[Tex/LaTex] Projection of included 2D graphics to a plane

3dasymptotepstrickstikz-pgf

General purpose

I want to project a graphic file from external sources (example.pdf saved on my computer e.g. a chip design) on the bottom of a 3D graphic (which I can draw in LaTeX by using TikZ, pstrick or asymptote).

I know that it works for text letters, see How to project text onto a plane?. So I guess that it would also work with an included graphics!

Example using TikZ

I also achieved a minor step towards this goal but I am not happy with performing a 2D rotation in 3D. How can I configure the command

/tikz/cm={a, b, c, d, coordinate}

in order to perform a 3D rotation? The command is given in the tikz-pgf manual (v3.0.0, p.363) in chapter 25.3. Or is there a simpler way to go? Also Canvas Transformation could be used…

By the way, I perform 3D rotations by using

\tdplotsetmaincoords{phi}{theta}

which is contained in the package tikz-3dplot.

My MWE:

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{3D,calc}

\begin{document}

\begin{tikzpicture}
\coordinate (chip) at (0,0,0);
\node[cm={1,0,cos(20),sin(20),(0,0)}] at (coordA){\includegraphics[width=20em]{example.pdf}};
\end{tikzpicture}
\end{document}

Asymptote

I am also interested whether I can include graphics with asymptote or not.

EDIT (not minimal tikz example):

I want to give you an impression what I am intended to do:

\documentclass[border=5pt]{standalone}
\usepackage{tikz,tikz-3dplot}
\usetikzlibrary{calc}

\newcommand{\drawrect}[4]{
    \fill[red!50,opacity=0.5] #1 -- #2 -- #3 -- #4 -- cycle;
}

\begin{document}

\begin{tikzpicture}
% Underlaying graphics:
\node[cm={cos(-20),sin(-20),sin(80),cos(80),(0,0)}]{\includegraphics[width=20em]{example-image.pdf}};
% Position of the box:
\tdplotsetmaincoords{75.3}{55}
\begin{scope}[tdplot_main_coords,scale=1]
    \coordinate (positionA) at (+2.2,0,0);
\end{scope}
% Draw the rotated box:
\tdplotsetmaincoords{75.3}{55+90+9};
\begin{scope}[tdplot_main_coords,scale=1]
    % Rectangle's (side's) half sizes
    \coordinate (RectangleX) at (1.15,0,0);
    \coordinate (RectangleY) at (0,1.15,0);
    \coordinate (RectangleZ) at (0,0,0.2);
    % Center of cube:
    \coordinate (root) at ($(positionA)+(RectangleZ)$);
    % Cube:
    \drawrect
        {($(root)-(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)+(RectangleZ)$)}
        {($(root)-(RectangleX)-(RectangleY)+(RectangleZ)$)}
    \drawrect
        {($(root)-(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)+(RectangleY)-(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)-(RectangleZ)$)}
    \drawrect
        {($(root)-(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)-(RectangleX)-(RectangleY)+(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)+(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)-(RectangleZ)$)}
    \drawrect
        {($(root)+(RectangleX)+(RectangleY)+(RectangleZ)$)}
        {($(root)+(RectangleX)+(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)-(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)+(RectangleZ)$)}
    \drawrect
        {($(root)+(RectangleX)+(RectangleY)+(RectangleZ)$)}
        {($(root)+(RectangleX)+(RectangleY)-(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)-(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)+(RectangleZ)$)}
    \drawrect
        {($(root)+(RectangleX)+(RectangleY)+(RectangleZ)$)}
        {($(root)-(RectangleX)+(RectangleY)+(RectangleZ)$)}
        {($(root)-(RectangleX)-(RectangleY)+(RectangleZ)$)}
        {($(root)+(RectangleX)-(RectangleY)+(RectangleZ)$)}
    \end{scope}
\end{tikzpicture}
\end{document}

which results in:

Simple example using expanded code

Other application

It is somehow similar to an architect's plan. A 2D plan below and a simple 3D structure on top of it.

