summaryrefslogtreecommitdiff
path: root/graphics/pgf/base/doc/text-en/pgfmanual-en-math-commands.tex
blob: 393c0842d00f8f9507d2d88362575f5496c20bb5 (plain)
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
246
% Copyright 2018 by Mark Wibrow
%
% 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{Additional Mathematical Commands}
\label{pgfmath-commands}

Instead of parsing and evaluating complex expressions, you can also use the
mathematical engine to evaluate a single mathematical operation. The macros
used for many of these computations are listed above in
Section~\ref{pgfmath-functions}. \pgfname{} also provides some additional
commands which are shown below:


\subsection{Basic arithmetic functions}
\label{pgfmath-commands-basic}

In addition to the commands described in Section~\ref{pgfmath-functions-basic},
the following command is provided:

\begin{command}{\pgfmathreciprocal\marg{x}}
    Defines |\pgfmathresult| as $1\div\meta{x}$. This provides greatest
    accuracy when \mvar{x} is small.
\end{command}


\subsection{Comparison and logical functions}

In addition to the commands described in
Section~\ref{pgfmath-functions-comparison}, the following command was provided
by Christian Feuers\"anger:

\begin{command}{\pgfmathapproxequalto\marg{x}\marg{y}}
    Defines |\pgfmathresult| 1.0 if $ \rvert \meta{x} - \meta{y} \lvert <
    0.0001$, but 0.0 otherwise. As a side-effect, the global boolean
    |\ifpgfmathcomparison| will be set accordingly.
\end{command}


\subsection{Pseudo-Random Numbers}
\label{pgfmath-random}

In addition to the commands described in
Section~\ref{pgfmath-functions-random}, the following commands are provided:

\begin{command}{\pgfmathgeneratepseudorandomnumber}
    Defines |\pgfmathresult| as a pseudo-random integer between 1 and
    $2^{31}-1$. This uses a linear congruency generator, based on ideas of
    Erich Janka.
\end{command}

\begin{command}{\pgfmathrandominteger\marg{macro}\marg{minimum}\marg{maximum}}
    This defines \meta{macro} as a pseudo-randomly generated integer from the
    range \meta{minimum} to \meta{maximum} (inclusive).
    %
\begin{codeexample}[]
\begin{pgfpicture}
   \foreach \x in {1,...,50}{
      \pgfmathrandominteger{\a}{1}{50}
      \pgfmathrandominteger{\b}{1}{50}
      \pgfpathcircle{\pgfpoint{+\a pt}{+\b pt}}{+2pt}
      \color{blue!40!white}
      \pgfsetstrokecolor{blue!80!black}
      \pgfusepath{stroke, fill}
   }
\end{pgfpicture}
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathdeclarerandomlist\marg{list name}{\ttfamily\{}\marg{item-1}\marg{item-2}...{\ttfamily\}}}
    This creates a list of items with the name \meta{list name}.
\end{command}

\begin{command}{\pgfmathrandomitem\marg{macro}\marg{list name}}
    Select an item from a random list \meta{list name}. The
    selected item is placed in \meta{macro}.
\end{command}

\begin{codeexample}[]
\begin{pgfpicture}
   \pgfmathdeclarerandomlist{color}{{red}{blue}{green}{yellow}{white}}
   \foreach \a in {1,...,50}{
      \pgfmathrandominteger{\x}{1}{85}
      \pgfmathrandominteger{\y}{1}{85}
      \pgfmathrandominteger{\r}{5}{10}
      \pgfmathrandomitem{\c}{color}
      \pgfpathcircle{\pgfpoint{+\x pt}{+\y pt}}{+\r pt}
      \color{\c!40!white}
      \pgfsetstrokecolor{\c!80!black}
      \pgfusepath{stroke, fill}
   }
\end{pgfpicture}
\end{codeexample}

\begin{command}{\pgfmathsetseed\marg{integer}}
    Explicitly sets the seed for the pseudo-random number generator. By default
    it is set to the value of |\time|$\times$|\year|.
\end{command}


\subsection{Base Conversion}
\label{pgfmath-bases}

\pgfname{} provides limited support for conversion between
\emph{representations} of numbers. Currently the numbers must be positive
integers in the range $0$ to $2^{31}-1$, and the bases in the range $2$ to
$36$. All digits representing numbers greater than 9 (in base ten), are
alphabetic, but may be upper or lower case.

In addition to the commands described in Section~\ref{pgfmath-functions-base},
the following commands are provided:

\begin{command}{\pgfmathbasetodec\marg{macro}\marg{number}\marg{base}}
    Defines \meta{macro} as the result of converting \meta{number} from base
    \meta{base} to base 10. Alphabetic digits can be upper or lower case.

