[Tex/LaTex] How to draw a transparent cube in 3D perspective

3dpstricks

I would like to draw a transparent, `flattened cube' in perspective with dotted lines from both vanishing points to each of the vertices of the 3D solid. Is there a PSTricks package for this?

It is much like Jan Hlavacek's answer to What is the easiest way to draw 3D cube with TikZ? but with the vanishing points and dotted lines from these, and then the `cube' should be transparent. Unfortunately I do not know TikZ.

Update

The following code shows what I would like to achieve:

screenshot

\documentclass{article}

\usepackage{auto-pst-pdf,pstricks-add}

\begin{document}

\begin{figure}
\def\HAa{-5.25 }
\def\HBa{12.5 }
\def\Ab{-0.85 }
\def\Bb{3.05 }
\def\Ia{-1.8 }
\def\Ja{2.65 }
 \centering
 \psset{unit=0.765cm}
  \begin{pspicture}(\HAa,\Ab)(\HBa,\Bb)
   \pnode(!\HAa 0){H1}
   \psdot(H1)
   \pnode(!\HBa 0){H2}
   \psdot(H2)
   \pnode(!\Ia 0){P9}
   \pnode(!\Ja 0){P10}
   \pcline[linestyle=dashed](H1)(P9)
   \pcline[linestyle=dashed](P10)(H2)
   \pnode(!0 \Ab){P1}
   \pnode(!0 \Bb){P2}
   \pnode(!\Ia \HAa \Ia sub \HAa div \Ab mul){P3}
   \pnode(!\Ia \HAa \Ia sub \HAa div \Bb mul){P4}
   \pnode(!\Ja \HBa \Ja sub \HBa div \Ab mul){P5}
   \pnode(!\Ja \HBa \Ja sub \HBa div \Bb mul){P6}
   \psIntersectionPoint(H1)(P5)(H2)(P3){P7}
   \psIntersectionPoint(H1)(P6)(H2)(P4){P8}
   \multido{\i=1+1}{8}{\psdot(P\i)}
   \pcline(P1)(P2)
   \pcline(P1)(P3)
   \pcline(P2)(P4)
   \pcline(P3)(P4)
   \pcline(P1)(P5)
   \pcline(P2)(P6)
   \pcline(P5)(P6)
  \psset{linestyle=dotted}
   \pcline(P3)(H1)
   \pcline(P4)(H1)
   \pcline(P5)(H1)
   \pcline(P6)(H1)
   \pcline(P3)(H2)
   \pcline(P4)(H2)
   \pcline(P5)(H2)
   \pcline(P6)(H2)
   \pcline(P7)(P8)
  \end{pspicture}
\end{figure}

\end{document}

I would like to make this drawing when knowing just the width, depth, and height of the box plus the point of view, instead of maunally calculating the \def values.

P.S. I do not know how to include images, sorry.

Update 2

I have changed the code a bit. (The \def names are changed and the hiddens lines in the cubiod are dashed instead of dotted.)

\documentclass{article}

\usepackage{pstricks-add}

\begin{document}

\begin{figure}
\def\venstre{-5.25 }
\def\hoejre{12.5 }
\def\vinkel{-0.85 }
\def\hoejde{3.05 }
\def\dybde{-1.8 }
\def\bredde{2.65 }
 \centering
 \psset{unit=0.684cm}
  \begin{pspicture}(\venstre,\vinkel)(\hoejre,\hoejde)
   \pnode(!\venstre 0){H1}
   \pnode(!\hoejre 0){H2}
   \psdot(H1)
   \psdot(H2)
   \pnode(!\dybde 0){P9}
   \pnode(!\bredde 0){P10}
   \pcline[linestyle=dashed](H1)(P9)
   \pcline[linestyle=dashed](P10)(H2)
   \pnode(!0 \vinkel){P1}
   \pnode(!0 \hoejde){P2}
   \pnode(!\dybde \venstre \dybde sub \venstre div \vinkel mul){P3}
   \pnode(!\dybde \venstre \dybde sub \venstre div \hoejde mul){P4}
   \pnode(!\bredde \hoejre \bredde sub \hoejre div \vinkel mul){P5}
   \pnode(!\bredde \hoejre \bredde sub \hoejre div \hoejde mul){P6}
   \psIntersectionPoint(H1)(P5)(H2)(P3){P7}
   \psIntersectionPoint(H1)(P6)(H2)(P4){P8}
   \multido{\i=1+1}{8}{\psdot(P\i)}
   \pcline(P1)(P2)
   \pcline(P1)(P3)
   \pcline(P2)(P4)
   \pcline(P3)(P4)
   \pcline(P1)(P5)
   \pcline(P2)(P6)
   \pcline(P5)(P6)
  \psset{linestyle=dotted}
   \pcline(P3)(H1)
   \pcline(P4)(H1)
   \pcline(P7)(H1)
   \pcline(P8)(H1)
   \pcline(P7)(H2)
   \pcline(P8)(H2)
   \pcline(P5)(H2)
   \pcline(P6)(H2)
  \psset{linestyle=dashed}
   \pcline(P7)(P3)
   \pcline(P7)(P5)
   \pcline(P7)(P8)
   \pcline(P8)(P4)
   \pcline(P8)(P6)
  \end{pspicture}
\end{figure}

