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| -rw-r--r-- | Master/texmf-dist/doc/latex/curve2e/manifest.txt | 34 | ||||
| -rw-r--r-- | Master/texmf-dist/source/latex/curve2e/curve2e.dtx | 1597 | ||||
| -rw-r--r-- | Master/texmf-dist/source/latex/curve2e/curve2e.ins | 42 | ||||
| -rw-r--r-- | Master/texmf-dist/tex/latex/curve2e/curve2e.sty | 660 | ||||
| -rw-r--r-- | Master/texmf-dist/tpm/curve2e.tpm | 29 |
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diff --git a/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf b/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf Binary files differnew file mode 100644 index 00000000000..f812e3f1e77 --- /dev/null +++ b/Master/texmf-dist/doc/latex/curve2e/curve2e.pdf diff --git a/Master/texmf-dist/doc/latex/curve2e/manifest.txt b/Master/texmf-dist/doc/latex/curve2e/manifest.txt new file mode 100644 index 00000000000..963f752522f --- /dev/null +++ b/Master/texmf-dist/doc/latex/curve2e/manifest.txt @@ -0,0 +1,34 @@ +The package bundle curve2e is composed of the following files + +curve2e.ins +curve2e.dtx +curve2e.pdf +mainfest.txt + +Maninfest.txt is this file. + +curve2e.dtx is the documented source file of package curve2e.sty; you get +curve2e.sty by running tex or latex on curve2e.ins. +You get the documentation by running latex on curve2e.dtx; curve2e.pdf already +contains the documentation in pdf format. + +The package has the lppl status of author maintained. + +Nevertheless this package is an extension to the standard LaTeX package pict2e, +so that this file is first of all submitted to the authors of pict2e, in case +they wanted to incorporate part or all of its contents in the official package +they maintain. Therefore any change must be controlled against the parent +package pict2e so as to avoid redefining what has already been incorporated in +the official package. Their e-mails are + +Rolf Niepraschk, Rolf.Niepraschk@ptb.de +Hubert Gaesslein, HubertJG@open.mind.de + + +If you prefer sending me your modifications, as long as I will maintain this +package, I will forward every (documented) suggestion or modification to the +authors of pict2e. + +Claudio Beccari + +claudio.beccari@polito.it
\ No newline at end of file diff --git a/Master/texmf-dist/source/latex/curve2e/curve2e.dtx b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx new file mode 100644 index 00000000000..0bfb7205754 --- /dev/null +++ b/Master/texmf-dist/source/latex/curve2e/curve2e.dtx @@ -0,0 +1,1597 @@ +% \iffalse +%% +%% File `curve2e.dtx'. +%% Copyright (C) 2005 Claudio Beccari all rights reserved. +%% +% What follows is the usual trick that is not typeset in the documentation +% dvi file that is produced by LaTeX; It is used to define the date, the version +% and the short descriptio that characterizes both this file and the package; +% the point is that |\ProvicesFile| is being read only by the driver, while +% |\ProvidePackage| goes to the stripped package file; It must be done before +% starting the documentation otherwise |\GetFileInfo| can't get the necessary +% information. +% \fi +%<*package> +% \begin{macrocode} +\NeedsTeXFormat{LaTeX2e} +%</package> +%<*driver> +\ProvidesFile{curve2e.dtx}% +%</driver> +%<+package>\ProvidesPackage{curve2e}% + [2005/08/15 v.0.10 Extension package for pict2e] +%<*package> +% \end{macrocode} +%</package> +% \iffalse +%<*driver> +\documentclass{ltxdoc} +\hfuzz 10pt +\usepackage{multicol} +\usepackage[ansinew]{inputenc} +\GetFileInfo{curve2e.dtx} +\title{The extension package \textsf{curve2e}\thanks{Version number +\fileversion; last revised \filedate.}} +\author{Claudio Beccari} +\begin{document} + \maketitle +\begin{multicols}{2} + \tableofcontents + \end{multicols} + \DocInput{curve2e.dtx} +\end{document} +%</driver> +% \fi +% +% \CheckSum{0} +% \begin{abstract} +% This file documents the |curve2e| extension package to the recent +% implementation of the |pict2e| bundle that has been described by Lamport +% himself in the second edition of his \LaTeX\ handbook. +% +% This extension redefines a couple of commands and introduces some more drawing +% facilities that allow to draw circular arcs and arbitrary curves with the +% minimum of user intervention. This beta version is open to the contribution of +% other users as well as it may be incorporated in other people's packages. +% Please cite the original author and the chain of contributors. +% \end{abstract} +% +% \section{Package \texttt{pict2e} and this extension \texttt{curve2e}} +% Package \texttt{pict2e} was announced in inssue 15 of \texttt{latexnews} +% around December 2003; it was declared that the new package would replace the +% dummy one that has been accompanying every realease of \LaTeXe\ since its +% beginnings in 1994. The dummy package was just issuing an info message that +% simply announced the temporary unavailability of the real package. +% +% Eventually Gäßlein and Niepraschk implemented what Lamport himself had already +% documented in the second edition of his \LaTeX\ handbook, that is a \LaTeX\ +% package that contained the macros capable of removing all the limitations +% contained in the standard commands of the original \texttt{picture} +% environment; specifically: +% \begin{enumerate} +% \item the line and vector slopes were limited to the ratios of relatively +% prime one digit integers of magnitude not exceeding 6 for lines and 4 for +% vectors; +% \item filled and unfilled full circles were limited by the necessarily +% bounded number of specific glyphs contained in the special \LaTeX\ +% \texttt{picture} fonts; +% \item quarter circles were also limited in their radii for the same reason; +% \item ovals (rectangles with rounded corners) could not be too small because +% of the unavailability of small radius quarter circles, nor could be too +% large, in the sense that after a certain radius the rounded corners remained +% the same and would not increase proportionally to the oval size. +% \item vector arrows had only one possible shape besides matching the limited +% number of vector slopes; +% \item for circles and inclined lines and vectors there were available just +% two possible thicknesses. +% \end{enumerate} +% +% The package \texttt{pict2e} removes most if not all the above limitations: +% \begin{enumerate} +% \item line and vector slopes are virtually unlimited; the only remainig +% limitation is that the direction coefficients must be three-digit integer +% numbers; they need not be relatively prime; +% \item filled and unfilled circles can be of any size; +% \item ovals can be designed with any specified corner curvature and there is +% virtually no limitation to such curvatures; of course corner radii should not +% exceed half the lower value between the base and the hight of the oval; +% \item there are two shapes for the arrow tips; the triangular one traditional +% with \LaTeX\ vectors, or the arrow tip with PostScript style. +% \item the |\linethicknes| command changes the thicknes of all lines, straight, +% curved, vertical, horizontal, arrow tipped, et cetera. +% \end{enumerate} +% +% This specific extension adds the following features +% \begin{enumerate} +% \item commands for setting the line terminations are introduced; the user can +% chose between square or rounded caps; the default is set to rounded caps; +% \item the |\line| macro is redefined so as to allow integer and fractional +% direction coefficients, but maintaining the same syntax as in the original +% \texttt{picture} environment; +% \item a new macro |\Line| is defined so as to avoid the need to specify the +% horizontal projection of inclined lines; +% \item a new macro |\LINE| joins two points specified with their coordinates; +% of course there is no need to use the |\put| command with this line +% specification; +% \item similar macros are redefined for vectors; |\vector| redefines the +% original macro but with the vector slope limitation removed; |\Vector| gets +% specified with its two horizontal and vertical components; |\VECTOR| +% joins two specified points (without using the |\put| command) with the arrow +% pointing to the second point; +% \item a new macro |\polyline| for drawing polygonal lines is defined that +% accepts from two vertices up to an arbitrary (reasonably limited) number of +% them; +% \item a new macro |\Arc| is defined in order to draw an arc with arbitrary +% radius and arbitrary angle amplitude; this amplitude is specified in +% sexagesimal degrees, not in radians; +% \item two new macros are defined in order to draw circular arcs with one +% arrow at one or both ends; +% \item a new macro |\Curve| is defined so as to draw arbitrary curved lines +% by means of third order Bézier splines; the |\Curve| macro requires only the +% curve nodes and the direction of the tangents at each node. +% \end{enumerate} +% +% In order to make the necessary calculations many macros have been defined so +% as to use complex number to manipulate point coordinates, directions, +% rotations and the like. The trigonometric functions have also been defined in +% a way that the author believes to be more efficient that that implied by the +% \texttt{trig} package; in any case the macro names are sufficiently +% different to accomodate both definitions in the same \LaTeX\ run. +% +% Many aspects of this extension could be fine tuned for better performance; +% many new commands could be defined in order to further extend this extension. +% If the new service macros are accepted by other \TeX\ and \LaTeX\ programmers, +% this beta version could become the start for a real extension of the +% \texttt{pict2e} package or even become a part of it. +% +% For this reason I suppose that every enhanceent should be submitted to +% Gäßlein and Niepraschk who are the prime maintainers of \texttt{pict2e}; +% they only can decide wether or not to incorporate new macros in their package. +% +% +% \StopEventually{% +% \begin{thebibliography}{9} +% \bibitem{pict2e} Gäßlein H.\ and Niepraschk R., \emph{The \texttt{pict2e} +% package}, PDF document attached to the ``new'' \texttt{pict2e} bundle; the +% bundle may be downloaded from any CTAN archive or one of their mirrors. +% \end{thebibliography} +% } +% +% \section{Source code} +% \subsection{Some preliminary extensions to the \texttt{pict2e} package} +% The necessary preliminary code has already been introduced. Here we require +% the \texttt{color} package and the \texttt{pict2e} one; for the latter one we +% make sure that a sufficiently recent version is used. +% \begin{macrocode} +\RequirePackage{color} +\RequirePackageWithOptions{pict2e}[2004/06/01] +% \end{macrocode} +% Next we define the line terminators and joins; the following definitions work +% correctly if the \texttt{dvips} or the \texttt{pdftex} driver are specified; +% probably other modes should be added so as to be consistent with +% \texttt{pict2e}. +% \begin{macrocode} +\ifcase\pIIe@mode\relax +\or %Postscript + \def\roundcap{\special{ps:: 1 setlinecap}}% + \def\squarecap{\special{ps:: 0 setlinecap}}% + \def\roundjoin{\special{ps:: 1 setlinejoin}}% + \def\beveljoin{\special{ps:: 2 setlinejoin}}% +\or %pdf + \def\roundcap{\pdfliteral{1 J}}% + \def\squarecap{\pdfliteral{0 J}}% + \def\roundjoin{\pdfliteral{1 j}}% + \def\beveljoin{\pdfliteral{2 j}}% +\fi +% \end{macrocode} +% +% The next macros are just for debugging. With the \texttt{tracing} package it +% would probably be better to define other macros, but this is not for the +% users, but for the devellopers. +% \begin{macrocode} +\def\TRON{\tracingcommands\tw@ \tracingmacros\tw@}% +\def\TROF{\tracingcommands\z@ \tracingmacros\z@}% +% \end{macrocode} +% +% Next we define some new dimension registers that will be used by the +% subsequent macros; should they be already defined, there will not be any +% redefinition; nevertheless the macros should be sufficiently protected so as +% avoid overwriting