% \iffalse
% +AMDG  This document was begun on 1E June 11EE, the vigil
% of the Nativity of St. John the Baptist, and it is humbly
% dedicated to him and to the Immaculate Heart of Mary, for
% their prayers, and to the Sacred Heart of Jesus, for His
% mercy.
% 
% This document is copyright 2015 by Donald P. Goodman, and is
% released publicly under the LaTeX Project Public License.  The
% distribution and modification of this work is constrained by the
% conditions of that license.  See
% 	http://www.latex-project.org/lppl.txt
% for the text of the license.  This document is released
% under version 1.3 of that license, and this work may be distributed
% or modified under the terms of that license or, at your option, any
% later version.
% 
% This work has the LPPL maintenance status 'maintained'.
% 
% The Current Maintainer of this work is Donald P. Goodman
% (dgoodmaniii@gmail.com).
% 
% This work consists of the files shapes.dtx and
% shapes.ins, along with the generated file shapes.mp
% and shapes.pdf, and the README.
% \fi

% \iffalse
%<*driver>

\documentclass{ltxdoc}
\usepackage{docmfp}
\usepackage{url}
\usepackage[typeone]{dozenal}
\usepackage{verbatim}
\usepackage{mflogo}
\usepackage[everymp={input shapes;},latex]{gmp}
\usepackage{makeidx}
\makeindex
\long\def\demonstrate#1#2{%
	\bigskip%
	\hrule%
	\hbox to\linewidth{%
		\hbox to0.65\linewidth{%
			\vbox to1.4in{\vfil#1\vfil}%
		}\hbox to0.35\linewidth{%
			\vbox to1.4in{\vfil#2\vfil}%
		}%
	}%
	\hrule%
	\bigskip%
}

\begin{document}
\DocInput{shapes.dtx}
\end{document}
%</driver>
% \fi
% \title{The \texttt{shapes} Macros, v1.0}
% \author{Donald P.\ Goodman III}
% \date{\today}
%
% \maketitle
% \begin{abstract}\noindent
% The |shapes| macros for \MP\ provide regular polygons,
% their corresponding reentrant stars, and images
% demonstrating fractions.  These macros are quite
% configurable.
% \end{abstract}
% 
% \tableofcontents
%
% \section{Introduction}
%
% The |shapes| macros are not revolutionary, and in fact are
% quite simple; however, I spent some time generalizing them
% for a text I'm currently working on, and so I thought they
% might be useful for the general populace.  They are
% divided into two main groups:  regular polygons and their
% corresponding reentrant star shapes; and fractionals,
% circles divided into a certain number of parts with the
% desired fraction filled in.
%
% This document was typeset in accordance with the
% |docstrip| utility, which allows the automatic extraction
% of code and documentation from the same document.
%
% \section{Prerequisites and Conventions}
%
% Some prerequesites for using this package are \MP\ itself
% (obviously).  If you're using the package with \LaTeX, the
% |gmp| package would probably be helpful; be sure to use
% the |latex| package option.  
% These should be packaged in any
% reasonably modern \LaTeX\ system, such as \TeX Live or
% Mik\TeX.
%
% This documentation assumes nothing about your personal
% \TeX\ or \MP\ environment.  Con\TeX t and the various
% forms of Lua\TeX\ have \MP\ built-in; with pdf\LaTeX, the
% author's choice, one can use the |gmp| package to
% include the source directly in one's document (that's
% what's been done in this documentation) or develop a
% simple script to compile them afterwards and include them
% in the source via |\includegraphics| (probably the
% quickest option, since compilation is done in advance).
% Here, we simply post the plain vanilla \MP\ code, and let
% you work out those details however you prefer.
%
% \section{The Shapes Macros}
%
% We begin with the simple shapes macros, which are about as
% basic as they can be.
%
% All of these shapes default to
% circles with a one inch diameter, so you can scaled them
% with that kept in mind.
