# 3d plot with reflected arrows in “planes” using TikZ

I'm trying to reproduce this picture in TikZ, but I don't know how to get those 3D "planes" of arrows shown.

Here is my attempt so far, which isn't remotely close to what I want (and mostly obtained from here anyway):

\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}
\draw (-4,0) arc (180:360:4 and 1);
\draw [dashed] (-4,0) arc (180:0:4 and 1);
\draw (-4,0) arc (180:0:4 and 4);
\draw (0,0,0) -- ++(0,-.5,-.5) -- ++(0,.5,0) -- ++(0,.5,.5) -- cycle;
\draw (0,0) -- ++(-.5,0) -- ++(0,.5) -- ++(.5,0) -- cycle;
\draw [thick, dashed] (0,0) -- ++(-5,0);
\draw [thick, {latex}-] (0,0) -- ++(172.5:5cm);
\draw [thick, dashed] (0,0) -- ++(0,5);
\draw [thick, dashed] (0,0,0) -- ++(0,-2.5,-2.5);
\draw [thick, -{latex}] (0,0) -- ++(45:5cm);
\draw [red, thick, <->] (0,0) ++(172.5:4.5cm) arc (172.5:180:4.5cm) node [midway, left] () {$\gamma_i$};
\draw [red, thick, <-] (0,0) ++(180:1.5cm) arc (180:532:1.5cm) node [midway, right] () {$\varphi_i$};
\end{tikzpicture}
\end{document}


EDIT: If TikZ isn't good for doing this, any other package will do at this point!

• (As an aside, I asked a TikZ related question a few days ago with a similar crap MWE; since I don't want to seem like I'm [ab]using the answerers here, is there maybe something I can pay them? Or give them points? I feel bad just asking for someone to help me solve a problem and then just saying thank you; also, I know this should be something asked in the meta board but I included it here in case someone were to bring it up.) – Alborz Apr 16 '16 at 0:34
• You can accept the answer to a question which helps you most. You can also vote up any answer which helps you (including the one you accept, if you wish). Also, if you use something in a later question which you learnt from an earlier answer, you can (and should) attribute it to the person who answered. (Within reason, obviously. For significant chunks of code.) Also, people appreciate your including MWEs, especially if they improve as you get more experience ;). – cfr Apr 16 '16 at 0:40
• TikZ is really not great for 3D. If you need to draw 3D stuff, you would be well-advised to learn to use one of the tools which is better suited to it. In particular, to use a tool which actually draws in 3D. TikZ can't do this. It draws in 2D. You can fake 3D but it is only fake. There's no 3D object there you can tweak, for example. If the perspective changes, you typically need to redo everything. tikz-3dplot can help in automating some of the calculations needed to fake 3D in TikZ 2D. But it is still fake e.g. you have to draw things in the right order. There's no real depth. – cfr Apr 16 '16 at 0:44
• Oh, and you can obviously hire people to draw things for you. But you can't hire them here ;). – cfr Apr 16 '16 at 0:45
• @cfr good point, just added where I based my code from :) also, hmm that's unfortunate then, what tools do you recommend? I've heard of asymptote and PSTricks but that's all I am aware of... [and darn! I wish I could hire them here lol] – Alborz Apr 16 '16 at 0:46

I am uploading the code that done from a friend of mine (@GeorgePapademetriou -not a member, but sure want to share)

\documentclass[svgnames,10pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
%\usepackage{xcolor}
%\usepackage{pgfplots}
\usetikzlibrary{arrows, 3d, decorations.markings}
\usetikzlibrary{calc}
\usepgflibrary{shapes.arrows}