register values loaded by other macro fpackages. +% \begin{macrocode} +\ifx\undefined\@tdA \newdimen\@tdA \fi +\ifx\undefined\@tdB \newdimen\@tdB \fi +\ifx\undefined\@tdC \newdimen\@tdC \fi +\ifx\undefined\@tdD \newdimen\@tdD \fi +\ifx\undefined\@tdE \newdimen\@tdE \fi +\ifx\undefined\@tdF \newdimen\@tdF \fi +\ifx\undefined\defaultlinewidth \newdimen\defaultlinewidth \fi +% \end{macrocode} +% +% It is better to define a macro for setting a different value for the line and +% curve thicknesses; the `|\defaultlinewidth| should contain the +% equivalent of |\@wholewidth|, that is the thickness of thick lines; thin lines +% are half as thick; so when the default line thickness is specified to, say, +% 1pt, thick lines will be 1pt thick and thin lines will be 0.5pt thick. The +% default whole width of thick lines is 0,8pt, but this is specified in the +% kernel of \LaTeX\ and\slash or in \texttt{pict2e}. +% \begin{macrocode} +\newcommand\defaultlinethickness[1]{\defaultlinewidth=#1\relax +\def\thicklines{\linethickness{\defaultlinewidth}}% +\def\thinlines{\linethickness{.5\defaultlinewidth}}% +\thinlines\ignorespaces} +% \end{macrocode} +% The |\ignorespaces| at the end of this and the subsequent macros is for +% avoiding spurious spaces to get into the picture that is being drawn, because +% these spaces introduce picture deformities often difficult to spot and +% eliminate. +% +% \subsubsection{Improved line and vector macros} +% The new macro |\Line| allows to draw an arbitrary inclination line as if it +% was a polygon with just two vertices. This line should be set by means of a +% |\put| command so that its starting point is always at a relative 0,0 +% coordinate point. The two arguments define the horizontal and the +% vertical component respectively. +% \begin{macrocode} +\def\Line(#1,#2){\pIIe@moveto\z@\z@ + \pIIe@lineto{#1\unitlength}{#2\unitlength}\pIIe@strokeGraph}% +% \end{macrocode} +% +% A similar macro |\LINE| operates between two explicit points with absolute +% coordinates, instead of relative to the position specified by a |\put| +% command; it resorts to the |\polyline| macro that is to be defined in a while. +% \begin{macrocode} +\def\LINE(#1)(#2){\polyline(#1)(#2)}% +% \end{macrocode} +% +% The |\line| macro is redefined by making use of a new division routine that +% receives in input two dimensions and yields on output their fractional ratio. +% The beginning of the macro definition is the same as that of \texttt{pict2e}: +% \begin{macrocode} +\def\line(#1)#2{\begingroup + \@linelen #2\unitlength + \ifdim\@linelen<\z@\@badlinearg\else +% \end{macrocode} +% but as soon as it is verified that the line length is not zero, things +% change remarkably; in facts the machinery for complex numbers is invoked: +% |\DirOfVect| takes the only macro argument (that actually contains a comma +% separated pair of fractional numbers) and copies it to |\Dir@line| (an +% arbitrarily named control sequence) after renormalizing to unit magnitude; +% this is passed to |GetCoord| that separates the two components into the +% control sequences |\d@mX| and|\d@mY|; these in turn are the values that are +% actually operated upon by the subsequent commands. +% \begin{macrocode} + \expandafter\DirOfVect#1to\Dir@line + \GetCoord(\Dir@line)\d@mX\d@mY +% \end{macrocode} +% The normalized vector direction is actually formed with the directing cosines +% of the line direction; since the line length is actually the horizontal +% component for non vertical lines, it is necessary to compute the actual line +% length for non vertical lines by dividing the given length by the +% magnitude of horizontal cosine |\d@mX|, and the line legth is accordingly +% scaled: +% \begin{macrocode} + \ifdim\d@mX\p@=\z@\else + \DividE\ifdim\d@mX\p@<\z@-\fi\p@ by\d@mX\p@ to\sc@lelen + \@linelen=\sc@lelen\@linelen + \fi +% \end{macrocode} +% Finally the \texttt{moveto}, \texttt{lineto} and \texttt{stroke} language +% keywords are involed by means of the internal \texttt{pict2e} commands in +% order to draw the line. Notice that even vertical lines are drawn with the +% ``PostScript'' commands instead of resorting to the dvi low level language +% that was used both in \texttt{pict2e} and in the original \texttt{picture} +% commands; it had a meaning in the old times, but it certainly does not have +% any when lines are drawn by the driver that drives the output to a visible +% document form, not by \TeX\ the program. +% \begin{macrocode} + \pIIe@moveto\z@\z@ + \pIIe@lineto{\d@mX\@linelen}{\d@mY\@linelen}% + \pIIe@strokeGraph +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% The new macro |\GetCoord| splits a vector (or complex number) specification +% into its components: +% \begin{macrocode} +\def\GetCoord(#1)#2#3{% +\expandafter\SplitNod@\expandafter(#1)#2#3\ignorespaces} +% \end{macrocode} +% But the macro that does the real work is |\SplitNod@|: +% \begin{macrocode} +\def\SplitNod@(#1,#2)#3#4{\edef#3{#1}\edef#4{#2}}% +% \end{macrocode} +% +% The redifinitions and the new definitions for vectors are a little more +% complicated than with segments, because each vector is drawn as a filled +% contour; the original \texttt{pict2e} macro checks if the slopes are +% corrsponding to the limitations specified by Lamport (integer three digit +% signed numbers) and sets up a transformation in order to make it possible to +% draw each vector as an horizontal left-to-right arrow and then to rotate it by +% its angle about its tail point; actually there are two macros for tracing the +% contours that are eventually filled by the principal macro; each contour +% macro draws the vector with a \LaTeX\ or a PostScript arrow whose parameters +% are specified by default or may be taken from the parameters taken from the +%\texttt{PSTricks} package if this one is loaded before \texttt{pict2e}; in any +% case we did not change the contour drawing macros because if they are +% modified the same modification is passed on to the arrows drawn with the +% \texttt{curve2e} package redefinitions. +% +% Because of these features the redefinitions and the new macros are different +% from those used for straight lines. +% +% We start with the redefinition of |\vector| and we use the machinery for +% vectors (as complex numbers) we used for |\line|. +% \begin{macrocode} + \def\vector(#1)#2{% + \begingroup + \GetCoord(#1)\d@mX\d@mY + \@linelen#2\unitlength +% \end{macrocode} +% As in \texttt{pict2e} we avoid tracing vectors if the slope parameters are +% both zero. +% \begin{macrocode} + \ifdim\d@mX\p@=\z@\ifdim\d@mY\p@=\z@\@badlinearg\fi\fi +% \end{macrocode} +% But we check only for the positive nature of the $l_x$ component; if it is +% negative, we simply change sign instead of blocking the typesetting process. +% This is useful also for macros |\Vector| and |\VECTOR| to be defined in a +% while. +% \begin{macrocode} + \ifdim\@linelen<\z@ \@linelen=-\@linelen\fi +% \end{macrocode} +% We now make a vector with the slope direction even if one or the other is +% zero and we determine its direction; the real and imaginary parts of the +% direction vector are also the values we need for the subsequent rotation. +% \begin{macrocode} + \MakeVectorFrom\d@mX\d@mY to\@Vect + \DirOfVect\@Vect to\Dir@Vect +% \end{macrocode} +% In order to be compatible with the original \texttt{pict2e} I need to +% transform the components of the vector direction in lengths with the specific +% names |\@xdim| and |\@ydim| +% \begin{macrocode} + \YpartOfVect\Dir@Vect to\@ynum \@ydim=\@ynum\p@ + \XpartOfVect\Dir@Vect to\@xnum \@xdim=\@xnum\p@ +% \end{macrocode} +% If the vector is really sloping we need to scale the $l_x$ component in order +% to get the vector total length; we have to divide by the cosine of the vector +% inclination wich is the real part of the vector direction. I use my division +% macro; since it yields a ``factor'' I directly use it to scale the lenght of +% the vector. I finally memorize the true vector lenth in the internal +% dimension |@tdB| +% \begin{macrocode} + \ifdim\d@mX\p@=\z@ + \else\ifdim\d@mY\p@=\z@ + \else + \DividE\ifdim\@xnum\p@<\z@-\fi\p@ by\@xnum\p@ to\sc@lelen + \@linelen=\sc@lelen\@linelen + \fi + \fi + \@tdB=\@linelen +% \end{macrocode} +% The remaining code is defintely similar to that of \texttt{pict2e}; the +% real difference consists in the fact that the arrow is designed by itself +% without the stem; but it is placed at the vector end; therefore the first +% statement is just the transformation matrix used by the output driver to +% rotate the arrow tip and to displace it the right amount. But in order +% to draw only the arrow tip I have to set the |\@linelen| length to zero. +% \begin{macrocode} +\pIIe@concat\@xdim\@ydim{-\@ydim}\@xdim{\@xnum\@linelen}{\@ynum\@linelen}% + \@linelen\z@ + \pIIe@vector + \pIIe@fillGraph +% \end{macrocode} +% Now we can restore the stem lenght that must be shortened by the dimension of +% the arrow; examinimng the documentation of \texttt{pict2e} we discover that +% we have to shorten it by an approximate amount of $AL$ (with the notations of +% \texttt{pict2e}, figs~10 and~11); the arrow tip paramenters are stored in +% certain variables with which we can determine the amount of the stem +% shortening; if the stem was too short and the new length is negative, we +% refrain from designing such stem. +% \begin{macrocode} + \@linelen=\@tdB + \@tdA=\pIIe@FAW\@wholewidth + \@tdA=\pIIe@FAL\@tdA + \advance\@linelen-\@tdA + \ifdim\@linelen>\z@ + \pIIe@moveto\z@\z@ + \pIIe@lineto{\@xnum\@linelen}{\@ynum\@linelen}% + \pIIe@strokeGraph\fi + \endgroup} +% \end{macrocode} +% +% Now we define the macro that does not require the specification of the length +% or the $l_x$ lenght component; the way the new |\vector| macro works does not +% actually require this specification, because \TeX\ can compute the vector +% length, provided the two direction components are exacly the horizontal and +% vertical vector components. +% \begin{macrocode} +\def\Vector(#1,#2){\vector(#1,#2){#1}} +% \end{macrocode} +% +% On the opposite the next macro specifies a vector by means of the coordinates +% of its end points; the first point is where the vector starts, and the second +% point is the arrow side. +% \begin{macrocode} +\def\VECTOR(#1)(#2){\begingroup +\SubVect#1 from #2 to \@tempa +\expandafter\put\expandafter(#1){\expandafter\Vector\expandafter(\@tempa)}% +\endgroup\ignorespaces} +% \end{macrocode} +% +% The \texttt{pict2e} documentation says that if the vector length is zero the +% macro designs only the arrow tip; this may work with macro |\vector|, +% certainly not with |\Vector| and |\VECTOR|. This might be useful for adding +% an arrow tip to a circular arc +% +% \subsubsection{Polygonal lines} +% We now define the polygonal line macro; its syntax is very simple +% \begin{flushleft}\ttfamily +% \cs{polygonal}(\rmfamily{P}$_0$)(\rmfamily{P}$_1$)\rmfamily{P}$_2$)\dots +% (\rmfamily{P}$_n$) +% \end{flushleft} +% In order to write a recursive macro we need aliases for the parentheses; +% actually we need only the left parenthesis, but some editors complain about +% unmathched delimiters, so we define an alias also for the right parenthesis. +% \begin{macrocode} +\let\lp@r( \let\rp@r) +% \end{macrocode} +% The first call to |\polyline| examines the first point coordinates and moves +% the drawing position to this point; afterwards it looks for the second point +% coordinates; they start with a left parenthesis; if this is found the +% coordinates should be there, but if the left parenthesis is missing (possibly +% preceeded by spaces that are ignored by the |\@ifnextchar| macro) then a +% warning message is output together with the line number where the missing +% parenthesis causes the warning: beware, this line number might point to +% several lines further on along the source file! +% \begin{macrocode} +\def\polyline(#1){\beveljoin\GetCoord(#1)\d@mX\d@mY + \pIIe@moveto{\d@mX\unitlength}{\d@mY\unitlength}% + \@ifnextchar\lp@r{\p@lyline}{% + \PackageWarning{curve2e}% + {Polygonal lines require at least two vertices!