%
% The simplest case is with a regular
% polygon, like so:
%
% \demonstrate{%
%	\hbox{|modfig(6,0);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modfig(6,0); draw modfigure;
%	\end{mpost}
% }%
%
% Of course, these drawn figures can be manipulated in the
% usual ways:
%
% \demonstrate{%
%	\hbox{|modfig(6,0);|}
%	\hbox{|draw modfigure rotated (45) withcolor red;|}
% }{%
% 	\begin{mpost}
%	modfig(6,0); draw modfigure rotated (45) withcolor red;
%	\end{mpost}
% }%
%
% The two arguments to |modfig| are simple:  the first tells
% the number of sides desired, while the second means
% \emph{no numbers are printed} if 0, and \emph{print
% numbers} if 1:
% 
% \demonstrate{%
%	\hbox{|modfig(8,1);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modfig(8,1); draw modfigure;
%	\end{mpost}
% }%
%
% If you don't want the circle to be printed, simply tell
% \MP\ with |modcircle := false;| and it will not print it:
%
% \demonstrate{%
%	\hbox{|modcircle := false;|}
%	\hbox{|modfig(8,1);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modcircle := false;
%	modfig(8,1); draw modfigure;
%	\end{mpost}
% }%
%
% |modcircle| defaults to |true|.
%
% Notice that |modfig| doesn't care if there's a circle or
% not; if you want numbers on the vertices, it will print
% them there.
%
% You can adjust the width of the lines by specifying
% |modcirclepen| and |modshapepen|:
%
% \demonstrate{%
%	\hbox{|modcirclepen := pencircle scaled 3;|}
%	\hbox{|modshapepen := pencircle scaled 2;|}
%	\hbox{|modfig(4,0);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modcirclepen := pencircle scaled 3;
%	modshapepen := pencircle scaled 2;
%	modfig(4,0); draw modfigure;
%	\end{mpost}
% }%
%
% Both |modcirclepen| and |modshapepen| default to 
% |pencircle scaled 1|.
%
% We can also put ticks around the outside of the circle,
% at whatever intervals we want.  The parameters here are
% \DescribeMacro{modticks}|modticks|, which is a boolean set
% to |false| by default.  Set it to |true| if you want
% ticks.  You can control the number of ticks with
% \DescribeMacro{nummodticks}|nummodticks|, which defaults
% to twelve.  You can control the length of those ticks with
% \DescribeMacro{ticklen}|ticklen|, which defaults to
% |0.1in|.  Finally, you can control the pen that is used to
% draw the ticks, which is \DescribeMacro{tickpen}|tickpen|,
% which defaults to |pencircle scaled 1|:
%
% \demonstrate{%
%	\hbox{|nummodticks := 6;|}
%	\hbox{|ticklen := 0.2in;|}
%	\hbox{|modticks := true;|}
%	\hbox{|tickpen := pensquare scaled 2;|}
%	\hbox{|modshapepen := pensquare scaled 4;|}
%	\hbox{|modfig(4,0);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	nummodticks := 6;
%	ticklen := 0.2in;
%	modticks := true;
%	tickpen := pensquare scaled 2;
%	modshapepen := pensquare scaled 4;
%	modfig(4,0); draw modfigure;
%	\end{mpost}
% }%
%
% We can do essentially the same thing with reentrant star
% figures with |modstar|.  Unlike |modfig|, |modstar| takes
% \emph{three} arguments:  the number of vertices, whether
% or not you want those vertices numbered, and how many
% points you want to skip as you go around the circle.
%
% \demonstrate{%
%	\hbox{|modstar(11,1,3);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modstar(11,1,3); draw modfigure;
%	\end{mpost}
% }%
%
% Note that the third argument actually skips $n - 1$
% points, not $n$ points.  But all the same parameters we
% saw when looking at |modfig| will still work in the same
% way:
% 
% \demonstrate{%
%	\hbox{|modcirclepen := pencircle scaled 1;|}
%	\hbox{|modshapepen := pencircle scaled 2;|}
%	\hbox{|modstar(11,1,4);|}
%	\hbox{|draw modfigure;|}
% }{%
% 	\begin{mpost}
%	modcirclepen := pencircle scaled 1;
%	modshapepen := pencircle scaled 2;
%	modstar(11,1,4); draw modfigure;
%	\end{mpost}
% }%
%
% And that's about all there is to it.