\begin{document}

%% plane with
\begin{tikzpicture} %
\def\R{1.8} % for phi angle
\begin{scope}  [x={(0.9cm,-0.15cm)}, y={(0.25cm,0.435cm)}, z={(0cm,0.8cm)}, scale=2.5]
\begin{scope} [every path/.style={thin}]
\begin{scope} [canvas is xy plane at z=0]
%the plane
\draw [fill=green!10] (-2.2,-2)--(-2,2)--(2,2)--(2.2,-2)--cycle;
\end{scope}
% x,y,z axis
\draw[-latex] (-2.1,0,0) -- (2.5,0,0) node[right]{$x$};
\draw[-latex] (0,-2,0) -- (0,2.5,0) node[right]{$y$};
\draw[-latex] (0,0,0) -- (0,0,2) node [above]{$z$};
\begin{scope}[canvas is xy plane at z=0]
% phi angle and vectors
\draw [->, thick, red] (0:\R-0.4) arc[start angle=0,delta angle=310,radius=\R-0.4] node[below] {$\phi_r$};
\draw [fill=yellow!20, thick] (0,0)--(0:\R-0.8) arc[start angle=0,delta angle=-90, radius=\R-0.8]-- cycle;
\draw[-latex,black] (0,0)--++(-80:\R-0.8);
\draw[-latex,black] (0,0)--++(-60:\R-0.8);
\draw[-latex,black] (0,0)--++(-40:\R-0.8);
\draw[-latex,black] (0,0)--++(-20:\R-0.8);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
%theta angle and vectors
\draw [fill=blue!10, thick] (0,0)-- (90:\R-0.8) arc (90:180:\R-0.8)--cycle;
\draw [-latex, blue!50!black, thick] (90:\R-0.65) arc (90:141:\R-0.65) node [midway, above] {$\theta_i$};
\draw[-latex,black] (0,0)--++(110:\R-0.8);
\draw[-latex,black] (0,0)--++(130:\R-0.8);
\draw[-latex,black] (0,0)--++(150:\R-0.8);
\draw[-latex,black] (0,0)--++(170:\R-0.8);
% node and vector to the theta angle
\draw[semithick,black,decoration={markings,mark=at position 0.5 with {\arrow{latex}}},
postaction=decorate] (0,0)++(141:2.5) node[above,align=center] {Incidence \\ direction} --++ (141:-2.5);
\end{scope}
% first lobe
\draw [fill=blue!5, thick] (0,0,0)--(0,0,1) to [bend left=25] (0.8,0.25, 0.6) to [bend left=20] (2,0.6, 0)
to [bend left=20] (1.5,0.4,0)--cycle;
\draw[-latex,black] (0,0)--++(95:1.76);
\draw[-latex,black] (0,0)--++(80:1.56);
\draw[-latex,black] (0,0)--++(60:1.5);
\draw[-latex,black] (0,0)--++(40:1.78);
\draw[-latex,black] (0,0)--++(25:1.97);
\draw[-latex,black] (0,0)--++(10:1.5);
\draw[-latex,black] (0,0)--++(-5:1.5);
\begin{scope}[canvas is xz plane at y=0]
%second lobe
\draw [fill=blue!18, thick] (0,0)-- (90:\R-0.8) arc(90:40:\R-0.8) to [bend left] (2.2,0.15) to [bend left] (1.5,0) --cycle;
\draw[-latex,black] (0,0)--++(80:\R-0.8);
\draw[-latex,black] (0,0)--++(60:\R-0.8);
\draw[-latex,black] (0,0)--++(40:\R-0.8);
\draw[-latex,black] (0,0)--++(30:1.32);
\draw[-latex,black] (0,0)--++(20:1.68);
\draw[-latex,black] (0,0)--++(10:2);
\draw[-latex,black] (0,0)--++(4:2.2);
\end{scope}
%third lobe
\draw [fill=blue!25, thick] (0,0,0)--(0,0,1) to [bend left] (0.75,-0.25, 0.6) to [bend left=20] (2.1,-0.6, 0.3)
to [bend left=20] (1.5,-0.5, 0)--cycle;
\draw[-latex,black] (0,0)--++(95:1.6);
\draw[-latex,black] (0,0)--++(80:1.23);
\draw[-latex,black] (0,0)--++(60:0.9);
\draw[-latex,black] (0,0)--++(40:1.1);
\draw[-latex,black] (0,0)--++(25:1.33);
\draw[-latex,black] (0,0)--++(10:1.64);
\draw[-latex,black] (0,0)--++(-3:1.95);
%forth lobe
\draw [fill=blue!30, thick] (0,0,0)--(0,0,1) to [bend left] (0.65,-0.45, 0.5) to [bend left=20] (1.8,-0.6,0,0.5)
to [bend left=20] (1.2,-0.8,0,0)--cycle;
\draw[-latex,black] (0,0)--++(100:1.58);
\draw[-latex,black] (0,0)--++(90:1.28);
\draw[-latex,black] (0,0)--++(75:0.9);
\draw[-latex,black] (0,0)--++(50:0.61);
\draw[-latex,black] (0,0)--++(20:0.8);
\draw[-latex,black] (0,0)--++(0:1.24);
\draw[-latex,black] (0,0)--++(-18:1.85);
\draw[-latex,black] (0,0)--++(-28:1.7);
%descriptions
\node at (2.4,-2.2,0) {$q(\phi_r)=q(\phi_r=0)\cos\phi_r$};
\draw[->, blue!50!black] (2.4,-2,0)--(2.2,-0.2,0);
\draw[->, blue!50!black] (1.9,-2.1,0)--(1.5,-1,0);
\node at (-2.6,0,0.5) {Measuring plane};
\draw[->, blue!50!black] (-2.2,0,0.5)--(-.4,-.2,0.4);
\node at (-1.6,-1.6,0) {Sample plane};
\end{scope}
\end{scope}

