path: root/Master/texmf-dist/tex/latex/lapdf/lapdf.sty

% =========================================================================
% LAPDF.STY: Version 1.1, Copyright(C) 2006-2011, Detlef Reimers
% Lapdf is distributed under the terms of the GNU general public licence
% -------------------------------------------------------------------------
% Email:   detlefreimers@gmx.de     Website: http://detlefreimers.de
% =========================================================================
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{lapdf}[2006/04/09 v1.0 Drawing with pdfTeX]
\RequirePackage{calc}

\newtoks\@c \newtoks\@d \newtoks\@e \newtoks\@f

\let\@ta\@tempcnta \let\@tb\@tempcntb \newcount\@@s
\newcount\@@i \newcount\@@k \newcount\@@n \newcount\col
\newcount\@az \newcount\@bz \newcount\@cz \newcount\@xz
\newcount\@ca \newcount\@cb \newcount\@cc \newcount\@cd
\newcount\@ce \newcount\@cf \newcount\@cg \newcount\@ch
\newcount\@ci \newcount\@ck \newcount\@cl \newcount\@cm
\newcount\@cn

\let\@tbox\@tempboxa
\let\@@a\@ovdx \let\@@b\@ovdy \let\@@t\@ovxx \let\@@u\@ovyy
\newdimen\wid \newdimen\tmp
\newdimen\@@d \newdimen\@@m \newdimen\@@x \newdimen\@@y
\newdimen\@@A \newdimen\@@B \newdimen\@@C \newdimen\@@D
\newdimen\@@T \newdimen\@@U \newdimen\@@X \newdimen\@@Y
\newdimen\@CR \newdimen\@CG \newdimen\@CB
\newdimen\@ax \newdimen\@ay \newdimen\@az
\newdimen\@bx \newdimen\@by \newdimen\@bz
\newdimen\@cx \newdimen\@cy \newdimen\@cz
\newdimen\@dx \newdimen\@dy \newdimen\@dz
\newdimen\@ex \newdimen\@ey \newdimen\@ez
\newdimen\@fx \newdimen\@fy \newdimen\@fz
\newdimen\@gx \newdimen\@gy \newdimen\@gz
\newdimen\@hx \newdimen\@hy \newdimen\@hz
\newdimen\@rx \newdimen\@ry \newdimen\@rz \newdimen\@rw
\newdimen\@sx \newdimen\@sy \newdimen\@tx \newdimen\@ty
\newdimen\@ux \newdimen\@uy \newdimen\@vx \newdimen\@vy
\newdimen\@wx \newdimen\@wy
\newdimen\@xx \newdimen\@xy \newdimen\@xz
\newdimen\@zx \newdimen\@zy \newdimen\@zz
\newdimen\@yx \newdimen\@yy

% -------------------------------------------------------------------------
\@ck=0
\wid=0.35pt

% -------------------------------------------------------------------------
\DeclareOption{black}{%
 \@cl=0
 \gdef\Resetcol{}
 \gdef\Stepcol(#1,#2,#3){}
 \gdef\Nextcol(#1,#2){}
}
\DeclareOption{color}{%
 \@cl=1
 \gdef\Resetcol{\col=-1}
 \gdef\Stepcol(#1,#2,#3){%
  \@cc=\col \Add(\@cc,#3)
  \ifnum#1<0 \@ca=0 \else \@ca=#1 \fi
  \ifnum#2>95 \@cb=95 \else \@cb=#2 \fi
  \ifnum\col<\@ca \col=\@ca \else
   \ifnum\col>\@cb \col=\@ca \else
    \ifnum\@cc<\@ca \col=\@ca \else
     \ifnum\@cc>\@cb \col=\@ca \else \col=\@cc \fi\fi\fi\fi
  \ifnum\col<96%
   \Colval(\col,8,\@rx)
   \Colval(\col,0,\@gx)
   \Colval(\col,16,\@bx)
   \Setcol(\Np\@rx,\Np\@gx,\Np\@bx) \fi}
 \gdef\Nextcol(#1,#2){\Stepcol(#1,#2,1)}
}

% -------------------------------------------------------------------------
% Calculates the cromatic intensity of a specific color. n is the color,
% d is the color offset (r: 8, g: 0, b: 16) and r is the result register.
%   \Colval(n,d,r)
% -------------------------------------------------------------------------
\gdef\Colval(#1,#2,#3){%
 \ifnum#1>71 \@cm=3 \else \ifnum#1>47 \@cm=2 \else
  \ifnum#1>23 \@cm=1 \else \@cm=0 \fi \fi \fi
 \@cn=#1 \Add(\@cn,#2) \Mod(\@cn,24)
 \Sub(\@cn,8) \Abs(\@cn)
 \ifnum\@cn<4 \Dset(#3,1) \else
  \ifnum\@cn<8 \Dset(#3,8) \Dsub(#3,\@cn)
   \Div(#3,4) \else \Dset(#3,0) \fi \fi
 \Dset(\@tx,5) \Dsub(\@tx,\@cm) \Dmul(#3,\@tx) \Div(#3,5) \Crnd(#3)}

% -------------------------------------------------------------------------
% This macro is only necessary, because my TeX compiler under MacOS9.2
% says 'out of color stack space' without the rounding. With this function,
% all color values have two digits or less. \Crnd(col)
% -------------------------------------------------------------------------
\gdef\Crnd(#1){\Ddiv(#1,0.0999pt) \Mul(#1,10) \Dint(#1) \Ddiv(#1,100pt)}

% -------------------------------------------------------------------------
\ExecuteOptions{black}
\ProcessOptions
 \ifnum\@cl>0 \AtBeginDocument{\Resetcol} \fi

% -------------------------------------------------------------------------
% Strips the pt dimension
% -------------------------------------------------------------------------
{\catcode`t=12\catcode`p=12\gdef\nP#1pt{#1}}
\gdef\Np#1{\expandafter\nP\the#1}%

% -------------------------------------------------------------------------
%   \Lapdf{}  the Lapdf logo
% -------------------------------------------------------------------------
\def\Lapdf{L\kern-.2em\lower.5ex\hbox{A}\kern-.15emPDF}

% -------------------------------------------------------------------------
%   \pdfTeX{}  a pdfTeX logo
% -------------------------------------------------------------------------
\def\pdfTeX{\hbox{pdf}\kern+.05em\TeX{}}

% -------------------------------------------------------------------------
%   \PDF{cmd} for the pdf specials, which are used here
% -------------------------------------------------------------------------
\gdef\PDF#1{\@killglue\special{pdf:#1}}

% -------------------------------------------------------------------------
%   \lapdf(x1,y1)(x2,y2)  the lapdf environment
% -------------------------------------------------------------------------
\newcommand{\pdf}{\Gsave \Scale(\Np\unitlength,\Np\unitlength)
 \Setwidth(0.02) \Setcap(1) \Setdash([] 0)}
\def\endpdf{\Grestore}

\newcommand{\lapdf}{\@pdfpict}
 \gdef\@pdfpict(#1,#2)(#3,#4){\begin{picture}(#1,#2)(#3,#4) \begin{pdf}}
\def\endlapdf{\end{pdf} \end{picture}}

% -------------------------------------------------------------------------
% Gets the unit length from document. Define and set a register.
% -------------------------------------------------------------------------
\gdef\Ul{\unitlength}
\gdef\Set(#1,#2){#1=#2}
\gdef\Dset(#1,#2){#1=#2pt}
\gdef\Defnum(#1,#2){\newcount#1 #1=#2}
\gdef\Defdim(#1,#2){\newdimen#1 #1=#2pt}