\MessageBreak + Control your polygonal line specification\MessageBreak}% + \ignorespaces}} +% \end{macrocode} +% But if there is a second or further point coordinate the recursive macro +% |\p@lyline| is called; it works on the next point and checks for a further +% point; if such a point exists it calls itself, otherwise it terminates the +% polygonal line by stroking it. +% \begin{macrocode} +\def\p@lyline(#1){\GetCoord(#1)\d@mX\d@mY + \pIIe@lineto{\d@mX\unitlength}{\d@mY\unitlength}% + \@ifnextchar\lp@r{\p@lyline}{\pIIe@strokeGraph\ignorespaces}} +% \end{macrocode} +% +% \subsubsection{The red service grid} +% The next command is very useful for debugging while editing one's drawings; +% it draws a red grid with square meshes that are ten drawing units apart; +% there is no graduation along the grid, since it is supposed to be a debugging +% aid and the user should know what he/she is doing; nevertheless it is +% advisable to displace the grid by means of a |\put| command so that its grid +% lines coincide with the graph coordinates multiples of 10. Missing to do so +% the readings become cumbersome. The |\RoundUp| macros provide to increase the +% grid dimensions to integer multiples of ten. +% \begin{macrocode} +\def\GraphGrid(#1,#2){\begingroup\textcolor{red}{\linethickness{.1\p@}% +\RoundUp#1modulo10to\@GridWd \RoundUp#2modulo10to\@GridHt +\@tempcnta=\@GridWd \divide\@tempcnta10\relax \advance\@tempcnta\@ne +\multiput(0,0)(10,0){\@tempcnta}{\line(0,1){\@GridHt}}% +\@tempcnta=\@GridHt \divide\@tempcnta10\advance\@tempcnta\@ne +\multiput(0,0)(0,10){\@tempcnta}{\line(1,0){\@GridWd}}\thinlines}% +\endgroup\ignorespaces} +% \end{macrocode} +% Rounding uo is useful because also the grid margins fall on coordinates +% multiples of 10. It resosrts to the |\Integer| macro that will be described in +% a while. +% \begin{macrocode} +\def\RoundUp#1modulo#2to#3{\expandafter\@tempcnta\Integer#1.??% +\count254\@tempcnta\divide\count254by#2\relax +\multiply\count254by#2\relax +\count252\@tempcnta\advance\count252-\count254 +\ifnum\count252>0\advance\count252-#2\relax +\advance\@tempcnta-\count252\fi\edef#3{\number\@tempcnta}\ignorespaces}% +% \end{macrocode} +% The |\Integer| macro takes a possibly fractional number whose decimal +% separator, if present, \textit{must} be the decimal point and uses the point +% as an argunent delimiter If one has the doubt that the number being passed +% to |\Integer| might be an integer, he/she should call the macro with a +% further point; +% if the argument is truly integer this point works as the delimiter of the +% integer part; if the argument being passed is fractional this extra point +% gets discarded as well as the fractional part of the number. +% \begin{macrocode} +\def\Integer#1.#2??{#1}% +% \end{macrocode} +% +% \subsection{The new division macro} +% Now comes one of the most important macros in the whole package: the division +% macro; it takes two lengths as imput values ant computes their fractional +% ratio. +% It must take care of the signs, so that it examines the operand signs and +% determines the result sign separately conserving this computed sign in the +% macro |\segno|; this done, we are sure that both operands are or are +% made positive; should the +% numerator be zero it directly issues the zero quotient; should the +% denominator be zero it ouputs a signed ``infinity'', that is the maximun +% allowable length measured in points that \TeX\ can deal with. +% Since the result is assigned a value, the calling statement must pass as the +% third argument eiter a control sequence or an active character. Of course the +% first operand is the dividend, the second the divisor and the third the +% quotient. +% \begin{macrocode} +\ifx\DividE\undefined + \def\DividE#1by#2to#3{% + \begingroup + \dimendef\Numer=254\relax \dimendef\Denom=252\relax + \countdef\Num 254\relax + \countdef\Den 252\relax + \countdef\I=250\relax + \Numer #1\relax \Denom #2\relax + \ifdim\Denom<\z@ \Denom -\Denom \Numer -\Numer\fi + \def\segno{}\ifdim\Numer<\z@ \def\segno{-}\Numer -\Numer\fi + \ifdim\Denom=\z@ + \ifdim\Numer>\z@\def\Q{16383.99999}\else\def\Q{-16383.99999}\fi + \else + \Num=\Numer \Den=\Denom \divide\Num\Den + \edef\Q{\number\Num.}% + \advance\Numer -\Q\Denom \I=6\relax + \@whilenum \I>\z@ \do{\DividEDec\advance\I\m@ne}% + \fi + \xdef#3{\segno\Q}\endgroup + }% +% \end{macrocode} +% The |\DividEDec| macro takes the remainder of the previous division, +% multiplies it by 10, computes a one digit quotient that postfixes to the +% previous overall quotient, and computes the next remainder; all operations +% are done on integer registers to whom the dimensional operands are assigned +% so that the mentioned registers acquire the measures of the dimensions in +% scaled points; \TeX\ is called to perform integer arithmetics, but the long +% division takes care of the decimal separator and of the suitable number of +% fractional digits. +% \begin{macrocode} + \def\DividEDec{\Numer=10\Numer \Num=\Numer \divide\Num\Den + \edef\q{\number\Num}\edef\Q{\Q\q}\advance\Numer -\q\Denom}% +\fi +% \end{macrocode} +% In the above code the |\begingroup|\dots|\endgroup| maintain all registers +% local so that ony the result must be globally defined. The |\ifx|\dots|\fi| +% construct assures the division machinery is not redefined; I use it in so +% many packages that its better not to mix up things even with slightly +% different definitions. +% +% The next two macros are one of the myriad variants of the dirty trick used by +% Knuth for separating a measure from its units that \textit{must} be points, +% ``\texttt{pt}''; One has to call |\Numero| with a control sequence and a +% dimension; the dimension value in points is assinged to the control sequence. +% \begin{macrocode} +\ifx\undefined\@Numero% s + {\let\cc\catcode \cc`p=12\cc`t=12\gdef\@Numero#1pt{#1}}% +\fi +\ifx\undefined\Numero + \def\Numero#1#2{\dimen254 +#2\edef#1{\expandafter\@Numero\the\dimen254}\ignorespaces}% +\fi +% \end{macrocode} +% For both macros the |\ifx|\dots|\fi| constructs avoids messing up the +% definitions I have in several packages. +% +% \subsection{Trigonometric functions} +% We now start with trigonometric functions. We define the macros |\SinOf|, +% |\CosOf| and |\TanOf| (we might define also |\CotOf|, but the cotangent does +% not appear so essential) by means of the parametric formulas that require the +% knowledge of the tangento of the half angle. We want to specify the angeles +% in sexagesimal degrees, not in radians, so we can make accurate reductions to +% the main quadrants. we use the fromulas +% \begin{eqnarray*} +% \sin\theta &=& \frac{2}{\cot x + \tan x}\\ +% \cos\theta &=& \frac{\cot x - \tan x}{\cot x + \tan x}\\ +% \tan\theta &=& \frac{2}{\cot x - \tan x}\\ +% \noalign{\hbox{where}} +% x &=& \theta/114.591559 +% \end{eqnarray*} +% is the half angle in degrees converted to radians. +% +% We use this slightly modified set of parametric formulas because the cotangent +% of $x$ is a by product of the computation of the tangent of $x$; in this way +% we avoid computing the squares of numbers that might lead to overflows. For +% the same reason we avoid computing the value of the trigonometric functions +% in proximity of the value zero (and the other values that might involve high +% tangent or cotangent values) and in that case we prefer to approximate the +% small angle function value with its first or second order truncation of the +% McLaurin series; in facts for angles whose magnitude is smaller than $1^\circ$ +% the magnitude of the independent variable $y=2x$ (the angle in degress +% converted to radians) is so small (less than 0.017) that the sine and tangent +% can be freely approximated with $y$ itself (the error being smaller than +% approximately $10^{-6}$), while the cosine can be freely approximated with +% the formula $1-0.5y^2$ (the error being smaller than about $4\cdot10^{-9}$). +% +% We keep using grouping so that internal variables are local to these groups +% and do not mess up other things. +% +% The first macro is the service routine that computes the tangent and the +% cotangent of the half angle in radians; since we have to use always the +% reciprocal if this value, we call it |\X| but ins spite of the similarity it +% is the reciprocal of $x$. Notice that parameter \texttt{\#1} must be a length. +% \begin{macrocode} +\def\g@tTanCotanFrom#1to#2and#3{% +\DividE 114.591559\p@ by#1to\X \@tdB=\X\p@ +% \end{macrocode} +% Computations are done with the help of counter |\I|, of the length |\@tdB|, +% and the auxiliary control sequences |\Tan| and |\Cot| whose meaning is +% transparent. The iterative process controlled by |\@whilenum| implements the +% (truncated) continued fraction expansion of the tangent function +% \[ +% \tan x = \frac{1}{\displaystyle \frac{1\mathstrut}{\displaystyle x} +% -\frac{1}{\displaystyle \frac{3\mathstrut}{\displaystyle x} +% -\frac{1}{\displaystyle \frac{5\mathstrut}{\displaystyle x} +% -\frac{1}{\displaystyle \frac{7\mathstrut}{\displaystyle x} +% -\frac{1}{\displaystyle \frac{9\mathstrut}{\displaystyle x} +% -\frac{1}{\displaystyle \frac{11\mathstrut}{\displaystyle x} +% -\cdots}}}}}} +% \] +% \begin{macrocode} +\countdef\I=254\def\Tan{0}\I=11\relax +\@whilenum\I>\z@\do{% + \@tdC=\Tan\p@ \@tdD=\I\@tdB + \advance\@tdD-\@tdC \DividE\p@ by\@tdD to\Tan + \advance\I-2\relax}% +\def#2{\Tan}\DividE\p@ by\Tan\p@ to\Cot \def#3{\Cot}% +\ignorespaces}% +% \end{macrocode} +% +% Now that we have the macro for computing the tangent and cotangent of the +% half angle, we can compute the real trigonometric functions we are interesed +% in. The sine value is computed after reducing the sine argument to the +% interval $0^\circ< \theta<180^\circ$; actually special values such as +% $0^\circ$,$90^\circ$, $180^\circ$, et cetera, are taken care separtely, so +% that CPU time is saved for these special cases. The sine sign is taken care +% separately accordinng to the quadrant of the sine argument. +% \begin{macrocode} +\def\SinOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>\z@% + \@whiledim\@tdA>180\p@\do{\advance\@tdA -360\p@}% +\else% + \@whiledim\@tdA<-180\p@\do{\advance\@tdA 360\p@}% +\fi \ifdim\@tdA=\z@ + \gdef#2{0}% +\else + \ifdim\@tdA>\z@ + \def\Segno{+}% + \else + \def\Segno{-}% + \@tdA=-\@tdA + \fi + \ifdim\@tdA>90\p@ + \@tdA=-\@tdA \advance\@tdA 180\p@ + \fi + \ifdim\@tdA=90\p@ + \xdef#2{\Segno1}% + \else + \ifdim\@tdA=180\p@ + \gdef#2{0}% + \else + \ifdim\@tdA<\p@ + \@tdA=\Segno0.0174533\@tdA + \DividE\@tdA by\p@ to#2% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA=\T\p@ \advance\@tdA \Tp\p@ + \DividE \Segno2\p@ by\@tdA to#2% + \fi + \fi + \fi +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% +% For the computation of the cosine we behave in a similar way. +% \begin{macrocode} +\def\CosOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>\z@% + \@whiledim\@tdA>360\p@\do{\advance\@tdA -360\p@}% +\else% + \@whiledim\@tdA<\z@\do{\advance\@tdA 360\p@}% +\fi +% +\ifdim\@tdA>180\p@ + \@tdA=-\@tdA \advance\@tdA 360\p@ +\fi +% +\ifdim\@tdA<90\p@ + \def\Segno{+}% +\else + \def\Segno{-}% + \@tdA=-\@tdA \advance\@tdA 180\p@ +\fi +\ifdim\@tdA=\z@ + \gdef#2{\Segno1}% +\else + \ifdim\@tdA<\p@ + \@tdA=0.0174533\@tdA \Numero\@tempA\@tdA + \@tdA=\@tempA\@tdA \@tdA=-.5\@tdA + \advance\@tdA \p@ + \DividE\@tdA by\p@ to#2% + \else + \ifdim\@tdA=90\p@ + \gdef#2{0}% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA=\Tp\p@ \advance\@tdA-\T\p@ + \@tdB=\Tp\p@ \advance\@tdB\T\p@ + \DividE\Segno\@tdA by\@tdB to#2% + \fi + \fi +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% +% For the tangent computation we behave in a similar way, except that we +% consider the fundamantal