\end{tikzpicture}
%

\end{document}


Output:

PS: We have been payed for this graphic, but I suppose that the OP would like to share since he is probably the one that asked and if someone asks for help from a forum we have to believe that he want to help the forum too. PS2: Ok... I mean this... that is not a forum!

This is similar to koleygr's answer but uses tikz-3dplot to obtain the rotated coordinate systems, and \foreach loops to make the code shorter. One reason to post this is that now, i.e. starting from version 3.1 of TikZ, the 3d library treat the xy plane on the same footing as all other planes.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\begin{document}
\tdplotsetmaincoords{70}{20}
\begin{tikzpicture}[tdplot_main_coords,font=\sffamily,%
funky shape/.style={insert path={%
(0,0) -- (2.5,-1) to[bend right] coordinate[pos=0.5] (#1-1) (3.5,0)
coordinate (#1-2) to[bend right] coordinate[pos=1/3] (#1-3)
coordinate[pos=2/3] (#1-4)(1,1) coordinate (#1-5)
to[bend right] coordinate[pos=0.5] (#1-6) (0,2)}}]
\draw[fill=yellow!70!gray,canvas is xy plane at z=0] (-5,-5) rectangle (5,5);
\node[transform shape,canvas is xy plane at z=0,anchor=south west]
at (-5,-5) {sample plane};
\draw[-stealth] (-5,0,0) -- (5,0,0) node[pos=1.05]{$x$};
\draw[-stealth] (0,-5,0) -- (0,5,0) node[pos=1.05]{$y$};
\draw[-stealth] (0,0,0) -- (0,0,5) node[pos=1.1]{$z$};
\begin{scope}[canvas is xy plane at z=0]
\draw[fill=yellow!90!gray] (-90:2.5) arc (-90:0:2.5) -- (0,0);
\foreach \Z in {-81,-72,...,-9}
{\draw[thick,-latex] (0,0) -- (\Z:2.5); }
\draw[-latex] (3.25,0) arc(0:300:3.25) node[below]{$\varphi_r$};
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
\draw[fill=blue!20] (90:2.5) arc (90:180:2.5) -- (0,0);
\foreach \Z in {105,120,...,165}
{\draw[thick,-latex] (0,0) -- (\Z:2.5); }
\draw[thick] (135:6.5) node[above,align=center]{incidence\\ direction} -- (135:2.5);
\draw[thick,-latex] (135:6.5) -- (135:4.5);
\node[anchor=south east] at (110:3) {$\theta_i$};
\draw[-latex] (90:3) arc(90:135:3);
\end{scope}
\foreach \X [count=\Y,evaluate=\Y as \Col using {int(\Y*20)}] in {30,0,-20,-40}
{\tdplotsetrotatedcoords{\X}{00}{0}
\begin{scope}[tdplot_rotated_coords]
\begin{scope}[canvas is xz plane at y=0]
\draw[fill=blue!\Col,funky shape=X-\Y];
\foreach \Z in {1,...,6}
{\draw[thick,-latex] (0,0) -- (X-\Y-\Z); }
\end{scope}
\end{scope}}
\node (q) at ([yshift=-2cm]X-2-2) {$q(\varphi_r)=q(\varphi_r=0)\cos\varphi_r$};
\foreach \Y in {2,3,4}
{\draw[thick,-latex] (q) -- (X-\Y-2);}
\end{tikzpicture}
\end{document}