1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
|
% Copyright 2019 by Till Tantau
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
\section{Three Dimensional Drawing Library}
\begin{tikzlibrary}{3d}
This package provides some styles and options for drawing three dimensional
shapes.
\end{tikzlibrary}
\subsection{Coordinate Systems}
\begin{coordinatesystem}{xyz cylindrical}
The |xyz cylindrical| coordinate system allows to you specify a point in
terms of cylindrical coordinates, sometimes also referred to as cylindrical
polar coordinates or polar cylindrical coordinates. It is very similar to
the |canvas polar| and |xy polar| coordinate systems with the difference
that you provide an elevation over the $xy$-plane using the |z| key.
%
\begin{key}{/tikz/cs/angle=\meta{degrees} (initially 0)}
The angle of the coordinate interpreted in the ellipse whose axes are
the $x$-vector and the $y$-vector.
\end{key}
%
\begin{key}{/tikz/cs/radius=\meta{number} (initially 0)}
A factor by which the $x$-vector and $y$-vector are multiplied prior to
forming the ellipse.
\end{key}
%
\begin{key}{/tikz/cs/z=\meta{number} (initially 0)}
Factor by which the $z$-vector is multiplied.
\end{key}
%
\begin{codeexample}[preamble={\usetikzlibrary{3d}}]
\begin{tikzpicture}[->]
\draw (0,0,0) -- (xyz cylindrical cs:radius=1);
\draw (0,0,0) -- (xyz cylindrical cs:radius=1,angle=90);
\draw (0,0,0) -- (xyz cylindrical cs:z=1);
\end{tikzpicture}
\end{codeexample}
%
\end{coordinatesystem}
\begin{coordinatesystem}{xyz spherical}
The |xyz spherical| coordinate system allows you to specify a point in
terms of spherical coordinates.
%
\begin{key}{/tikz/cs/radius=\meta{number} (initially 0)}
Factor by which the $x$-, $y$-, and $z$-vector are multiplied.
\end{key}
%
\begin{key}{/tikz/cs/latitude=\meta{degrees} (initially 0)}
Angle of the coordinate between the $y$- and $z$-vector, measured from
the $y$-vector.
\end{key}
%
\begin{key}{/tikz/cs/longitude=\meta{degrees} (initially 0)}
Angle of the coordinate between the $x$- and $y$-vector, measured from
the $y$-vector.
\end{key}
%
\begin{key}{/tikz/cs/angle=\meta{degrees} (initially 0)}
Same as |longitude|.
\end{key}
%
\begin{codeexample}[preamble={\usetikzlibrary{3d}}]
\begin{tikzpicture}[->]
\draw (0,0,0) -- (xyz spherical cs:radius=1);
\draw (0,0,0) -- (xyz spherical cs:radius=1,latitude=90);
\draw (0,0,0) -- (xyz spherical cs:radius=1,longitude=90);
\end{tikzpicture}
\end{codeexample}
%
\end{coordinatesystem}
\subsection{Coordinate Planes}
Sometimes drawing with full three dimensional coordinates is not necessary and
it suffices to draw in two dimensions but in a different coordinate plane. The
following options help you to switch to a different plane.
\subsubsection{Switching to an arbitrary plane}
\begin{key}{/tikz/plane origin=\meta{point} (initially {(0,0)})}
Origin of the plane.
\end{key}
\begin{key}{/tikz/plane x=\meta{point} (initially {(1,0)})}
Unit vector of the $x$-direction in the new plane.
\end{key}
\begin{key}{/tikz/plane y=\meta{point} (initially {(0,1)})}
Unit vector of the $y$-direction in the new plane.
\end{key}
\begin{key}{/tikz/canvas is plane}
Perform the transformation into the new canvas plane using the units above.
Note that you have to set the units \emph{before} calling
|canvas is plane|.