%
% \section{Fraction Images}
% \label{sect:fraimg}
%
% The following macros are useful for demonstrating the
% nature and size of fractions in a visible way.  The name
% of the game here is |fraccirc|, which takes two arguments:
% the number of parts to be filled, and the number of parts
% in the whole:
%
% \demonstrate{%
%	\hbox{|fraccirc(7)(12);|}
%	\hbox{|draw thefrac;|}
% }{%
% 	\begin{mpost}
%	fraccirc(7)(12);
%	draw thefrac;
%	\end{mpost}
% }
%
% Note that, due to the internal implementation, these two
% arguments must each be enclosed in their own parentheses.
%
% We can adjust these things as appropriate.  For example,
% we can fill with blue rather than red, and use thicker
% lines:
%
% \demonstrate{%
%	\hbox{|fracfillcolor := blue;|}
%	\hbox{|fraccirclepen := pencircle scaled 1;|}
%	\hbox{|fractionpen := pencircle scaled 2;|}
%	\hbox{|fraccirc(4)(7);|}
%	\hbox{|draw thefrac;|}
% }{%
% 	\begin{mpost}
%	fracfillcolor := blue;
% 	fraccirclepen := pencircle scaled 1;
%	fractionpen := pencircle scaled 2;
%	fraccirc(4)(7);
%	draw thefrac;
%	\end{mpost}
% }
%
% As the above example suggests, |fracfillcolor| gives the
% color with which the portion of the fraction should be
% filled; it defaults to |red|.  |fraccirclepen| is the pen
% used to draw the circle around the fraction; it defaults
% to |pencircle scaled 1.5|.  Finally, |fractionpen| is the
% pen used to draw the partition and the circle immediately
% surrounding them; it defaults to |pencircle scaled 1|.
%
% \section{Implementation}
% \label{sect:implem}
%
%    \begin{macrocode}
color fracfillcolor; fracfillcolor := red;
pen fraccirclepen; fraccirclepen := pencircle scaled 1.5;
pen fractionpen; fractionpen := pencircle scaled 1;
def fraccirc(suffix x)(expr y) =
	radius := 1in;
	ticklen := radius/24;
	path circ; circ := fullcircle scaled radius;
	pair p[]; pair q[]; pair r[]; pair s[];
	p[0] := (0,0) shifted (0,radius/2);
	q[0] := p[0] shifted (0,ticklen);
	r[0] := p[0] shifted (0,-ticklen);
	s[0] := r[0];
	picture thefrac;
	picture addition;
	thefrac := image(pickup fraccirclepen; draw circ;);
	addition := image(pickup fractionpen; draw p[0]--q[0];);
	addto thefrac also addition;
	for i=1 upto 12:
		p[i] := p[i-1] rotatedaround ((0,0),-30);
		q[i] := q[i-1] rotatedaround ((0,0),-30);
		addition := image(pickup fractionpen; draw p[i]--q[i];);
		addto thefrac also addition;
	endfor;
	addition := image(pickup fractionpen; draw (0,0)--r[0];);
	addto thefrac also addition;
	pair t; pair q;
	addition := image(
		t = r[0] rotatedaround ((0,0),-((360/y)*x)/2);
		q = r[0] rotatedaround ((0,0),-((360/y)*x));
		fill r[0]--(0,0)--q..t..cycle withcolor fracfillcolor;
		draw r[0]--(0,0)--q..t..cycle;
	);
	addto thefrac also addition;
	for i=1 upto y:
		r[i] := r[i-1] rotatedaround ((0,0),-(360/y));
		s[i] := r[i-1] rotatedaround ((0,0),-(360/y)/2);
		addition := image(%
			pickup fractionpen;%
			draw (0,0)--r[i];
			draw r[i-1]..s[i]..r[i];
		);
		addto thefrac also addition;
	endfor;
enddef;
% put in the pens for the modular shapes
boolean modcircle; modcircle := true;
