at (1.35,-1.1) [point, label = left:$R_{3}$] {};
\node (n4) at (-0.2, -1.9) [point, label = left:$R_{4}$] {};

\draw[<-] (n1) -- node (a) [label = {below right:$d_{1}$}] {} (n0);
\draw[<-] (n2) -- node (b) [label = {above right:$d_{2}$}] {} (n0);
\draw[<-] (n3) -- node (c) [label = {above right:$d_{3}$}] {} (n0);
\draw[<-] (n4) -- node (d) [label = {above right:$d_{4}$}] {} (n0);

\end{tikzpicture}
\end{document}

la imagen tikz

Respuesta1

Si no quieres dibujar en 3D, lo cual es posible contikz-3dplotpaquete, entonces una solución muy sencilla es llenar los planos con algunos colores muy claros. Vea la imagen de abajo.

ingrese la descripción de la imagen aquí

Este es el código para tu caso.

\documentclass[landscape]{article}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{10pt}%
\usetikzlibrary{calc}


\begin{document}
\begin{tikzpicture}
[
scale=3,
>=stealth,
point/.style = {draw, circle,  fill = black, inner sep = 1pt},
dot/.style   = {draw, circle,  fill = black, inner sep = .2pt},
]

%% Vanishing points for perspective handling
\coordinate (P1) at (-9cm,1.5cm); % left vanishing point (To pick)
\coordinate (P2) at (9cm,1.5cm); % right vanishing point (To pick)

%% (A1) and (A2) defines the 2 central points of the cuboid
\coordinate (A1) at (0em,3cm); % central top point (To pick)
\coordinate (A2) at (0em,-3cm); % central bottom point (To pick)

%% (A3) to (A8) are computed given a unique parameter (or 2) .8
% You can vary .8 from 0 to 1 to change perspective on left side
\coordinate (A3) at ($(P1)!.8!(A2)$); % To pick for perspective 
\coordinate (A4) at ($(P1)!.8!(A1)$);

% You can vary .8 from 0 to 1 to change perspective on right side
\coordinate (A7) at ($(P2)!.7!(A2)$);
\coordinate (A8) at ($(P2)!.7!(A1)$);

%% Automatically compute the last 2 points with intersections
\coordinate (A5) at
  (intersection cs: first line={(A8) -- (P1)},
            second line={(A4) -- (P2)});
\coordinate (A6) at
  (intersection cs: first line={(A7) -- (P1)}, 
            second line={(A3) -- (P2)});



%% Possibly draw back faces
\fill[gray!90] (A2) -- (A3) -- (A6) -- (A7) -- cycle; % face 6
\node at (barycentric cs:A2=1,A3=1,A6=1,A7=1) {\tiny };
\fill[gray!50] (A3) -- (A4) -- (A5) -- (A6) -- cycle; % face 3
\node at (barycentric cs:A3=1,A4=1,A5=1,A6=1) {\tiny };
\fill[gray!30] (A5) -- (A6) -- (A7) -- (A8) -- cycle; % face 4
\node at (barycentric cs:A5=1,A6=1,A7=1,A8=1) {\tiny };

\draw[thick] (A5) -- (A6);
\draw[thick] (A3) -- (A6);
\draw[thick] (A7) -- (A6);

\node (n0) at (0,0) [point, label = left:$S$] {};
\node (n1) at (1.2,1.7) [point, label = left:$R_{1}$] {};
\node (n2) at (-0.5, 1.2) [point, label = left:$R_{2}$] {};
\node (n3) at (1.35,-1.1) [point, label = left:$R_{3}$] {};
\node (n4) at (-0.2, -1.9) [point, label = left:$R_{4}$] {};



\draw[fill, green, opacity=.1] (0,0) -- (1.2,1.7) -- (-0.5, 1.2);
\draw[fill, green, opacity=.1] (0,0) -- (-0.2, -1.9) -- (1.35,-1.1);
\draw[fill, red, opacity=.05] (0,0) -- (1.2,1.7) -- (1.35,-1.1);