interval as $0^\circ<\theta<90^\circ$; for the odd +% multiples of $90^\circ$ we assign the result a \TeX\ infinity value, that is +% the maximum number in points a dimension can be. +% \begin{macrocode} +\def\TanOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>90\p@% + \@whiledim\@tdA>90\p@\do{\advance\@tdA -180\p@}% +\else% + \@whiledim\@tdA<-90\p@\do{\advance\@tdA 180\p@}% +\fi% +\ifdim\@tdA=\z@% + \gdef#2{0}% +\else + \ifdim\@tdA>\z@ + \def\Segno{+}% + \else + \def\Segno{-}% + \@tdA=-\@tdA + \fi + \ifdim\@tdA=90\p@ + \xdef#2{\Segno16383.99999}% + \else + \ifdim\@tdA<\p@ + \@tdA=\Segno0.0174533\@tdA + \DividE\@tdA by\p@ to#2% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA\Tp\p@ \advance\@tdA -\T\p@ + \DividE\Segno2\p@ by\@tdA to#2% + \fi + \fi +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% +% \subsection{Arcs and curves preliminary information} +% We would like to define now a macro for drawing circular arcs of any radius +% and any angular aperture; the macro should require the arc center, the +% arc starting point and the angular aperture. The command should have the +% following syntax: +% \begin{flushleft}\ttfamily +% \cs{Arc}(\meta{{\rmfamily center}})(\meta{{\rmfamily starting +% point}}){\meta{{\rmfamily angle}}} +% \end{flushleft} +% If the \meta{angle} is positive the arc runs counterclokwise from the +% starting point; clockwise if it's negative. +% +% It's necessary to detrmine the end point and the control points of the +% Bézier spline(s) that make up the circular arc. +% +% The end point is obtained from the rotation of the starting point around the +% center; but the \texttt{pict2e} comand |\pIIe@rotate| is such that the +% pivoting point appears to be non relocatable. +% It is therefore necessary to resort to low level \TeX\ commands and the +% defined trigonometric functions and a set of macros that operate on complex +% numbers used as vector scale-rotate operators. +% +% \subsection{Complex number macros} +% We need therefore macros for summing, subtracting, multiplying, dividing +% complex numbers, for determining they directions (unit vectors); a unit vector +% is the complex number divided by its magnitude so that the result is the +% cartesian form of the Euler's equation +% \[ +% \mathrm{e}^{\mathrm{j}\phi} = \cos\phi+\mathrm{j}\sin\phi +% \] +% +% The magnitude of a vector id determined by taking a clever square root of a +% function of the real and the imaginary parts; see further on. +% +% It's better to represent each complex number with one control sequence; this +% implies frequent assembling and disassembling the pair of real numbers that +% make up a complex number. These real components are assembled into the +% defining control sequence as a couple of coordinates, i.e.\ two comma +% separated integer or fractional signed decimal numbers. +% +% For assembling two real numbers into a complex number we use the following +% elementary macro: +% \begin{macrocode} +\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}\ignorespaces}% +% \end{macrocode} +% Another elementary macro copies a complex number into another one: +% \begin{macrocode} +\def\CopyVect#1to#2{\edef#2{#1}\ignorespaces}% +% \end{macrocode} +% The magnitude is determined with the macro |\ModOfVect| with delimited +% arguments; as usual it is assumed that the results are retrieved by means of +% control sequences, not used directly. +% +% The magnitude $M$ is determined by taking the moduli of the real and +% immaginary parts, changing their signs if necessary; the larger component is +% then taken as the reference one so that, if $a$ is larger than $b$, the +% square root of the sum of their squares is computed as such: +% \[ +% M = \sqrt{a^2+b^2} = a\sqrt{1+(b/a)^2} +% \] +% In this way the radicand never exceeds 2 and its is quite easy taking its +% square root by means of the Newton iterative process; due to the quadratic +% convergence, five iterations are more than sufficient. When one of the +% components is zero, the Newton iterative process is skipped. The overall +% macro is the following: +% \begin{macrocode} +\def\ModOfVect#1to#2{\GetCoord(#1)\t@X\t@Y +\@tempdima=\t@X\p@ \ifdim\@tempdima<\z@ \@tempdima=-\@tempdima\fi +\@tempdimb=\t@Y\p@ \ifdim\@tempdimb<\z@ \@tempdimb=-\@tempdimb\fi +\ifdim\@tempdima>\@tempdimb + \DividE\@tempdimb by\@tempdima to\@T + \@tempdimc=\@tempdima +\else + \DividE\@tempdima by\@tempdimb to\@T + \@tempdimc=\@tempdimb +\fi +\ifdim\@T\p@>\z@ + \@tempdima=\@T\p@ \@tempdima=\@T\@tempdima + \advance\@tempdima\p@ % + \@tempdimb=\p@% + \@tempcnta=5\relax + \@whilenum\@tempcnta>\z@\do{\DividE\@tempdima by\@tempdimb to\@T + \advance\@tempdimb \@T\p@ \@tempdimb=.5\@tempdimb + \advance\@tempcnta\m@ne}%\ + \@tempdimc=\@T\@tempdimc +\fi +\Numero#2\@tempdimc +\ignorespaces}% +% \end{macrocode} +% As a byproduct of the computation the control sequence |\@tempdimc| contains +% the vector or complex number magnitude multiplied by the length of one point. +% +% Since the macro for determining the magnitude of a vector is available, we +% can now normalize the vector to its magnitude, therefore getting the cartesian +% form of the direction vector. If by any chance the direction of the null +% vector is requested, the output is again the null vector, without +% normalization. +% \begin{macrocode} +\def\DirOfVect#1to#2{\GetCoord(#1)\t@X\t@Y +\ModOfVect#1to\@tempa +\ifdim\@tempdimc=\z@\else + \DividE\t@X\p@ by\@tempdimc to\t@X + \DividE\t@Y\p@ by\@tempdimc to\t@Y + \MakeVectorFrom\t@X\t@Y to#2\relax +\fi\ignorespaces}% +% \end{macrocode} +% +% A cumulative macro uses the above ones for determining with one call both the +% magnitude and the direction of a complex number. The first argument is the +% input complex number, the second its magnitude, and the third is again a +% complex number normalized to unit magnitude (unless the input was the null +% complex number); remember always that output quantities must be specified +% with control sequences to be used at a later time. +% \begin{macrocode} +\def\ModAndDirOfVect#1to#2and#3{% +\GetCoord(#1)\t@X\t@Y +\ModOfVect#1to#2% +\DividE\t@X\p@ by\@tempdimc to\t@X \DividE\t@Y\p@ by\@tempdimc to\t@Y +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +% \end{macrocode} +% The next macro computes the magnitude and the direction of the difference of +% two complex numbers; the first input argument is the minuend, the second is +% the subtraend; the output quantities are the third argument containing the +% magnitude of the difference and the fourth is the direction of the difference. +% The service macro |\SubVect| executes the difference of two complex numbers +% and is described further on. +% \begin{macrocode} +\def\DistanceAndDirOfVect#1minus#2to#3and#4{% +\SubVect#2from#1to\@tempa \ModAndDirOfVect\@tempa to#3and#4\relax +\ignorespaces}% +% \end{macrocode} +% We now have two macros intended to fetch just the real or, respectively, the +% imaginary part of the input complex number. +% \begin{macrocode} +\def\XpartOfVect#1to#2{% +\GetCoord(#1)#2\@tempa +\ignorespaces}% +% +\def\YpartOfVect#1to#2{% +\GetCoord(#1)\@tempa#2\relax +\ignorespaces}% +% \end{macrocode} +% With the next macro we create a direction vector (second argument) from a +% given angle (first argument). +% \begin{macrocode} +\def\DirFromAngle#1to#2{\CosOf#1to\t@X% +\SinOf#1to\t@Y\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}% +% \end{macrocode} +% +% Sometimes it is necessary to scale a vector by an arbatrary real factor; this +% implies scaling both the real and imaginary part of the input given vector. +% \begin{macrocode} +\def\ScaleVect#1by#2to#3{\GetCoord(#1)\t@X\t@Y +\@tempdima=\t@X\p@ \@tempdima=#2\@tempdima\Numero\t@X\@tempdima +\@tempdima=\t@Y\p@ \@tempdima=#2\@tempdima\Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +% \end{macrocode} +% Again, sometimes it is necessary to reverse the direction of rotation; this +% implies changing the sign of the imaginary part of a given complex number; +% this operation produces the complex conjugate of the given number. +% \begin{macrocode} +\def\ConjVect#1to#2{\GetCoord(#1)\t@X\t@Y +\@tempdima=-\t@Y\p@\Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}% +% \end{macrocode} +% +% With all the low level elementary operations we can now proceed to the +% definitions of the binary operations on complex numbers. We start with the +% addition: +% \begin{macrocode} +\def\AddVect#1and#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ +\advance\@tempdima\td@X\p@ \Numero\t@X\@tempdima \@tempdima\tu@Y\p@ +\advance\@tempdima\td@Y\p@ \Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +% \end{macrocode} +% Then the subtraction: +% \begin{macrocode} +\def\SubVect#1from#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\td@X\p@ +\advance\@tempdima-\tu@X\p@ \Numero\t@X\@tempdima \@tempdima\td@Y\p@ +\advance\@tempdima-\tu@Y\p@ \Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +% \end{macrocode} +% +% For the multiplication we need to split the operation according to the fact +% that we want to multiply by the second operand or by the complex comjugate of +% the second operand; it would be nice if we could use the usual +% postfixed asterisk notation for the complex conjugate, but I could not find +% a simple means for doing so; therefore I use the prefixed notation, that is +% I put the asterisk before the second operand. The first part of the +% multiplication macro just takes care of the multiplicand and then checks for +% the asterisk; if there is no asterisk it calls a second service macro that +% performs a regular complex multiplication, otherwise it calls a third +% service macro that executes the conjugate multiplication. +% \begin{macrocode} +\def\MultVect#1by{\@ifstar{\@ConjMultVect#1by}{\@MultVect#1by}}% +% +\def\@MultVect#1by#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ +\@tempdimb\tu@Y\p@ +\@tempdimc=\td@X\@tempdima\advance\@tempdimc-\td@Y\@tempdimb +\Numero\t@X\@tempdimc +\@tempdimc=\td@Y\@tempdima\advance\@tempdimc\td@X\@tempdimb +\Numero\t@Y\@tempdimc +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +% +\def\@ConjMultVect#1by#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ \@tempdimb\tu@Y\p@ +\@tempdimc=\td@X\@tempdima\advance\@tempdimc+\td@Y\@tempdimb +\Numero\t@X\@tempdimc +\@tempdimc=\td@X\@tempdimb\advance\@tempdimc-\td@Y\@tempdima +\Numero\t@Y\@tempdimc +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces} +% \end{macrocode} +% +% The division of two complex numbers implies scaling down the dividend by the +% magnitude of the divisor and by rotating the dividend scaled vector by the +% opposite direction of the divisor; therefore: +% \begin{macrocode} +\def\DivVect#1by#2to#3{\ModAndDirOfVect#2to\@Mod and\@Dir +\DividE\p@ by\@Mod\p@ to\@Mod \ConjVect\@Dir to\@Dir +\ScaleVect#1by\@Mod to\@tempa +\MultVect\@tempa by\@Dir to#3\ignorespaces}% +% \end{macrocode} +% +% \subsection{Arcs and curved vectors} +% We are now in the position of really doing graphic work We start with tracing +% a circular arc of arbitrary center, arbitrary starting point and arbitrary +% aperture; The first macro checks the aperture; if this is not zero it +% actually proceeds with the necessary computations, otherwise it does +% nothing. +% \begin{macrocode} +\def\Arc(#1)(#2)#3{\begingroup +\@tdA=#3\p@ \ifdim\@tdA=\z@\else + \@Arc(#1)(#2)% +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% The aperture is already memorized in |\@tdA|; the |\@Arc| macro receives +% the center coordinates in the first argument and the coordinates of the +% starting point in the second argument. +% \begin{macrocode} +\def\@Arc(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi +% \end{macrocode} +% The rotation angle sign is memorized in |\Segno| and |\@tdA| now contains the +% absolute value of the arc aperture. +% If the rotation angle is larger than $360^\circ$ a message is issued that +% informs