% -------------------------------------------------------------------------
% Two macros for count or dimen registers. If nested, you have to use
% brackets around the inner looop.
%  \whilenum{num condition}{commands}  \whiledim{dim condition}{commands}
% -------------------------------------------------------------------------
\gdef\Whilenum#1#2{\loop\ifnum#1#2\repeat}
\gdef\Whiledim#1#2{\loop\ifdim#1pt#2\repeat}

% -------------------------------------------------------------------------
% Arithmetic with count registers.
% -------------------------------------------------------------------------
\gdef\Add(#1,#2){\advance#1#2}
\gdef\Sub(#1,#2){\advance#1-#2}
\gdef\Mul(#1,#2){\multiply#1#2}
\gdef\Div(#1,#2){\divide#1#2}
\gdef\@Abs(#1){\ifnum#1<\z@ #1=-#1 \@@s=-1 \else \@@s=1 \fi}
\gdef\Abs(#1){\ifnum#1<\z@ #1=-#1 \fi}
\gdef\Sig(#1,#2){\ifnum#1<\z@ \Set(#2,-1) \else \Set(#2,1) \fi}
\gdef\Mod(#1,#2){\@@i=#1 \Div(\@@i,#2) \Mul(\@@i,#2) \Sub(#1,\@@i)}

% -------------------------------------------------------------------------
% Arithmetic with dimen registers. Dmul & Ddiv use the calc package.
% -------------------------------------------------------------------------
\gdef\Dadd(#1,#2){\advance#1#2pt}
\gdef\Dsub(#1,#2){\advance#1-#2pt}
\gdef\Dmul(#1,#2){\setlength{#1}{#1*\ratio{#2}{1pt}}}
\gdef\Ddiv(#1,#2){\setlength{#1}{1pt*\ratio{#1}{#2}}}
\gdef\@Dabs(#1){\ifdim#1<\z@ #1=-#1 \@@s=-1 \else \@@s=1 \fi}
\gdef\Dabs(#1){\ifdim#1<\z@ #1=-#1 \fi}
\gdef\Dint(#1){\@@i=#1 \Div(\@@i,65536) \Dset(#1,\@@i)}
\gdef\Dsig(#1,#2){\ifdim#1<\z@ \Set(#2,-1) \else \Set(#2,1) \fi}
\gdef\Dmod(#1,#2){\@@m=#1 \Ddiv(\@@m,#2pt)
 \Dint(\@@m) \Dmul(\@@m,#2pt) \Sub(#1,\@@m)}

% -------------------------------------------------------------------------
% Conversion to radian or degree.
%   \Rad(x,result)   \Deg(x,result)
% -------------------------------------------------------------------------
\gdef\Rad(#1,#2){\Dset(#2,#1) #2=0.017453#2}
\gdef\Deg(#1,#2){\Dset(#2,#1) #2=57.29578#2}

% -------------------------------------------------------------------------
% Calculates the sinus of an angle r in radian. The result is returned
% in register r. First, we reduce the argument to [0,2pi]. \Sin(x,r)
% -------------------------------------------------------------------------
\gdef\Sin(#1,#2){%
 \Dset(\@@x,#1) \Dmod(\@@x,6.2832)
 \@@y=\@@x \@@a=\@@x
 \Dset(\@@d,1) \@ta=1
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@a,\@@x) \Add(\@ta,1) \Div(\@@a,\@ta)
  \Dmul(\@@a,\@@x) \Add(\@ta,1) \Div(\@@a,\@ta)
  \@@a=-\@@a \Add(\@@y,\@@a) \@@d=\@@a \Dabs(\@@d)} #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the cosinus of an angle r in radian. The result is returned
% in register r. First, we reduce the argument to [0,2pi]. \Cos(x,r)
% -------------------------------------------------------------------------
\gdef\Cos(#1,#2){%
 \Dset(\@@x,#1) \Dmod(\@@x,6.2832)
 \Dset(\@@d,1) \@ta=0
 \Dset(\@@y,1) \Dset(\@@a,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@a,\@@x) \Add(\@ta,1) \Div(\@@a,\@ta)
  \Dmul(\@@a,\@@x) \Add(\@ta,1) \Div(\@@a,\@ta)
  \@@a=-\@@a \Add(\@@y,\@@a) \@@d=\@@a \Dabs(\@@d)} #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the tangens of an angle r in radian. The result is returned
% in register r.  First, we reduce the argument to [0,2pi]. We limit the
% maximum value at |n/2*pi| to 5. \Tan(x,r)
% -------------------------------------------------------------------------
\gdef\Tan(#1,#2){%
 \Dset(\@@U,#1) \Dmod(\@@U,6.2832)
 \Sin(\Np\@@U,\@@X) \Cos(\Np\@@U,\@@Y)
 \ifdim\@@Y=0pt \Dset(\@@X,5) \else \Ddiv(\@@X,\@@Y) \fi
 #2=\@@X}

% -------------------------------------------------------------------------
% Calculates the arcus sinus of x. The result is returned in register r.
% \Asin(x,r)
% -------------------------------------------------------------------------
\gdef\Asin(#1,#2){%
 \Dset(\@@x,#1) \@ta=1
 \ifdim\@@x<1.0pt
  \ifdim\@@x>-1.0pt
   \@@y=\@@x \@@t=\@@x \Dset(\@@d,1)
   \@whiledim{\@@d>0pt}\do{%
    \Mul(\@@t,\@ta) \Dmul(\@@t,\@@x) \Add(\@ta,1)
    \Div(\@@t,\@ta) \Dmul(\@@t,\@@x) \Add(\@ta,1)
    \@@u=\@@t \Div(\@@t,\@ta) \Add(\@@y,\@@t)
    \@@d=\@@t \Dabs(\@@d) \@@t=\@@u}
  \else \Dset(\@@y,-1.5708) \fi
 \else \Dset(\@@y,1.5708) \fi #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the arcus cosinus of x. The result is returned in register r.
% \Acos(x,r)
% -------------------------------------------------------------------------
\gdef\Acos(#1,#2){%
 \Asin(#1,\@@y) \Dset(#2,1.5708) \Sub(#2,\@@y)}

