From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 2 Sep 2019 13:46:59 +0900 Subject: Initial commit --- macros/latex/contrib/coordsys/README | 8 + macros/latex/contrib/coordsys/coordsys.dtx | 3318 ++++++++++++++++++++++++++ macros/latex/contrib/coordsys/coordsys.ins | 51 + macros/latex/contrib/coordsys/coordsys.pdf | 3497 ++++++++++++++++++++++++++++ 4 files changed, 6874 insertions(+) create mode 100644 macros/latex/contrib/coordsys/README create mode 100644 macros/latex/contrib/coordsys/coordsys.dtx create mode 100644 macros/latex/contrib/coordsys/coordsys.ins create mode 100644 macros/latex/contrib/coordsys/coordsys.pdf (limited to 'macros/latex/contrib/coordsys') diff --git a/macros/latex/contrib/coordsys/README b/macros/latex/contrib/coordsys/README new file mode 100644 index 0000000000..f44f40d824 --- /dev/null +++ b/macros/latex/contrib/coordsys/README @@ -0,0 +1,8 @@ +The coordsys and logsys packages draw Cartesian and logarithmic +coordinate systems, number lines, and grids in a variety of +styles. Moreover, these packages include commands for drawing +intervals and for exporting curves from Maple to LaTeX. + +This material is subject to the LaTeX Project Public License. +See http://www.ctan.org/tex-archive/help/Catalogue/licenses.lppl.html +for the details of that license. diff --git a/macros/latex/contrib/coordsys/coordsys.dtx b/macros/latex/contrib/coordsys/coordsys.dtx new file mode 100644 index 0000000000..1221d4950f --- /dev/null +++ b/macros/latex/contrib/coordsys/coordsys.dtx @@ -0,0 +1,3318 @@ +% \iffalse +% This is the coordsys package, coordsys.dtx +% Copyright 2000--06 by Mogens Lemvig Hansen. +% +% Run first coordsys.ins then this file, coordsys.dtx, +% through LaTeX and read the documentation in coordsys.dvi +% +% This program may be distributed and/or modified under the +% conditions of the LaTeX Project Public License, either version 1.2 +% of this license or (at your option) any later version. +% The latest version of this license is in +% http://www.latex-project.org/lppl.txt +% and version 1.2 or later is part of all distributions of LaTeX +% version 2003/12/01 or later. +% +% This program consists of the files coordsys.dtx and coordsys.ins +% +%<*docdriver> +\documentclass{ltxdoc}[1996/01/11] +\usepackage{url,varioref,color,coordsys,logsys} +\IfFileExists{eepic.sty}{\usepackage{epic,eepic}}{\relax} +\CodelineIndex%\EnableCrossrefs +%\OnlyDescription +\MakeShortVerb{\"} +\makeatletter +\DoNotIndex{\@circlefnt, \@empty, \@ifpackageloaded, \@ifstar, +\@tempcnta, \@tempcntb, \@tempdima, \@tempdimb, \@tempdimc, +\@wholewidth, \\, \addtocounter, \addtolength, \advance, +\afterassignment, \arabic, \baselineskip, \char, +\color@begingroup, \color@endgroup, \colorbox, \count@, +\DeclareOption, \def, \divide, \edef, \ensuremath, +\ExecuteOptions, \fontdimen, \frac, \hbox, \hfill, \hrule, \hskip, +\hspace, \hss, +\if, \else, \fi, \ifdim, \fi, \ifnum, \fi, \ifx, \repeat, +\ignorespaces, \leaders, \leavevmode, \let, \line, 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+\end{filecontents*} + +\begin{document} \DocInput{coordsys.dtx} \end{document} +% +% \fi +% \CheckSum{2292} +% \CharacterTable +% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z +% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z +% Digits \0\1\2\3\4\5\6\7\8\9 +% Exclamation \! Double quote \" Hash (number) \# +% Dollar \$ Percent \% Ampersand \& +% Acute accent \' Left paren \( Right paren \) +% Asterisk \* Plus \+ Comma \, +% Minus \- Point \. Solidus \/ +% Colon \: Semicolon \; Less than \< +% Equals \= Greater than \> Question mark \? +% Commercial at \@ Left bracket \[ Backslash \\ +% Right bracket \] Circumflex \^ Underscore \_ +% Grave accent \` Left brace \{ Vertical bar \| +% Right brace \} Tilde \~} +% +% \def\fileversion{1.4} \def\filedate{2006/02/03} \def\docdate{\filedate} +% \title{The \textsf{coordsys} and \textsf{logsys} Packages\thanks{This +% file describes version \fileversion, \filedate.}} +% \author{\copyright\ Mogens Lemvig Hansen\thanks{% +% The \textsf{coordsys} and \textsf{logsys} packages are distributed under +% the \LaTeX\ Project +% Public License; please see Section~\ref{sec:license}.}\\ +% mlhansen@uniserve.com} +% \date{\docdate} +% \maketitle +% \begin{abstract} +% The \textsf{coordsys} package provides commands for typesetting +% number lines (coordinate axes), coordinate systems, and grids +% in the \textsf{picture} environment. +% The \textsf{logsys} package extends the \textsf{coordsys} package by +% providing logarithmic, semi-logarithmic, and double-logarithmic +% coordinate systems and grids. +% \end{abstract} +% +% \tableofcontents +% +% \section{Regular Coordinate Systems} +% Load the \textsf{coordsys} package with the "\usepackage" command. +% \begin{quote} +% "\usepackage"\oarg{options}"{coordsys}" +% \end{quote} +% The \textsf{coordsys} package has three \meta{options}, +% \textsf{centred} (the default), \textsf{outside}, and \textsf{inside}, that +% control the +% appearance of tick marks; see Section~\ref{sec:tickstyle} on +% page~\pageref{sec:tickstyle}. +% +% \subsection{One Dimension} +% \DescribeMacro{\numbline} +% The "\numbline" command typesets a number line.\index{number line|(usage} +% For example, +% \begin{quote} +% \begin{verbatim} +% \begin{picture}(200,20)(-75,-15) +% \numbline{-75}{125} +% \end{picture} +% \end{verbatim} +% \begin{picture}(200,20)(-75,-15) +% \numbline{-75}{125} +% \end{picture} +% \end{quote} +% You should always use the "\numbline" command inside a +% \textsf{picture} environment. +% Do not forget to leave room for the labels on the number line. +% In the following examples I omit the "\begin{picture}" +% and "\end{picture}" commands to reduce clutter. +% +% The tick marks are by default separated by 10 units; +% give "\numbline" an optional first argument to change that. +% For example +% \begin{quote} +% \begin{verbatim} +% \numbline[7]{-75}{125} +% \end{verbatim} +% \begin{picture}(200,20)(-75,-15) +% \numbline[7]{-75}{125} +% \end{picture} +% \end{quote} +% +% \DescribeMacro{\numbline*} +% The starred version of "\numbline" omits the labels. +% \begin{quote} +% \begin{verbatim} +% \numbline*[7]{-75}{125} +% \end{verbatim} +% \begin{picture}(200,6)(-75,-3) +% \numbline*[7]{-75}{125} +% \end{picture} +% \end{quote} +% +% Thus, +% \begin{quote} +% "\numbline"\oarg{spacing}\marg{from}\marg{to}\\ +% "\numbline*"\oarg{spacing}\marg{from}\marg{to} +% \end{quote} +% typeset\label{numblinesyntax} (horizontal) number lines +% from \meta{from} to \meta{to} with +% \meta{spacing} +% units between the tick marks (the default is 10); +% use the starred command to suppresses the labels. +% All the arguments must be integers. +% +% \DescribeMacro{\vnumbline}\DescribeMacro{\vnumbline*} +% The "\vnumbline" and "\vnumbline*" commands similarly +% typeset vertical number lines. +% \begin{quote} +% "\vnumbline"\oarg{spacing}\marg{from}\marg{to}\\ +% "\vnumbline*"\oarg{spacing}\marg{from}\marg{to} +% \end{quote} +% The syntax is similar to that of the "\numbline" command +% \vpageref[above]{numblinesyntax}.\index{number line|)usage} +% \begin{quote} +% \begin{minipage}{.2\linewidth} +% \begin{picture}(20,100)(-17,20) +% \vnumbline{20}{120} +% \end{picture} +% \end{minipage} +% \qquad +% \begin{minipage}{.6\linewidth} +% \begin{verbatim} +% \vnumbline{20}{120} +% \end{verbatim} +% \end{minipage} +% \end{quote} +% +% \subsection{Two Dimensions} +% \DescribeMacro{\coordsys} +% Use the "\coordsys"\index{coordinate system>with intersecting axes|usage} +% command to typeset coordinate systems. +% \begin{quote} +% \begin{picture}(200,110)(-50,-50) +% \coordsys(-50,-50)(150,60) +% \put(75,25){\texttt{\textbackslash coordsys(-50,-50)(150,60)}} +% \end{picture} +% \end{quote} +% \DescribeMacro{\coordsys*} +% Thus, +% \begin{quote} +% "\coordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\coordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset\label{coordsyssyntax} coordinate systems where +% \parg{ll} is the lower-left corner +% and \parg{ur} is the upper-right corner. +% The optional argument \meta{h-spacing} gives the spacing between the +% tick marks on the horizontal axis; the default is 10 units. +% The optional argument \meta{v-spacing} gives the spacing between the +% tick marks on the vertical axis; the default is to use the same +% spacing as on the horizontal axis. +% The starred version omits the labels. +% All the arguments must be integers. +% +% Regular coordinate systems with intersecting axes are not always +% appropriate, for example when the point $(0,0)$ is not in the range +% of the coordinate system. +% The \textsf{coordsys} package therefore provides some alternative +% styles. All the coordinate-system-drawing commands have similar syntax. +% +% \DescribeMacro{\fcoordsys}\DescribeMacro{\fcoordsys*} +% The "\fcoordsys"\index{coordinate system>framed|usage} +% command typesets framed coordinate systems; that is, the +% axes are at the left and bottom edges of the system. +% \begin{quote} +% "\fcoordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\fcoordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% The syntax is similar to that of the "\coordsys" command +% \vpageref[above]{coordsyssyntax}. +% \begin{quote} +% \begin{picture}(220,125)(30,35) +% \fcoordsys[5](50,50)(250,160) +% \put(155,125){\texttt{\textbackslash fcoordsys[5](-50,-50)(150,60)}} +% \end{picture} +% \end{quote} +% +% \DescribeMacro{\bcoordsys}\DescribeMacro{\bcoordsys*} +% The "\bcoordsys"\index{coordinate system>boxed|usage} +% command typesets boxed coordinate systems. +% \begin{quote} +% "\bcoordsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\bcoordsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% The syntax is similar to that of the "\coordsys" command +% \vpageref[above]{coordsyssyntax}. +% \begin{quote} +% \begin{picture}(265,125)(-70,-65) +% \bcoordsys[15][5](-50,-50)(195,60) +% \put(-30,25){\texttt{\textbackslash bcoordsys[15][5](-50,-50)(195,60)}} +% \end{picture} +% \end{quote} +% +% \DescribeMacro{\window}\DescribeMacro{\window*} +% The "\window" command typesets a plotting window as on a graphing +% calculator. +% \begin{quote} +% "\window"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\window*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% The syntax is similar to that of the "\coordsys" command +% \vpageref[above]{coordsyssyntax}. +% \begin{quote} +% \begin{picture}(302,127)(-107,-67) +% \window(-50,-50)(195,60) +% \put(15,25){\texttt{\textbackslash window(-50,-50)(195,60)}} +% \end{picture} +% \end{quote} +% The labels will look nicer if you use the \textsf{amstext} package (which is +% part of the \textsf{amsmath} package). +% +% \DescribeMacro{\coordgrid} +% The "\coordgrid"\index{grid|(usage}\index{grid>dotted|usage} +% command typesets a coordinate grid. +% \begin{quote} +% \begin{picture}(300, 125) +% \coordgrid(0,0)(300,125) +% \put(15,25){\texttt{\textbackslash coordgrid(0,0)(300,125)}} +% \end{picture} +% \end{quote} +% The "\coordgrid" command does not print any labels +% but you can superimpose a coordinate system. +% \begin{quote} +% \begin{verbatim} +% \coordgrid[15][5](-50,-50)(195,60) +% \coordsys[15][5](-50,-50)(195,60) +% \end{verbatim} +% \begin{picture}(245,110)(-50,-50) +% \coordgrid[15][5](-50,-50)(195,60) +% \coordsys[15][5](-50,-50)(195,60) +% \end{picture} +% \end{quote} +% If you load the \textsf{color} package before the \textsf{coordsys} +% package, the labels will be printed on a +% white background.\index{labels>background of|usage} +% +% Typesetting pretty grids with dotted lines is not easy. +% If a grid does come out ugly,\index{grid>ugly|usage} +% try to increase "\unitlength" +% to allow for more dots between the lines. +% You may also reduce the size of the dots; +% see the "\gridstyle" command \vpageref[below]{gridstyle}. +% \DescribeMacro{\coordgrid*} +% Alternatively you can use the "\coordgrid*" command which +% typesets a coordinate grid with solid lines.\index{grid>solid|usage} +% You could then use the +% \textsf{color} package to colour the grid, say, gray; again, see +% the "\gridstyle" command \vpageref[below]{gridstyle}. +% +% Thus, +% \begin{quote} +% "\coordgrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\coordgrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset coordinate grids with a syntax similar to that of +% the "\coordsys" command \vpageref[above]{coordsyssyntax}. +% The starred version uses solid lines; +% the un-starred version uses dotted lines.