the user that the angle will be reduced modulo $360^\circ$; this +% operation is performed by succesive subtractions rather than with modular +% arithmetics on the assumption that in general one subtraction suffices. +% \begin{macrocode} +\Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +% \end{macrocode} +% Now the radius is determined and the drawing point is moved to the stating +% point. +% \begin{macrocode} +\SubVect#2from#1to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +% \end{macrocode} +% From now on it's better to define a new macro that will be used also in the +% subsequent macros that trace arcs; here we already have the starting poin +% coordinates and the angle to draw the arc, therefore we just call the new +% macro, stroke the line and exit. +% \begin{macrocode} +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +% \end{macrocode} +% And the new macro |\@@Arc| starts with moving the drawing point to the first +% point and does everything needed for tracing the requested arc, except +% stroking it; I leave the \texttt{stroke} command to the completion of the +% calling macro and nobody forbids to use the |\@@Arc| macro for other purposes. +% \begin{macrocode} +\def\@@Arc{% +\pIIe@moveto{\@pPunX\unitlength}{\@pPunY\unitlength}% +% \end{macrocode} +% If the aperture is larger than $180^\circ$ it traces a semicircle in thr +% right direction and correspondingly reduces the overall aperture. +% \begin{macrocode} +\ifdim\@tdA>180\p@ + \advance\@tdA-180\p@ + \Numero\@gradi\@tdA + \SubVect\@pPun from\@Cent to\@V + \AddVect\@V and\@Cent to\@sPun + \MultVect\@V by0,-1.3333333to\@V \if\Segno-\ScaleVect\@V by-1to\@V\fi + \AddVect\@pPun and\@V to\@pcPun + \AddVect\@sPun and\@V to\@scPun + \GetCoord(\@pcPun)\@pcPunX\@pcPunY + \GetCoord(\@scPun)\@scPunX\@scPunY + \GetCoord(\@sPun)\@sPunX\@sPunY + \pIIe@curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}% + {\@scPunX\unitlength}{\@scPunY\unitlength}% + {\@sPunX\unitlength}{\@sPunY\unitlength}% + \CopyVect\@sPun to\@pPun +\fi +% \end{macrocode} +% If the remaining aperture is not zero it contiues tracing the rest of the arc. +% Here we need the extrema of the arc and the coordinates of the control points +% of the Bézier cubic spline that traces the arc. The control points lay on the +% perpendicular to the vectors that join the arc center to the stating +% and end points respectively. Their distance $K$ from the adiacent nodes is +% determined with the formula +% \[ +% K= \frac{4}{3}(1-\cos\theta)R +% \] +% where $\theta$ is half the arc aperture and $R$ is its radius. +% \begin{macrocode} +\ifdim\@tdA>\z@ + \DirFromAngle\@gradi to\@Dir \if\Segno-\ConjVect\@Dir to\@Dir \fi + \SubVect\@Cent from\@pPun to\@V + \MultVect\@V by\@Dir to\@V + \AddVect\@Cent and\@V to\@sPun + \@tdA=.5\@tdA \Numero\@gradi\@tdA + \DirFromAngle\@gradi to\@Phimezzi + \GetCoord(\@Phimezzi)\@cosphimezzi\@sinphimezzi + \@tdB=1.3333333\p@ \@tdB=\@Raggio\@tdB + \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@ \Numero\@tempa\@tdC + \@tdB=\@tempa\@tdB + \DividE\@tdB by\@sinphimezzi\p@ to\@cZ + \ScaleVect\@Phimezzi by\@cZ to\@Phimezzi + \ConjVect\@Phimezzi to\@mPhimezzi + \if\Segno-% + \let\@tempa\@Phimezzi + \let\@Phimezzi\@mPhimezzi + \let\@mPhimezzi\@tempa + \fi + \SubVect\@sPun from\@pPun to\@V + \DirOfVect\@V to\@V + \MultVect\@Phimezzi by\@V to\@Phimezzi + \AddVect\@sPun and\@Phimezzi to\@scPun + \ScaleVect\@V by-1to\@V + \MultVect\@mPhimezzi by\@V to\@mPhimezzi + \AddVect\@pPun and\@mPhimezzi to\@pcPun + \GetCoord(\@pcPun)\@pcPunX\@pcPunY + \GetCoord(\@scPun)\@scPunX\@scPunY + \GetCoord(\@sPun)\@sPunX\@sPunY + \pIIe@curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}% + {\@scPunX\unitlength}{\@scPunY\unitlength}% + {\@sPunX\unitlength}{\@sPunY\unitlength}% +\fi} +% \end{macrocode} +% +% We exploit much of the above definitions for the |\Arc| macro for drawing +% circular arcs with an arrow at one or both ends; the first macro +% |\VerctorArc| draws an arrow at the ending point of the arc; the second macro +% |\VectorARC| draws arrows at both ends; the arrows have the same shape as +% those for vectors; actually they are drawn by putting a vector of zero +% length at the proper arc end(s), thereore they are styled as traditional or +% PostScript arrows according to the option of the \texttt{pict2e} package. +% +% But the specific drawing done here shortens the arc so as not to overlap on +% the arrow(s); the only or both arrows are also lightly tilted in order to +% avoid the impression of a corner where the arc enters the arrow tip. +% +% All these operations require a lot of ``playing'' with vector directions, +% but even if the operations are numerous, they do not do anything else but: +% (a) determining the end point and its direction ; (b) determining the arrow +% length as an angular quantity, i.e. the arc amplitude that must be subtracted +% from the total arc to be drawn; (c) the direction of the arrow should be +% corresponding to the tangent to the arc at the point where the arrow tip is +% attached;(d) tiltilng the arrow tip by half its angular amplitude; (e) +% determining the resulting position and direction of the arrow tip so as to +% draw a zero length vector; (f) possibly repeating the same procedure for the +% other end of the arc; shortening the total arc angular amplitude by the +% amount of the arrow tip(s) already set, and then drawing the final circular +% arc that joins the starting point to the final arrow or one arrow to the other +% one. +% +% The calling macros are very similar to the |\Arc| macro initial one: +% \begin{macrocode} +\def\VectorArc(#1)(#2)#3{\begingroup +\@tdA=#3\p@ \ifdim\@tdA=\z@\else + \@VArc(#1)(#2)% +\fi +\endgroup\ignorespaces}% +% +\def\VectorARC(#1)(#2)#3{\begingroup +\@tdA=#3\p@ +\ifdim\@tdA=\z@\else + \@VARC(#1)(#2)% +\fi +\endgroup\ignorespaces}% +% \end{macrocode} +% The single arrowed arc is defined with the following long macro where all the +% described operations are performed more or less in the described succession; +% probably the macro requires a little cleaning, but since it work fine I did +% not try to optimize it for time or number of tokens. The final part of the +% macro is almost identical to that of the plain arc; the beginning also is +% quite similar; The central part is dedicated to the positioning of the arrow +% tip and to the necessary calculations for determining the tip tilt and the +% reduction of the total arc length. The already defined |\@@Arc| macro actually +% draws the curved vector stem without stroking it. +% \begin{macrocode} +\def\@VArc(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi \Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\@tdE=\pIIe@FAW\@wholewidth \@tdE=\pIIe@FAL\@tdE +\Numero\@Freccia\@tdE +\DividE\@Freccia\p@ by \@Raggio\p@ to\DeltaGradi +\@tdD=\DeltaGradi\p@ +\@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD +\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD +\DirFromAngle\@tempa to\@Dir +\MultVect\@V by\@Dir to\@sPun +\edef\@tempA{\ifx\Segno-\m@ne\else\@ne\fi}% +\MultVect\@sPun by 0,\@tempA to\@vPun +\DirOfVect\@vPun to\@Dir +\AddVect\@sPun and #1 to \@sPun +\GetCoord(\@sPun)\@tdX\@tdY +\@tdD\ifx\Segno--\fi\DeltaGradi\p@ +\@tdD=.5\@tdD \Numero\DeltaGradi\@tdD +\DirFromAngle\DeltaGradi to\@Dird +\MultVect\@Dir by*\@Dird to\@Dir +\GetCoord(\@Dir)\@xnum\@ynum +\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}% +\@tdE =\ifx\Segno--\fi\DeltaGradi\p@ +\advance\@tdA -\@tdE \Numero\@gradi\@tdA +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +% \end{macrocode} +% +% The macro for the arc terminated with arrow tips at both ends is again very +% similar, except it is necessary to repeat the arrow tip positioning also at +% the starting point. The |\@@Arc| macro draws the curved stem. +% \begin{macrocode} +\def\@VARC(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi \Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\@tdE=\pIIe@FAW\@wholewidth \@tdE=0.8\@tdE +\Numero\@Freccia\@tdE +\DividE\@Freccia\p@ by \@Raggio\p@ to\DeltaGradi +\@tdD=\DeltaGradi\p@ \@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD +\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD +\DirFromAngle\@tempa to\@Dir +\MultVect\@V by\@Dir to\@sPun +\edef\@tempA{\ifx\Segno-\m@ne\else\@ne\fi}% +\MultVect\@sPun by 0,\@tempA to\@vPun +\DirOfVect\@vPun to\@Dir +\AddVect\@sPun and #1 to \@sPun +\GetCoord(\@sPun)\@tdX\@tdY +\@tdD\ifx\Segno--\fi\DeltaGradi\p@ +\@tdD=.5\@tdD \Numero\@tempB\@tdD +\DirFromAngle\@tempB to\@Dird +\MultVect\@Dir by*\@Dird to\@Dir +\GetCoord(\@Dir)\@xnum\@ynum +\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}% +\@tdE =\DeltaGradi\p@ +\advance\@tdA -2\@tdE \Numero\@gradi\@tdA +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +\SubVect\@Cent from\@pPun to \@V +\edef\@tempa{\ifx\Segno-\else-\fi\@ne}% +\MultVect\@V by0,\@tempa to\@vPun +\@tdE\ifx\Segno--\fi\DeltaGradi\p@ +\Numero\@tempB{0.5\@tdE}% +\DirFromAngle\@tempB to\@Dird +\MultVect\@vPun by\@Dird to\@vPun +\DirOfVect\@vPun to\@Dir\GetCoord(\@Dir)\@xnum\@ynum +\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}} +\edef\@tempa{\ifx\Segno--\fi\DeltaGradi}% +\DirFromAngle\@tempa to \@Dir +\SubVect\@Cent from\@pPun to\@V +\MultVect\@V by\@Dir to\@V +\AddVect\@Cent and\@V to\@pPun +\GetCoord(\@pPun)\@pPunX\@pPunY +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +% \end{macrocode} +% +% It must be understood that the curved vectors, tha above circular arcs +% terminated with an arrow tip at one or both ends, have a nice appearance only +% if the arc radius is not too small, or, said in a different way, if the arrow +% tip angular width does not exceed a maximum of a dozen degrees (and this is +% probably already too much); the tip does not get curved as the arc is, +% therefore there is not a smooth transition from the curved stem and the +% straight arrow tip if this one is large in comparison to the arc radius. +% +% \subsection{General curves} +% Now we define a macro for tracing a general, not necessarily circular arc. +% This macro resorts to a general triplet of macros with which it is possible +% to draw almost anything. It traces a single Bézier spline from a first point +% where the tangent direction is specified to a second point where again it is +% specified the tangent direction. Actually this is a special (possibly useless) +% case where the general |\Curve| macro could do the same or a better job. In +% any case\dots +% \begin{macrocode} +\def\CurveBetween#1and#2WithDirs#3and#4{% +\StartCurveAt#1WithDir{#3}\relax +\CurveTo#2WithDir{#4}\CurveFinish}% +% \end{macrocode} +% +% Actually the above macro is a special case of concatenation of the triplet +% formed by macros |\StartCurve|, |\CurveTo| and|\CurveFinish|; the second of +% which can be repeated an arbitrary number of times. +% +% The first macro initializes the drawing and the third one strokes it; the +% real work is done by the second macro. The first macro inizializes the +% drawing but also memorizes the starting direction; the second macro traces +% the current Bézier arc reaching the destination point with the sepcified +% direction, but memorizes this direction as the one with which to start the +% next arc. The overall curve is then always smooth because the various +% Bézier arcs join with continuous tangents. If a cusp is desired it is +% necessary to change the memorized direction at the end of the arc before the +% cusp and before the start of the next arc; this is better than stroking the +% curve before the cusp and then starting another curve, because the curve +% jointure at the cusp is not stroked with the same command, therefore we get +% two superimposed curve terminations. We therefore need another small macro +% |\ChangeDir| to perform this task. +% +% It is necessary to recall that the directions point to the control points, +% but they do not define the