% -------------------------------------------------------------------------
% Calculates the arcus tangens of x. The result is returned in register r.
% Because the power series of atan converges too slowly, we use the
% addition theorem of atan and split the calculation to get accurate
% results. \Atan(x,r)
% -------------------------------------------------------------------------
\gdef\Atan(#1,#2){%
 \Dset(\@@x,#1) \@ta=1 \@Dabs(\@@x)
 \ifdim\@@x<0.2500pt \Dset(\@@u,0.00000)
  \@@a=1.0\@@x \Dsub(\@@a,0) \@@b=0.0\@@x \Dadd(\@@b,1)
 \else
  \ifdim\@@x<0.6875pt \Dset(\@@u,0.46365)
   \@@a=2.0\@@x \Dsub(\@@a,1) \@@b=1.0\@@x \Dadd(\@@b,2)
  \else
   \ifdim\@@x<1.1875pt \Dset(\@@u,0.78540)
    \@@a=1.0\@@x \Dsub(\@@a,1) \@@b=1.0\@@x \Dadd(\@@b,1)
   \else
    \ifdim\@@x<3.375pt \Dset(\@@u,0.98279)
     \@@a=2.0\@@x \Dsub(\@@a,3) \@@b=3.0\@@x \Dadd(\@@b,2)
    \else \Dset(\@@u,1.57080)
     \@@a=0.0\@@x \Dsub(\@@a,1) \@@b=1.0\@@x \Dadd(\@@b,0)
    \fi\fi\fi\fi
 \Ddiv(\@@a,\@@b) \@@x=\@@a \@@y=\@@x \@@t=\@@x \Dset(\@@d,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@t,\@@x) \Add(\@ta,2)
  \Dmul(\@@t,\@@x) \Div(\@@t,\@ta)
  \@@t=-\@@t \Add(\@@y,\@@t)
  \@@d=\@@t \ifdim\@@d<0pt \@@d=-\@@d \fi}
 \Add(\@@y,\@@u) \Mul(\@@y,\@@s) #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the sinus hyperbolicus. The result is returned in register r.
% \Sinh(x,r)
% -------------------------------------------------------------------------
\gdef\Sinh(#1,#2){%
 \Dset(\@@x,#1) \@ta=1
 \@@y=\@@x \@@t=\@@x \Dset(\@@d,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@t,\@@x) \Add(\@ta,1) \Div(\@@t,\@ta)
  \Dmul(\@@t,\@@x) \Add(\@ta,1) \Div(\@@t,\@ta)
  \Add(\@@y,\@@t) \@@d=\@@t \Dabs(\@@d)} #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the cosinus hyperbolicus. The result is returned in register
% r. \Cosh(x,r)
% -------------------------------------------------------------------------
\gdef\Cosh(#1,#2){%
 \Dset(\@@x,#1) \@ta=0
 \Dset(\@@y,1) \Dset(\@@t,1) \Dset(\@@d,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@t,\@@x) \Add(\@ta,1) \Div(\@@t,\@ta)
  \Dmul(\@@t,\@@x) \Add(\@ta,1) \Div(\@@t,\@ta)
  \Add(\@@y,\@@t) \@@d=\@@t \Dabs(\@@d)} #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the tangens hyperbolicus. The result is returned in register
% r. \Tanh(x,r)
% -------------------------------------------------------------------------
\gdef\Tanh(#1,#2){%
 \Dset(\@@a,#1) \Dset(\@@b,#1)
 \Cosh(#1,\@@a) \Sinh(#1,\@@b)
 \Ddiv(\@@b,\@@a) #2=\@@b}

% -------------------------------------------------------------------------
% Calculates the area sinus of x. The result is returned register r.
% \Asinh(x,r)
% -------------------------------------------------------------------------
\gdef\Asinh(#1,#2){%
 \Dset(\@@a,#1) \Dmul(\@@a,\@@a)
 \Dadd(\@@a,1) \Sqrt(\Np\@@a,\@@a)
 \Dadd(\@@a,#1) \Ln(\Np\@@a,\@@a) #2=\@@a}

% -------------------------------------------------------------------------
% Calculates the area cosinus of x. The result is returned register r.
% \Acosh(x,r)
% -------------------------------------------------------------------------
\gdef\Acosh(#1,#2){%
 \Dset(\@@a,#1)
 \ifdim\@@a<12pt \Dmul(\@@a,\@@a)
  \Dsub(\@@a,1) \Sqrt(\Np\@@a,\@@a)
  \Dadd(\@@a,#1) \Ln(\Np\@@a,\@@a)
 \else \Add(\@@a,\@@a) \Ln(\Np\@@a,\@@a) \fi #2=\@@a}

% -------------------------------------------------------------------------
% Calculates the area tangens of x. The result is returned register r.
% We limit the maximum value of atanh to 5. \Atanh(x,r)
% -------------------------------------------------------------------------
\gdef\Atanh(#1,#2){%
 \Dset(\@@a,#1) \@Dabs(\@@a)
 \ifdim\@@a>0.9999pt \Dset(\@@a,5) \else
  \Dset(\@@b,1) \Sub(\@@b,\@@a) \Dadd(\@@a,1)
  \Ln(\Np\@@a,\@@a) \Ln(\Np\@@b,\@@b)
  \Sub(\@@a,\@@b) \Div(\@@a,2) \fi
 \Mul(\@@a,\@@s) #2=\@@a}

% -------------------------------------------------------------------------
% Calculates the natural logarithm. The result is returned in register r.
% For large numbers we reduce the argument x, using  ln(x)=ln(x/e^k)+k.
% For small numbers we enlarge the argument x, using ln(x)=ln(x*e^k)-k.
% The value of k is added at the end. \Ln(x,r)
% -------------------------------------------------------------------------
\gdef\Ln(#1,#2){%
 \Dset(\@@x,#1) \Dset(\@@t,2.71828) \@ta=1 \@tb=0
 \@whiledim{\@@x>\@@t}\do{\Ddiv(\@@x,\@@t) \Add(\@tb,1)}
 \@whiledim{\@@x<1pt}\do{\Dmul(\@@x,\@@t) \Sub(\@tb,1)}
 \@@t=\@@x \Dadd(\@@t,1)
 \Dsub(\@@x,1) \Ddiv(\@@x,\@@t)
 \@@y=\@@x \@@t=\@@x \Dset(\@@d,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@t,\@@x) \Dmul(\@@t,\@@x)
  \@@u=\@@t \Add(\@ta,2) \Div(\@@t,\@ta)
  \Add(\@@y,\@@t) \@@d=\@@t \ifdim\@@d<0pt \@@d=-\@@d \fi
  \@@t=\@@u} \Mul(\@@y,2) \Dadd(\@@y,\@tb) #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the logarithm of x to basis a. The result is returned in
% register r. \Log(a,x,r)
% -------------------------------------------------------------------------
\gdef\Log(#1,#2,#3){%
 \Ln(#1,\@ax) \Ln(#2,\@@x)
 \Ddiv(\@@x,\@ax) #3=\@@x}

% -------------------------------------------------------------------------
% Calculates the natural power of x. The result is returned in register r.
% \Exp(x,r)
% -------------------------------------------------------------------------
\gdef\Exp(#1,#2){%
 \Dset(\@@x,#1) \@ta=1
 \Dset(\@@y,1) \Dset(\@@t,1) \Dset(\@@d,1)
 \@whiledim{\@@d>0pt}\do{%
  \Dmul(\@@t,\@@x) \Div(\@@t,\@ta) \Add(\@ta,1)
  \Add(\@@y,\@@t) \@@d=\@@t \Dabs(\@@d)} #2=\@@y}

% -------------------------------------------------------------------------
% Calculates the x-th power of number a. The result is returned in
% register r. \Pow(a,x,r)
% -------------------------------------------------------------------------
\gdef\Pow(#1,#2,#3){%
 \Dset(\@@x,#1) \Dset(\@@y,#2)
 \ifdim\@@y=1.0pt #3=\@@x \else
  \ifdim\@@x>0pt
   \Ln(#1,\@@y) \Dset(\@@x,#2) \Dmul(\@@x,\@@y) \@ta=1
   \Dset(\@@y,1) \Dset(\@@t,1) \Dset(\@@d,1)
   \@whiledim{\@@d>0pt}\do{%
    \Dmul(\@@t,\@@x) \Div(\@@t,\@ta) \Add(\@ta,1)
    \Add(\@@y,\@@t) \@@d=\@@t \Dabs(\@@d)}
   #3=\@@y \else #3=\@@x \fi \fi}