%
\begin{codeexample}[preamble={\usetikzlibrary{3d}}]
\begin{tikzpicture}[
->,
plane x={(0.707,-0.707)},
plane y={(0.707,0.707)},
canvas is plane,
]
\draw (0,0) -- (1,0);
\draw (0,0) -- (0,1);
\end{tikzpicture}
\end{codeexample}
%
\end{key}
\subsubsection{Predefined planes}
\begin{key}{/tikz/canvas is xy plane at z=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(0,0,|\meta{dimension}|)}|,
\item |plane x={(1,0,|\meta{dimension}|)}|, and
\item |plane y={(0,1,|\meta{dimension}|)}|.
\end{itemize}
\end{key}
\begin{key}{/tikz/canvas is yx plane at z=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(0,0,|\meta{dimension}|)}|,
\item |plane x={(0,1,|\meta{dimension}|)}|, and
\item |plane y={(1,0,|\meta{dimension}|)}|.
\end{itemize}
\end{key}
\begin{key}{/tikz/canvas is xz plane at y=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(0,|\meta{dimension}|,0)}|,
\item |plane x={(1,|\meta{dimension}|,0)}|, and
\item |plane y={(0,|\meta{dimension}|,1)}|.
\end{itemize}
\end{key}
\begin{key}{/tikz/canvas is zx plane at y=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(0,|\meta{dimension}|,0)}|,
\item |plane x={(0,|\meta{dimension}|,1)}|, and
\item |plane y={(1,|\meta{dimension}|,0)}|.
\end{itemize}
\end{key}
\begin{key}{/tikz/canvas is yz plane at x=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(|\meta{dimension}|,0,0)}|,
\item |plane x={(|\meta{dimension}|,1,0)}|, and
\item |plane y={(|\meta{dimension}|,0,1)}|.
\end{itemize}
\end{key}
\begin{key}{/tikz/canvas is zy plane at x=\meta{dimension}}
A plane with
%
\begin{itemize}
\item |plane origin={(|\meta{dimension}|,0,0)}|,
\item |plane x={(|\meta{dimension}|,0,1)}|, and
\item |plane y={(|\meta{dimension}|,1,0)}|.
\end{itemize}
\end{key}
\subsection{Examples}
\begin{codeexample}[preamble={\usetikzlibrary{3d}}]
\begin{tikzpicture}[z={(10:10mm)},x={(-45:5mm)}]
\def\wave{
\draw[fill,thick,fill opacity=.2]
(0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0)
sin (5,1) cos (6,0) sin (7,-1) cos (8,0)
sin (9,1) cos (10,0)sin (11,-1)cos (12,0);
\foreach \shift in {0,4,8}
{
\begin{scope}[xshift=\shift cm,thin]
\draw (.5,0) -- (0.5,0 |- 45:1cm);
\draw (1,0) -- (1,1);
\draw (1.5,0) -- (1.5,0 |- 45:1cm);
\draw (2.5,0) -- (2.5,0 |- -45:1cm);
\draw (3,0) -- (3,-1);
\draw (3.5,0) -- (3.5,0 |- -45:1cm);
\end{scope}
}
}
\begin{scope}[canvas is zy plane at x=0,fill=blue]
\wave
\node at (6,-1.5) [transform shape] {magnetic field};
\end{scope}
\begin{scope}[canvas is zx plane at y=0,fill=red]
\draw[help lines] (0,-2) grid (12,2);
\wave
\node at (6,1.5) [rotate=180,xscale=-1,transform shape] {electric field};
\end{scope}
\end{tikzpicture}
\end{codeexample}
\begin{codeexample}[preamble={\usetikzlibrary{3d}}]
\begin{tikzpicture}
\begin{scope}[canvas is zy plane at x=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\begin{scope}[canvas is zx plane at y=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\begin{scope}[canvas is xy plane at z=0]
\draw (0,0) circle (1cm);
\draw (-1,0) -- (1,0) (0,-1) -- (0,1);
\end{scope}
\end{tikzpicture}
\end{codeexample}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: "pgfmanual-pdftex-version"
%%% End:
|