control points themselves; they are just +% directions, or, even better, they are simply vectors with the desired +% direction; the macros themselves provide to the normalization and +% memorization. +% +% The next desirable poit would be to design a macro that accepts optional node +% directions and computes the missing ones according to a suitable strategy. I +% can think of many such strategies, but none seems to be generally applicable, +% in the sense that one strategy might give good results, say, with sinusoids +% and another one,say, with cardioids, but neither one is suitable for both +% cases. +% +% For the moment we refrain from automatic direction computation, but we design +% the general macro as if directions were iptional. +% +% Here we begin with the first initializing macro that receives in the first +% argument the starting point and in the second argument the direction of the +% tangent (not necessarily normalized to a unit vector) +% \begin{macrocode} +\def\StartCurveAt#1WithDir#2{% +\begingroup +\GetCoord(#1)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Pzero +\pIIe@moveto{\@tempa\unitlength}{\@tempb\unitlength}% +\GetCoord(#2)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Dzero +\DirOfVect\@Dzero to\@Dzero} +% \end{macrocode} +% And this reinitializes the direction after a cusp +% \begin{macrocode} +\def\ChangeDir<#1>{% +\GetCoord(#1)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Dzero +\DirOfVect\@Dzero to\@Dzero +\ignorespaces} +% \end{macrocode} +% +% The next macro is the finishing one; it strokes the whole curve and closes the +% group that was opened with |\StartCurve|. +% \begin{macrocode} +\def\CurveFinish{\pIIe@strokeGraph\endgroup\ignorespaces}% +% \end{macrocode} +% +% The ``real'' curve macro comes next; it is supposed to determine the control +% points for joining the previous point (initial node) with the specified +% direction to the next point with another specified direction (final node). +% Since the control points are along the sepcified directions, it is necessary +% to determine the distances from the adiacent curve nodes. This must work +% correctly even if nodes and directions imply an inflection point somewhere +% along the arc. +% +% The strategy I devised consists in determining each control point as if it +% were the control point of a circular arc, precisely an arc of an +% osculating circle, a circle tangent to the curve at that node. The ambiguity +% of the stated problem may be solved by establishing that the chord of the +% osculating circle has the same direction as the chord of the arc being drawn, +% and that the curve chord is divided into two parts each of which should be +% interpreted as half the chord of the osculating circle; this curve chord +% division is made proportionally to the projection of the tangent directions +% on the chord itself. Excluding degenerate cases that may be dealt with +% directly, immagine the triangle built with the chord and the two tangents; +% this triangle is staightforward if there is no inflection point; otherwise it +% is necessary to change one of the two directions by reflecting it about the +% chord. This is much simpler to view if a general rotation of the whole +% contruction is made so as to bring the curve chord on the $x$ axis, because +% the reflection about the chord amounts to taking the complex conjugate of one +% of the directions. In facts with a concave curve the ``left'' direction +% vector arrow and the ``right'' direction vector tail lay in the same half +% plane, while with an inflected curve, they lay in opposite half plains, so +% that taking the complex conjugate of one of directions re-establishes the +% correct situation for the triangle we are looking for. +% +% This done the perpendicular from the triangle vertex to the cord divides the +% chord in two parts (the foot of this perpendicular may lay outside the chord, +% but this is no problem since we are looking for positive solutions, so that +% if we get negative numbers we just negate tem); these two parts are taken as +% the half chords of the osculating circles, therefore there is no problem +% determining the distances $K_{\mathrm{left}}$ and $K_{\mathrm{rigth}}$ from +% the left and right +% nodes by using the same formula we used with circular arcs. Well\dots\ the +% same formula means that we have to determine the radius from the half chord +% and its inclination with the node tangent; all things we can do with the +% complex number algebra and macros we already have at our disposal. If we look +% carefully at this computation done for the circular arc we discover that in +% practice we used the half chord length instead of the radius; so the coding +% is actually the same, may be just with different variable names. +% +% We therefore start with getting the points and directions and calculating the +% chord and its direction +% \begin{macrocode} +\def\CurveTo#1WithDir#2{% +\def\@Puno{#1}\def\@Duno{#2}\DirOfVect\@Duno to\@Duno +\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord +% \end{macrocode} +% Then we rotate everything about the starting point so as to bring the chord on +% the real axis +% \begin{macrocode} +\MultVect\@Dzero by*\@DirChord to \@Dpzero +\MultVect\@Duno by*\@DirChord to \@Dpuno +\GetCoord(\@Dpzero)\@Xpzero\@Ypzero +\GetCoord(\@Dpuno)\@Xpuno\@Ypuno +% \end{macrocode} +% The chord needs not be actually rotated because it suffices its length +% along the real axis; the chord length is memorized in |\@Chord|. +% +% We now examine the various degenerate cases, when either tangent is +% perpendicular to che chord, or when it is parallel pointing invard or outward, +% with or without inflection. +% +% We start with the $90^\circ$ case for the ``left'' direction +% separating the cases when the other direction is or is not $90^\circ$~\dots +% \begin{macrocode} +\ifdim\@Xpzero\p@=\z@ + \ifdim\@Xpuno\p@=\z@ + \@tdA=0.666666\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \edef\@Mcpuno{\@Mcpzero}% + \else + \@tdA=0.666666\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \SetCPmodule\@Mcpuno from\@ne\@Chord\@Dpuno% + \fi +% \end{macrocode} +% \dots\ from when the ``left'' direction is not perpendicular to the chord; it +% might +% be parallel and we must distinguish the cases for the other direction~\dots +% \begin{macrocode} +\else + \ifdim\@Xpuno\p@=\z@ + \@tdA=0.666666\p@ + \Numero\@Mcpuno{\@Chord\@tdA}% + \SetCPmodule\@Mcpzero from\@ne\@Chord\@Dpzero% + \else + \ifdim\@Ypzero\p@=\z@ + \@tdA=0.333333\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \ifdim\@Ypuno\p@=\z@ + \edef\@Mcpuno{\@Mcpzero}% + \fi +% \end{macrocode} +% \dots\ from when the left direction is oblique and the other direction is +% either parallel to the chord~\dots +% \begin{macrocode} + \else + \ifdim\@Ypuno\p@=\z@ + \@tdA=0.333333\p@ + \Numero\@Mcpuno{\@Chord\@tdA}% + \SetCPmodule\@Mcpzero from\@ne\@Chord\@Dpzero +% \end{macrocode} +% \dots\ and, finally, from when both directions are oblique with respect to +% the chord; we must see if there is an inflection point; if both direction +% point to the same half plane we have to take the complex conjugate of une +% direction so as to define the triangle we were speaking about above. +% \begin{macrocode} + \else + \@tdA=\@Ypzero\p@ \@tdA=\@Ypuno\@tdA + \ifdim\@tdA>\z@ + \ConjVect\@Dpuno to\@Dwpuno + \else + \edef\@Dwpuno{\@Dpuno}% + \fi +% \end{macrocode} +% The control sequence |\@Dwpuno| contains the right direction for forming the +% triangle; we cam make the weighed subdivision of the chord according to the +% horizontal components of the directions; we eventually turn negative values +% to positive ones since we are intersted in the magnitudes of the control +% vectors. +% \begin{macrocode} + \GetCoord(\@Dwpuno)\@Xwpuno\@Ywpuno + \@tdA=\@Xpzero\p@ \@tdA=\@Ywpuno\@tdA + \@tdB=\@Xwpuno\p@ \@tdB=\@Ypzero\@tdB + \DividE\@tdB by\@tdA to\@Fact + \@tdC=\p@ \advance\@tdC-\@Fact\p@ + \ifdim\@tdC<\z@ \@tdC=-\@tdC\fi + \DividE\p@ by \@Fact\p@ to\@Fact + \@tdD=\p@ \advance\@tdD-\@Fact\p@ + \ifdim\@tdD<\z@ \@tdD=-\@tdD\fi +% \end{macrocode} +% before dividing by the denominator we have to check the directions, although +% oblique to the chord are not parallel to one another; in this case there is +% no question of a weighed subdivision of the chord +% \begin{macrocode} + \ifdim\@tdD<0.0001\p@ + \def\@factzero{1}% + \def\@factuno{1}% + \else + \DividE\p@ by\@tdC to\@factzero + \DividE\p@ by\@tdD to\@factuno + \fi +% \end{macrocode} +% We now have the subdivision factors and we call another macro for determining +% the required magnitudes +% \begin{macrocode} + \SetCPmodule\@Mcpzero from\@factzero\@Chord\@Dpzero + \SetCPmodule\@Mcpuno from\@factuno\@Chord\@Dwpuno + \fi + \fi + \fi +\fi +% \end{macrocode} +% Now we have all data we need and we determine the positions of the control +% points; we do not work any more on the rotated diagram of the horizontal +% chord, but we operate on the original points and directions; all we had to +% compute, after all, were the distances of the control point along the +% specified directions; remember that the ``left'' control point is along the +% positive ``left'' direction, while the ``right'' conptrol point precedes the +% curve node along the ``rigth'' direction, so that a vector subtraction must +% be done. +% \begin{macrocode} +\ScaleVect\@Dzero by\@Mcpzero to\@CPzero +\AddVect\@Pzero and\@CPzero to\@CPzero +\ScaleVect\@Duno by\@Mcpuno to\@CPuno +\SubVect\@CPuno from\@Puno to\@CPuno +% \end{macrocode} +% Now we have the four points and we can instruct the internal \texttt{pict2e} +% macros to do the path tracing. +% \begin{macrocode} +\GetCoord(\@Puno)\@XPuno\@YPuno +\GetCoord(\@CPzero)\@XCPzero\@YCPzero +\GetCoord(\@CPuno)\@XCPuno\@YCPuno +\pIIe@curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}% + {\@XCPuno\unitlength}{\@YCPuno\unitlength}% + {\@XPuno\unitlength}{\@YPuno\unitlength}% +% \end{macrocode} +% It does not have to stroke the curve because other Bézier splines might still +% be added to the path. On the opposite it memorizes the final point as the +% initial point of the next spline +% \begin{macrocode} +\CopyVect\@Puno to\@Pzero +\CopyVect\@Duno to\@Dzero +\ignorespaces}% +% \end{macrocode} +% +% The next macro is used to determine the control vectors lengths when we have +% the chord fraction, the chord length and the direction along which to compute +% the vector; all the input data (arguments from \#2 to \#4) may be passed as +% control sequences so the calling statement needs not use any curly braces. +% \begin{macrocode} +\def\SetCPmodule#1from#2#3#4{% +\GetCoord(#4)\t@X\t@Y +\@tdA=#3\p@ +\@tdA=#2\@tdA +\@tdA=1.333333\@tdA +\@tdB=\p@ \advance\@tdB +\t@X\p@ +\DividE\@tdA by\@tdB to#1\relax +\ignorespaces}% +% \end{macrocode} +% +% We finally define the overall |\Curve| macro that recursively examines an +% arbitrary list of nodes and directions; node coordinates are grouped within +% regular parentheses while direction components are grouped within angle +% brackets. The first call of the macro initializes the drawing process and +% checks for the next node and direction; if a second node is missing, it issues +% a warning message and does not draw anything. The second macro defines the +% path to the next point and checks for another node; if the next list item is +% a square bracket delimited argument, it iterprets it as a change of +% direction, while if it is another parentesis delinite argument it inpterprets +% it as a new node-direction specification; +% if the node and direction list is terminated, it issues the stroking command +% and exits the recursive process. The |@ChangeDir| macro is just an interface +% for executing the regular |\ChangeDir| macro, but also for recursing again by +% recalling |\@Curve|. +% \begin{macrocode} +\def\Curve(#1)<#2>{% + \StartCurveAt#1WithDir{#2}% + \@ifnextchar\lp@r\@Curve{% + \PackageWarning{curve2e}{% + Curve specifications must contain at least two nodes!