pen modcirclepen; modcirclepen := pencircle scaled 1;
pen modshapepen; modshapepen := pencircle scaled 1;
boolean modticks; modticks := false;
numeric nummodticks; nummodticks := 12;
numeric ticklen; ticklen := 0.1in;
pen tickpen; tickpen := pencircle scaled 1;
def modstar(expr numpoints,numbers,numstar) =
	picture modfigure;
	if (modcircle = true):
		modfigure := image(draw fullcircle scaled 1in withpen modcirclepen;);
	else:
		modfigure := image();
	fi;
	picture modtickpic;
	if (modticks = true):
		modtickpic := image(
			pair tickstart[]; pair tickend[];
			tickstart[0] = (0,0) shifted (0,0.5in);
			tickend[0] = tickstart[0] shifted (0,ticklen);
			draw tickstart[0]--tickend[0] withpen tickpen;
			for i=1 upto (nummodticks-1):
				tickstart[i] = tickstart[i-1] rotatedaround
					((0,0), (360/nummodticks));
				tickend[i] = tickend[i-1] rotatedaround
					((0,0), (360/nummodticks));
				draw tickstart[i]--tickend[i] withpen tickpen;
			endfor;
		);
		addto modfigure also modtickpic;
	fi
	pickup modshapepen;
	pair p[]; pair q[];
	picture addition;
	p[0] = (0,0.5in);
	q[0] = (0,0.6in);
	if (numbers = 1):
		addition := image(label("0",q[0]));
		addto modfigure also addition;
	fi
	for i=1 upto numpoints:
		p[i] = p[i-1] rotatedaround ((0,0),-(360/numpoints));
		q[i] = q[i-1] rotatedaround ((0,0),-(360/numpoints));
		if (numbers = 1):
			if (i <> numpoints):
				addition := image(label(decimal i,q[i]));
				addto modfigure also addition;
			fi
		fi
	endfor
	for i=0 upto numpoints:
		if (i < numstar):
			addition := image(%
				draw p[i]--p[i+numstar];
				draw p[i]--p[numpoints - numstar + i];
			);
			addto modfigure also addition;
		elseif (i >= (numstar*2)):
			addition := image(draw p[i-numstar]--p[i]);
			addto modfigure also addition;
		fi
	endfor
	addto modfigure also addition;
enddef;
def modfig(expr numpoints,numbers) =
	picture modfigure;
	if (modcircle = true):
		modfigure := image(draw fullcircle scaled 1in withpen modcirclepen);
	else:
		modfigure := image();
	fi
	picture modtickpic;
	if (modticks = true):
		modtickpic := image(
			pair tickstart[]; pair tickend[];
			tickstart[0] = (0,0) shifted (0,0.5in);
			tickend[0] = tickstart[0] shifted (0,ticklen);
			draw tickstart[0]--tickend[0] withpen tickpen;
			for i=1 upto (nummodticks-1):
				tickstart[i] = tickstart[i-1] rotatedaround
					((0,0), (360/nummodticks));
				tickend[i] = tickend[i-1] rotatedaround
					((0,0), (360/nummodticks));
				draw tickstart[i]--tickend[i] withpen tickpen;
			endfor;
		);
		addto modfigure also modtickpic;
	fi
	pair p[]; pair q[];
	picture addition;
	pickup modshapepen;
	p[0] = (0,0.5in);
	q[0] = (0,0.6in);
	if (numbers = 1):
		addition := image(label("0",q[0]));
		addto modfigure also addition;
	fi
	for i=1 upto numpoints:
		p[i] = p[i-1] rotatedaround ((0,0),-(360/numpoints));
		q[i] = q[i-1] rotatedaround ((0,0),-(360/numpoints));
		addition := image(draw p[i-1]--p[i]);
		addto modfigure also addition;
		if (numbers = 1):
			if (i <> numpoints):
				addition := image(label(decimal i,q[i]));
				addto modfigure also addition;
			fi
		fi
	endfor;
enddef;
%    \end{macrocode}