enter image description here

Best Answer

In a cube the bottom is invisible, the reason why I define an own plane P2inner. Needs the lates pst-solides3d and an eps image which has only basic line elements, like lineto curveto and moveto:

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}
\begin{document}

\psset{viewpoint=20 -120 30 rtp2xyz,Decran=20,unitPicture=15,lightsrc=viewpoint}
\begin{pspicture}[solidmemory](-7,-9)(8,3)
\psSolid[object=plan,definition=normalpoint,base=-6 6 -6 6,args={0 0 -4 [0 0.1 1]},
  fillstyle=solid,linecolor=black!15,fillcolor=black!10,name=P2inner]
\psImage[unitPicture=30,file=tiger.eps,origine=0 0 -4,normal=0 0 1,phi=180](-4,0)
\psSolid[object=cube,a=4,name=Cube,linecolor=red,numfaces=all,fontsize=100,
  RotZ=20,action=draw]
\psImage[unitPicture=30,file=tiger.eps,origine=Cube 0 solidcentreface,normal=Cube 0 solidnormaleface,phi=-90]
\psImage[unitPicture=30,file=tiger.eps,origine=Cube 3 solidcentreface,normal=Cube 3 solidnormaleface]
\psImage[unitPicture=30,file=tiger.eps,origine=Cube 2 solidcentreface,normal=Cube 2 solidnormaleface]
\end{pspicture}

\end{document}

enter image description here

Related Solutions

[Tex/LaTex] What packages or tools best support any 3D line, plane, surface intersections

You mention that you've been tasked with drawing simple 3D structures. For that, a visually intuitive tool is Google Sketchup. 3D geometry for cubes is obtained by extruding (using the Push/Pull tool) a square, and model components can be intersected with one another.

enter image description here

Geometric perspective to the desired viewpoint is easily achieved via the orbiting tool. Print to PDF provides a means to include the resulting 3D structure to be included into your LaTeX document:

enter image description here

More complex figures and intersections are also possible using basic constructions of rectangles/circles and extrusions in 3D. Here the two pieces from the intersected cube has been separated:

enter image description here

[Tex/LaTex] Projection of Circle onto Spherical Surface

Well, no prizes for speed (not just because there is some duplication of calculations: TikZ is slow for this kind of stuff), but this shows one way of doing it. I expect asymptote/PSTricks could do it quicker, but I don't see any other way of doing it in TikZ.

The maths is straightforward "back-of-the-envelope" trigonometry (in this case literally). The only "insight" is to draw the circles manually.

EDIT 1 inspired by Jake's missing (at the time of writing) PGF Plots answer, I've changed most of the \foreach statements to TikZ plot commands which makes things a bit quicker.

EDIT 2 changed the critical function to sqrt(\R^2-(\cx+\r*cos(\t))^2-(\cy+\r*sin(\t))^2) as this provides better accuracy than veclen when the circles get near to the edge.

EDIT 3 a second version has been added which uses layers to add both circles at the same time.

\documentclass{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}[x=(-30:4cm),y=(30:4cm),z=(90:4cm)]

\def\R{1}

\draw (-\R,0,0) -- (\R,0,0);
\draw (0,-\R,0) -- (0,\R,0);
\draw (0,0,0) -- (0,0,\R);
\draw plot [domain=0:360, samples=60, variable=\i] 
    (\R*cos \i, \R*sin \i, 0) -- cycle;

\def\r{0.075}

\foreach \cr in {0.3, 0.5, 0.7, 0.9}
    \foreach \ca [evaluate={\cx=\cr*cos \ca; \cy=\cr*sin \ca;}]in {-90,-60,-30,0,30, 60, 90}
        \draw [green!85!black, fill=green!85!black, fill opacity=0.25]
            plot [domain=0:360, samples=40, variable=\i] 
                (\cx+\r*cos \i, \cy+\r*sin \i, 0) -- cycle;

\foreach \i in {0, 30,...,150}
    \draw [dotted] plot [domain=-90:90, samples=30, variable=\j]        
        (\R*cos \i*sin \j,\R*sin \i*sin \j, \R*cos \j);