\end{document}

enter image description here

Update 3

Here is what I ended up with:

\documentclass{article}

\usepackage{pst-solides3d}

\begin{document}

\begin{figure}
 \psset{viewpoint=10 45 8 rtp2xyz,Decran=5}
  \begin{pspicture}[solidmemory](-5,-5)(6,12)
   \psSolid[object=point,args=6 0 1.42,name=L]
   \psSolid[object=point,args=-12 9.75 1.42,name=R]
   \psSolid[object=line,linecolor=red!40,linestyle=dashed,linewidth=2pt,args=R L]
   \psSolid[object=parallelepiped,a=4.56,b=4.56,c=3.90,RotZ=-8,fillcolor=yellow!40,name=Cube,action=draw*](0 0 2)
   \multido{\iA=0+1}{8}{%
     \psSolid[object=point,definition=solidgetsommet,args=Cube \iA,name=C\iA]
   }
   \multido{\iA=0+1}{8}{%
     \psSolid[object=line,linecolor=blue!40,linestyle=dotted,args=L C\iA]
     \psSolid[object=line,linecolor=blue!40,linestyle=dotted,args=R C\iA]
   }
   \psSolid[object=parallelepiped,a=4.56,b=4.56,c=3.90,RotZ=-8,name=Cube,action=draw](0 0 2)
  \end{pspicture}
\end{figure}

\end{document}

Best Answer

\documentclass{article}
\usepackage{pst-solides3d}    
\begin{document}

\psset{viewpoint=10 60 15 rtp2xyz,Decran=5}
\begin{pspicture}[solidmemory](-5,-5)(6,12)
\psSolid[object=point,args=10 -36 0,name=L]
\psSolid[object=point,args=-36 10 0,name=R]
\psSolid[object=line,linecolor=blue,linestyle=dashed,linewidth=2pt,args=R L]
\psSolid[object=parallelepiped,a=6,b=3,c=3,RotZ=30,name=Cube,action=draw*](0 0 2)
\multido{\iA=0+1}{8}{%
  \psSolid[object=point,definition=solidgetsommet,args=Cube \iA,name=C\iA]}
\multido{\iA=0+1}{8}{%
  \psSolid[object=line,linecolor=blue!40,linestyle=dotted,args=L C\iA]
  \psSolid[object=line,linecolor=blue!40,linestyle=dotted,args=R C\iA]}
\psSolid[object=parallelepiped,a=6,b=3,c=3,RotZ=30,name=Cube,action=draw](0 0 2)
\end{pspicture}

\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Perspective transform

I have some code that I wrote to do a slightly more "proper" handling of 3D coordinates than TikZ currently does. Amusingly, it's in the TeX-SX launchpad package already despite not (until now) being part of an answer. It's the tikz3d.dtx package. The idea of it is twofold:

More advanced handling of 3D coordinates. In particular, remembering all three coordinates longer than TikZ currently does. The point of this is that if you do (1,2,3) -- +(3,4,5) then TikZ first converts the coordinates to 2D and then does the relative calculation. This is fine if the conversion from 3D to 2D is linear, but if you want to do a perspective transformation then this isn't linear so converting to 2D and then adding gives the wrong results.
The ability to modify the conversion from 3D to 2D. TikZ can handle a linear 3D to 2D conversion, but there are many interesting transformations that aren't linear. This code allows one to specify an arbitrary transformation. I've built it with a perspective transformation, but anything could be done. Because the coordinates are remembered as 3D, not 2D, there is greater flexibility in the choice of transformation.