% -------------------------------------------------------------------------
% Calculates the n-th root of a number x. The result is returned in
% register r. \Root(x,n,r)
% -------------------------------------------------------------------------
\gdef\Root(#1,#2,#3){%
 \Dset(\@@x,#1) \Dset(\@@y,#2)
 \ifdim\@@y=1pt #3=\@@x \else
  \ifdim\@@x>0pt
   \Ln(#1,\@@x) \Dset(\@@y,#2) \Ddiv(\@@x,\@@y) \@ta=1
   \Dset(\@@y,1) \Dset(\@@t,1) \Dset(\@@d,1)
   \@whiledim{\@@d>0pt}\do{%
    \Dmul(\@@t,\@@x) \Div(\@@t,\@ta) \Add(\@ta,1)
    \Add(\@@y,\@@t) \@@d=\@@t \Dabs(\@@d)}
   #3=\@@y \else #3=\@@x \fi \fi}

% -------------------------------------------------------------------------
% Calculates the n-th potenz (pos or neg integer) of a number a. The
% result is returned in register r. \Pot(a,n,r)
% -------------------------------------------------------------------------
\gdef\Pot(#1,#2,#3){%
  \Dset(\@@x,1) \@cm=#2 \@Abs(\@cm) \@ta=0
  \@whilenum{\@ta<\@cm}\do{%
   \Dmul(\@@x,#1pt) \Add(\@ta,1)}
  \ifnum\@@s<0 \Dset(#3,1) \Ddiv(#3,\@@x) \else #3=\@@x \fi}

% -------------------------------------------------------------------------
% Calculates the square root of a number x. The result is returned in
% register r. First we reduce the argument to get fewer steps. \Sqrt(x,r)
% -------------------------------------------------------------------------
\gdef\Sqrt(#1,#2){%
 \Dset(\@@t,#1) \Dset(\@@x,1) \@@d=\@@x \@@b=\@@x
 \ifdim\@@t=0pt \Dset(#2,0) \else
  \@whiledim{\@@t>4pt}\do{\Div(\@@t,4) \Mul(\@@b,2)}
  \@whiledim{\@@d>0pt}\do{\@@y=\@@t
   \Ddiv(\@@y,\@@x) \Sub(\@@y,\@@x) \Div(\@@y,2)
   \@@d=\@@y \Dabs(\@@d) \Add(\@@x,\@@y)} #2=\Np\@@b\@@x \fi}

% -------------------------------------------------------------------------
% Calculates the distance between two points. The result is returned in
% register r. \Len(x1,y1)(x2,y2)(r)
% -------------------------------------------------------------------------
\gdef\Len(#1,#2)(#3,#4)(#5){%
 \Dset(\@@a,#3) \Sub(\@@a,#1pt)
 \Dset(\@@b,#4) \Sub(\@@b,#2pt)
 \Dmul(\@@a,\@@a) \Dmul(\@@b,\@@b)
 \Add(\@@a,\@@b) \Sqrt(\Np\@@a,#5)}

% -------------------------------------------------------------------------
% Calculates the hypothenuse of a rectangular triangle. The result is
% returned in register r. \Hypot(a,b,r)
% -------------------------------------------------------------------------
\gdef\Hypot(#1,#2,#3){%
 \Dset(\@@a,#1) \Dset(\@@b,#2)
 \Dmul(\@@a,\@@a) \Dmul(\@@b,\@@b)
 \Add(\@@a,\@@b) \Sqrt(\Np\@@a,#3)}

% -------------------------------------------------------------------------
% Calculates the directional angle between two points. The result in rad
% is returned in register r. The first point is the reference point.
% \Direc(x1,y1)(x2,y2)(r)
% -------------------------------------------------------------------------
\gdef\Direc(#1,#2)(#3,#4)(#5){%
 \Dset(\@@X,#3) \Dset(\@@A,#1) \Sub(\@@X,\@@A)
 \Dset(\@@Y,#4) \Dset(\@@B,#2) \Sub(\@@Y,\@@B)
 \@@U=\@@X \Abs(\@@U)
 \ifdim\@@U<0.001pt \Dset(\@@A,1.5708)
  \ifdim\@@Y<0pt \Dadd(\@@A,3.1416) \fi
 \else \@@A=\@@Y \Ddiv(\@@A,\@@X) \Atan(\Np\@@A,\@@A)
  \ifdim\@@X<0pt \Dadd(\@@A,3.1416)
  \else \ifdim\@@Y<0pt \Dadd(\@@A,6.2832) \fi\fi\fi #5=\@@A}

% -------------------------------------------------------------------------
% Rotate a point around the origin by angle a. The result is returned in
% x2,y2. \Rotpoint(a)(x1,y1)(x2,y2)
% -------------------------------------------------------------------------
\gdef\Rotpoint(#1)(#2,#3)(#4,#5){%
 \Dset(\@zx,#2) \Dset(\@zy,#3)
 \Dset(\@yx,#2) \Dset(\@yy,#3)
 \Rad(#1,\@@U)
 \Sin(\Np\@@U,\@@A) \Cos(\Np\@@U,\@@B)
 \Dmul(\@zx,\@@B) \Dmul(\@zy,\@@A)
 \Dmul(\@yx,\@@A) \Dmul(\@yy,\@@B)
 \Sub(\@zx,\@zy) \Add(\@yx,\@yy)
 #4=\@zx #5=\@yx}

% -------------------------------------------------------------------------
% Draws a small point, filled with gray value g (0..1) at x,y.
%   \Point(g)(x,y)
% -------------------------------------------------------------------------
\gdef\Point(#1)(#2,#3){\Gsave \Setwidth(0.01) \Setcol(0,0,0)%
 \Circle(32)(#2,#3,0.065) \Fill(#1,#1,#1) \Grestore}

% -------------------------------------------------------------------------
% TeX typesetting a text at x,y with positional specification s. We have
% to temporary leave lapdf and reenter afterwords. If you want to add any
% macro from the picture environment, you have to use the same procedure.
%   \Text(x,y,s){text}
% -------------------------------------------------------------------------
\gdef\Text(#1,#2,#3)#4{%
 \end{pdf} \normalsize \put(#1,#2){\makebox(0,0)[#3]{#4}} \begin{pdf}}

% -------------------------------------------------------------------------
%   \Setcol(r,g,b) set a color
%   \Setgray(v) set a gray
%   \@setcol(switch,r,g,b) helper function
%      rg and g are fore filling  (f is first param)
%      RG and G are fore stroking (s is first param)
% -------------------------------------------------------------------------
\gdef\@setcol(#1,#2,#3,#4){\def\@c{#1}
 \Dset(\@CR,#2) \Dset(\@CG,#3) \Dset(\@CB,#4)
 \ifnum\@cl=1
  \if\@c f \@f={rg} \else \@f={RG} \fi
  \def\@e{#2 #3 #4}
 \else
   \ifdim\@ax=1.0pt \def\@e{1} \else \def\@e{0} \fi
 \fi
 \PDF{\@e\space \the\@f}}

\gdef\Setcol(#1,#2,#3){\@setcol(s,#1,#2,#3)}
\gdef\Setgray(#1){\@setcol(s,#1,#1,#1)}