\foreach \j in {0, 15,...,90}
    \draw [dotted] plot [domain=0:360, samples=60, variable=\i]  
            (\R*cos \i*sin \j,\R*sin \i*sin \j, \R*cos \j);

\foreach \cr in {0.3, 0.5, 0.7, 0.9}
    \foreach \ca [evaluate={\cx=\cr*cos \ca; \cy=\cr*sin \ca;}]in {-90,-60,-30,0,30, 60, 90}
        \draw [red, fill=red, fill opacity=.25] 
            plot [domain=0:360, samples=40, variable=\t] 
                (\cx+\r*cos \t,\cy+\r*sin \t, {sqrt(\R^2-(\cx+\r*cos(\t))^2-(\cy+\r*sin(\t))^2)})
                    -- cycle;

\end{tikzpicture}

\end{document}

enter image description here

And here's a version using layers and Cartesian rather than polar coordinates for the circles:

\documentclass{standalone}
\usepackage{tikz}
\begin{document}

\pgfdeclarelayer{dome floor}
\pgfdeclarelayer{dome}
\pgfdeclarelayer{dome surface}
\pgfsetlayers{dome floor,main,dome,dome surface}

\def\addcircle#1#2#3#4{%
    \begingroup%
        \pgfmathparse{#1}\let\R=\pgfmathresult
        \pgfmathparse{#2}\let\cx=\pgfmathresult
        \pgfmathparse{#3}\let\cy=\pgfmathresult
        \pgfmathparse{#4}\let\r=\pgfmathresult
        \begin{pgfonlayer}{dome floor}
            \draw [blue!45!black, fill=blue!45, fill opacity=0.25]
                            plot [domain=0:360, samples=40, variable=\i] 
                                (\cx+\r*cos \i, \cy+\r*sin \i, 0) -- cycle;
        \end{pgfonlayer}
        \begin{pgfonlayer}{dome surface}
            \draw [red!75!black, fill=red!75, fill opacity=0.25] 
                plot [domain=0:360, samples=60, variable=\t] 
                    (\cx+\r*cos \t,\cy+\r*sin \t, {sqrt(max(\R^2-(\cx+\r*cos(\t))^2-(\cy+\r*sin(\t))^2, 0))})
                        -- cycle;
        \end{pgfonlayer}
    \endgroup%
}
\begin{tikzpicture}[x=(-30:1cm),y=(30:1cm),z=(90:1cm)]


\def\R{6}

\begin{pgfonlayer}{dome floor}
    \draw (-\R,0,0) -- (\R,0,0);
    \draw (0,-\R,0) -- (0,\R,0);
    \draw plot [domain=0:360, samples=90, variable=\i] 
        (\R*cos \i, \R*sin \i, 0) -- cycle;
\end{pgfonlayer}

\draw (0,0,0) -- (0,0,\R);

\begin{pgfonlayer}{dome surface}
    \foreach \i in {0, 30,...,150}
            \draw [dotted] plot [domain=-90:90, samples=60, variable=\j]        
                (\R*cos \i*sin \j,\R*sin \i*sin \j, \R*cos \j);
    \foreach \j in {0, 15,...,90}
            \draw [dotted] plot [domain=0:360, samples=60, variable=\i]  
                    (\R*cos \i*sin \j,\R*sin \i*sin \j, \R*cos \j);
\end{pgfonlayer}

\def\r{0.5}
\foreach \m [evaluate={\N=max(-4, \m-7);}]in {0,...,5}{
    \foreach \n in {0,-1,...,\N}
        {\addcircle{\R}{\m*sin 60}{\n-mod(abs(\m),2)*\r}{\r}}}


\end{tikzpicture}

\end{document}

enter image description here

General purpose

Example using TikZ

Asymptote

EDIT (not minimal tikz example):

Other application

Best Answer

Related Solutions

[Tex/LaTex] What packages or tools best support any 3D line, plane, surface intersections

[Tex/LaTex] Projection of Circle onto Spherical Surface

Related Question