The big drawback is that, as with TikZ, this only works on the coordinates, not on the actual paths. However, to properly transform the paths would involve quite considerable work because, for example, the perspective transformation of a bezier curve is not a bezier curve. Since the output formats of TikZ can only handle at best cubic beziers, one would need to approximate the projection by a family of bezier cubics.

On the other hand, the perspective projection of a straight line is still a straight line and it takes quite a considerable perspective effect to deform a bezier curve significantly away from a bezier curve. Here's a couple of examples: the curves are done by projecting the coordinates and then drawing the resulting bezier curve. The jointed-up dots are what the curve really ought to look like (sort of). As you can see, there's not a lot of difference.

projected bezier curve

The basic shapes do need some modification to take into account the 3D coordinates, so I've got some methods for doing that. Circles and arcs don't need much modification, but for the rectangle I made a to path to handle it.

Here are a few more examples (from the file tikz3d_test.tex in the TeX-SX launchpad project).

\begin{tikzpicture}[3d/perspective eye={5,5,-10}]
\draw (3d cs:0,0,0) to[3d rectangle] (3d cs:7,7,0);
\draw (3d cs:0,0,0) to[3d rectangle] (3d cs:7,0,7);
\draw (3d cs:7,7,7) to[3d rectangle] (3d cs:0,7,0);
\draw (3d cs:7,7,7) to[3d rectangle] (3d cs:0,0,7);
\end{tikzpicture}

3D Cube with perspective

Node sizes don't change

\begin{tikzpicture}[3d/perspective eye={5,5,10}]
\foreach \y in {0,.5,...,5}
  \draw (3d cs:0,\y,1) -- (3d cs:0,\y,-31);
  \draw[ultra thick] (3d cs:0,0,0) -- +(0,1) node[thin,fill=white,draw,text width=5em,rounded corners,align=center,anchor=south] {How big is this sign?};
  \draw[ultra thick] (3d cs:0,0,-25) -- +(0,1) node[thin,fill=white,draw,text width=5em,rounded corners,align=center,anchor=south] {How big is this sign?};
\end{tikzpicture}

3D coordinates with nodes

More examples in the TeX-SX launchpad project.

[Tex/LaTex] How to draw parallelepiped and cube with LaTeX

You can annotate the diagram in various ways. Here's one approach.

coordinates are placed when constructing the cuboid. These are then used in a later path as starting points. Further coordinates are placed offset from the originals (a little below, a little left, a little right...) which are then used to draw the lines. Drawing these with the edge operation makes it possible to add arrow tips for the start and end of each line without using separate paths, and the quotes library is then used to label these edges using the edge ["<label>"] syntax. The options for these labels are set to auto to offset them. Where TikZ would 'jump the wrong way', a ' is added after the quoted label to 'swap' the offset e.g. left rather than right.

\documentclass[border=5pt, multi, tikz]{standalone}
\usetikzlibrary{quotes,arrows.meta}
\begin{document}
\begin{tikzpicture}[every edge quotes/.append style={auto, text=blue}]
  \pgfmathsetmacro{\cubex}{5}
  \pgfmathsetmacro{\cubey}{1}
  \pgfmathsetmacro{\cubez}{3}
  \draw [draw=blue, every edge/.append style={draw=blue, densely dashed, opacity=.5}, fill=magenta]
    (0,0,0) coordinate (o) -- ++(-\cubex,0,0) coordinate (a) -- ++(0,-\cubey,0) coordinate (b) edge coordinate [pos=1] (g) ++(0,0,-\cubez)  -- ++(\cubex,0,0) coordinate (c) -- cycle
    (o) -- ++(0,0,-\cubez) coordinate (d) -- ++(0,-\cubey,0) coordinate (e) edge (g) -- (c) -- cycle
    (o) -- (a) -- ++(0,0,-\cubez) coordinate (f) edge (g) -- (d) -- cycle;
  \path [every edge/.append style={draw=blue, |-|}]
    (b) +(0,-5pt) coordinate (b1) edge ["30cm"'] (b1 -| c)
    (b) +(-5pt,0) coordinate (b2) edge ["5cm"] (b2 |- a)
    (c) +(3.5pt,-3.5pt) coordinate (c2) edge ["10cm"'] ([xshift=3.5pt,yshift=-3.5pt]e)
    ;
\end{tikzpicture}
\end{document}