\index{grid|)usage} +% +% \DescribeMacro{\gridstyle}\label{gridstyle} +% The default size of the dots is the with of "\thinlines" +% and "\thicklines".\index{grid>size of dots|usage}\index{grid>style|(usage} +% If you intend to print your grids at a +% sufficiently high resolution, you should reduce the size of the +% dots by issuing a "\gridstyle" command. On my 600\,dpi printer, +% these sizes look nice for points: +% \begin{quote} +% \begin{verbatim} +% \gridstyle{\linethickness{0.24pt}}{\linethickness{0.48pt}} +% \end{verbatim} +% \gridstyle{\linethickness{0.24pt}}{\linethickness{0.48pt}} +% \begin{picture}(245,110)(-50,-50) +% \coordgrid[15][5](-50,-50)(195,60) +% \coordsys[15][5](-50,-50)(195,60) +% \end{picture} +% \end{quote} +% When I use solid lines, I can get away with half that, +% \begin{quote} +% \begin{verbatim} +% \gridstyle{\linethickness{0.12pt}}{\linethickness{0.24pt}} +% \end{verbatim} +% \gridstyle{\linethickness{0.12pt}}{\linethickness{0.24pt}} +% \begin{picture}(245,110)(-50,-50) +% \coordgrid*[15][5](-50,-50)(195,60) +% \coordsys[15][5](-50,-50)(195,60) +% \end{picture} +% \end{quote} +% +% If you make grids for the screen, I recommend using +% colour.\index{grid>coloured|usage} For example, +% \begin{quote} +% \begin{verbatim} +% \definecolor{gray}{gray}{0.5} +% \definecolor{lightgray}{gray}{0.75} +% \gridstyle{\thinlines\color{lightgray}}{\thinlines\color{gray}} +% \coordgrid*(-109,-65)(200,100) +% \coordsys(-109,-65)(200,100) +% \end{verbatim} +% \begin{picture}(245,110)(-50,-50) +% \definecolor{gray}{gray}{0.5} +% \definecolor{lightgray}{gray}{0.75} +% \gridstyle{\thinlines\color{lightgray}}{\thinlines\color{gray}} +% \coordgrid*[15][5](-50,-50)(195,60) +% \coordsys[15][5](-50,-50)(195,60) +% \end{picture} +% \end{quote} +% +% In general, +% \begin{quote} +% "\gridstyle"\marg{thin declaration}\marg{thick declaration} +% \end{quote} +% Note that these are \emph{declarations}: the \meta{thin declarations} +% apply also to the thick grid lines unless explicitly overruled by the +% \meta{thick declaration}. +% The current "\gridstyle" applies to all types of grids: +% dotted, solid, regular, or logarithmic. +% The default style is +% "\gridstyle{\thinlines}{\thicklines}".\label{defaultgridstyle}\index{grid>style|)usage} +% +% +% \subsection{Bells and Whistles} +% \subsubsection{Manual Labels} +% \DescribeMacro{\sethlabel}\DescribeMacro{\setvlabel} +% All the number-line and coordinate-system commands format the +% labels\index{labels>manual|usage}\index{manual labels|usage} using +% the commands "\sethlabel" (for labels on horizontal axes) and +% "\setvlabel" (for labels on vertical axes). If you set labels manually, +% you should use the same commands for a uniform appearance. +% \begin{quote} +% \begin{verbatim} +% \numbline{-75}{125} +% \put(125,0){\sethlabel{x}} +% \end{verbatim} +% \begin{picture}(200,20)(-75,-15) +% \numbline{-75}{125} +% \put(125,0){\sethlabel{x}} +% \end{picture} +% \end{quote} +% The syntax is +% \begin{quote} +% "\sethlabel"\oarg{alignment}\marg{label}\\ +% "\setvlabel"\oarg{alignment}\marg{label} +% \end{quote} +% The \meta{label} is set in math mode. +% The default \meta{alignment} is "[t]" for "\sethlabel" and +% "[r]" for "\setvlabel". You may want to add to these defaults +% (as in "\sethlabel[tl]"); you probably do not want to replace the +% defaults. +% +% If you want your labels set in some other style, you must re-define +% "\sethlabel" and "\setvlabel". +% +% \subsubsection{Thick Tick Density} +% \DescribeMacro{\hthickratio} +% \DescribeMacro{\vthickratio} +% By default every fifth tick mark is +% thick.\index{thick ticks|usage}\index{ticks>ratio of thick|usage} +% You can change that by redefining +% the commands "\hthickratio" and "\vthickratio". +% \begin{quote} +% \begin{verbatim} +% \renewcommand{\hthickratio}{4} +% \numbline[25]{0}{350} +% \end{verbatim} +% \setlength{\unitlength}{.3pt} +% \begin{picture}(350,80)(0,-50) +% \renewcommand{\hthickratio}{4} +% \numbline[25]{0}{350} +% \end{picture} +% \end{quote} +% +% \subsubsection{Different Scales on the Two Axes} +% \DescribeMacro{\rescaleby} +% LaTeX\ (the \textsf{picture} environment) does not support different +% scales\index{labels>re-scaled|usage}\index{scaling labels|usage} +% on the two axes; "\unitlength" is used for both the +% horizontal and the vertical direction. +% However, you may create the \emph{appearance} of different scales by +% scaling the labels on the axes. +% Here is a coordinate system that has been rigged to contain the graph of +% $y=x^2$ for $x$ between $-10$ and $10$. +% \begin{quote} +% \setlength{\unitlength}{5pt} +% \rescaleby{10}{1}{\vlabel} +% \begin{picture}(22,15)(-10,-3) +% \coordsys[1](-10,0)(12,12) +% \end{picture} +% \begin{minipage}[b]{.5\linewidth} +% \begin{verbatim} +% \rescaleby{10}{1}{\vlabel} +% \coordsys[1](-10,0)(12,12) +% \end{verbatim} +% \end{minipage} +% \end{quote} +% That is, +% \begin{quote} +% "\rescaleby"\oarg{symb}\marg{num}\marg{den}\marg{cmd} +% \end{quote} +% multiplies the labels by $\frac{\meta{num}}{\meta{den}}\meta{symb}$; +% both \meta{num} and \meta{den} must be integers; +% and \meta{den} must be positive.\footnote{Multiplying the labels by +% a negative number does not reverse the arrows, so I suggest using +% boxed coordinate systems in that case.} +% The optional argument, if present, represents a symbolic +% (non-numeric) scale factor; see the example below. +% The last argument, \meta{cmd}, must be one of "\hlabel" +% or "\vlabel". +% +% The following coordinate system has been rigged for graphing $\sin$ or +% $\cos$. Note that only that labels have been scaled; +% the real coordinates of the small circle are still $(90,50)$. +% \begin{quote} +% \begin{verbatim} +% \renewcommand{\hthickratio}{6} +% \rescaleby[\pi]{1}{180}{\hlabel} +% \rescaleby{1}{100}{\vlabel} +% \coordsys[15][10](0,-100)(400,115) +% \put(90,50){\circle{6}} +% \end{verbatim} +% \setlength{\unitlength}{.5pt} +% \begin{picture}(435,215)(-35,-100) +% \renewcommand{\hthickratio}{6} +% \rescaleby[\pi]{1}{180}{\hlabel} +% \rescaleby{1}{100}{\vlabel} +% \coordsys[15][10](0,-100)(400,115) +% \put(90,50){\circle{6}} +% \end{picture} +% \end{quote} +% +% \subsubsection{Different Styles of Tick Marks} +% \label{sec:tickstyle} +% \DescribeMacro{\tickstyle} +% As you can affect the width of the dots or lines of a +% "\coordgrid" with a "\gridstyle" command, +% so you can affect the width of the tick marks with a +% "\tickstyle"\index{ticks>style of|usage} command: +% \begin{quote} +% "\tickstyle"\marg{thin declaration}\marg{thick declaration} +% \end{quote} +% Note that these are \emph{declarations}: the \meta{thin declarations} +% apply also to the thick tick marks unless explicitly overruled by the +% \meta{thick declaration}.\footnote{And the declarations that apply +% to the thick tick marks spill over to the labels which maybe they +% shouldn't, so let's not talk about that.} +% The default style is +% "\tickstyle{\thinlines}{\thicklines}".\footnote{When +% I wrote \vpageref[above]{defaultgridstyle} that the default grid style is +% \texttt{\textbackslash gridstyle\{\textbackslash thinlines\}\{\textbackslash +% thicklines\}} I lied. The default grid style is the follow the current +% \texttt{\textbackslash tickstyle}.} +% +% \DescribeMacro{\ticklength} +% The "\ticklength" command controls the length of the +% tick marks.\index{ticks>length of|usage} +% \begin{quote} +% \begin{verbatim} +% \tickstyle{\thinlines\renewcommand{\ticklength}{4pt}} +% {\thinlines\renewcommand{\ticklength}{8pt}} +% \end{verbatim} +% \tickstyle{\thinlines\renewcommand{\ticklength}{4pt}} +% {\thinlines\renewcommand{\ticklength}{8pt}} +% \begin{picture}(200,20)(-75,-15) +% \numbline{-75}{125} +% \end{picture} +% \end{quote} +% Note that the \emph{command} "\ticklength" must be changed with +% "\renewcommand". +% +% If you prefer tick marks\index{ticks>style of|usage} +% just on the outside of the coordinate axes, load +% \textsf{coordsys} with the \textsf{outside} option. +% \begin{quote} +% \begin{verbatim} +% \usepackage[outside]{coordsys} +% \end{verbatim} +% \makeatletter +% \renewcommand{\vtickmark}{\makebox(0,0)[t]{\rule{\@wholewidth}{3pt}}} +% \renewcommand{\htickmark}{\makebox(0,0)[r]{\rule{3pt}{\@wholewidth}}} +% \makeatother +% \begin{picture}(200,110)(-50,-50) +% \coordsys(-50,-50)(150,60) +% \end{picture} +% \end{quote} +% +% Similarly, the \textsf{inside} option puts the tick marks on the inside of +% the axes. The default option is \textsf{centred}. +% +% +% +% \section{Logarithmic Coordinate Systems} +% Load the \textsf{logsys} package with the "\usepackage" command. +% \begin{quote} +% "\usepackage"\oarg{options}"{coordsys,logsys}" +% \end{quote} +% The \textsf{logsys} package supports the same options, \textsf{centred}, +% \textsf{outside}, and \textsf{inside}, as the \textsf{coordsys} package. +% +% \subsection{One Dimension} +% \DescribeMacro{\logline} +% The "\logline" command typesets a horizontal, logarithmic number +% line.\index{number line>logarithmic|(usage} +% \begin{quote} +% \begin{verbatim} +% \logline{-60}{210} +% \end{verbatim} +% \begin{picture}(270,20)(-60,-15) +% \logline{-60}{210} +% \end{picture} +% \end{quote} +% The "\logline" command typesets only whole blocks of tick marks +% (whole powers of $10$). +% Making the axis long enough that the tick marks do not +% collide with the arrow and yet not so long that it looks ridiculous is the +% users responsibility. +% The default distance between the thick tick marks (the powers of $10$) is +% 50~units. +% Therefore I made the axis above extend from $-60$ (a bit below $-50$ which +% appears as $10^{-1} = \frac1{10}$) to $210$ (a bit above $200$ which appears +% as $10^4$). +% +% \DescribeMacro{\logline*} +% Thus,\label{loglinesyntax} +% \begin{quote} +% "\logline"\oarg{spacing}\marg{from}\marg{to}\\ +% "\logline*"\oarg{spacing}\marg{from}\marg{to} +% \end{quote} +% typeset horizontal, logarithmic number lines from \meta{from} to +% \meta{to} with \meta{spacing} units between the powers of $10$; the default +% is 50. +% The starred version omits the labels. +% All the arguments must be integers. +% +% The "\logline" command only typesets an axis; it does not change the +% way \LaTeX\ and the \textsf{picture} environment interprets coordinates. +% The equation below gives the relationship between the coordinate to +% "\put", $x_p$, and the apparent coordinate, +% $x_a$.\index{labels>logarithmic|usage} +% \[ +% x_p = \meta{spacing} \log_{10} x_a. +% \] +% For example: +% \begin{quote} +% \begin{verbatim} +% \logline[40]{-50}{210} +% \put(87.04,10){\makebox(0,0)[b]{150}} % 40*log(150) = 87.04 +% \put(87.04,10){\vector(0,-1){10}} +% \end{verbatim} +% \begin{picture}(260, 40)(-50,-15) +% \logline[40]{-50}{210} +% \put(87.04,10){\makebox(0,0)[b]{150}} ^^A% 40*log(150) = 87.04 +% \put(87.04,10){\vector(0,-1){10}} +% \end{picture} +% \end{quote} +% +% \DescribeMacro{\vlogline} +% \DescribeMacro{\vlogline*} +% The vertical equivalent is "\vlogline": +% \begin{quote} +% "\vlogline"\oarg{spacing}\marg{from}\marg{to}\\ +% "\vlogline*"\oarg{spacing}\marg{from}\marg{to} +% \end{quote} +% The syntax is similar to that of the "\logline" command +% \vpageref[above]{loglinesyntax}.