\draw[<-,very thick] (n1) -- node (a) [label = {below right:$d_{1}$}] {} (n0);
\draw[<-,very thick] (n2) -- node (b) [label = {above right:$d_{2}$}] {} (n0);
\draw[<-,very thick] (n3) -- node (c) [label = {above right:$d_{3}$}] {} (n0);
\draw[<-,very thick] (n4) -- node (d) [label = {above right:$d_{4}$}] {} (n0);


\end{tikzpicture}
\end{document}

Respuesta2

Usaría las macros de transformación de coordenadas disponibles en TikZ que básicamente permiten definir un nuevo conjunto de coordenadas x, y y z en función del "antiguo" sistema u, v como se muestra a continuación:

ingrese la descripción de la imagen aquí

Encuentro este código menos complicado y con menos cálculo:

\documentclass[tikz,convert]{standalone}
\begin{document}
\def\rot{30}
\begin{tikzpicture}[x={(180+\rot:1cm)},y={(-\rot:1cm)},z={(90:1cm)},scale=.7,>=stealth,thick]


\draw [fill=gray,draw=none] (0,0,0)--(10,0,0)--(10,5,0)--(0,5,0)--cycle;
\draw [fill=gray!50!white,draw=none] (0,0,0)--(10,0,0)--(10,0,15)--(0,0,15)--cycle;
\draw [fill=gray!30!white,draw=none] (0,0,0)--(0,5,0)--(0,5,15)--(0,0,15)--cycle;
\draw (0,0,0)--(10,0,0) (0,0,0)--(0,5,0) (0,0,0)--(0,0,15);


\node [fill=black,circle,inner sep=1pt] (pt0) at (5,0.5,5) {};
\node [fill=black,circle,inner sep=1pt] (pt1) at (0,1,10) {};
\node [fill=black,circle,inner sep=1pt] (pt2) at (9,0,9) {};
\node [fill=black,circle,inner sep=1pt] (pt3) at (0,2,1) {};
\node [fill=black,circle,inner sep=1pt] (pt4) at (8,2,0) {};

\draw [->] (pt0)--(pt1) node [pos=.5,right] {$d_1$};
\draw [->] (pt0)--(pt2) node [pos=.5,right] {$d_2$};
\draw [->] (pt0)--(pt3) node [pos=.5,below] {$d_3$};
\draw [->] (pt0)--(pt4) node [pos=.5,right] {$d_4$};

\node at (pt0) [left] {$S$}; 
\node at (pt1) [above] {$R1$}; 
\node at (pt2) [left] {$R2$}; 
\node at (pt3) [right] {$R3$}; 
\node at (pt4) [below] {$R4$}; 
\end{tikzpicture}
\end{document}

y esta es la salida:

Imagen con transformación 3d y ángulo=20

Tenga en cuenta que definí un número llamado \rot. Si cambias su valor hasta 30 (por ejemplo) obtendrás automáticamente otra perspectiva. Además, si quieres más profundidad, también puedes dibujar líneas discontinuas. Otra cosa que puedes hacer, dado que la falta de profundidad se debe principalmente a los pequeños cambios en la coordenada y, es posible que desees cambiar la escala de esa dirección, por ejemploy={((-\rot:3cm))}

Más profundidad con línea discontinua y perspectiva diferente

simplemente agregando al código anterior estas pocas líneas (nota \def\rot{30}en el preámbulo):

\begin{tikzpicture}[x={(180+\rot:1cm)},y={(-\rot:3cm)},z={(90:1cm)},...]
...
\draw [dashed] (pt1)--+(0,-1,0) (pt1)--+(0,0,-10);
\draw [dashed] (pt2)--+(0,0,-9) (pt2)--+(-9,0,0);
\draw [dashed] (pt3)--+(0,-2,0) (pt3)--+(0,0,-1);
\draw [dashed] (pt4)--+(-8,0,0) (pt4)--+(0,-2,0);
...
\end{tikzpicture}

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