\medskip{\def\medskip{}

\begin{codeexample}[]
\pgfmathbasetodec\mynumber{107f}{16} \mynumber
\end{codeexample}

    \noindent Note that, as usual in \TeX, the braces around an argument can be
    omitted if the argument is just a single token (a macro name is a single
    token).
    %
\begin{codeexample}[]
\pgfmathbasetodec\mynumber{33FC}{20} \mynumber
\end{codeexample}

}\medskip
    %
\end{command}

\begin{command}{\pgfmathdectobase\marg{macro}\marg{number}\marg{base}}
    Defines \meta{macro} as the result of converting \meta{number} from base 10
    to base \meta{base}. Any resulting alphabetic digits are in \emph{lower
    case}.
    %
\begin{codeexample}[]
\pgfmathdectobase\mynumber{65535}{16} \mynumber
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathdectoBase\marg{macro}\marg{number}\marg{base}}
    Defines \meta{macro} as the result of converting \meta{number} from base 10
    to base \meta{base}. Any resulting alphabetic digits are in \emph{upper
    case}.
    %
\begin{codeexample}[]
\pgfmathdectoBase\mynumber{65535}{16} \mynumber
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathbasetobase\marg{macro}\marg{number}\marg{base-1}\marg{base-2}}
    Defines \meta{macro} as the result of converting \meta{number} from base
    \meta{base-1} to base \meta{base-2}. Alphabetic digits in \meta{number} can
    be upper or lower case, but any resulting alphabetic digits are in
    \emph{lower case}.
    %
\begin{codeexample}[]
\pgfmathbasetobase\mynumber{11011011}{2}{16} \mynumber
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathbasetoBase\marg{macro}\marg{number}\marg{base-1}\marg{base-2}}
    Defines \meta{macro} as the result of converting \meta{number} from base
    \meta{base-1} to base \meta{base-2}. Alphabetic digits in \meta{number} can
    be upper or lower case, but any resulting alphabetic digits are in
    \emph{upper case}.
    %
\begin{codeexample}[]
\pgfmathbasetoBase\mynumber{121212}{3}{12} \mynumber
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathsetbasenumberlength\marg{integer}}
    Sets the number of digits in the result of a base conversion to
    \meta{integer}. If the result of a conversion has less digits than this
    number, it is prefixed with zeros.
    %
\begin{codeexample}[]
\pgfmathsetbasenumberlength{8}
\pgfmathdectobase\mynumber{15}{2} \mynumber
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathtodigitlist\marg{macro}\marg{number}}
    This command converts \meta{number} into a comma-separated list of digits
    and stores the result in \meta{macro}. The \marg{number} is \emph{not}
    parsed before processing.
    %
\begin{codeexample}[]
\pgfmathsetbasenumberlength{8}
\begin{tikzpicture}[x=0.25cm, y=0.25cm]
  \foreach \n [count=\y] in {0, 60, 102, 102, 126, 102, 102, 102, 0}{
    \pgfmathdectobase{\binary}{\n}{2}
    \pgfmathtodigitlist{\digitlist}{\binary}
    \foreach \digit [count=\x, evaluate={\c=\digit*50+15;}] in \digitlist
      \fill [fill=black!\c] (\x, -\y) rectangle ++(1,1);
  }
\end{tikzpicture}
\end{codeexample}
    %
\end{command}


\subsection{Angle Computations}

Unlike the rest of the math engine, which is a ``standalone'' package, the
following commands only work in conjunction with the core of \pgfname.

\begin{command}{\pgfmathanglebetweenpoints\marg{p}\marg{q}}
    Returns the angle of a line from \meta{p} to \meta{q} relative to a line
    going straight right from \meta{p}.
    %
\begin{codeexample}[]
\pgfmathanglebetweenpoints{\pgfpoint{1cm}{3cm}}{\pgfpoint{2cm}{4cm}}
\pgfmathresult
\end{codeexample}
    %
\end{command}

\begin{command}{\pgfmathanglebetweenlines\marg{$p_1$}\marg{$q_1$}\marg{$p_2$}\marg{$q_2$}}
    Returns the clockwise angle between a line going through $p_1$ and $q_1$
    and a line going through $p_2$ and $q_2$.
    %
\begin{codeexample}[]
\pgfmathanglebetweenlines{\pgfpoint{1cm}{3cm}}{\pgfpoint{2cm}{4cm}}
                         {\pgfpoint{0cm}{1cm}}{\pgfpoint{1cm}{0cm}}
\pgfmathresult
\end{codeexample}
    %
\end{command}