\index{number line>logarithmic|)usage} +% +% +% \subsection{Two Dimensions} +% \DescribeMacro{\logsys} +% Use the "\logsys"\index{coordinate system>logarithmic|(usage} +% command to typeset logarithmic coordinate systems. +% \begin{quote} +% \begin{picture}(220,125)(-70,-65) +% \logsys[5](-50,-50)(150,60) +% \put(55,25){\texttt{\textbackslash logsys[5](-50,-50)(150,60)}} +% \end{picture} +% \end{quote} +% \DescribeMacro{\logsys*} +% Thus, +% \begin{quote} +% "\logsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\logsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset coordinate systems with logarithmic vertical axis, +% where \parg{ll} is the lower-left corner +% and \parg{ur} is the upper-right corner. +% The optional argument \meta{h-spacing} gives the spacing between the +% tick marks on the horizontal axis; the default is 10 units. +% The optional argument \meta{v-spacing} gives the spacing between the +% thick tick marks (powers of $10$) on the vertical axis; +% the default is 50 units. +% The starred version omits the labels. +% All the arguments must be integers. +% +% \DescribeMacro{\semilogsys} +% Use the "\semilogsys" command to typeset semi-logarithmic +% coordinate systems. +% \begin{quote} +% \begin{picture}(230,125)(-70,-65) +% \semilogsys[25](-50,-50)(160,60) +% \put(55,25){\texttt{\textbackslash semilogsys[25](-50,-50)(160,60)}} +% \end{picture} +% \end{quote} +% \DescribeMacro{\semilogsys*} +% Thus, +% \begin{quote} +% "\semilogsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\semilogsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset coordinate systems with logarithmic horizontal axis, +% where \parg{ll} is the lower-left corner +% and \parg{ur} is the upper-right corner. +% The optional argument \meta{h-spacing} gives the spacing between the +% thick tick marks (powers of $10$) on the horizontal axis; +% the default is 50 units. +% The optional argument \meta{v-spacing} gives the spacing between the +% tick marks on the vertical axis; +% the default is 10 units. +% The starred version omits the labels. +% All the arguments must be integers. +% +% \DescribeMacro{\loglogsys} +% Use the "\loglogsys" command to typeset double-logarithmic +% coordinate systems. +% \begin{quote} +% \begin{picture}(230,125)(-70,-65) +% \loglogsys(-50,-50)(160,60) +% \put(55,25){\texttt{\textbackslash loglogsys(-50,-50)(150,60)}} +% \end{picture} +% \end{quote} +% \DescribeMacro{\loglogsys*} +% Thus, +% \begin{quote} +% "\loglogsys"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\loglogsys*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset coordinate systems with two logarithmic axes, +% where \parg{ll} is the lower-left corner +% and \parg{ur} is the upper-right corner. +% The optional argument \meta{h-spacing} gives the spacing between the +% thick tick marks (powers of $10$) on the horizontal axis; +% the default is 50 units. +% The optional argument \meta{v-spacing} gives the spacing between the +% thick tick marks (powers of $10$) on the vertical axis; +% the default is 50 units. +% The starred version omits the labels. +% All the arguments must be +% integers.\index{coordinate system>logarithmic|)usage} +% +% \DescribeMacro{\loggrid} +% \DescribeMacro{\loggrid*} +% \DescribeMacro{\semiloggrid} +% \DescribeMacro{\semiloggrid*} +% \DescribeMacro{\logloggrid} +% \DescribeMacro{\logloggrid*} +% The "\loggrid",\index{grid>logarithmic|(usage} +% "\loggrid*", "\semiloggrid", +% "\semiloggrid*", "\logloggrid", and "\logloggrid*" commands +% typeset logarithmic grids. +% \begin{quote} +% \begin{verbatim} +% \logloggrid*(0,0)(300,100) +% \end{verbatim} +% \begin{picture}(300, 100) +% \logloggrid*(0,0)(300,100) +% \end{picture} +% \end{quote} +% Thus, +% \begin{quote} +% "\loggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\loggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\semiloggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\semiloggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\logloggrid"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur}\\ +% "\logloggrid*"\oarg{h-spacing}\oarg{v-spacing}\parg{ll}\parg{ur} +% \end{quote} +% typeset logarithmic, semi-logarithmic, and double-logarithmic +% coordinate grids where \parg{ll} is the lower-left corner +% and \parg{ur} is the upper-right corner. +% The optional argument \meta{h-spacing} gives the spacing between the +% vertical grid lines and +% the optional argument \meta{v-spacing} gives the spacing between the +% horizontal grid lines; +% The default spacing is 10 units on linear axes and 50 units between the +% thick tick marks (the powers of $10$) on logarithmic axes. +% The starred versions use solid lines; +% the un-starred versions use dotted lines. +% All the arguments must be integers.\index{grid>logarithmic|)usage} +% +% +% \section{Filling the Coordinate Systems} +% The purpose of the \textsf{coordsys} and \textsf{logsys} packages +% is to typeset coordinate systems, so maybe the package should end here. +% However, I have had to write a bit of code to help me fill my +% coordinate systems, so I'll share that. +% +% \subsection{Intervals} +% \DescribeMacro{\interval} +% The "\interval" command takes as argument an interval in standard notation +% and draws it on the horizontal coordinate axis or number line. +% \begin{quote} +% \begin{verbatim} +% \numbline{-15}{65} +% \interval[-7.5,30) +% \end{verbatim} +% \begin{picture}(80,15)(-15,-12) +% \numbline{-15}{65} +% \interval[-7.5,30) +% \end{picture} +% \end{quote} +% The interval can be open, half-open, or closed as in +% $(a,b)$, $(a,b]$, $[a,b)$, and $[a,b]$\footnote{The notation +% $\left]a,b\right[$ for open (or half-open) intervals is also +% supported.} You can specify infinite intervals with "<" or ">". +% \begin{quote} +% \begin{verbatim} +% \numbline{-15}{65} +% \interval<-14,30[ +% \end{verbatim} +% \begin{picture}(80,15)(-15,-12) +% \numbline{-15}{65} +% \interval<-14,30[ +% \end{picture} +% \end{quote} +% \DescribeMacro{\intervalthickness} +% The "\intervalthickness" command sets the thickness of the fat line +% that marks the interval. +% An optional argument allows you to draw the fat line off centre. +% \begin{quote} +% \begin{verbatim} +% \numbline{-15}{65} +% \intervalthickness[0.5pt]{1pt} +% \interval[-7.5,30] +% \color{red} +% \intervalthickness[-0.5pt]{1pt} +% \interval(10,55> +% \end{verbatim} +% \begin{picture}(80,15)(-15,-12) +% \numbline{-15}{65} +% \intervalthickness[0.5pt]{1pt} +% \interval[-7.5,30] +% \color{red} +% \intervalthickness[-0.5pt]{1pt} +% \interval(10,55> +% \end{picture} +% \end{quote} +% \DescribeMacro{\vinterval} +% The "\vinterval" command similarly draws intervals on the vertical axis. +% \begin{quote} +% \begin{verbatim} +% \fcoordsys[5](150,50)(350,160) +% \interval[200,300] +% \vinterval(75,150> +% \end{verbatim} +% \begin{picture}(220,125)(130,35) +% \fcoordsys[5](150,50)(350,160) +% \interval[200,300] +% \vinterval(75,150> +% \end{picture} +% \end{quote} +% +% To sum up: +% \begin{quote} +% "\interval"\meta{L-delim}\meta{from}","\meta{to}\meta{R-delim}\\ +% "\vinterval"\meta{L-delim}\meta{from}","\meta{to}\meta{R-delim}\\ +% "\intervalthickness"\oarg{offset}\marg{width} +% \end{quote} +% Here \meta{L-delim} must be one of "[", "(", "<", or "]", and +% \meta{R-delim} must be one of "]", ")", ">", or "[". +% Both \meta{from} and \meta{to} are numbers, integers or +% decimals\footnote{Due to implementation details, a decimal +% must have at least one digit on either side of the decimal point. +% Thus \texttt{0.5} is ok but \texttt{.5} is not.} +% Both \meta{offset} and \meta{width} must be lengths. +% The centre of the fat interval line will drawn \meta{offset} above the +% horizontal axis or \meta{offset} to the right of the vertical axis. +% +% +% \subsection{Curves} +% For plotting curves\index{curves|(usage} +% I recommend the \textsf{epic} and +% \textsf{eepic} packages.\footnote{Both are old \LaTeX209 packages that work +% fine in \LaTeXe. The \textsf{eepic} package re-implements the \textsf{epic} +% package making use of \textsc{PostScript}. The \textsf{eepic} package +% works well with dvips and dvipdfm but not with pdf\LaTeX.} +% I especially like \textsf{(e)epic}'s "\putfile" command which allows +% you to calculate your plot with some external program, export the points to +% plot to a text file, and import that file to have \LaTeX\ draw the plot. +% For external program I use Maple.\index{curves>with Maple|usage} +% The \textsf{coordsys} package includes a piece of +% Maple code that exports a Maple plot in the form "\putfile" expects. +% You can therefore take advantage of Maple adaptive plotting +% algorithm\footnote{Maple cleverly calculates more points where the curve +% wiggles.} in your \LaTeX\ plots. +% +% Here is how it works:\index{putfile|usage} +% In Maple, read in the file \url{putfile} which is part of the +% \textsf{coordsys} package. +% \begin{verbatim} +% > read "/where/you/placed/putfile"; +% \end{verbatim} +% Make your plot, here $y=\frac{x^2}{10}$. +% \begin{verbatim} +% > plot( x^2/10, x=-10..10, title="x^2/10"); +% \end{verbatim} +% When you are happy with your plot, assign it to a variable. +% \begin{verbatim} +% > P := %: +% \end{verbatim} +% Then use the "putfile" command to export the curve to the file +% \url{parabola.put}. +% \begin{verbatim} +% > putfile( "parabola.put", P ); +% \end{verbatim} +% +% In \LaTeX, use the "\putfile" command to put "\picsquare"s at each +% point listed in \url{parabola.put}. +% \begin{quote} +% \begin{verbatim} +% \coordsys[1](-10,0)(11,11) +% \putfile{parabola.put}{\picsquare} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{7pt} +% \begin{picture}(21,13)(-10,-2) +% \coordsys[1](-10,0)(11,11) +% \putfile{parabola.put}{\picsquare} +% \end{picture} +% \fi +% \end{quote} +% +% The \textsf{(e)epic} package provides an environment, +% \textsf{drawjoin}, that joins all points set with the +% special "\put" command "\jput". +% Thus, to draw a curve with the "\putfile" command you enter a +% \textsf{drawjoin} environment, let "\put" be a synonym for +% "\jput", and call "\putfile". +% \begin{quote} +% \begin{verbatim} +% \coordsys[1](-10,0)(11,11) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{parabola.put}{\picsquare} +% \end{drawjoin} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{7pt} +% \begin{picture}(21,13)(-10,-2) +% \coordsys[1](-10,0)(11,11) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{parabola.put}{\picsquare} +% \end{drawjoin} +% \end{picture} +% \fi +% \end{quote} +% +% To draw a curve that requires (or looks best with) different scales on +% the two axes, you can use the "scale" option to +% "putfile"\index{curves>scaled|(usage}\index{putfile>scale|(usage} +% in Maple: +% \begin{verbatim} +% > plot( (x+2)*(x-1)*(x-2), x=-3..4 ); +% > putfile( "cubic.put", %, scale=[10, 1] ); +% \end{verbatim} +% Now all the $x$-coordinates in "cubic.put" are $10$ times larger +% than they should be. Thus re-scale the horizontal labels +% by~$\frac{1}{10}$.\index{labels>re-scaled|(usage}\index{scaling labels|(usage} +% \begin{quote} +% \begin{verbatim} +% \rescaleby{1}{10}{\hlabel} +% \coordsys[2](-30,-20)(40,36) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{cubic.put}{\picsquare} +% \end{drawjoin} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{2.3pt} +% \begin{picture}(70,56)(-30,-20) +% \rescaleby{1}{10}{\hlabel} +% \coordsys[2](-30,-20)(40,36) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{cubic.put}{\picsquare} +% \end{drawjoin} +% \end{picture} +% \fi +% \end{quote} +% +% Scaling can be necessary even when the two axes do use the same +% scale. Consider the graph of $r=1+\sin\theta$ in polar coordinates. The +% graph is $2.6$ units wide and $2.25$ units tall. All the arguments to the +% "\coordsys" command must be integers, so the smallest distance between +% tick marks is $1$ unit; the coordinate system will have very few tick marks. +% Instead scale up by, say, a factor $100$. +% In Maple: +% \begin{verbatim} +% > polarplot( 1+sin(theta), theta=0..2*Pi ); +% > putfile( "cardioid.put", %, scale=[100,100] ); +% \end{verbatim} +% In \LaTeX: +% \begin{quote} +% \begin{verbatim} +% \rescaleby{1}{100}{\hlabel} +% \rescaleby{1}{100}{\vlabel} +% \coordsys(-130,-25)(130,215) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{cardioid.put}{\picsquare} +% \end{drawjoin} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{0.5pt} +% \begin{picture}(260,240)(-130,-25) +% \rescaleby{1}{100}{\hlabel} +% \rescaleby{1}{100}{\vlabel} +% \coordsys(-130,-25)(130,215) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{cardioid.put}{\picsquare} +% \end{drawjoin} +% \end{picture} +% \fi +% \end{quote} +% +% If the plot contains more than one curve, +% "putfile"\index{putfile>multiple curves|usage} generates +% one file for each. You can of course specify multiple curves +% directly, but they can also be the result of the "discont" +% option to "plot". +% \begin{verbatim} +% > plot( csc(x), x=0..2*Pi, y=-10..10, discont=true ); +% > putfile( "csc.put", %, scale=[180/Pi, 10] ); +% \end{verbatim} +% Here "putfile" wrote two files calling them "csc1.put" +% and "csc2.put". These two curves must be drawn by different +% \textsf{drawjoin} environments. +% \begin{quote} +% \begin{verbatim} +% \renewcommand{\hthickratio}{3} +% \rescaleby[\pi]{1}{180}{\hlabel} +% \rescaleby{1}{10}{\vlabel} +% \coordsys(0,-100)(360,115) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{csc1.put}{\picsquare} +% \end{drawjoin} +% \begin{drawjoin} +% \let\put=\jput +% \putfile{csc2.put}{\picsquare} +% \end{drawjoin} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{0.5pt} +% \begin{picture}(400,215)(-40,-100) +% \renewcommand{\hthickratio}{3} +% \rescaleby[\pi]{1}{180}{\hlabel} +% \rescaleby{1}{10}{\vlabel} +% \coordsys(0,-100)(360,115) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{csc1.put}{\picsquare} +% \end{drawjoin} +% \begin{drawjoin} +% \let\put=\jput +% \putfile{csc2.put}{\picsquare} +% \end{drawjoin} +% \end{picture} +% \fi +% \end{quote} +% +% For logarithmic plots +% scaling\index{curves>logarithmic|usage}\index{scaling labels>logarithmic|usage} +% is almost always necessary. +% Consider the +% graph of $y=\frac{1}{1+e^{-x}}$ for $x$ running from $-10$ to $10$. +% The $y$-coordinates extend over five powers of $10$, so scale by $4$ +% to make it comparable to the range of $x$-coordinates. +% \begin{verbatim} +% > logplot(1/(1+exp(-x)), x=-10..10); +% > putfile("logistic.put", %, scale=[1,4]); +% \end{verbatim} +% The "\rescaleby" command is not suitable for logarithmic axes. +% Instead set the optional \meta{spacing} argument to the correct +% distance between the powers of~$10$, in this case~$4$. +% \begin{quote} +% \begin{verbatim} +% \logsys[1][4](-10,-20)(11,1) +% \begin{drawjoin} +% \let\put=\jput +% \putfile{logistic.put}{\picsquare} +% \end{drawjoin} +% \end{verbatim} +% \ifx\putfile\undefined +% You do not have the \textsf{epic} and \textsf{eepic} packages, +% so \LaTeX\ cannot generate the result of the above commands. +% \else +% \setlength{\unitlength}{7pt} +% \begin{picture}(25,23)(-14,-22) +% \definecolor{gray}{gray}{0.5} +% \definecolor{lightgray}{gray}{0.75} +% \gridstyle{\linethickness{0.12pt}\color{lightgray}}% +% {\linethickness{0.12pt}\color{gray}} +% \loggrid*[1][4](-10,-20)(11,1) +% \logsys[1][4](-10,-20)(11,1) +% \color{red} +% \begin{drawjoin} +% \let\put=\jput +% \putfile{logistic.put}{\picsquare} +% \end{drawjoin} +% \end{picture} +% \fi +% \end{quote} +% \index{curves>scaled|)usage}\index{putfile>scale|)usage}% +% \index{labels>re-scaled|)usage}\index{scaling labels|)usage} +% +% Use the "putfile" command as follows:\index{putfile>syntax|usage} +% \begin{quote} +% "putfile(" \meta{filename}"," \meta{PLOT structure} ["," +% \meta{options} ] ");" +% \end{quote} +% If \meta{filename} is a string and the \meta{PLOT structure} contains +% more than one curve, "putfile" will append $1, 2, 3, \dots$ as needed; +% "putfile" also appends an extension of ".tex" if the \meta{filename} +% has no extension. +% If the \meta{filename} is a list or set of filenames, they are used +% as is. (So if you do not want "putfile" to meddle with your filename, +% give it in a set.) +% +% The only possible option is\index{putfile>scale|(usage} +% \begin{quote} +% "scale" "=" "[" \meta{number}"," \meta{number} "]" +% \end{quote} +% The "putfile" command will multiply all $x$-coordinates by the first +% number and all $y$-coordinates by the second number. +% Both numbers must be "evalf"able. +% +% If you scale the coordinates of a curve, you must +% of course compensate for that to get an honest +% representation of your data in \LaTeX. +% \begin{itemize} +% \item If you scale a regular (linear) axis by, say, +% "scale=[3/5,1]", you should use "\rescaleby{5}{3}{\hlabels}" +% to re-scale the labels. +% +% \item If you scale a logarithmic axis by, say, "scale=[1,30]" +% you should use the optional \meta{spacing} argument to +% the command that draws the coordinate system, say +% "\logsys[30]("\dots +% \end{itemize}\index{putfile>scale|)usage}\index{curves|)usage} +% +% +% \section{Installation} +% Extract\index{installation|usage} the \url{.sty} files from +% the \url{.dtx} file by running \url:coordsys.ins: through \LaTeX. +% Then generate the documentation for the \textsf{coordsys} and +% \textsf{logsys} packages +% by running the file \url:coordsys.dtx: through +% \LaTeX---thrice to resolve cross references.\footnote{If you want an index, +% you must run MakeIndex +% (\texttt{makeindex -s gind.ist coordsys}) between the second and third +% \LaTeX{} run.} +% +% You now have to decide what to do with several files. +% \begin{itemize} +% \item Move the files \url:coordsys.sty: and \url:logsys.sty: to some +% directory where \LaTeX\ can find it; +% \url:(local)texmf/tex/latex/misc: would be +% the natural choice. +% \item Move the documentation, \url:coordsys.dvi: or \url:coordsys.pdf:, to +% \url:(local)texmf/doc/latex/misc:. +% \item You may discard the source files, \url:coordsys.dtx: and +% \url:coordsys.ins:, or store them in +% \url:(local)texmf/source/latex/misc:. +% \item If you ran \url{coordsys.dtx} through \LaTeX, several \url{.put} +% were created. You can discard those. +% \end{itemize} +% +% +% +% \section{License}\label{sec:license} +% This program may be distributed and/or modified under the +% conditions of the \LaTeX\ Project Public License, either version 1.3 +% of this license or (at your option) any later version. +% The latest version of this license is in +% \url;http://www.latex-project.org/lppl.txt; +% and version 1.2 or later is part of all distributions of \LaTeX \ +% version 2003/12/01 or later. +% +% This program consists of the files \url:coordsys.dtx: and +% \url:coordsys.ins:. +% +% +% \section{Acknowledgements} +% Thank you to Scott Pakin +% for his input on the implementation of Euclid's +% algorithm. +% +% Thank you to Svend Daugaard Pedersen +% for catching an error in the logarithmic systems +% and for suggestions that led to "\gridstyle". +% +% Thank you to Staffan Lundberg +% who found an error in my understanding +% of Maple's structured types and thus prompted me to polish the +% Maple code for "putfile". +% +% Thank you to Jan Hegewald +% whose questions led to an improved description and implementation +% of "\rescaleby". +% +% +% \StopEventually{ +% \PrintIndex +% } +% +% \section{Implementation} +% +% \subsection{The \textsf{coordsys} Package} +% \subsubsection{Identification} +% First we must declare ourselves. +% \begin{macrocode} +%<*coordsys> +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{coordsys}[2006/02/03 version 1.4] +% \end{macrocode} +% +% \subsubsection{Declaration of Options} +% \begin{macro}{\ticklength} +% \begin{macro}{\vtickmark} +% \begin{macro}{\htickmark} +% The options define "\ticklength", "vtickmark", and +% "\htickmark". First check that these three commands are not defined +% elsewhere. +% \begin{macrocode} +\newcommand{\ticklength}{\relax} +\newcommand{\vtickmark}{\relax} +\newcommand{\htickmark}{\relax} +% \end{macrocode} +% The "\vtickmark" and "\htickmark" commands set the individual +% ticks; "\vtickmark" sets vertical ticks on a horizontal axis, +% and "\htickmark" sets horizontal ticks on a vertical axis. +% "\@wholewidth" is the current line width, +% that is, the width of "\thinlines" or "\thicklines". +% \begin{macrocode} +\DeclareOption{centred}{% + \def\vtickmark{\makebox(0,0){\rule{\@wholewidth}{\ticklength}}}% + \def\htickmark{\makebox(0,0){\rule{\ticklength}{\@wholewidth}}}% + \def\ticklength{6\p@}% +} +\DeclareOption{outside}{% + \def\vtickmark{\makebox(0,0)[t]{\rule{\@wholewidth}{\ticklength}}}% + \def\htickmark{\makebox(0,0)[r]{\rule{\ticklength}{\@wholewidth}}}% + \def\ticklength{3\p@}% +} +\DeclareOption{inside}{% + \def\vtickmark{\makebox(0,0)[b]{\rule{\@wholewidth}{\ticklength}}}% + \def\htickmark{\makebox(0,0)[l]{\rule{\ticklength}{\@wholewidth}}}% + \def\ticklength{3\p@}% +} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \subsubsection{Execution of Options} +% The default option is \textsf{centred}. +% \begin{macrocode} +\ExecuteOptions{centred} +\ProcessOptions +% \end{macrocode} +% +% \subsubsection{Main Code} +% \begin{macro}{\vgridfromto} +% \begin{macro}{\hgridfromto} +% The "\vgridfromto" and "\hgridfromto" commands typeset vertical +% and horizontal dotted lines for the dotted coordinate grids. +% \begin{quote} +% "\vgridfromto"\marg{from}\marg{to}\\ +% "\hgridfromto"\marg{from}\marg{to} +% \end{quote} +% The dotted line is to run from ($y$- or $x$-coordinate) \meta{from} to ($y$- +% or $x$-coordinate) \meta{to}. The two commands set the lines by means of +% leaders in a box. The box is set at $y$- or $x$-coordinate zero and the +% leaders extend to the right length by skipping back and forth. This way the +% dots line up nicely in a predictable manner. When "\vgridfromto" or +% "\hgridfromto" is called, "\coordsys@w" should contain the size +% (height or width) of the box containing each dot. +% \begin{macrocode} +\newcommand{\vgridfromto}[2]{% + \vbox to \z@{\vskip -#2\unitlength + \leaders\vbox to \coordsys@w{\vss\hbox{\picsquare}\vss} + \vfill + \vskip #1\unitlength}} +\newcommand{\hgridfromto}[2]{% + \hbox to \z@{\hskip #1\unitlength + \leaders\hbox to \coordsys@w{\hss\picsquare\hss}\hfill + \hskip-#2\unitlength}} +% \end{macrocode} +% \end{macro}\end{macro} +% \begin{macro}{\vgridlength} +% \begin{macro}{\hgridlength} +% The "\vgriglength" and "\hgridlength" command typesets +% solid vertical and horizontal lines. +% \begin{quote} +% "\vgridlength"\marg{length}\\ +% "\hgridlength"\marg{length} +% \end{quote} +% The line is to have length \meta{length} and is set at the left-hand or +% bottom edge of the coordinate system. +% \begin{macrocode} +\newcommand{\vgridlength}[1]{\line(0,1){#1}} +\newcommand{\hgridlength}[1]{\line(1,0){#1}} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\setvlabel} +% \begin{macro}{\sethlabel} +% The "\setvlabel" and "\sethlabel" commands typeset the labels on +% the vertical and horizontal axes, respectively. +% The "\setvlabel" command sets 5\,pt of space between the label and the +% axis, which is about right, considering that the tick marks extend 3\,pt on +% either side of the axis. +% The "\sethlabel" command places the labels on a baseline 3\,pt plus +% the current "\baselineskip" below the axis by means of a strut (a +% zero-width rule).\nextlinelabel{cl:setlabels} +% \begin{macrocode} +\@ifpackageloaded{color}{% + \newcommand{\setvlabel}[2][r]{% + \makebox(0,0)[#1]{\colorbox{white}{$#2$}\hspace{5pt}}} + \newcommand{\sethlabel}[2][t]{% + \makebox(0,0)[#1]{% + \setlength{\@tempdimc}{3pt}% + \addtolength{\@tempdimc}{\baselineskip}% + \rule{0pt}{\@tempdimc}\colorbox{white}{$#2$}}}% +}{% no colour + \newcommand{\setvlabel}[2][r]{% + \makebox(0,0)[#1]{$#2$\hspace{5\p@}}} + \newcommand{\sethlabel}[2][t]{% + \makebox(0,0)[#1]{% + \setlength{\@tempdimc}{3\p@}% + \addtolength{\@tempdimc}{\baselineskip}% + \rule{\z@}{\@tempdimc}$#2$}}% +}% end if color package +% \end{macrocode} +% You may want to redefine "\setvlabel" and "\sethlabel" to present +% the labels in a different way---use a smaller font, increase the distance to +% the axes,\dots. Your redefined commands must take one optional and one +% mandatory argument---the "\window" command uses the optional argument. +% Do not assume that the mandatory argument is always a number---the +% "\window" command uses "\setvlabel" and "\sethlabel" to +% typeset the min\slash max labels. +% \end{macro}\end{macro} +% +% \begin{macro}{\hlabel} +% \begin{macro}{\vlabel} +% The "\hlabel" and "\vlabel" commands calculate the labels that +% "\setvlabel" and "\sethlabel" typeset. The default definitions +% of "\hlabel" and "\vlabel" do nothing, but you can redefine them +% with the "\rescaleby" command. +% \begin{macrocode} +\newcommand{\hlabel}[1]{#1}% +\newcommand{\vlabel}[1]{#1}% +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\rescaleby} +% The "\rescaleby" command redefines it's fourth argument +% (the third mandatory argument) +% which should be either "\hlabel" or "\vlabel". +% After +% \begin{quote} +% "\rescaleby"\oarg{symb}\marg{num}\marg{den}"{\hlabel}" +% \end{quote} +% the result of "\hlabel"\marg{x} should be +% $\frac{\meta{num}\times \meta{x}}{\meta{den}} \meta{symb}$. +% \begin{macrocode} +\newcommand{\rescaleby}[4][]{\renewcommand{#4}[1]{{% + \count@=##1\relax + \ifnum\count@=0\relax + \@tempcntb=1\relax + \else + \multiply\count@ #2\relax + \ifnum\count@<0\count@=-\count@\fi + \@EuclidGCD{\count@}{#3}% + \count@=##1\relax + \multiply\count@ #2\relax + \divide\count@\@tempcnta + \@tempcntb=#3\relax + \divide\@tempcntb\@tempcnta + \fi +% \end{macrocode} +% We have reduced the fraction. Now print it nicely. +% \begin{macrocode} + \ifnum\count@<0\relax + -% + \count@=-\count@ + \fi + \def\coordsys@a{#1}% + \ifx\coordsys@a\@empty\relax + \ifnum\@tempcntb=1\relax + \the\count@ + \else + \frac{\the\count@}{\the\@tempcntb}% + \fi + \else + \ifnum\@tempcntb=1\relax + \ifnum\count@=1\relax + \coordsys@a + \else + \the\count@\coordsys@a + \fi + \else + \ifnum\count@=1\relax + \frac{\coordsys@a}{\the\@tempcntb}% + \else + \frac{\the\count@}{\the\@tempcntb}\coordsys@a + \fi + \fi + \fi +}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\hthickratio} +% \begin{macro}{\vthickratio} +% By default every fifth tick mark is thick. +% \begin{macrocode} +\newcommand{\hthickratio}{5} +\newcommand{\vthickratio}{5} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\text} +% Hopefully the \textsf{amstext} package will override this very simple +% "\text" command intended for subscripts only. +% \begin{macrocode} +\providecommand{\text}[1]{\mbox{\scriptsize #1}} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\picsquare} +% The "\picsquare" command typesets a square of size the current line +% width---as in the \textsf{epic} package. +% \begin{macrocode} +\providecommand{\picsquare}{% + \makebox(0,0){\rule{\@wholewidth}{\@wholewidth}}} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\count@} +% \begin{macro}{\c@@coord} +% \begin{macro}{\@tenpcnta} +% \begin{macro}{\@tenpcntb} +% \begin{macro}{\if@numbline} +% We need three counters. \LaTeX\ inherits one, "\count@", from plain +% \TeX\ and defines two more, "\@tempcnta" and "\@tempcntb". +% We create a \LaTeX\ counter, "@coord",\nextlinelabel{cl:@coord} without +% allocating a new counter +% by making "\c@@coord" a synonym for "\count@"\footnote{I don't +% quite understand why I bother do that; I copied the idea from Lamport's +% \textsf{graphpap} package, which is where the \textsf{coordsys} package +% began.