% -------------------------------------------------------------------------
% Some useful predefined colors. All names start with capital letters.
% -------------------------------------------------------------------------
\gdef\Black{\Setcol(0,0,0)}
\gdef\Dred{\Setcol(0.7,0,0)}
\gdef\Dgreen{\Setcol(0,0.7,0)}
\gdef\Dblue{\Setcol(0,0,0.7)}
\gdef\Dcyan{\Setcol(0,0.7,0.7)}
\gdef\Dmagenta{\Setcol(0.7,0,0.7)}
\gdef\Dyellow{\Setcol(0.7,0.7,0)}
\gdef\Dgray{\Setcol(0.4,0.4,0.4)}
\gdef\Gray{\Setcol(0.8,0.8,0.8)}
\gdef\Red{\Setcol(1,0,0)}
\gdef\Green{\Setcol(0,1,0)}
\gdef\Blue{\Setcol(0,0,1)}
\gdef\Cyan{\Setcol(0,1,1)}
\gdef\Magenta{\Setcol(1,0,1)}
\gdef\Yellow{\Setcol(1,1,0)}
\gdef\White{\Setcol(1,1,1)}

% -------------------------------------------------------------------------
% The first macro strokes with current and fills with specified color.
%   \Fill(r,g,b)
% The second macro simply uses gray instead of a color value
%   \Gfill(gr)
% The third strokes and fills with the current color (CR, CG, CB).
%   \Sfill
% -------------------------------------------------------------------------
\gdef\Fill(#1,#2,#3){\@setcol(f,#1,#2,#3) \PDF{B*}}
\gdef\Gfill(#1){\@setcol(f,#1,#1,#1) \PDF{B*}}
\gdef\Sfill{\Fill(\Np\@CR,\Np\@CG,\Np\@CB)}

% -------------------------------------------------------------------------
% The main PDF commands, please read a PDF-Specification fore their meaning
% and also the documentation of Lapdf
% -------------------------------------------------------------------------
\gdef\Gsave{\PDF{q}}
\gdef\Grestore{\PDF{Q}}
\gdef\Setclip{\PDF{W* n}}
\gdef\Stroke{\PDF{S}}
\gdef\Closepath{\PDF{h}}
\gdef\Setwidth(#1){\PDF{#1 w}}
\gdef\Thick{\PDF{0.03 w}}
\gdef\Thin{\PDF{0.01 w}}
\gdef\Setcap(#1){\PDF{#1 J}}
\gdef\Setjoin(#1){\PDF{#1 j}}
\gdef\Setflat(#1){\PDF{#1 i}}
\gdef\Setmiter(#1){\PDF{#1 M}}
\gdef\Setdash(#1){\PDF{#1 d}}
\gdef\Bezier(#1,#2,#3,#4,#5,#6){\PDF{#1 #2 #3 #4 #5 #6 c}}
\gdef\Concat(#1,#2,#3,#4,#5,#6){\PDF{#1 #2 #3 #4 #5 #6 cm}}
\gdef\Translate(#1,#2){\PDF{1 0 0 1 #1 #2 cm}}
\gdef\Scale(#1,#2){\PDF{#1 0 0 #2 0 0 cm}}
\gdef\Rotate(#1){\Cos(#1,\@ax) \Sin(#1,\@bx)
 \@cx=-\@bx \@rotate(\Np\@ax,\Np\@bx,\Np\@cx)}
 \gdef\@rotate(#1,#2,#3){\PDF{#1 #2 #3 #1 0 0 cm}}
\gdef\Rect(#1,#2,#3,#4){\PDF{#1 #2 #3 #4 re}}

% -------------------------------------------------------------------------
%   \Dash(n) 4 predefined standard dashes (0..3).
% -------------------------------------------------------------------------
\gdef\Dash(#1){\def\@c{#1}
 \ifnum\@c=0 \PDF{[] 0 d} \fi
 \ifnum\@c=1 \PDF{[0.1 0.1] 0 d} \fi
 \ifnum\@c=2 \PDF{[0.1 0.1 0.025 0.1] 0 d} \fi
 \ifnum\@c=3 \PDF{[0.025 0.1] 0 d} \fi}

% -------------------------------------------------------------------------
% Move to point and line drawing in affine space.
%   \Moveto(x1,y1)   \Lineto(x1,y1)   \Line(x1,y1,x2,y2)
% -------------------------------------------------------------------------
\gdef\Moveto(#1,#2){\Dset(\@xx,#1) \Dset(\@xy,#2) \PDF{#1 #2 m}}
\gdef\Lineto(#1,#2){\Dset(\@xx,#1) \Dset(\@xy,#2) \PDF{#1 #2 l}}
\gdef\Line(#1,#2)(#3,#4){\Moveto(#1,#2) \Lineto(#3,#4)}

% -------------------------------------------------------------------------
% Move to point in homogeneous space.
%   \Rmoveto(x1,y1,z1)
% -------------------------------------------------------------------------
\gdef\Rmoveto(#1,#2,#3){\Dset(\@xx,#1) \Dset(\@xy,#2) \Dset(\@xz,#3)
 \PDF{#1 #2 m}}

% -------------------------------------------------------------------------
% Helper macros for all the grid drawings.
% -------------------------------------------------------------------------
\gdef\@Putline(#1,#2)(#3,#4)(#5){\put(#1,#2){\line(#3,#4){#5}}}
\gdef\@Putvector(#1,#2)(#3,#4)(#5){\put(#1,#2){\vector(#3,#4){#5}}}
\gdef\@Puttext(#1,#2)[#3]#4{\put(#1,#2){\makebox(0,0)[#3]{#4}}}

% -------------------------------------------------------------------------
% Helper: Draws a graphic dot at point (x,y).
%   \@Gdot(x,y)
% -------------------------------------------------------------------------
\gdef\@Gbox{\setbox\@tbox\hbox{\hskip-\@halfwidth%
 \vrule\@height\@halfwidth\@depth\@halfwidth\@width\@wholewidth}}