If you need to draw a group of these or several in different places, defining a pic may be a convenient solution. As I've defined it, the pic annotated cuboid takes a single, optional argument which can set various parameters: width, height, depth, units (for the labels) and scale. To set colours, fills etc., you can pass an optional argument to the \pic to specify pic actions e.g. \pic [draw=red, fill=yellow, text=green] {annotated cuboid={width=10, height=45, depth=89.6, scale=.05, units=mm}};. Defaults are the current defaults for colours etc., a cuboid 10x10x10, scaled to one tenth natural size, with unit labels in centimetres.

For example:

\begin{tikzpicture}
  \pic {annotated cuboid};
  \pic [fill=magenta, text=blue, draw=blue] at (5,0) {annotated cuboid={width=30, height=5, depth=10}};
  \pic [fill=green, text=green!50!black, draw=green!25!black] at (5,-2) {annotated cuboid={width=6, height=20, depth=15, units=mm}};
  \pic at (1,-3) {annotated cuboid={width=150, height=200, depth=250, scale=.01, units=m}};
  \pic [fill=cyan, text=blue!75!cyan, draw=blue!75!cyan] at (-3,-2) {annotated cuboid={width=15, height=18, depth=13.5, units=}};
\end{tikzpicture}

produces

Complete code:

\documentclass[border=5pt, multi, tikz]{standalone}
\usetikzlibrary{quotes,arrows.meta}
\tikzset{
  annotated cuboid/.pic={
    \tikzset{%
      every edge quotes/.append style={midway, auto},
      /cuboid/.cd,
      #1
    }
    \draw [every edge/.append style={pic actions, densely dashed, opacity=.5}, pic actions]
    (0,0,0) coordinate (o) -- ++(-\cubescale*\cubex,0,0) coordinate (a) -- ++(0,-\cubescale*\cubey,0) coordinate (b) edge coordinate [pos=1] (g) ++(0,0,-\cubescale*\cubez)  -- ++(\cubescale*\cubex,0,0) coordinate (c) -- cycle
    (o) -- ++(0,0,-\cubescale*\cubez) coordinate (d) -- ++(0,-\cubescale*\cubey,0) coordinate (e) edge (g) -- (c) -- cycle
    (o) -- (a) -- ++(0,0,-\cubescale*\cubez) coordinate (f) edge (g) -- (d) -- cycle;
    \path [every edge/.append style={pic actions, |-|}]
    (b) +(0,-5pt) coordinate (b1) edge ["\cubex \cubeunits"'] (b1 -| c)
    (b) +(-5pt,0) coordinate (b2) edge ["\cubey \cubeunits"] (b2 |- a)
    (c) +(3.5pt,-3.5pt) coordinate (c2) edge ["\cubez \cubeunits"'] ([xshift=3.5pt,yshift=-3.5pt]e)
    ;
  },
  /cuboid/.search also={/tikz},
  /cuboid/.cd,
  width/.store in=\cubex,
  height/.store in=\cubey,
  depth/.store in=\cubez,
  units/.store in=\cubeunits,
  scale/.store in=\cubescale,
  width=10,
  height=10,
  depth=10,
  units=cm,
  scale=.1,
}
\begin{document}
\begin{tikzpicture}
  \pic {annotated cuboid};
  \pic [fill=magenta, text=blue, draw=blue] at (5,0) {annotated cuboid={width=30, height=5, depth=10}};
  \pic [fill=green, text=green!50!black, draw=green!25!black] at (5,-2) {annotated cuboid={width=6, height=20, depth=15, units=mm}};
  \pic at (1,-3) {annotated cuboid={width=150, height=200, depth=250, scale=.01, units=m}};
  \pic [fill=cyan, text=blue!75!cyan, draw=blue!75!cyan] at (-3,-2) {annotated cuboid={width=15, height=18, depth=13.5, units=}};
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Perspective transform

[Tex/LaTex] How to draw parallelepiped and cube with LaTeX

Related Question