} +% The "\if" controls whether to set labels. +% \begin{macrocode} +\let\c@@coord\count@ +\newif\if@numbline +% \end{macrocode} +% \end{macro}\end{macro}\end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\tickstyle} +% \begin{macro}{\thin@ticks} +% \begin{macro}{\thick@ticks} +% The commands "\thin@ticks" and "\thick@ticks" store the style of +% the tick marks. The "\tickstyle" command defines those two. The +% default is "\thinlines" for the thin tick marks and "\thicklines" +% for the thick tick marks. +% \begin{macrocode} +\newcommand{\tickstyle}[2]{% + \def\thin@ticks{#1}% + \def\thick@ticks{#2}} +\tickstyle{\thinlines}{\thicklines} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\@set@ticks} +% The "\@set@ticks" command calculates the positions of the +% tick marks. +% \begin{quote} +% "\@set@ticks"\marg{thickratio}\marg{spacing}^^A +% \marg{from}\marg{to}\marg{tickfree}\marg{cmd} +% \end{quote} +% \begin{macro}{\coordsys@a} +% \begin{macro}{\coordsys@b} +% \begin{macro}{\coordsys@c} +% The "\@set@ticks" command calculates three parameters: +% "\coordsys@a" is the position of the first tick; +% "\coordsys@b" is the number of ticks to set; and +% "\coordsys@c" is the spacing between the ticks (that is, +% \meta{spacing} for the thin ticks and $\meta{thickratio}\meta{spacing}$ +% for the thick ticks). +% \end{macro}\end{macro}\end{macro} +% Then "\@set@ticks" calls \meta{cmd} to actually set the ticks using +% these parameters.\nextlinelabel{cl:BeginTickCalc} +% \begin{macrocode} +\newcommand{\@set@ticks}[6]{% + \thin@ticks + \edef\coordsys@c{#2}% +% \end{macrocode} +% First we must round \meta{from} up to a multiple of \meta{spacing}. +% Knuth's implementation of integer division +% always rounds toward zero, +% so for negative \meta{from} we can simply divide and multiply +% by \meta{spacing}. If \meta{from} is positive, we must play around a +% little to round up instead of down. +% \begin{macrocode} + \@tempcnta=#3\relax + \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi + \divide\@tempcnta \coordsys@c\relax + \ifnum #3>0\advance\@tempcnta 1\relax\fi + \multiply\@tempcnta \coordsys@c\relax + \edef\coordsys@a{\the\@tempcnta}% +% \end{macrocode} +% Then we must calculate how many ticks to set. +% To avoid collision between ticks and arrowheads, +% there is to be no ticks in the last \meta{tickfree} length. +% \begin{macrocode} + \@tempcntb=#4\relax + \advance\@tempcntb -\@tempcnta\relax + \setlength{\@tempdima}{\@tempcntb\unitlength}% + \addtolength{\@tempdima}{-#5}% + \ifdim\@tempdima<\z@\relax + \def\coordsys@b{0}% + \else + \divide\@tempdima\unitlength\relax + \divide\@tempdima\coordsys@c\relax + \@tempcntb=\@tempdima% + \advance\@tempcntb 1\relax% + \edef\coordsys@b{\the\@tempcntb}% + \fi + #6% +% \end{macrocode} +% \nextlinelabel[0]{cl:EndTickCalc} +% Then the thick ticks. +% This time the spacing is $\meta{thickratio}\meta{spacing}$, so calculate +% that number +% and store it in "\coordsys@c". +% \begin{macrocode} + \thick@ticks + \@tempcntb=#1\relax + \multiply\@tempcntb \coordsys@c\relax + \edef\coordsys@c{\the\@tempcntb}% +% \end{macrocode} +% Calculate the position of the first (thick) tick as above. +% \begin{macrocode} + \@tempcnta=#3\relax + \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi + \divide\@tempcnta \coordsys@c\relax + \ifnum #3>0\advance\@tempcnta 1\relax\fi + \multiply\@tempcnta \coordsys@c\relax + \edef\coordsys@a{\the\@tempcnta}% +% \end{macrocode} +% Then calculate the number of \emph{thin} ticks +% between the first thick tick ("\@tempcnta") and +% \meta{to} less \meta{tickfree}, namely +% $\left\lfloor\frac{\meta{to}-\meta{first}-\meta{tickless}}{\meta{spacing}}\right\rfloor+1$. +% \begin{macrocode} + \@tempcntb=#4\relax + \advance\@tempcntb -\@tempcnta\relax + \setlength{\@tempdima}{\@tempcntb\unitlength}% + \addtolength{\@tempdima}{-#5}% + \ifdim\@tempdima<\z@\relax + \def\coordsys@b{0}% + \else + \divide\@tempdima\unitlength\relax + \divide\@tempdima#2\relax + \@tempcntb=\@tempdima% +% \advance\@tempcntb 1\relax +% \end{macrocode} +% The number of thick ticks is then +% $\left\lceil\frac{\meta{number of thin ticks}}{\meta{thickratio}}\right\rceil$. +% \begin{macrocode} +% \advance\@tempcntb -1\relax + \divide\@tempcntb #1\relax + \advance\@tempcntb 1\relax + \edef\coordsys@b{\the\@tempcntb}% + \fi + #6% +} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\numbline} +% The "\numbline" command checks for a star, +% \begin{macrocode} +\newcommand{\numbline}{% + \@ifstar{\@numblinefalse\hnumbline@i} + {\@numblinetrue \hnumbline@i}} +% \end{macrocode} +% \begin{macro}{\hnumbline@i} +% then "\hnumbline@i" picks up the optional argument, +% \begin{macrocode} +\newcommand{\hnumbline@i}[1][10]{\leavevmode\hnumbline@ii{#1}} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\hnumbline@ii} +% and "\hnumbline@ii" does the work: +% Calculate the length of the arrow and set it, then call "\@set@ticks" +% to set the tick marks. The extra set of braces localizes the +% "\tickstyle" declarations. +% \begin{macrocode} +\newcommand{\hnumbline@ii}[3]{{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#2,0){\vector(1,0){\coordsys@w}}% + \@set@ticks{\hthickratio}{#1}{#2}{#3}{6\p@}{ + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b\vtickmark}% +% \end{macrocode} +% Set the labels if we have to. +% The parameters "\coordsys@a", "\coordsys@b", and +% "\coordsys@c" that "\@set@ticks" calculated for the thick tick +% marks are still available. In particular, "\coordsys@a" is the +% position and, hence, the value of the first label. +% \begin{macrocode} + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \sethlabel{\hlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}} + \fi + \color@endgroup}% +% \end{macrocode} +% Finally store the vertical coordinate of the number line in +% "\coordsys@w" for the sake of the "\interval" command. +% \begin{macrocode} + \def\coordsys@w{0}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\vnumbline} +% \begin{macro}{\vnumbline@i} +% \begin{macro}{\vnumbline@ii} +% The "\vnumbline" command and friends work in much the same way. +% \begin{macrocode} +\newcommand{\vnumbline}{% + \@ifstar{\@numblinefalse\vnumbline@i} + {\@numblinetrue \vnumbline@i}} +\newcommand{\vnumbline@i}[1][10]{\leavevmode\vnumbline@ii{#1}} +\newcommand{\vnumbline@ii}[3]{{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(0,#2){\vector(0,1){\coordsys@h}}% + \@set@ticks{\vthickratio}{#1}{#2}{#3}{6\p@}{% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \setvlabel{\vlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}} + \fi + \color@endgroup}% + \def\coordsys@h{0}% +} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\coordsys} +% All the coordinate-system drawing command use similar syntax, so we use a +% unified approach for picking up the arguments. +% The "\coordsys" command defines the temporary variable +% "\coordsys@c" to be the name of the command that does the real work. +% Then "\coordsys" checks for the presence of a star. +% \begin{macrocode} +\newcommand{\coordsys}{% + \def\coordsys@c{\coordsys@i}% + \@ifstar{\@numblinefalse\coordsys@args@i} + {\@numblinetrue \coordsys@args@i}} +% \end{macrocode} +% \begin{macro}{\coordsys@args@i} +% \begin{macro}{\@hticksep} +% The "\coordsys@args@i" command picks up the first optional argument +% storing it +% in "\@hticksep" so that we can use that variable as the default for the +% second optional argument. +% \begin{macrocode} +\newcommand{\coordsys@args@i}[1][10]{\leavevmode + \def\@hticksep{#1}% + \coordsys@args@ii} +% \end{macrocode} +% \end{macro}\end{macro} +% \begin{macro}{\coordsys@args@ii} +% \begin{macro}{\@vticksep} +% Then "\coordsys@args@ii" picks up the second optional argument, +% \begin{macrocode} +\newcommand{\coordsys@args@ii}[1][\@hticksep]{% + \def\@vticksep{#1}% + \coordsys@args@iii} +% \end{macrocode} +% \end{macro}\end{macro} +% \begin{macro}{\coordsys@args@iii} +% and the "\coordsys@args@iii" command picks up the first point and +% brutally +% replaces whatever the following may be with a "(". Since \TeX\ ignores +% spaces when looking for an argument, this allows the user to leave a space +% between the first and the second point. +% \begin{macrocode} +\def\coordsys@args@iii(#1,#2)#3{\coordsys@c{#1}{#2}(} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\coordsys@i} +% Finally the real command, "\coordsys@c", that is "\coordsys@i", +% picks up the second point (as well as the first), and gets to work: +% First calculate the length of each axis and set it. +% \begin{macrocode} +\def\coordsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,0){\vector(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(0,#2){\vector(0,1){\coordsys@h}}% +% \end{macrocode} +% Then set the tick marks on the horizontal axis. +% \begin{macrocode} + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{% + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b\vtickmark}% +% \end{macrocode} +% This style of coordinate system has intersecting axes, so we must suppress +% the label ``0''. +% \begin{macrocode} + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b{% + \ifnum\value{@coord}=0\relax\else + \edef\coordsys@a{\arabic{@coord}}% + \sethlabel{\hlabel{\coordsys@a}}% + \fi + \addtocounter{@coord}{\coordsys@c}}% + \fi +% \end{macrocode} +% Then do the tick marks and labels on the vertical axis. +% \begin{macrocode} + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b{% + \ifnum\value{@coord}=0\relax\else + \edef\coordsys@a{\arabic{@coord}}% + \setvlabel{\vlabel{\coordsys@a}}% + \fi + \addtocounter{@coord}{\coordsys@c}}% + \fi + \color@endgroup}% +% \end{macrocode} +% Finally store the location of the axis in "\coordsys@w" and "\coordsys@h" +% for the sake of the "\interval" command. +% \begin{macrocode} + \def\coordsys@w{0}% + \def\coordsys@h{0}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\fcoordsys} +% \begin{macro}{\fcoordsys@i} +% The "\fcoordsys" and "\fcoordsys@i" commands work much like +% "\coordsys" and "\coordsys@i" above. +% \begin{macrocode} +\newcommand{\fcoordsys}{% + \def\coordsys@c{\fcoordsys@i}% + \@ifstar{\@numblinefalse\coordsys@args@i} + {\@numblinetrue \coordsys@args@i}} +\def\fcoordsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,#2){\vector(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\vector(0,1){\coordsys@h}}% + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \sethlabel{\hlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \setvlabel{\vlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi + \color@endgroup}% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\bcoordsys} +% \begin{macro}{\bcoordsys@i} +% The "\bcoordsys" and "\bcoordsys@i" commands work much like +% "\coordsys" and "\coordsys@i" above. +% \begin{macrocode} +\newcommand{\bcoordsys}{% + \def\coordsys@c{\bcoordsys@i}% + \@ifstar{\@numblinefalse\coordsys@args@i} + {\@numblinetrue \coordsys@args@i}} +\def\bcoordsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,#2){\line(1,0){\coordsys@w}}% + \put(#1,#4){\line(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\line(0,1){\coordsys@h}}% + \put(#3,#2){\line(0,1){\coordsys@h}}% + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \sethlabel{\hlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \setvlabel{\vlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi + \color@endgroup}% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\window} +% \begin{macro}{\window@i} +% And yet another modification of the same old thing. +% \begin{macrocode} +\newcommand{\window}{% + \def\coordsys@c{\window@i}% + \@ifstar{\let\coordsys@a\phantom\coordsys@args@i} + {\let\coordsys@a\relax \coordsys@args@i}} +\def\window@i#1#2(#3,#4){{% + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta-#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \@tempcnta=#4\relax + \advance\@tempcnta-#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\line(1,0){\coordsys@w}}% + \put(#1,#2){\line(0,1){\coordsys@h}}% + \put(#3,#4){\line(-1,0){\coordsys@w}}% + \put(#3,#4){\line(0,-1){\coordsys@h}}% +% \end{macrocode} +% Set the labels; "\ensuremath" for the sake of the +% subscripts. +% \begin{macrocode} + \put(#1,#2){\sethlabel[tl]% + {\ensuremath{x_{\text{min}}=\coordsys@a{#1}}}}% + \put(#3,#2){\sethlabel[tr]% + {\ensuremath{x_{\text{max}}=\coordsys@a{#3}}}}% + \put(#1,#2){\setvlabel[rb]% + {\ensuremath{y_{\text{min}}=\coordsys@a{#2}}}}% + \put(#1,#4){\setvlabel[rt]% + {\ensuremath{y_{\text{max}}=\coordsys@a{#4}}}}% +% \end{macrocode} +% If the axes are in the window, typeset them (without labels). +% \begin{macrocode} + \ifnum #1<0\relax\ifnum #3>0\relax + \vnumbline*[\@vticksep]{#2}{#4}% + \fi\fi + \ifnum #2<0\relax\ifnum #4>0\relax + \numbline*[\@hticksep]{#1}{#3}% + \fi\fi + }% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro} +% \end{macro} +% +% \begin{macro}{\gridstyle} +% \begin{macro}{\grid@style} +% The "\gridstyle" command defines "\grid@style" to issue a suitable +% "\tickstyle" command at the proper time. The default +% "\grid@style" is to do nothing---that is, use the current +% "\tickstyle" unchanged. +% \begin{macrocode} +\newcommand{\gridstyle}[2]{\def\grid@style{\tickstyle{#1}{#2}}} +\newcommand{\grid@style}{\relax} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\coordgrid} +% The "\coordgrid" command chooses between the starred version, +% "\coordgrid@ii", with solid lines and the un-starred version, +% "\coordgrid@i", with dotted lines. +% \begin{macrocode} +\newcommand{\coordgrid}{% + \@ifstar{\def\coordsys@c{\coordgrid@ii}\coordsys@args@i} + {\def\coordsys@c{\coordgrid@i}\coordsys@args@i}} +% \end{macrocode} +% \begin{macro}{\coordgrid@i} +% The "\coordgrid@i" command calls "\coordgrid@calc" to calculate +% the size, "\coordsys@w", of the box containing each dot of the dotted +% lines based on the values of "\@hticksep" and "\@vticksep". Then +% set the dotted lines with "\@set@ticks". +% \begin{macrocode} +\def\coordgrid@i#1#2(#3,#4){{\color@begingroup + \coordgrid@calc + \grid@style + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{% + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b + {\vgridfromto{#2}{#4}}}% + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b + {\hgridfromto{#1}{#3}}}% + \color@endgroup}} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\coordgrid@ii} +% The "\coordgrid@ii" command is similar to "\fcoordsys@i" above. +% \begin{macrocode} +\def\coordgrid@ii#1#2(#3,#4){{\color@begingroup + \grid@style + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b + {\vgridlength{\coordsys@h}}}% + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b + {\hgridlength{\coordsys@w}}}% + \color@endgroup}} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\coordgrid@calc} +% To typeset pretty grids of dots the number of dots between lines must be an +% integer. Thus, the number of dots must be a factor of the greatest common +% divisor of "\@vticksep" and "\@hticksep". The "\@EuclidGCD" +% command returns the $\gcd$ in the counter "\@tempcnta" +% \begin{macrocode} +\newcommand{\coordgrid@calc}{% + \@EuclidGCD{\@vticksep}{\@hticksep}% + \@tempdima=\unitlength + \multiply\@tempdima\@tempcnta +% \end{macrocode} +% Now "\@tempdima" is the longest length that fits an integer number of +% times between lines. The dots should not be closer than 2\,pt. +% \begin{macrocode} + \@tempdimb=2\p@\relax + \ifdim\@tempdima<\@tempdimb + \PackageWarning{coordsys}{The tick marks are too + close\MessageBreak for a pretty grid}% + \else +% \end{macrocode} +% However, "\@tempdima" may be able to contain multiple dots. +% \begin{macrocode} + \divide\@tempdima \@tempdimb\relax + \@tempdimb=\unitlength + \multiply\@tempdimb\@tempcnta + \divide\@tempdimb\@tempdima + \fi +% \end{macrocode} +% In either case store the box size in "\coordsys@w". +% \begin{macrocode} + \edef\coordsys@w{\the\@tempdimb}% +} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\interval} +% We use "\newcommand" to check that "\interval" is not already defined; +% then we need plain \TeX's "\def" because "\interval" picks up its +% arguments in a non-standard way. +% \begin{macrocode} +\newcommand{\interval}{} +\def\interval#1#2,{% + \def\coordsys@a{#1}% + \def\coordsys@b{#2}% + \def\coordsys@c{}% +% \end{macrocode} +% Now "\coordsys@a" is the \meta{L-delim} and "\coordsys@b" is whatever follows +% up to the first comma, that is \meta{from}. +% Then define "\coordsys@a" to be the correct symbol suitably aligned +% in a box. Note that the characters in \LaTeX's circle font are placed +% rather peculiarly inside their bounding box. +% \begin{macrocode} + \if\coordsys@a]\def\coordsys@a{(}\fi + \if\coordsys@a[% + \def\coordsys@a{% + \makebox[0.5\width][l]{\@circlefnt\char'163}}% + \else\if\coordsys@a(% + \def\coordsys@a{% + \makebox[0.5\width][l]{\@circlefnt\char'143}}% + \else\if\coordsys@a<% + \def\coordsys@a{% + \raisebox{-\fontdimen22\textfont2}{% + \makebox[\z@]{$<$}}}% + \else + \PackageError{coordsys} + {Bad delimiter} + {\string\interval\space expects [, (, <, or ] % + but got \coordsys@a}% + \def\coordsys@a{}% + \fi\fi\fi +% \end{macrocode} +% Picking up the \meta{from} was easy because we know the +% number ends at the comma. But we do not know where the \meta{to} number ends. +% \TeX\ knows how to read an integer, so do that and proceed with "\interv@l" +% which picks up either the right-hand delimiter or a decimal point as its +% first argument. +% \begin{macrocode} + \afterassignment\interv@l\count@=} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\interv@l} +% If we got a decimal point, store the integer part of the number in +% "\coordsys@c" and try again. +% \begin{macrocode} +\newcommand{\interv@l}[1]{% + \if#1.% + \edef\coordsys@c{\the\count@.}% + \def\next{\afterassignment\interv@l\count@=}% +% \end{macrocode} +% Otherwise, append the number we just read to "\coordsys@c". +% Now "\coordsys@c" contains \meta{to}. So calculate the +% length (in~pt) of the interval. +% \begin{macrocode} + \else + \edef\coordsys@c{\coordsys@c\the\count@}% + \setlength{\@tempdima}{\coordsys@b\unitlength}% + \setlength{\@tempdima}{-\@tempdima}% + \addtolength{\@tempdima}{\coordsys@c\unitlength}% +% \end{macrocode} +% Define "\coordsys@c" to be the correct symbol for the \meta{R-delim}. +% \begin{macrocode} + \def\coordsys@c{#1}% + \if\coordsys@c[\def\coordsys@c{)}\fi + \if\coordsys@c]% + \def\coordsys@c{\mbox{% + \@circlefnt + \settowidth{\@tempdima}{\char'163}% + \hskip 0.5\@tempdima + \char'163% + \hskip -\@tempdima}% + }% + \else\if\coordsys@c)% + \def\coordsys@c{\mbox{% + \@circlefnt + \settowidth{\@tempdima}{\char'143}% + \hskip 0.5\@tempdima + \char'143% + \hskip -\@tempdima}% + }% + \else\if\coordsys@c>% + \def\coordsys@c{% + \raisebox{-\fontdimen22\textfont2}{% + \makebox[\z@]{$>$}}}% + \else + \PackageError{coordsys} + {Bad delimiter} + {\string\interval\space expects ], ), <, or [ % + but got \coordsys@c}% + \def\coordsys@c{}% + \fi\fi\fi +% \end{macrocode} +% \begin{macro}{\coordsys@w}\begin{macro}{\coordsys@h} +% Finally, "\put" the pieces down. Here "\coordsys@w" is the vertical +% coordinate of the last typeset horizontal axis (usually~$0$), +% and "\interval@line" is defined by "\intervalthickness" below. +% \begin{macrocode} + \put(\coordsys@b,\coordsys@w){\makebox[\@tempdima][s]{% + \coordsys@a + \interval@line + \coordsys@c + }}% + \let\next=\ignorespaces + \fi + \next} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\vinterval} +% \begin{macro}{\vinterv@l} +% The "\vinterval" and "\vinterv@l" commands work as their horizontal cousins. +% \begin{macrocode} +\newcommand{\vinterval}{} +\def\vinterval#1#2,{% + \def\coordsys@a{#1}% + \def\coordsys@b{#2}% + \def\coordsys@c{}% + \if\coordsys@a]\def\coordsys@a{(}\fi + \if\coordsys@a[% + \def\coordsys@a{\hbox to\z@{% + \@circlefnt + \settowidth{\@tempdima}{\char'163}% + \hskip 0.5\@tempdima minus 1fil + \char'163% + \hskip -0.5\@tempdima minus 1fil + \vrule width \z@ depth \z@ height 0.5\@tempdima + }}% + \else\if\coordsys@a(% + \def\coordsys@a{\hbox to\z@{% + \@circlefnt + \settowidth{\@tempdima}{\char'143}% + \hskip 0.5\@tempdima minus 1fil + \char'143% + \hskip -0.5\@tempdima minus 1fil + \vrule width \z@ depth \z@ height 0.5\@tempdima + }}% + \else\if\coordsys@a<% + \def\coordsys@a{\hbox to\z@{\hss + \raisebox{-\fontdimen22\textfont2}[\z@][\z@]{% + $\vee$}\hss}}% + \else + \PackageError{coordsys} + {Bad delimiter} + {\string\vinterval\space expects [, (, <, or ] % + but got \coordsys@a}% + \def\coordsys@a{}% + \fi\fi\fi + \afterassignment\vinterv@l\count@=} +\newcommand{\vinterv@l}[1]{% + \if#1.% + \edef\coordsys@c{\the\count@.}% + \def\next{\afterassignment\interv@l\count@=}% + \else + \edef\coordsys@c{\coordsys@c\the\count@}% + \setlength{\@tempdima}{\coordsys@b\unitlength}% + \setlength{\@tempdima}{-\@tempdima}% + \addtolength{\@tempdima}{\coordsys@c\unitlength}% + \def\coordsys@c{#1}% + \if\coordsys@c[\def\coordsys@c{)}\fi + \if\coordsys@c]% + \def\coordsys@c{\hbox to\z@{% + \@circlefnt + \settowidth{\@tempdima}{\char'163}% + \hskip 0.5\@tempdima minus 1fil + \char'163% + \hskip -0.5\@tempdima minus 1fil + \vrule width \z@ depth 0.5\@tempdima height \z@ + }}% + \else\if\coordsys@c)% + \def\coordsys@c{\hbox to\z@{% + \@circlefnt + \settowidth{\@tempdima}{\char'143}% + \hskip 0.5\@tempdima minus 1fil + \char'143% + \hskip -0.5\@tempdima minus 1fil + \vrule width \z@ depth 0.5\@tempdima height \z@ + }}% + \else\if\coordsys@c>% + \def\coordsys@c{\hbox to\z@{\hss% + \raisebox{-\fontdimen22\textfont2}[\z@][\z@]{% + $\wedge$}\hss}}% + \else + \PackageError{coordsys} + {Bad delimiter} + {\string\vinterval\space expects ], ), <, or [ % + but got \coordsys@c}% + \def\coordsys@c{}% + \fi\fi\fi + \put(\coordsys@h,\coordsys@b){\vbox{% + \setlength{\baselineskip}{\z@}% + \setlength{\lineskip}{\z@}% + \settoheight{\@tempdimb}{\coordsys@a}% + \addtolength{\@tempdima}{-\@tempdimb}% + \settodepth {\@tempdimb}{\coordsys@c}% + \addtolength{\@tempdima}{-\@tempdimb}% + \coordsys@c + \vinterval@line + \coordsys@a + }}% + \let\next=\ignorespaces + \fi + \next} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\intervalthickness} +% \begin{macro}{interval@line}\begin{macro}{\vinterval@line} +% The "\intervalthickness" command defines the two commands "\interval@line" +% and "\vinterval@line" that draw the thick line indicating the interval. +% \begin{macrocode} +\newcommand{\intervalthickness}[2][\z@]{% + \setlength{\@tempdima}{#2}% + \setlength{\@tempdima}{0.5\@tempdima}% + \setlength{\@tempdimb}{-\@tempdima}% + \addtolength{\@tempdima}{#1}% + \addtolength{\@tempdimb}{#1}% + \edef\coordsys@a{\the\@tempdima}% + \edef\coordsys@b{-\the\@tempdimb}% + \edef\interval@line{% + \leaders\hrule depth \coordsys@b height \coordsys@a\hss}% + \setlength{\@tempdima}{#2}% + \setlength{\@tempdima}{-0.5\@tempdima}% + \addtolength{\@tempdima}{#1}% + \edef\coordsys@a{\the\@tempdima}% + \edef\vinterval@line{% + \hbox to\z@{% + \hskip \coordsys@a + \vrule height\@tempdima width #2% + \hss + }% + }% +} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% Then a few defaults for "\interval" and "\vinterval". +% \begin{macrocode} +\intervalthickness{1.6\p@} +\def\coordsys@w{0} +\def\coordsys@h{0} +% +% \end{macrocode} +% +% \iffalse Don't document this fragment of code. +% \begin{macrocode} +%<*euclid> +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{euclidgcd}[2006/02/03 version 1.4] +\newcommand{\EuclidGCD}[2]{% + \@EuclidGCD{#1}{#2}% + \the\@tempcnta} +% +% \end{macrocode} +% \fi +% +% \begin{macro}{\@EuclidGCD} +% The "\@EuclidGCD" command calculates the greatest common divisor +% of two positive integers using Euclid's algorithm.