\gdef\@Gdot(#1,#2){\@killglue
 \raise#2\hb@xt@\z@{\kern#1\unhcopy\@tbox\hss}}

% -------------------------------------------------------------------------
% Helper: Draws a dashed line with n points per unitlength from current
% point to x,y. \@Gline(n)(x,y)
% -------------------------------------------------------------------------
\gdef\@Gline(#1)(#2,#3){%
 \@cm=#1 \@ci=0
 \@dx=#2\Ul \@dy=#3\Ul
 \Div(\@dx,\@cm) \Div(\@dy,\@cm)
 \Add(\@cm,1) \@Gbox
 \@whilenum{\@ci<\@cm}\do{%
  \@@X=\@ci\@dx \@@Y=\@ci\@dy
  \@Gdot(\@@X,\@@Y) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Helper: Draws a dashed circle of radius r with 10 points per unitlength.
%   \@Gcircle(r)
% -------------------------------------------------------------------------
\gdef\@Gcircle(#1){%
 \@cm=#1 \Mul(\@cm,63) \@ci=0
 \Dset(\@dx,6.2832) \Div(\@dx,\@cm) \@Gbox
 \@whilenum{\@ci<\@cm}\do{%
  \@dy=\@ci\@dx
  \Cos(\Np\@dy,\@@X) \@@X=#1\@@X
  \Sin(\Np\@dy,\@@Y) \@@Y=#1\@@Y
  \@Gdot(\Np\@@X\Ul,\Np\@@Y\Ul) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a linear grid with n points per unitlength. A grid is drawn if g>0.
% Value a may be 0 (no axes), 1 (simple axes), 2 (additional tickmarks)
% or 3 (additional values). \Lingrid(n)(g,a)(xmin,max)(ymin,ymax)
% -------------------------------------------------------------------------
\gdef\Lingrid(#1)(#2,#3)(#4,#5)(#6,#7){%
 \end{pdf}
 \scriptsize
 \linethickness{\wid}
 \@cd=#7 \Sub(\@cd,#6) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=#4 \@cc=#5 \Add(\@cc,1)
 \ifnum#4=0
  \ifnum#3>1 \@Putline(-0.1,0)(1,0)(0.1) \fi
  \ifnum#3>2 \@Puttext(-0.15,0)[rc]{0} \fi \fi
 \ifnum#6=0
  \ifnum#3>1 \@Putline(0,-0.1)(0,1)(0.1) \fi
  \ifnum#3>2 \@Puttext(0,-0.15)[ct]{0} \fi \fi
 \@whilenum{\@cb<\@cc}\do{%
  \ifnum#2=1 \put(\@cb,#6){\@Gline(\@cg)(0,\@cd)} \fi
  \ifnum\@cb=0 \else
   \ifnum#3>1 \@Putline(\@cb,-0.1)(0,1)(0.1) \fi
   \ifnum#3>2 \@Puttext(\@cb,-0.15)[ct]{\the\@cb} \fi \fi
  \Add(\@cb,1)}
 \@cd=#5 \Sub(\@cd,#4) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=#6 \@cc=#7 \Add(\@cc,1)
 \@whilenum{\@cb<\@cc}\do{%
  \ifnum#2=1 \put(#4,\@cb){\@Gline(\@cg)(\@cd,0)} \fi
  \ifnum\@cb=0 \else
   \ifnum#3>1 \@Putline(-0.1,\@cb)(1,0)(0.1) \fi
   \ifnum#3>2 \@Puttext(-0.15,\@cb)[rc]{\the\@cb} \fi \fi
  \Add(\@cb,1)}
 \Dset(\@@X,#5) \Dsub(\@@X,#4) \Dadd(\@@X,0.4)
 \Dset(\@@Y,#7) \Dsub(\@@Y,#6) \Dadd(\@@Y,0.4)
 \ifnum#3>0 \@Putvector(#4,0)(1,0)(\Np\@@X)
  \@Putvector(0,#6)(0,1)(\Np\@@Y) \fi
 \begin{pdf}}

% -------------------------------------------------------------------------
% Draws a grid with n points per unitlength. It is horizontal logarithmic
% and vertical linear. A grid is drawn if g>0. Value a may be 0 (no axes),
% 1 (simple axes), 2 (additional tickmarks) or 3 (additional values).
% \Logxgrid(n)(g,a)(xmin,max)(ymin,ymax)
% -------------------------------------------------------------------------
\gdef\Logxgrid(#1)(#2,#3)(#4,#5)(#6,#7){%
 \end{pdf}
 \scriptsize
 \linethickness{\wid}
 \@cd=#7 \Sub(\@cd,#6) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=1 \@cc=0 \@ca=#4
 \ifnum#6=0
  \ifnum#3>1 \@Putline(0,-0.1)(0,1)(0.1) \fi
  \ifnum#3>2 \@Puttext(0,-0.15)[ct]{$10^{\the\@ca}$} \fi \fi
 \@whilenum{\@ca<#5}\do{\Log(10,\@cb,\@@X) \Dadd(\@@X,\@cc) \Mul(\@@X,5)
  \ifnum#2=1 \put(\Np\@@X,#6){\@Gline(\@cg)(0,\@cd)} \fi
  \ifnum\@cb<10 \Add(\@cb,1)
  \else \@cb=2 \Add(\@cc,1) \Add(\@ca,1)
   \ifnum#3>1 \@Putline(\Np\@@X,-0.1)(0,1)(0.1) \fi
   \ifnum#3>2 \@Puttext(\Np\@@X,-0.15)[ct]{$10^{\the\@ca}$} \fi \fi}
 \@cd=#5 \Sub(\@cd,#4) \Mul(\@cd,5) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=#6 \@cc=#7 \Add(\@cc,1)
 \@whilenum{\@cb<\@cc}\do{%
  \ifnum#2=1 \put(0,\@cb){\@Gline(\@cg)(\@cd,0)} \fi
  \ifnum#3>1 \@Putline(-0.1,\@cb)(1,0)(0.1) \fi
  \ifnum#3>2 \@Puttext(-0.15,\@cb)[rc]{\the\@cb} \fi \Add(\@cb,1)}
 \Dset(\@@X,#5) \Dsub(\@@X,#4) \Mul(\@@X,5) \Dadd(\@@X,0.4)
 \Dset(\@@Y,#7) \Dsub(\@@Y,#6) \Dadd(\@@Y,0.4)
 \ifnum#3>0 \@Putvector(-0.1,0)(1,0)(\Np\@@X)
  \@Putvector(0,#6)(0,1)(\Np\@@Y) \fi
 \begin{pdf}}

% -------------------------------------------------------------------------
% Draws a grid with n points per unitlength. It is horizontal linear and
% vertical logarithmic. A grid is drawn if g>0. Value a may be 0 (no axes),
% 1 (simple axes), 2 (additional tickmarks) or 3 (additional values).
% \Logygrid(n)(g,a)(xmin,max)(ymin,ymax)
% -------------------------------------------------------------------------
\gdef\Logygrid(#1)(#2,#3)(#4,#5)(#6,#7){%
 \end{pdf}
 \scriptsize
 \linethickness{\wid}
 \@cd=#7 \Sub(\@cd,#6) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=1 \@cc=0 \@ca=#4
 \ifnum#6=0
  \ifnum#3>1 \@Putline(-0.1,0)(1,0)(0.1) \fi
  \ifnum#3>2 \@Puttext(-0.15,0)[rc]{$10^{\the\@ca}$} \fi \fi
 \@whilenum{\@ca<#5}\do{\Log(10,\@cb,\@@Y) \Dadd(\@@Y,\@cc) \Mul(\@@Y,5)
  \ifnum#2=1 \put(#6,\Np\@@Y){\@Gline(\@cg)(\@cd,0)} \fi
  \ifnum\@cb<10 \Add(\@cb,1)
  \else \@cb=2 \Add(\@cc,1) \Add(\@ca,1)
   \ifnum#3>1 \@Putline(-0.1,\Np\@@Y)(1,0)(0.1) \fi
   \ifnum#3>2 \@Puttext(-0.15,\Np\@@Y)[rc]{$10^{\the\@ca}$} \fi \fi}
 \@cd=#5 \Sub(\@cd,#4) \Mul(\@cd,5) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=#6 \@cc=#7 \Add(\@cc,1)
 \@whilenum{\@cb<\@cc}\do{%
  \ifnum#2=1 \put(\@cb,0){\@Gline(\@cg)(0,\@cd)} \fi
  \ifnum#3>1 \@Putline(\@cb,-0.1)(0,1)(0.1) \fi
  \ifnum#3>2 \@Puttext(\@cb,-0.15)[ct]{\the\@cb} \fi \Add(\@cb,1)}
 \Dset(\@@Y,#5) \Dsub(\@@Y,#4) \Mul(\@@Y,5) \Dadd(\@@Y,0.4)
 \Dset(\@@X,#7) \Dsub(\@@X,#6) \Dadd(\@@X,0.4)
 \ifnum#3>0 \@Putvector(#6,0)(1,0)(\Np\@@X)
  \@Putvector(0,-0.1)(0,1)(\Np\@@Y) \fi
 \begin{pdf}}