\Messagebreak + Please, control your Curve specifications\MessageBreak}}} +\def\@Curve(#1)<#2>{% + \CurveTo#1WithDir{#2}% + \@ifnextchar\lp@r\@Curve{% + \@ifnextchar[\@ChangeDir\CurveFinish}} +\def\@ChangeDir[#1]{\ChangeDir<#1>\@Curve} +% \end{macrocode} +% +% As a concluding remark, please notice the the |\Curve| macro is certainly the +% most confortable to use, but it is sort of frozen in its possibilities. The +% user may certainly use the |\StartCurve|, |\CurveTo|, |\ChangeDir|, and +% |\CurveFinish| for a more versatile set of drawing macros; evidently nobody +% forbids to exploit the full power of the |\cbezier| original macro for cubic +% splines. +% +% I believe that the set of new macros can really help the user to draw his/her +% diagrams with more agility; it will be the accumulated experience to decide if +% this is true. +% \Finale +% \endinput + diff --git a/Master/texmf-dist/source/latex/curve2e/curve2e.ins b/Master/texmf-dist/source/latex/curve2e/curve2e.ins new file mode 100644 index 00000000000..037eca128ef --- /dev/null +++ b/Master/texmf-dist/source/latex/curve2e/curve2e.ins @@ -0,0 +1,42 @@ +%% +%% --------------- start of docstrip commands ------------------ +%% +\def\batchfile{curve2e.ins} +\input docstrip.tex +\preamble + +Copyright 2005 Claudio Beccari All rights reserved. + + This system is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. + + +IMPORTANT NOTICE: + +This work 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 1.3 or later is part of all distributions of LaTeX +version 2003/12/01 or later. + +This work has the LPPL maintenance status "author-maintained". + +This work consists of all files listed in manifest.txt. + + +If you receive only some of these files from someone, complain! + +\endpreamble +\def\batchfile{curve2e.dst} % ignored in distribution +\input docstrip.tex % ignored in distribution + +\keepsilent + +\Msg{*** Generating package curve2e ***} + +\generateFile{curve2e.sty}{t}{\from{curve2e.dtx}{package}} + +\endinput diff --git a/Master/texmf-dist/tex/latex/curve2e/curve2e.sty b/Master/texmf-dist/tex/latex/curve2e/curve2e.sty new file mode 100644 index 00000000000..e01f0e2d27b --- /dev/null +++ b/Master/texmf-dist/tex/latex/curve2e/curve2e.sty @@ -0,0 +1,660 @@ +%% +%% This is file `curve2e.sty', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% curve2e.dtx (with options: `package') +%% +%% Copyright 2005 Claudio Beccari All rights reserved. +%% +%% This system is distributed in the hope that it will be useful, +%% but WITHOUT ANY WARRANTY; without even the implied warranty of +%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +%% +%% +%% IMPORTANT NOTICE: +%% +%% This work 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 1.3 or later is part of all distributions of LaTeX +%% version 2003/12/01 or later. +%% +%% This work has the LPPL maintenance status "author-maintained". +%% +%% This work consists of all files listed in manifest.txt. +%% +%% +%% If you receive only some of these files from someone, complain! +%% +%% +%% File `curve2e.dtx'. +%% Copyright (C) 2005 Claudio Beccari all rights reserved. +%% +\NeedsTeXFormat{LaTeX2e} +\ProvidesPackage{curve2e}% + [2005/08/15 v.0.10 Extension package for pict2e] +\RequirePackage{color} +\RequirePackageWithOptions{pict2e}[2004/06/01] +\ifcase\pIIe@mode\relax +\or %Postscript + \def\roundcap{\special{ps:: 1 setlinecap}}% + \def\squarecap{\special{ps:: 0 setlinecap}}% + \def\roundjoin{\special{ps:: 1 setlinejoin}}% + \def\beveljoin{\special{ps:: 2 setlinejoin}}% +\or %pdf + \def\roundcap{\pdfliteral{1 J}}% + \def\squarecap{\pdfliteral{0 J}}% + \def\roundjoin{\pdfliteral{1 j}}% + \def\beveljoin{\pdfliteral{2 j}}% +\fi +\def\TRON{\tracingcommands\tw@ \tracingmacros\tw@}% +\def\TROF{\tracingcommands\z@ \tracingmacros\z@}% +\ifx\undefined\@tdA \newdimen\@tdA \fi +\ifx\undefined\@tdB \newdimen\@tdB \fi +\ifx\undefined\@tdC \newdimen\@tdC \fi +\ifx\undefined\@tdD \newdimen\@tdD \fi +\ifx\undefined\@tdE \newdimen\@tdE \fi +\ifx\undefined\@tdF \newdimen\@tdF \fi +\ifx\undefined\defaultlinewidth \newdimen\defaultlinewidth \fi +\newcommand\defaultlinethickness[1]{\defaultlinewidth=#1\relax +\def\thicklines{\linethickness{\defaultlinewidth}}% +\def\thinlines{\linethickness{.5\defaultlinewidth}}% +\thinlines\ignorespaces} +\def\Line(#1,#2){\pIIe@moveto\z@\z@ + \pIIe@lineto{#1\unitlength}{#2\unitlength}\pIIe@strokeGraph}% +\def\LINE(#1)(#2){\polyline(#1)(#2)}% +\def\line(#1)#2{\begingroup + \@linelen #2\unitlength + \ifdim\@linelen<\z@\@badlinearg\else + \expandafter\DirOfVect#1to\Dir@line + \GetCoord(\Dir@line)\d@mX\d@mY + \ifdim\d@mX\p@=\z@\else + \DividE\ifdim\d@mX\p@<\z@-\fi\p@ by\d@mX\p@ to\sc@lelen + \@linelen=\sc@lelen\@linelen + \fi + \pIIe@moveto\z@\z@ + \pIIe@lineto{\d@mX\@linelen}{\d@mY\@linelen}% + \pIIe@strokeGraph +\fi +\endgroup\ignorespaces}% +\def\GetCoord(#1)#2#3{% +\expandafter\SplitNod@\expandafter(#1)#2#3\ignorespaces} +\def\SplitNod@(#1,#2)#3#4{\edef#3{#1}\edef#4{#2}}% + \def\vector(#1)#2{% + \begingroup + \GetCoord(#1)\d@mX\d@mY + \@linelen#2\unitlength + \ifdim\d@mX\p@=\z@\ifdim\d@mY\p@=\z@\@badlinearg\fi\fi + \ifdim\@linelen<\z@ \@linelen=-\@linelen\fi + \MakeVectorFrom\d@mX\d@mY to\@Vect + \DirOfVect\@Vect to\Dir@Vect + \YpartOfVect\Dir@Vect to\@ynum \@ydim=\@ynum\p@ + \XpartOfVect\Dir@Vect to\@xnum \@xdim=\@xnum\p@ + \ifdim\d@mX\p@=\z@ + \else\ifdim\d@mY\p@=\z@ + \else + \DividE\ifdim\@xnum\p@<\z@-\fi\p@ by\@xnum\p@ to\sc@lelen + \@linelen=\sc@lelen\@linelen + \fi + \fi + \@tdB=\@linelen +\pIIe@concat\@xdim\@ydim{-\@ydim}\@xdim{\@xnum\@linelen}{\@ynum\@linelen}% + \@linelen\z@ + \pIIe@vector + \pIIe@fillGraph + \@linelen=\@tdB + \@tdA=\pIIe@FAW\@wholewidth + \@tdA=\pIIe@FAL\@tdA + \advance\@linelen-\@tdA + \ifdim\@linelen>\z@ + \pIIe@moveto\z@\z@ + \pIIe@lineto{\@xnum\@linelen}{\@ynum\@linelen}% + \pIIe@strokeGraph\fi + \endgroup} +\def\Vector(#1,#2){\vector(#1,#2){#1}} +\def\VECTOR(#1)(#2){\begingroup +\SubVect#1 from #2 to \@tempa +\expandafter\put\expandafter(#1){\expandafter\Vector\expandafter(\@tempa)}% +\endgroup\ignorespaces} +\let\lp@r( \let\rp@r) +\def\polyline(#1){\beveljoin\GetCoord(#1)\d@mX\d@mY + \pIIe@moveto{\d@mX\unitlength}{\d@mY\unitlength}% + \@ifnextchar\lp@r{\p@lyline}{% + \PackageWarning{curve2e}% + {Polygonal lines require at least two vertices!\MessageBreak + Control your polygonal line specification\MessageBreak}% + \ignorespaces}} +\def\p@lyline(#1){\GetCoord(#1)\d@mX\d@mY + \pIIe@lineto{\d@mX\unitlength}{\d@mY\unitlength}% + \@ifnextchar\lp@r{\p@lyline}{\pIIe@strokeGraph\ignorespaces}} +\def\GraphGrid(#1,#2){\begingroup\textcolor{red}{\linethickness{.1\p@}% +\RoundUp#1modulo10to\@GridWd \RoundUp#2modulo10to\@GridHt +\@tempcnta=\@GridWd \divide\@tempcnta10\relax \advance\@tempcnta\@ne +\multiput(0,0)(10,0){\@tempcnta}{\line(0,1){\@GridHt}}% +\@tempcnta=\@GridHt \divide\@tempcnta10\advance\@tempcnta\@ne +\multiput(0,0)(0,10){\@tempcnta}{\line(1,0){\@GridWd}}\thinlines}% +\endgroup\ignorespaces} +\def\RoundUp#1modulo#2to#3{\expandafter\@tempcnta\Integer#1.??% +\count254\@tempcnta\divide\count254by#2\relax +\multiply\count254by#2\relax +\count252\@tempcnta\advance\count252-\count254 +\ifnum\count252>0\advance\count252-#2\relax +\advance\@tempcnta-\count252\fi\edef#3{\number\@tempcnta}\ignorespaces}% +\def\Integer#1.#2??{#1}% +\ifx\DividE\undefined + \def\DividE#1by#2to#3{% + \begingroup + \dimendef\Numer=254\relax \dimendef\Denom=252\relax + \countdef\Num 254\relax + \countdef\Den 252\relax + \countdef\I=250\relax + \Numer #1\relax \Denom #2\relax + \ifdim\Denom<\z@ \Denom -\Denom \Numer -\Numer\fi + \def\segno{}\ifdim\Numer<\z@ \def\segno{-}\Numer -\Numer\fi + \ifdim\Denom=\z@ + \ifdim\Numer>\z@\def\Q{16383.99999}\else\def\Q{-16383.99999}\fi + \else + \Num=\Numer \Den=\Denom \divide\Num\Den + \edef\Q{\number\Num.}% + \advance\Numer -\Q\Denom \I=6\relax + \@whilenum \I>\z@ \do{\DividEDec\advance\I\m@ne}% + \fi + \xdef#3{\segno\Q}\endgroup + }% + \def\DividEDec{\Numer=10\Numer \Num=\Numer \divide\Num\Den + \edef\q{\number\Num}\edef\Q{\Q\q}\advance\Numer -\q\Denom}% +\fi +\ifx\undefined\@Numero% s + {\let\cc\catcode \cc`p=12\cc`t=12\gdef\@Numero#1pt{#1}}% +\fi +\ifx\undefined\Numero + \def\Numero#1#2{\dimen254 +#2\edef#1{\expandafter\@Numero\the\dimen254}\ignorespaces}% +\fi +\def\g@tTanCotanFrom#1to#2and#3{% +\DividE 114.591559\p@ by#1to\X \@tdB=\X\p@ +\countdef\I=254\def\Tan{0}\I=11\relax +\@whilenum\I>\z@\do{% + \@tdC=\Tan\p@ \@tdD=\I\@tdB + \advance\@tdD-\@tdC \DividE\p@ by\@tdD to\Tan + \advance\I-2\relax}% +\def#2{\Tan}\DividE\p@ by\Tan\p@ to\Cot \def#3{\Cot}% +\ignorespaces}% +\def\SinOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>\z@% + \@whiledim\@tdA>180\p@\do{\advance\@tdA -360\p@}% +\else% + \@whiledim\@tdA<-180\p@\do{\advance\@tdA 360\p@}% +\fi \ifdim\@tdA=\z@ + \gdef#2{0}% +\else + \ifdim\@tdA>\z@ + \def\Segno{+}% + \else + \def\Segno{-}% + \@tdA=-\@tdA + \fi + \ifdim\@tdA>90\p@ + \@tdA=-\@tdA \advance\@tdA 180\p@ + \fi + \ifdim\@tdA=90\p@ + \xdef#2{\Segno1}% + \else + \ifdim\@tdA=180\p@ + \gdef#2{0}% + \else + \ifdim\@tdA<\p@ + \@tdA=\Segno0.0174533\@tdA + \DividE\@tdA by\p@ to#2% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA=\T\p@ \advance\@tdA \Tp\p@ + \DividE \Segno2\p@ by\@tdA to#2% + \fi + \fi + \fi +\fi +\endgroup\ignorespaces}% +\def\CosOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>\z@% + \@whiledim\@tdA>360\p@\do{\advance\@tdA -360\p@}% +\else% + \@whiledim\@tdA<\z@\do{\advance\@tdA 360\p@}% +\fi +\ifdim\@tdA>180\p@ + \@tdA=-\@tdA \advance\@tdA 360\p@ +\fi +\ifdim\@tdA<90\p@ + \def\Segno{+}% +\else + \def\Segno{-}% + \@tdA=-\@tdA \advance\@tdA 180\p@ +\fi +\ifdim\@tdA=\z@ + \gdef#2{\Segno1}% +\else + \ifdim\@tdA<\p@ + \@tdA=0.0174533\@tdA \Numero\@tempA\@tdA + \@tdA=\@tempA\@tdA \@tdA=-.5\@tdA + \advance\@tdA \p@ + \DividE\@tdA by\p@ to#2% + \else + \ifdim\@tdA=90\p@ + \gdef#2{0}% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA=\Tp\p@ \advance\@tdA-\T\p@ + \@tdB=\Tp\p@ \advance\@tdB\T\p@ + \DividE\Segno\@tdA by\@tdB to#2% + \fi + \fi +\fi +\endgroup\ignorespaces}% +\def\TanOf#1to#2{\begingroup% +\@tdA=#1\p@% +\ifdim\@tdA>90\p@% + \@whiledim\@tdA>90\p@\do{\advance\@tdA -180\p@}% +\else% + \@whiledim\@tdA<-90\p@\do{\advance\@tdA 180\p@}% +\fi% +\ifdim\@tdA=\z@% + \gdef#2{0}% +\else + \ifdim\@tdA>\z@ + \def\Segno{+}% + \else + \def\Segno{-}% + \@tdA=-\@tdA + \fi + \ifdim\@tdA=90\p@ + \xdef#2{\Segno16383.99999}% + \else + \ifdim\@tdA<\p@ + \@tdA=\Segno0.0174533\@tdA + \DividE\@tdA by\p@ to#2% + \else + \g@tTanCotanFrom\@tdA to\T and\Tp + \@tdA\Tp\p@ \advance\@tdA -\T\p@ + \DividE\Segno2\p@ by\@tdA to#2% + \fi + \fi +\fi +\endgroup\ignorespaces}% +\def\MakeVectorFrom#1#2to#3{\edef#3{#1,#2}\ignorespaces}% +\def\CopyVect#1to#2{\edef#2{#1}\ignorespaces}% +\def\ModOfVect#1to#2{\GetCoord(#1)\t@X\t@Y +\@tempdima=\t@X\p@ \ifdim\@tempdima<\z@ \@tempdima=-\@tempdima\fi +\@tempdimb=\t@Y\p@ \ifdim\@tempdimb<\z@ \@tempdimb=-\@tempdimb\fi +\ifdim\@tempdima>\@tempdimb + \DividE\@tempdimb by\@tempdima to\@T + \@tempdimc=\@tempdima +\else + \DividE\@tempdima by\@tempdimb to\@T + \@tempdimc=\@tempdimb +\fi +\ifdim\@T\p@>\z@ + \@tempdima=\@T\p@ \@tempdima=\@T\@tempdima + \advance\@tempdima\p@ % + \@tempdimb=\p@% + \@tempcnta=5\relax + \@whilenum\@tempcnta>\z@\do{\DividE\@tempdima by\@tempdimb to\@T + \advance\@tempdimb \@T\p@ \@tempdimb=.5\@tempdimb + \advance\@tempcnta\m@ne}%\ + \@tempdimc=\@T\@tempdimc +\fi +\Numero#2\@tempdimc +\ignorespaces}% +\def\DirOfVect#1to#2{\GetCoord(#1)\t@X\t@Y +\ModOfVect#1to\@tempa +\ifdim\@tempdimc=\z@\else + \DividE\t@X\p@ by\@tempdimc to\t@X + \DividE\t@Y\p@ by\@tempdimc to\t@Y + \MakeVectorFrom\t@X\t@Y to#2\relax +\fi\ignorespaces}% +\def\ModAndDirOfVect#1to#2and#3{% +\GetCoord(#1)\t@X\t@Y +\ModOfVect#1to#2% +\DividE\t@X\p@ by\@tempdimc to\t@X \DividE\t@Y\p@ by\@tempdimc to\t@Y +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +\def\DistanceAndDirOfVect#1minus#2to#3and#4{% +\SubVect#2from#1to\@tempa \ModAndDirOfVect\@tempa to#3and#4\relax +\ignorespaces}% +\def\XpartOfVect#1to#2{% +\GetCoord(#1)#2\@tempa +\ignorespaces}% +\def\YpartOfVect#1to#2{% +\GetCoord(#1)\@tempa#2\relax +\ignorespaces}% +\def\DirFromAngle#1to#2{\CosOf#1to\t@X% +\SinOf#1to\t@Y\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}% +\def\ScaleVect#1by#2to#3{\GetCoord(#1)\t@X\t@Y +\@tempdima=\t@X\p@ \@tempdima=#2\@tempdima\Numero\t@X\@tempdima +\@tempdima=\t@Y\p@ \@tempdima=#2\@tempdima\Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +\def\ConjVect#1to#2{\GetCoord(#1)\t@X\t@Y +\@tempdima=-\t@Y\p@\Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#2\ignorespaces}% +\def\AddVect#1and#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ +\advance\@tempdima\td@X\p@ \Numero\t@X\@tempdima \@tempdima\tu@Y\p@ +\advance\@tempdima\td@Y\p@ \Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +\def\SubVect#1from#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\td@X\p@ +\advance\@tempdima-\tu@X\p@ \Numero\t@X\@tempdima \@tempdima\td@Y\p@ +\advance\@tempdima-\tu@Y\p@ \Numero\t@Y\@tempdima +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +\def\MultVect#1by{\@ifstar{\@ConjMultVect#1by}{\@MultVect#1by}}% +\def\@MultVect#1by#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ +\@tempdimb\tu@Y\p@ +\@tempdimc=\td@X\@tempdima\advance\@tempdimc-\td@Y\@tempdimb +\Numero\t@X\@tempdimc +\@tempdimc=\td@Y\@tempdima\advance\@tempdimc\td@X\@tempdimb +\Numero\t@Y\@tempdimc +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces}% +\def\@ConjMultVect#1by#2to#3{\GetCoord(#1)\tu@X\tu@Y +\GetCoord(#2)\td@X\td@Y \@tempdima\tu@X\p@ \@tempdimb\tu@Y\p@ +\@tempdimc=\td@X\@tempdima\advance\@tempdimc+\td@Y\@tempdimb +\Numero\t@X\@tempdimc +\@tempdimc=\td@X\@tempdimb\advance\@tempdimc-\td@Y\@tempdima +\Numero\t@Y\@tempdimc +\MakeVectorFrom\t@X\t@Y to#3\ignorespaces} +\def\DivVect#1by#2to#3{\ModAndDirOfVect#2to\@Mod and\@Dir +\DividE\p@ by\@Mod\p@ to\@Mod \ConjVect\@Dir to\@Dir +\ScaleVect#1by\@Mod to\@tempa +\MultVect\@tempa by\@Dir to#3\ignorespaces}% +\def\Arc(#1)(#2)#3{\begingroup +\@tdA=#3\p@ \ifdim\@tdA=\z@\else + \@Arc(#1)(#2)% +\fi +\endgroup\ignorespaces}% +\def\@Arc(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi +\Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +\SubVect#2from#1to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +\def\@@Arc{% +\pIIe@moveto{\@pPunX\unitlength}{\@pPunY\unitlength}% +\ifdim\@tdA>180\p@ + \advance\@tdA-180\p@ + \Numero\@gradi\@tdA + \SubVect\@pPun from\@Cent to\@V + \AddVect\@V and\@Cent to\@sPun + \MultVect\@V by0,-1.3333333to\@V \if\Segno-\ScaleVect\@V by-1to\@V\fi + \AddVect\@pPun and\@V to\@pcPun + \AddVect\@sPun and\@V to\@scPun + \GetCoord(\@pcPun)\@pcPunX\@pcPunY + \GetCoord(\@scPun)\@scPunX\@scPunY + \GetCoord(\@sPun)\@sPunX\@sPunY + \pIIe@curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}% + {\@scPunX\unitlength}{\@scPunY\unitlength}% + {\@sPunX\unitlength}{\@sPunY\unitlength}% + \CopyVect\@sPun to\@pPun +\fi +\ifdim\@tdA>\z@ + \DirFromAngle\@gradi to\@Dir \if\Segno-\ConjVect\@Dir to\@Dir \fi + \SubVect\@Cent from\@pPun to\@V + \MultVect\@V by\@Dir to\@V + \AddVect\@Cent and\@V to\@sPun + \@tdA=.5\@tdA \Numero\@gradi\@tdA + \DirFromAngle\@gradi to\@Phimezzi + \GetCoord(\@Phimezzi)\@cosphimezzi\@sinphimezzi + \@tdB=1.3333333\p@ \@tdB=\@Raggio\@tdB + \@tdC=\p@ \advance\@tdC -\@cosphimezzi\p@ \Numero\@tempa\@tdC + \@tdB=\@tempa\@tdB + \DividE\@tdB by\@sinphimezzi\p@ to\@cZ + \ScaleVect\@Phimezzi by\@cZ to\@Phimezzi + \ConjVect\@Phimezzi to\@mPhimezzi + \if\Segno-% + \let\@tempa\@Phimezzi + \let\@Phimezzi\@mPhimezzi + \let\@mPhimezzi\@tempa + \fi + \SubVect\@sPun from\@pPun to\@V + \DirOfVect\@V to\@V + \MultVect\@Phimezzi by\@V to\@Phimezzi + \AddVect\@sPun and\@Phimezzi to\@scPun + \ScaleVect\@V by-1to\@V + \MultVect\@mPhimezzi by\@V to\@mPhimezzi + \AddVect\@pPun and\@mPhimezzi to\@pcPun + \GetCoord(\@pcPun)\@pcPunX\@pcPunY + \GetCoord(\@scPun)\@scPunX\@scPunY + \GetCoord(\@sPun)\@sPunX\@sPunY + \pIIe@curveto{\@pcPunX\unitlength}{\@pcPunY\unitlength}% + {\@scPunX\unitlength}{\@scPunY\unitlength}% + {\@sPunX\unitlength}{\@sPunY\unitlength}% +\fi} +\def\VectorArc(#1)(#2)#3{\begingroup +\@tdA=#3\p@ \ifdim\@tdA=\z@\else + \@VArc(#1)(#2)% +\fi +\endgroup\ignorespaces}% +\def\VectorARC(#1)(#2)#3{\begingroup +\@tdA=#3\p@ +\ifdim\@tdA=\z@\else + \@VARC(#1)(#2)% +\fi +\endgroup\ignorespaces}% +\def\@VArc(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi \Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\@tdE=\pIIe@FAW\@wholewidth \@tdE=\pIIe@FAL\@tdE +\Numero\@Freccia\@tdE +\DividE\@Freccia\p@ by \@Raggio\p@ to\DeltaGradi +\@tdD=\DeltaGradi\p@ +\@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD +\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD +\DirFromAngle\@tempa to\@Dir +\MultVect\@V by\@Dir to\@sPun +\edef\@tempA{\ifx\Segno-\m@ne\else\@ne\fi}% +\MultVect\@sPun by 0,\@tempA to\@vPun +\DirOfVect\@vPun to\@Dir +\AddVect\@sPun and #1 to \@sPun +\GetCoord(\@sPun)\@tdX\@tdY +\@tdD\ifx\Segno--\fi\DeltaGradi\p@ +\@tdD=.5\@tdD \Numero\DeltaGradi\@tdD +\DirFromAngle\DeltaGradi to\@Dird +\MultVect\@Dir by*\@Dird to\@Dir +\GetCoord(\@Dir)\@xnum\@ynum +\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}% +\@tdE =\ifx\Segno--\fi\DeltaGradi\p@ +\advance\@tdA -\@tdE \Numero\@gradi\@tdA +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +\def\@VARC(#1)(#2){% +\ifdim\@tdA>\z@ + \let\Segno+% +\else + \@tdA=-\@tdA \let\Segno-% +\fi \Numero\@gradi\@tdA +\ifdim\@tdA>360\p@ + \PackageWarning{curve2e}{The arc aperture is \@gradi\space degrees + and gets reduced\MessageBreak% + to the range 0--360 taking the sign into consideration}% + \@whiledim\@tdA>360\p@\do{\advance\@tdA-360\p@}% +\fi +\SubVect#1from#2to\@V \ModOfVect\@V to\@Raggio \CopyVect#2to\@pPun +\@tdE=\pIIe@FAW\@wholewidth \@tdE=0.8\@tdE +\Numero\@Freccia\@tdE +\DividE\@Freccia\p@ by \@Raggio\p@ to\DeltaGradi +\@tdD=\DeltaGradi\p@ \@tdD=57.29578\@tdD \Numero\DeltaGradi\@tdD +\@tdD=\ifx\Segno--\fi\@gradi\p@ \Numero\@tempa\@tdD +\DirFromAngle\@tempa to\@Dir +\MultVect\@V by\@Dir to\@sPun +\edef\@tempA{\ifx\Segno-\m@ne\else\@ne\fi}% +\MultVect\@sPun by 0,\@tempA to\@vPun +\DirOfVect\@vPun to\@Dir +\AddVect\@sPun and #1 to \@sPun +\GetCoord(\@sPun)\@tdX\@tdY +\@tdD\ifx\Segno--\fi\DeltaGradi\p@ +\@tdD=.5\@tdD \Numero\@tempB\@tdD +\DirFromAngle\@tempB to\@Dird +\MultVect\@Dir by*\@Dird to\@Dir +\GetCoord(\@Dir)\@xnum\@ynum +\put(\@tdX,\@tdY){\vector(\@xnum,\@ynum){0}}% +\@tdE =\DeltaGradi\p@ +\advance\@tdA -2\@tdE \Numero\@gradi\@tdA +\CopyVect#1to\@Cent \GetCoord(\@pPun)\@pPunX\@pPunY +\SubVect\@Cent from\@pPun to \@V +\edef\@tempa{\ifx\Segno-\else-\fi\@ne}% +\MultVect\@V by0,\@tempa to\@vPun +\@tdE\ifx\Segno--\fi\DeltaGradi\p@ +\Numero\@tempB{0.5\@tdE}% +\DirFromAngle\@tempB to\@Dird +\MultVect\@vPun by\@Dird to\@vPun +\DirOfVect\@vPun to\@Dir\GetCoord(\@Dir)\@xnum\@ynum +\put(\@pPunX,\@pPunY){\vector(\@xnum,\@ynum){0}} +\edef\@tempa{\ifx\Segno--\fi\DeltaGradi}% +\DirFromAngle\@tempa to \@Dir +\SubVect\@Cent from\@pPun to\@V +\MultVect\@V by\@Dir to\@V +\AddVect\@Cent and\@V to\@pPun +\GetCoord(\@pPun)\@pPunX\@pPunY +\@@Arc +\pIIe@strokeGraph\ignorespaces}% +\def\CurveBetween#1and#2WithDirs#3and#4{% +\StartCurveAt#1WithDir{#3}\relax +\CurveTo#2WithDir{#4}\CurveFinish}% +\def\StartCurveAt#1WithDir#2{% +\begingroup +\GetCoord(#1)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Pzero +\pIIe@moveto{\@tempa\unitlength}{\@tempb\unitlength}% +\GetCoord(#2)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Dzero +\DirOfVect\@Dzero to\@Dzero} +\def\ChangeDir<#1>{% +\GetCoord(#1)\@tempa\@tempb +\CopyVect\@tempa,\@tempb to\@Dzero +\DirOfVect\@Dzero to\@Dzero +\ignorespaces} +\def\CurveFinish{\pIIe@strokeGraph\endgroup\ignorespaces}% +\def\CurveTo#1WithDir#2{% +\def\@Puno{#1}\def\@Duno{#2}\DirOfVect\@Duno to\@Duno +\DistanceAndDirOfVect\@Puno minus\@Pzero to\@Chord and\@DirChord +\MultVect\@Dzero by*\@DirChord to \@Dpzero +\MultVect\@Duno by*\@DirChord to \@Dpuno +\GetCoord(\@Dpzero)\@Xpzero\@Ypzero +\GetCoord(\@Dpuno)\@Xpuno\@Ypuno +\ifdim\@Xpzero\p@=\z@ + \ifdim\@Xpuno\p@=\z@ + \@tdA=0.666666\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \edef\@Mcpuno{\@Mcpzero}% + \else + \@tdA=0.666666\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \SetCPmodule\@Mcpuno from\@ne\@Chord\@Dpuno% + \fi +\else + \ifdim\@Xpuno\p@=\z@ + \@tdA=0.666666\p@ + \Numero\@Mcpuno{\@Chord\@tdA}% + \SetCPmodule\@Mcpzero from\@ne\@Chord\@Dpzero% + \else + \ifdim\@Ypzero\p@=\z@ + \@tdA=0.333333\p@ + \Numero\@Mcpzero{\@Chord\@tdA}% + \ifdim\@Ypuno\p@=\z@ + \edef\@Mcpuno{\@Mcpzero}% + \fi + \else + \ifdim\@Ypuno\p@=\z@ + \@tdA=0.333333\p@ + \Numero\@Mcpuno{\@Chord\@tdA}% + \SetCPmodule\@Mcpzero from\@ne\@Chord\@Dpzero + \else + \@tdA=\@Ypzero\p@ \@tdA=\@Ypuno\@tdA + \ifdim\@tdA>\z@ + \ConjVect\@Dpuno to\@Dwpuno + \else + \edef\@Dwpuno{\@Dpuno}% + \fi + \GetCoord(\@Dwpuno)\@Xwpuno\@Ywpuno + \@tdA=\@Xpzero\p@ \@tdA=\@Ywpuno\@tdA + \@tdB=\@Xwpuno\p@ \@tdB=\@Ypzero\@tdB + \DividE\@tdB by\@tdA to\@Fact + \@tdC=\p@ \advance\@tdC-\@Fact\p@ + \ifdim\@tdC<\z@ \@tdC=-\@tdC\fi + \DividE\p@ by \@Fact\p@ to\@Fact + \@tdD=\p@ \advance\@tdD-\@Fact\p@ + \ifdim\@tdD<\z@ \@tdD=-\@tdD\fi + \ifdim\@tdD<0.0001\p@ + \def\@factzero{1}% + \def\@factuno{1}% + \else + \DividE\p@ by\@tdC to\@factzero + \DividE\p@ by\@tdD to\@factuno + \fi + \SetCPmodule\@Mcpzero from\@factzero\@Chord\@Dpzero + \SetCPmodule\@Mcpuno from\@factuno\@Chord\@Dwpuno + \fi + \fi + \fi +\fi +\ScaleVect\@Dzero by\@Mcpzero to\@CPzero +\AddVect\@Pzero and\@CPzero to\@CPzero +\ScaleVect\@Duno by\@Mcpuno to\@CPuno +\SubVect\@CPuno from\@Puno to\@CPuno +\GetCoord(\@Puno)\@XPuno\@YPuno +\GetCoord(\@CPzero)\@XCPzero\@YCPzero +\GetCoord(\@CPuno)\@XCPuno\@YCPuno +\pIIe@curveto{\@XCPzero\unitlength}{\@YCPzero\unitlength}% + {\@XCPuno\unitlength}{\@YCPuno\unitlength}% + {\@XPuno\unitlength}{\@YPuno\unitlength}% +\CopyVect\@Puno to\@Pzero +\CopyVect\@Duno to\@Dzero +\ignorespaces}% +\def\SetCPmodule#1from#2#3#4{% +\GetCoord(#4)\t@X\t@Y +\@tdA=#3\p@ +\@tdA=#2\@tdA +\@tdA=1.333333\@tdA +\@tdB=\p@ \advance\@tdB +\t@X\p@ +\DividE\@tdA by\@tdB to#1\relax +\ignorespaces}% +\def\Curve(#1)<#2>{% + \StartCurveAt#1WithDir{#2}% + \@ifnextchar\lp@r\@Curve{% + \PackageWarning{curve2e}{% + Curve specifications must contain at least two nodes!\Messagebreak + Please, control your Curve specifications\MessageBreak}}} +\def\@Curve(#1)<#2>{% + \CurveTo#1WithDir{#2}% + \@ifnextchar\lp@r\@Curve{% + \@ifnextchar[\@ChangeDir\CurveFinish}} +\def\@ChangeDir[#1]{\ChangeDir<#1>\@Curve} + +\endinput +%% +%% End of file `curve2e.sty'. diff --git a/Master/texmf-dist/tpm/curve2e.tpm b/Master/texmf-dist/tpm/curve2e.tpm new file mode 100644 index 00000000000..338a40c2e44 --- /dev/null +++ b/Master/texmf-dist/tpm/curve2e.tpm @@ -0,0 +1,29 @@ +<!DOCTYPE rdf:RDF SYSTEM "../../support/tpm.dtd"> +<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:TPM="http://texlive.dante.de/"> + <rdf:Description about="http://texlive.dante.de/texlive/Package/curve2e.zip"> + <TPM:Name>curve2e</TPM:Name> + <TPM:Type>Package</TPM:Type> + <TPM:Date>2005/08/28 08:58:00</TPM:Date> + <TPM:Version></TPM:Version> + <TPM:Creator>karl</TPM:Creator> + <TPM:Title>The curve2e package.</TPM:Title> + <TPM:Description></TPM:Description> + <TPM:Author></TPM:Author> + <TPM:Size>315193</TPM:Size> + <TPM:Build/> + <TPM:RunFiles size="22672"> +texmf-dist/tex/latex/curve2e/curve2e.sty +texmf-dist/tpm/curve2e.tpm + </TPM:RunFiles> + <TPM:DocFiles size="221395"> +texmf-dist/doc/latex/curve2e/curve2e.pdf +texmf-dist/doc/latex/curve2e/manifest.txt + </TPM:DocFiles> + <TPM:SourceFiles size="72153"> +texmf-dist/source/latex/curve2e/curve2e.dtx +texmf-dist/source/latex/curve2e/curve2e.ins + </TPM:SourceFiles> + <TPM:Provides>Package/curve2e</TPM:Provides> + </rdf:Description> +</rdf:RDF> + |