\footnote{Euclid's +% algorithm uses the fact that $\gcd(n, d) = \gcd(d, r)$, where $r$ is +% the remainder after dividing $n$ by $d$. Since $r +\newcommand{\@EuclidGCD}[2]{% + \@tempcnta=#1\relax + \@tempcntb=#2\relax + \loop + \count@=\@tempcntb + \divide\count@\@tempcnta + \multiply\count@\@tempcnta + \advance\count@ -\@tempcntb +% \end{macrocode} +% Now "\count@" is $-r$, where $r$ is the remainder after dividing +% "\@tempcntb" by "\@tempcnta". +% \begin{macrocode} + \ifnum\count@<0\relax + \@tempcntb=\@tempcnta + \@tempcnta=-\count@ + \repeat +} +% +% \end{macrocode} +% \end{macro} +% +% +% \subsection{The \textsf{logsys} Package} +% \subsubsection{Identification} +% First we must declare ourselves. +% \begin{macrocode} +%<*logsys> +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{logsys}[2006/02/03 version 1.4] +% \end{macrocode} +% +% \subsubsection{Options} +% Pass all options to \textsf{coordsys}. +% \begin{macrocode} +\DeclareOption{centred}{\PassOptionsToPackage{centred}{coordsys}} +\DeclareOption{outside}{\PassOptionsToPackage{outside}{coordsys}} +\DeclareOption{inside}{\PassOptionsToPackage{inside}{coordsys}} +\ProcessOptions +% \end{macrocode} +% +% \subsubsection{Package Loading} +% The \textsf{logsys} package extends the \textsf{coordsys} package. +% \begin{macrocode} +\RequirePackage{coordsys}[2006/02/03] +% \end{macrocode} +% +% \subsubsection{Main Code} +% \begin{macro}{\loglabel} +% The "\loglabel" command typesets logarithmic labels. +% \begin{macrocode} +\newcommand{\loglabel}[1]{% + \ifnum #1=-2\relax \frac{1}{100}% + \else\ifnum #1=-1\relax \frac{1}{10}% + \else\ifnum #1= 0\relax 1% + \else\ifnum #1= 1\relax 10% + \else\ifnum #1= 2\relax 100% + \else 10^{#1}% + \fi\fi\fi\fi\fi} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\v@logbox} +% \begin{macro}{\h@logbox} +% The "\v@logbox" and "\h@logbox" commands each typeset one block +% of logarithmic tick marks. Each take two arguments: the size of a block and +% the tick mark to typeset. +% The glue in the boxes is (10000 times) $\log10-\log9$, $\log9-\log8$, +% $\log8-\log7$, \dots, and $\log2-\log1$. +% \begin{macrocode} +\newcommand{\v@logbox}[2]{% + \vbox to #1\unitlength{% + \offinterlineskip + \vskip \z@ plus 458fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 9 + \vskip \z@ plus 512fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 8 + \vskip \z@ plus 580fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 7 + \vskip \z@ plus 669fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 6 + \vskip \z@ plus 792fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 5 + \vskip \z@ plus 969fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 4 + \vskip \z@ plus 1249fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 3 + \vskip \z@ plus 1761fil\relax + \vbox to \z@{\vss\hbox{#2}\vss}% 2 + \vskip \z@ plus 3010fil\relax + }} +\newcommand{\h@logbox}[2]{% + \hbox to #1\unitlength{% + \hskip \z@ plus 3010fill\relax + \hbox to \z@{\hss #2\hss}% 2 + \hskip \z@ plus 1761fill\relax + \hbox to \z@{\hss #2\hss}% 3 + \hskip \z@ plus 1249fill\relax + \hbox to \z@{\hss #2\hss}% 4 + \hskip \z@ plus 969fill\relax + \hbox to \z@{\hss #2\hss}% 5 + \hskip \z@ plus 792fill\relax + \hbox to \z@{\hss #2\hss}% 6 + \hskip \z@ plus 669fill\relax + \hbox to \z@{\hss #2\hss}% 7 + \hskip \z@ plus 580fill\relax + \hbox to \z@{\hss #2\hss}% 8 + \hskip \z@ plus 512fill\relax + \hbox to \z@{\hss #2\hss}% 9 + \hskip \z@ plus 458fill\relax + }} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\@sethlogticks} +% In the linear case we got away with using one command, "\@set@ticks", +% to calculate the positions of the tick marks on both horizontal and vertical +% axes. The logarithmic case is more complicated, so we create separate +% command for the horizontal and vertical case. This split then allows the +% logarithmic commands to do more than just calculate the positions of the +% ticks: +% \begin{quote} +% "\@sethlogticks"\marg{spacing}\marg{from}\marg{to}^^A +% \marg{y0}\marg{tick} +% \end{quote} +% \emph{typesets} the logarithmic tick marks on a horizontal axis at +% $y$-coordinate \meta{y0}. Moreover, it typesets the labels. +% +% The calculation is much like the calculation for thin tick marks in the +% linear case; compare with code +% lines~\ref{cl:BeginTickCalc}--\ref{cl:EndTickCalc}. +% \begin{macrocode} +\newcommand{\@sethlogticks}[5]{% + \thin@ticks + \@tempcnta=#2\relax + \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi + \divide\@tempcnta #1\relax + \ifnum #2>0\advance\@tempcnta 1\relax\fi + \multiply\@tempcnta #1\relax + \edef\coordsys@a{\the\@tempcnta}% + \@tempcntb=#3\relax + \ifnum\@tempcnta<\@tempcntb\relax + \advance\@tempcntb -\@tempcnta\relax + \divide\@tempcntb #1\relax + \edef\coordsys@b{\the\@tempcntb}% + \multiput(\coordsys@a,#4)(#1,0)\coordsys@b + {\h@logbox{#1}{#5}}% +% \end{macrocode} +% In the linear case we took some measure against colliding tick marks and +% arrow heads; in +% the logarithmic case we leave that worry to the user\footnote{Because +% calculating the position of individual logarithmic tick mark is difficult; +% this code works by setting blocks of tick marks.}. Therefore we can (and +% should) set one more thick tick mark than we have blocks. +% \begin{macrocode} + \thick@ticks + \@tempcntb=\coordsys@b\relax + \advance\@tempcntb 1\relax + \edef\coordsys@b{\the\@tempcntb}% + \multiput(\coordsys@a,#4)(#1,0)\coordsys@b + {#5}% +% \end{macrocode} +% Then set the labels: First set the counter "@coord" to\footnote{The +% calculation uses a horrible mixture of \LaTeX\ syntax and plain \TeX\ since +% \LaTeX\ does not provide a division command. Maybe I should avoid the +% \LaTeX\ style counter and just use plain \TeX. See the note to code +% line~\ref{cl:@coord}.} +% $\frac{\meta{from}}{\meta{spacing}}$, then step that counter by one. +% \begin{macrocode} + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \divide\c@@coord #1\relax + \multiput(\coordsys@a,#4)(#1,0)\coordsys@b{% + \sethlabel{\loglabel{\arabic{@coord}}}% + \stepcounter{@coord}}% + \fi + \fi +} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\@setvlogticks} +% The vertical version works in much the same way. +% \begin{macrocode} +\newcommand{\@setvlogticks}[5]{% + \thin@ticks + \@tempcnta=#2\relax + \ifnum\@tempcnta>0\advance\@tempcnta -1\relax\fi + \divide\@tempcnta #1\relax + \ifnum #2>0\advance\@tempcnta 1\relax\fi + \multiply\@tempcnta #1\relax + \edef\coordsys@a{\the\@tempcnta}% + \@tempcntb=#3\relax + \ifnum\@tempcnta<\@tempcntb\relax + \advance\@tempcntb -\@tempcnta\relax + \divide\@tempcntb #1\relax + \edef\coordsys@b{\the\@tempcntb}% + \multiput(#4,\coordsys@a)(0,#1)\coordsys@b + {\v@logbox{#1}{#5}}% + \thick@ticks + \@tempcntb=\coordsys@b\relax + \advance\@tempcntb 1\relax + \edef\coordsys@b{\the\@tempcntb}% + \multiput(#4,\coordsys@a)(0,#1)\coordsys@b + {#5}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \divide\c@@coord #1\relax + \multiput(#4,\coordsys@a)(0,#1)\coordsys@b{% + \setvlabel{\loglabel{\arabic{@coord}}}% + \stepcounter{@coord}}% + \fi + \fi +} +% \end{macrocode} +% \end{macro} +% +% \begin{macro}{\logline} +% The "\logline" command checks for a star, +% \begin{macrocode} +\newcommand{\logline}{% + \@ifstar{\@numblinefalse\hlogline@i} + {\@numblinetrue \hlogline@i}} +% \end{macrocode} +% \begin{macro}{\hlogline@i} +% then "\hlogline@i" picks up the optional argument, +% \begin{macrocode} +\newcommand{\hlogline@i}[1][50]{\leavevmode\hlogline@ii{#1}} +% \end{macrocode} +% \begin{macro}{\hlogline@ii} +% and "\hlogline@ii" does the work---which isn't much since +% "\@sethlogticks" does almost everything. +% \begin{macrocode} +\newcommand{\hlogline@ii}[3]{{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#2,0){\vector(1,0){\coordsys@w}}% + \@sethlogticks{#1}{#2}{#3}{0}{\vtickmark} + \color@endgroup}% + \def\coordsys@w{0}% +} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\vlogline} +% \begin{macro}{\vlogline@i} +% \begin{macro}{\vlogline@ii} +% The "\vlogline" command and friends work in much the same way. +% \begin{macrocode} +\newcommand{\vlogline}{% + \@ifstar{\@numblinefalse\vlogline@i} + {\@numblinetrue \vlogline@i}} +\newcommand{\vlogline@i}[1][50]{\leavevmode\vlogline@ii{#1}} +\newcommand{\vlogline@ii}[3]{{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(0,#2){\vector(0,1){\coordsys@h}}% + \@setvlogticks{#1}{#2}{#3}{0}{\htickmark} + \color@endgroup}% + \def\coordsys@h{0}% +} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% \begin{macro}{\logsys} +% The logarithmic coordinate system commands have different default values for +% the optional arguments than their linear cousins. We therefore need a new +% approach for picking up optional arguments. +% +% The "\logsys" command defines "\coordsys@c" to be the command that +% eventually sets the coordinate system. Then "\logsys" define +% "\@hticksep" and "\@vticksep" to be the default values for the +% optional arguments. (Each logarithmic coordinate system type has a different +% set of default values.) Then "\logsys" checks for a star and calls +% "\logsys@args@i". +% \begin{macrocode} +\newcommand{\logsys}{% + \def\coordsys@c{\logsys@i}% + \def\@hticksep{10}% + \def\@vticksep{50}% + \@ifstar{\@numblinefalse\logsys@args@i} + {\@numblinetrue \logsys@args@i}} +% \end{macrocode} +% \begin{macro}{\logsys@args@i} +% The "\logsys@args@i" command picks up the first optional argument +% storing it in "\@hticksep" for later processing. +% \begin{macrocode} +\newcommand{\logsys@args@i}[1][\@hticksep]{\leavevmode + \edef\@hticksep{#1}% + \logsys@args@ii} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\logsys@args@ii} +% Then "\logsys@args@ii" picks up the second optional argument and calls +% the good old "\coordsys@args@iii" command to pick up (some of) the +% remaining arguments. +% \begin{macrocode} +\newcommand{\logsys@args@ii}[1][\@vticksep]{% + \edef\@vticksep{#1}% + \coordsys@args@iii} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\logsys@i} +% Finally "\logsys@i" sets the coordinate system: +% First calculate the width and height of the system, then set the axes +% and the tick marks and labels on the linear (horizontal) axis---all of it +% much like "\fcoordsys@i" above. +% \begin{macrocode} +\def\logsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,#2){\vector(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\vector(0,1){\coordsys@h}}% + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{6\p@}{% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b\vtickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \sethlabel{\hlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi +% \end{macrocode} +% Finally call "\@setvlogticks" to set the tick marks and labels on the +% logarithmic (vertical) axis. +% \begin{macrocode} + \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\htickmark}% + \color@endgroup}% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\semilogsys} +% \begin{macro}{\semilogsys@i} +% The "\semilogsys" and "\semilogsys@i" commands work in much the +% same manner. +% \begin{macrocode} +\newcommand{\semilogsys}{% + \def\coordsys@c{\semilogsys@i}% + \def\@hticksep{50}% + \def\@vticksep{10}% + \@ifstar{\@numblinefalse\logsys@args@i} + {\@numblinetrue \logsys@args@i}} +\def\semilogsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,#2){\vector(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\vector(0,1){\coordsys@h}}% + \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vtickmark}% + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{6\p@}{% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b\htickmark}% + \if@numbline + \setcounter{@coord}{\coordsys@a}% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b{% + \edef\coordsys@a{\arabic{@coord}}% + \setvlabel{\vlabel{\coordsys@a}}% + \addtocounter{@coord}{\coordsys@c}}% + \fi + \color@endgroup}% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\loglogsys} +% \begin{macro}{\loglogsys@i} +% The "\loglogsys" and "\loglogsys@i" commands work in much the +% same manner. +% \begin{macrocode} +\newcommand{\loglogsys}{% + \def\coordsys@c{\loglogsys@i}% + \def\@hticksep{50}% + \def\@vticksep{50}% + \@ifstar{\@numblinefalse\logsys@args@i} + {\@numblinetrue \logsys@args@i}} +\def\loglogsys@i#1#2(#3,#4){{\color@begingroup + \thinlines + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \put(#1,#2){\vector(1,0){\coordsys@w}}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \put(#1,#2){\vector(0,1){\coordsys@h}}% + \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vtickmark}% + \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\htickmark}% + \color@endgroup}% + \def\coordsys@h{#1}% + \def\coordsys@w{#2}% +} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\loggrid} +% The "\loggrid" command is the obvious cross between "\logsys" and +% "\coordgrid". +% \begin{macrocode} +\newcommand{\loggrid}{% + \def\@hticksep{10}% + \def\@vticksep{50}% + \@numblinefalse + \@ifstar{\def\coordsys@c{\loggrid@ii}\logsys@args@i} + {\def\coordsys@c{\loggrid@i}\logsys@args@i}} +% \end{macrocode} +% \begin{macro}{\loggrid@i} +% Similarly, "\loggrid@i" is a cross between "\logsys@i" and +% "\coordgrid@i", +% \begin{macrocode} +\def\loggrid@i#1#2(#3,#4){{\color@begingroup + \coordgrid@calc + \grid@style + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{% + \multiput(\coordsys@a,0)(\coordsys@c,0)\coordsys@b + {\vgridfromto{#2}{#4}}}% + \@setvlogticks{\@vticksep}{#2}{#4}{0}{\hgridfromto{#1}{#3}}% + \color@endgroup}} +% \end{macrocode} +% \end{macro} +% \begin{macro}{\loggrid@ii} +% and "\loggrid@ii" is a cross between "\logsys@i" and +% "\coordgrid@ii". +% \begin{macrocode} +\def\loggrid@ii#1#2(#3,#4){{\color@begingroup + \grid@style + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \@set@ticks{\hthickratio}{\@hticksep}{#1}{#3}{\z@}{% + \multiput(\coordsys@a,#2)(\coordsys@c,0)\coordsys@b + {\vgridlength{\coordsys@h}}}% + \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\hgridlength{\coordsys@w}}% + \color@endgroup}} +% \end{macrocode} +% \end{macro}\end{macro} +% +% \begin{macro}{\semiloggrid} +% \begin{macro}{\semiloggrid@i} +% \begin{macro}{\semiloggrid@ii} +% Semi-logarithmic grids provide no surprises, +% \begin{macrocode} +\newcommand{\semiloggrid}{% + \def\@hticksep{50}% + \def\@vticksep{10}% + \@numblinefalse + \@ifstar{\def\coordsys@c{\semiloggrid@ii}\logsys@args@i} + {\def\coordsys@c{\semiloggrid@i}\logsys@args@i}} +\def\semiloggrid@i#1#2(#3,#4){{\color@begingroup + \coordgrid@calc + \grid@style + \@sethlogticks{\@hticksep}{#1}{#3}{0}{\vgridfromto{#2}{#4}}% + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{% + \multiput(0,\coordsys@a)(0,\coordsys@c)\coordsys@b + {\hgridfromto{#1}{#3}}}% + \color@endgroup}} +\def\semiloggrid@ii#1#2(#3,#4){{\color@begingroup + \grid@style + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vgridlength{\coordsys@h}}% + \@set@ticks{\vthickratio}{\@vticksep}{#2}{#4}{\z@}{% + \multiput(#1,\coordsys@a)(0,\coordsys@c)\coordsys@b + {\hgridlength{\coordsys@w}}}% + \color@endgroup}} +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% \begin{macro}{\logloggrid} +% \begin{macro}{\logloggrid@i} +% \begin{macro}{\logloggrid@ii} +% and nor do double-logarithmic grids. +% \begin{macrocode} +\newcommand{\logloggrid}{% + \def\@hticksep{50}% + \def\@vticksep{50}% + \@numblinefalse + \@ifstar{\def\coordsys@c{\logloggrid@ii}\logsys@args@i} + {\def\coordsys@c{\logloggrid@i}\logsys@args@i}} +\def\logloggrid@i#1#2(#3,#4){{\color@begingroup + \coordgrid@calc + \grid@style + \@sethlogticks{\@hticksep}{#1}{#3}{0}{\vgridfromto{#2}{#4}}% + \@setvlogticks{\@vticksep}{#2}{#4}{0}{\hgridfromto{#1}{#3}}% + \color@endgroup}} +\def\logloggrid@ii#1#2(#3,#4){{\color@begingroup + \grid@style + \@tempcnta=#3\relax + \advance\@tempcnta -#1\relax + \edef\coordsys@w{\the\@tempcnta}% + \@tempcnta=#4\relax + \advance\@tempcnta -#2\relax + \edef\coordsys@h{\the\@tempcnta}% + \@sethlogticks{\@hticksep}{#1}{#3}{#2}{\vgridlength{\coordsys@h}}% + \@setvlogticks{\@vticksep}{#2}{#4}{#1}{\hgridlength{\coordsys@w}}% + \color@endgroup}} +% +% \end{macrocode} +% \end{macro}\end{macro}\end{macro} +% +% +% \subsection{The \texttt{putfile} Maple Code} +% \begin{macrocode} +%<*putfile> +putfile := proc(fn::{string, list(string), set(string)}, + P::specfunc(anything, PLOT) ) + option `Copyright 2000-06 by Mogens Lemvig Hansen`; + description "version 1.1"; + local L, fns, i, V, scl, FH, ttl, pt, path, ext; + global StringTools; +% \end{macrocode} +% Process the options. +% \begin{macrocode} + L := [args[3..-1]]; + if hasoption(L, 'scale', scl, 'L') then + scl := evalf(scl); + if not type(scl, ['numeric', 'numeric']) then + error "the scale option must be [numeric, numeric] but got %1", + scl; + fi; + else + scl := [1,1]; + fi; + if L <> [] then + error "unknown options: %1", L; + fi; +% \end{macrocode} +% Pull the "CURVES" from the "PLOT" structure. +% \begin{macrocode} + L := map( `putfile/grabcurves`, [op(P)] ); +% \end{macrocode} +% If a single filename is given, we can construct a suitable list of filenames: +% The path ends with the last backslash, slash, or colon in "fn"; +% the extension begins with the last period after that. +% \begin{macrocode} + if type(fn, 'string') then + path := map(StringTools:-FirstFromRight, ["\\", "/", ":"], fn); + path := max(op(path)); + ext := StringTools:-FirstFromRight(".", fn[path+1..-1]); +% \end{macrocode} +% If there is not extension, prepare to append +% ".tex";\footnote{The extension \texttt{.tex} for these data files +% may not be logical, but it is what \TeX\ assumes in the +% \texttt{\bslash putfile} command, so at least we have consistent +% assumptions.} +% otherwise save and strip the extension. +% \begin{macrocode} + if ext = 0 then + ext := ".tex"; + fns := fn; + else + ext := fn[path+ext..-1]; + fns := fn[1..-length(ext)-1] + fi; +% \end{macrocode} +% Multiply the filename if necessary, and append the extension. +% \begin{macrocode} + if nops(L) = 1 then + fns := [fns]; + else + fns := [ seq(cat(fns, i), i=1..nops(L)) ]; + fi; + fns := map(cat, fns, ext); +% \end{macrocode} +% If we have a set or list or filenames, their number must match the number of +% "CURVES". +% \begin{macrocode} + else + fns := fn; + if nops(fns) <> nops(L) then + error "the number of filenames must match " + "the number of curves, " + "received %1 names but %2 curves.", + nops(fns), nops(L); + fi; + fi; +% \end{macrocode} +% Extract the view-port from the "PLOT" structure. +% \begin{macrocode} + V := select(type, [op(P)], 'specfunc'('anything', 'VIEW')); + if nops(V) <> 1 then + V := ['DEFAULT', 'DEFAULT']; + else + V := [ op([1,1], V), op([1,2], V) ]; + fi; + V := subs('DEFAULT'=Float(-infinity)..Float(infinity), V); +% \end{macrocode} +% Finally, extract the title, if any. +% The title will be included as a comment. +% Since the title could be a multi-line string, we must insert "%" characters +% after any new-lines. +% \begin{macrocode} + ttl := select(type, [op(P)], 'specfunc'('anything', 'TITLE')); + if nops(ttl) = 1 then + ttl := op([1,1], ttl); + ttl := StringTools:-SubstituteAll(ttl, "\n", "\n%% "); + fi; +% \end{macrocode} +% Fit the curves to the view-port, and scale as requested. +% \begin{macrocode} + L := map( `putfile/cleancurve`, L, V); + L := map2( map, u->[scl[1]*u[1], scl[2]*u[2]], L ); +% \end{macrocode} +% For each curve, write the title (if any), the view-port, and all the points to +% the file. +% \begin{macrocode} + for i from 1 to nops(L) do try + FH := fopen(fns[i], 'WRITE', 'TEXT'); + if type(ttl, 'string') then fprintf(FH, "%%%% %s\n", ttl) fi; + if scl <> [1,1] then fprintf(FH, "%% scaled %a\n", scl) fi; + V := [ map2(op, 1, L[i]), map2(op, 2, L[i]) ]; + V := map( u-> min(op(u))..max(op(u)), V ); + fprintf(FH, "%% horizontal range: %f .. %f\n", op(V[1])); + fprintf(FH, "%% vertical range: %f .. %f\n", op(V[2])); + for pt in L[i] do + fprintf(FH, "%f \t%f\n", op(pt)); + od; + finally fclose(FH); + end try end do; +end; +% \end{macrocode} +% +% The sub-routines that follow use Maple's naming convention for such. +% +% We are interested in "CURVES" objects in a "PLOT" structure. +% A "CURVES" object contains options (which we ignore) and lists of +% \meta{curve}s, where a \meta{curve} is a list of \meta{point}s and a +% \meta{point} is a list of length two usually containing two numeric values. +% If "x" is not a "CURVES", return nothing. If "x" is a +% "CURVES", extract the list of \meta{curve}s and return the +% corresponding sequence of \meta{curve}s. If the "PLOT" structure +% contains more than one "CURVES" object, the sequences returned by +% "putfile/grabcurves" will flatten to one sequence of \meta{curve}s +% \begin{macrocode} +`putfile/grabcurves` := proc(x) + option `Copyright 2000-06 by Mogens Lemvig Hansen`; + description "version 1.1"; + local L; + if op(0, x) = 'CURVES' then + L := [ op(x) ]; + L := select(type, L, 'list'); + RETURN(op(L)); + else + RETURN(NULL); + fi; +end; +% \end{macrocode} +% Each curve has to be fitted inside the view-port. +% The curve, "CC", is a list of points. +% The view-port, "V", is a list of the form +% \texttt{[numeric..numeric, numeric..numeric]}. +% \begin{macrocode} +`putfile/cleancurve` := proc(CC::list, V::list) + local C, B, pts, pt, m, i; + option `Copyright 2004-06 by Mogens Lemvig Hansen`; + description "version 1.1"; +% \end{macrocode} +% Remove any non-numeric points. +% \begin{macrocode} + C := select(type, CC, ['numeric', 'numeric']); + if nops(C) < 1 then error "no numeric points in %1", C fi; +% \end{macrocode} +% Then build a new list of point: each time a consecutive pair of points in +% "C" straddles a boundary of the view-port, add the point of intersection +% between the line through the two points and the view-port. +% \begin{macrocode} + B := C[1]; + for i from 2 to nops(C) do + if C[i] = C[i-1] then next fi; + pts := NULL; + if ( C[i-1][1] < lhs(V[1]) and C[i][1] > lhs(V[1]) ) + or ( C[i-1][1] > lhs(V[1]) and C[i][1] < lhs(V[1]) ) then + m := ( C[i-1][2] - C[i][2] ) / ( C[i-1][1] - C[i][1] ); + pt := lhs(V[1]); + pt := [ pt, m*(pt-C[i][1]) + C[i][2] ]; + pts := pts, pt; + fi; + if ( C[i-1][1] < rhs(V[1]) and C[i][1] > rhs(V[1]) ) + or ( C[i-1][1] > rhs(V[1]) and C[i][1] < rhs(V[1]) ) then + m := ( C[i-1][2] - C[i][2] ) / ( C[i-1][1] - C[i][1] ); + pt := rhs(V[1]); + pt := [ pt, m*(pt-C[i][1]) + C[i][2] ]; + pts := pts, pt; + fi; + if ( C[i-1][2] < lhs(V[2]) and C[i][2] > lhs(V[2]) ) + or ( C[i-1][2] > lhs(V[2]) and C[i][2] < lhs(V[2]) ) then + m := ( C[i-1][1] - C[i][1] ) / ( C[i-1][2] - C[i][2] ); + pt := lhs(V[2]); + pt := [ m*(pt-C[i][2]) + C[i][1], pt ]; + pts := pts, pt; + fi; + if ( C[i-1][2] < rhs(V[2]) and C[i][2] > rhs(V[2]) ) + or ( C[i-1][2] > rhs(V[2]) and C[i][2] < rhs(V[2]) ) then + m := ( C[i-1][1] - C[i][1] ) / ( C[i-1][2] - C[i][2] ); + pt := rhs(V[2]); + pt := [ m*(pt-C[i][2]) + C[i][1], pt ]; + pts := pts, pt; + fi; +% \end{macrocode} +% If the two points straddle more than one view-port boundary, we add one point +% for each boundary. The order of the added points must be in the direction +% of the curve. +% \begin{macrocode} + pts := [pts]; + if C[i-1][1] < C[i][1] then + pts := sort(pts, (u,v)->evalb(u[1] C[i][1] then + pts := sort(pts, (u,v)->evalb(u[1]>v[1])); + elif C[i-1][2] < C[i][2] then + pts := sort(pts, (u,v)->evalb(u[2] C[i][2] then + pts := sort(pts, (u,v)->evalb(u[2]>v[2])); + else + error "cannot happen"; + fi; + B := B, op(pts), C[i]; + od; + C := [B]; +% \end{macrocode} +% Finally remove the point outside the view-port. +% \begin{macrocode} + C := select( u->evalb(lhs(V[1])<=u[1] and u[1] <= rhs(V[1])), C); + C := select( u->evalb(lhs(V[2])<=u[2] and u[2] <= rhs(V[2])), C); + C; +end; +% +% \end{macrocode} +% +% \Finale +% diff --git a/macros/latex/contrib/coordsys/coordsys.ins b/macros/latex/contrib/coordsys/coordsys.ins new file mode 100644 index 0000000000..6533a29459 --- /dev/null +++ b/macros/latex/contrib/coordsys/coordsys.ins @@ -0,0 +1,51 @@ +% The coordsys and logsys packages, version 1.4. +% Run first this file, coordsys.ins, then coordsys.dtx +% through LaTeX and read the documentation in coordsys.dvi +% +\input docstrip.tex +\preamble + + + This is the coordsys and logsys packages + Copyright 2000-06 by Mogens Lemvig Hansen, + mlhansen@uniserve.com + +This program may be distributed and/or modified under the +conditions of the LaTeX Project Public License, either version 1.3 +of this license or (at your option) any later version. The latest +version of this license is in + http://www.latex-project.org/lppl.txt +and version 1.2 or later is part of all distributions of LaTeX +version 2003/12/01 or later. + +This program consists of the files coordsys.dtx and coordsys.ins + +\endpreamble +\generate{\file{coordsys.sty} {\from{coordsys.dtx}{coordsys}} + \file{logsys.sty} {\from{coordsys.dtx}{logsys}} +% \file{euclidgcd.sty}{\from{coordsys.dtx}{euclid}} + } + +{\catcode`\#=12\gdef\MetaPrefix{##}} +\preamble + + + This is the coordsys and logsys packages + Copyright 2000-06 by Mogens Lemvig Hansen, + mlhansen@uniserve.com + +This program may be distributed and/or modified under the +conditions of the LaTeX Project Public License, either version 1.3 +of this license or (at your option) any later version. 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