% -------------------------------------------------------------------------
% Draws a grid with n points per unitlength. It is logarithmic in both
% directions. A grid is drawn if g>0. Value a may be 0 (no axes),
% 1 (simple axes), 2 (additional tickmarks) or 3 (additional values).
% \Logxygrid(n)(g,a)(xmin,max)(ymin,ymax)
% -------------------------------------------------------------------------
\gdef\Logxygrid(#1)(#2,#3)(#4,#5)(#6,#7){%
 \end{pdf}
 \scriptsize
 \linethickness{\wid}
 \@cd=#7 \Sub(\@cd,#6) \Mul(\@cd,5) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=1 \@cc=0 \@ca=#4
 \ifnum#6=0
  \ifnum#3>1 \@Putline(0,-0.1)(0,1)(0.1) \fi
  \ifnum#3>2 \@Puttext(0,-0.15)[ct]{$10^{\the\@ca}$} \fi \fi
 \@whilenum{\@ca<#5}\do{\Log(10,\@cb,\@@X) \Dadd(\@@X,\@cc) \Mul(\@@X,5)
  \ifnum#2=1 \put(\Np\@@X,#6){\@Gline(\@cg)(0,\@cd)} \fi
  \ifnum\@cb<10 \Add(\@cb,1)
  \else \@cb=2 \Add(\@cc,1) \Add(\@ca,1)
   \ifnum#3>1 \@Putline(\Np\@@X,-0.1)(0,1)(0.1) \fi
   \ifnum#3>2 \@Puttext(\Np\@@X,-0.15)[ct]{$10^{\the\@ca}$} \fi \fi}
 \@cd=#5 \Sub(\@cd,#4) \Mul(\@cd,5) \@cg=\@cd \Mul(\@cg,#1)
 \@cb=1 \@cc=0 \@ca=#6
 \ifnum#6=0
  \ifnum#3>1 \@Putline(-0.1,0)(1,0)(0.1) \fi
  \ifnum#3>2 \@Puttext(-0.15,0)[rc]{$10^{\the\@ca}$} \fi \fi
 \@whilenum{\@ca<#7}\do{\Log(10,\@cb,\@@Y) \Dadd(\@@Y,\@cc) \Mul(\@@Y,5)
  \ifnum#2=1 \put(#6,\Np\@@Y){\@Gline(\@cg)(\@cd,0)} \fi
  \ifnum\@cb<10 \Add(\@cb,1)
  \else \@cb=2 \Add(\@cc,1) \Add(\@ca,1)
   \ifnum#3>1 \@Putline(-0.1,\Np\@@Y)(1,0)(0.1) \fi
   \ifnum#3>2 \@Puttext(-0.15,\Np\@@Y)[rc]{$10^{\the\@ca}$} \fi \fi}
 \Dset(\@@X,#5) \Dsub(\@@X,#4) \Mul(\@@X,5) \Dadd(\@@X,0.4)
 \Dset(\@@Y,#7) \Dsub(\@@Y,#6) \Mul(\@@Y,5) \Dadd(\@@Y,0.4)
 \ifnum#3>0 \@Putvector(-0.1,0)(1,0)(\Np\@@X)
  \@Putvector(0,-0.1)(0,1)(\Np\@@Y) \fi
 \begin{pdf}}

% -------------------------------------------------------------------------
% Draws a polar grid with 10 points per unitlength and maximum radius r.
% If g>0, a grid is drawn. Value a may be 0 (no axes), 1 (simple axes),
% 2 (additional tickmarks), 3 (additional values, angles in degree) or
% 4 (like 3, but angles in multiples of pi). \Polgrid(g,a)(r)
% -------------------------------------------------------------------------
\gdef\Polgrid(#1,#2)(#3){%
 \end{pdf}
 \scriptsize
 \linethickness{\wid}
 \@ca=0
 \@whilenum{\@ca<#3}\do{%
  \Add(\@ca,1) \ifnum#1>0 \@Gcircle(\@ca) \fi
  \ifnum#2>1
   \ifnum\@ca=0 \else
    \@Putline(\@ca,-0.1)(0,1)(0.1) \@Putline(-\@ca,-0.1)(0,1)(0.1)
     \@Putline(-0.1,\@ca)(1,0)(0.1) \@Putline(-0.1,-\@ca)(1,0)(0.1)
     \ifnum#2>2 \@Puttext(\@ca,-0.15)[tc]{\the\@ca} \fi \fi \fi}
 \@ca=0 \@cb=0
 \@whilenum{\@ca<360}\do{%
  \@cb=#3 \Mul(\@cb,10) \Rad(\@ca,\@ax)
  \ifnum#1>0
   \Cos(\Np\@ax,\@@X) \Mul(\@@X,#3)
   \Sin(\Np\@ax,\@@Y) \Mul(\@@Y,#3)
   \put(0,0){\@Gline(\@cb)(\Np\@@X,\Np\@@Y)} \fi
  \ifnum#2>2
   \Dset(\@@U,#3) \Dadd(\@@U,0.35)
   \Cos(\Np\@ax,\@@X) \Dmul(\@@X,\@@U)
   \Sin(\Np\@ax,\@@Y) \Dmul(\@@Y,\@@U)
   \ifnum#2>3 \@cb=\@ca \Div(\@cb,15)
    \ifnum\@ca=0 \@Puttext(\Np\@@X,\Np\@@Y)[cc]{0}
    \else \@cc=\@cb \Mod(\@cc,6)
     \ifnum\@cc=0 \Div(\@cb,6)
      \ifnum\@cb=2 \@Puttext(\Np\@@X,\Np\@@Y)[cc]{$\pi$}
      \else \@Puttext(\Np\@@X,\Np\@@Y)[cc]{$\frac{\the\@cb}{2}\pi$} \fi
     \else \@Puttext(\Np\@@X,\Np\@@Y)[cc]{$\frac{\the\@cb}{12}\pi$} \fi \fi
    \else \@Puttext(\Np\@@X,\Np\@@Y)[cc]{$\the\@ca^{\circ}$} \fi \fi
   \Add(\@ca,15)}
 \ifnum#2>0 \Dset(\@@X,#3) \Mul(\@@X,2)
  \@Putline(-#3,0)(1,0)(\Np\@@X) \@Putline(0,-#3)(0,1)(\Np\@@X) \fi
 \begin{pdf}}

% -------------------------------------------------------------------------
% Plots a function with n line segments from x1 to x2. You have to define
% a function \Fx with the command: \def\Fx(#1,#2){..}. #1 is the x value
% and #2 is the result register. \Fplot(n)(x1,x2)             Examples:
% \def\Fx(#1,#2){\Sin(#1,#2) \Mul(#2,3) \Dadd(#2,1)}          y=3*sin(x)+1
% \def\Fx(#1,#2){\Dset(\x,#1) \Dsub(\x,2) \Exp(\Np\x,#2)}     y=exp(x-2)
% -------------------------------------------------------------------------
\gdef\Fplot(#1)(#2,#3){%
 \Dset(\@dx,#3) \Dsub(\@dx,#2) \Div(\@dx,#1)
 \Dset(\@ux,#2) \Fx(\Np\@ux,\@uy)
 \Moveto(\Np\@ux,\Np\@uy)
 \@whiledim{\@ux<#3pt}\do{\Add(\@ux,\@dx)
  \ifdim\@ux>#3pt \Dset(\@ux,#3) \fi
  \Fx(\Np\@ux,\@uy) \Lineto(\Np\@ux,\Np\@uy)}}

% -------------------------------------------------------------------------
% Plots a parametric function with n line segments for t1 to t2. You have
% to define two functions \Tx and \Ty with the commands: \def\Tx(#1,#2){..}
% and \def\Ty(#1,#2){..}. Here #1 is the t value and #2 is the result
% register. \Tplot(n)(t1,t2)                                    Example:
% \def\Tx(#1,#2){\Dset(#2,#1) \Mul(#2,2) \Dsub(#2,1)}           x=2*t-1
% \def\Ty(#1,#2){\Dset(\t,#1) #2=\t \Dmul(#2,#2) \Add(#2,\t)}   y=t^2+t
% -------------------------------------------------------------------------
\gdef\Tplot(#1)(#2,#3){%
 \Dset(\@dx,#3) \Dsub(\@dx,#2) \Div(\@dx,#1)
 \Dset(\@@U,#2) \Tx(\Np\@@U,\@ux)
 \Dset(\@@U,#2) \Ty(\Np\@@U,\@uy)
 \Moveto(\Np\@ux,\Np\@uy)
 \@whiledim{\@@U<#3pt}\do{\Add(\@@U,\@dx)
  \ifdim\@@U>#3pt \Dset(\@@U,#3) \fi
  \Tx(\Np\@@U,\@ux) \Ty(\Np\@@U,\@uy)
  \Lineto(\Np\@ux,\Np\@uy)}}

% -------------------------------------------------------------------------
% Converts a polar function r=f(a) to parametric cartesian form with:
% x=f(a)*cos(a), y=f(a)*sin(a). The result is returned in regs x and y.
% \Pxy(a,x,y)
% -------------------------------------------------------------------------
\gdef\Pxy(#1,#2,#3){%
 \Px(#1,#2) #3=#2
 \Cos(#1,\@@T) \Dmul(#2,\@@T)
 \Sin(#1,\@@T) \Dmul(#3,\@@T)}

% -------------------------------------------------------------------------
% Plots a polar function with n line segments from a1 to a2. You have to
% define a function \Px with the command: \def\Px(#1,#2){..}. #1 is the x
% value and #2 is the result register. \Pplot(n)(a1,a2)      Examples:
% \def\Px(#1,#2){\Dset(\a,#1) #2=2\a \Sin(\Np#2,#2)}         r=cos(2a)
% \def\Px(#1,#2){\Dset(\Sin(#1,#2) \Dadd(#2,1)}              r=1+sin(a)
% -------------------------------------------------------------------------
\gdef\Pplot(#1)(#2,#3){%
 \Dset(\@tx,#2) \Dset(\@ty,#3)
 \Dmul(\@tx,3.14159pt) \Dmul(\@ty,3.14159pt)
 \@dx=\@ty \Sub(\@dx,\@tx) \Div(\@dx,#1)
 \@@U=\@tx \Pxy(\Np\@@U,\@ux,\@uy)
 \Moveto(\Np\@ux,\Np\@uy)
 \@whiledim{\@@U<\@ty}\do{\Add(\@@U,\@dx)
  \ifdim\@@U>\@ty \@@U=\@ty \fi
  \Pxy(\Np\@@U,\@ux,\@uy)
  \Lineto(\Np\@ux,\Np\@uy)}}

% -------------------------------------------------------------------------
% Calculates the derivative dy/dx of a predefined real function \Fx.
% The value is x and the result is stored in register n. \Df(x,n)
% -------------------------------------------------------------------------
\gdef\Df(#1,#2){%
 \Dset(\@dx,#1) \@dy=\@dx \Dadd(\@dy,0.015625) \Dsub(\@dx,0.015625)
 \Fx(\Np\@dy,#2) \Fx(\Np\@dx,\@dx) \Sub(#2,\@dx) #2=32#2}

% -------------------------------------------------------------------------
% Calculates the partial derivative dx/dt of a predefined parameter curve
% \Tx. The value is t and the result is stored in register n. \Dtx(t,n)
% -------------------------------------------------------------------------
\gdef\Dtx(#1,#2){%
 \Dset(\@dx,#1) \@dy=\@dx \Dadd(\@dy,0.015625) \Dsub(\@dx,0.015625)
 \Tx(\Np\@dy,#2) \Tx(\Np\@dx,\@dx) \Sub(#2,\@dx) #2=32#2}

% -------------------------------------------------------------------------
% Calculates the partial derivative dy/dt of a predefined parameter curve
% \Ty. The value is t and the result is stored in register n. \Dty(t,n)
% -------------------------------------------------------------------------
\gdef\Dty(#1,#2){%
 \Dset(\@dx,#1) \@dy=\@dx \Dadd(\@dy,0.015625) \Dsub(\@dx,0.015625)
 \Ty(\Np\@dy,#2) \Ty(\Np\@dx,\@dx) \Sub(#2,\@dx) #2=32#2}

% -------------------------------------------------------------------------
% Calculates the total derivative dy/dx of a predefined parameter curve
% \Ty, \Tx. The value is t and the result is stored in register n. \Dtt(t,n)
% -------------------------------------------------------------------------
\gdef\Dtt(#1,#2){%
 \Dty(#1,#2) \Dtx(#1,\@dz) \Ddiv(#2,\@dz)}

% -------------------------------------------------------------------------
% Calculates the partial derivative dx/da of a predefined polar curve \Px.
% The value is a and the result is stored in register n. \Dpx(a,n)
% -------------------------------------------------------------------------
\gdef\Dpx(#1,#2){%
 \Dset(\@dx,#1) \@dy=\@dx \Dadd(\@dy,0.015625) \Dsub(\@dx,0.015625)
 \Px(\Np\@dy,#2) \Cos(\Np\@dy,\@dy) \Dmul(#2,\@dy)
 \Px(\Np\@dx,\@tx) \Cos(\Np\@dx,\@dx) \Dmul(\@tx,\@dx)
 \Sub(#2,\@tx) #2=32#2}

% -------------------------------------------------------------------------
% Calculates the partial derivative dy/da of a predefined polar curve \Px.
% The value is a and the result is stored in register n. \Dpy(a,n)
% -------------------------------------------------------------------------
\gdef\Dpy(#1,#2){%
 \Dset(\@dx,#1) \@dy=\@dx \Dadd(\@dy,0.015625) \Dsub(\@dx,0.015625)
 \Px(\Np\@dy,#2) \Sin(\Np\@dy,\@dy) \Dmul(#2,\@dy)
 \Px(\Np\@dx,\@tx) \Sin(\Np\@dx,\@dx) \Dmul(\@tx,\@dx)
 \Sub(#2,\@tx) #2=32#2}

% -------------------------------------------------------------------------
% Calculates the total derivative dy/dx of a predefined polar curve \Px.
% The value is a and the result is stored in register n. \Dtp(a,n)
% -------------------------------------------------------------------------
\gdef\Dtp(#1,#2){%
 \Dpy(#1,#2) \Dpx(#1,\@dz) \Ddiv(#2,\@dz)}

% -------------------------------------------------------------------------
% Draws a full ellipse with two rational quadratic bezier curves. x,y is
% the center, a and b are the diameters, n is the number of segments and c
% is the rotation angle in degree. \Ellipse(n)(x,y)(a,b,c)
% -------------------------------------------------------------------------
\gdef\Ellipse(#1)(#2,#3)(#4,#5,#6){%
 \@tb=#1 \Mul(\@tb,3) \Rad(#6,\@sx)
 \Dset(\@ux,#2) \Dset(\@uy,#3)
 \Dset(\@vx,#2) \Dset(\@vy,#3)
 \Dset(\@wx,#2) \Dset(\@wy,#3)
 \Dset(\@ax,#4) \Dset(\@ay,#5)
 \Sin(\Np\@sx,\@sy) \Cos(\Np\@sx,\@sx)
 \@bx=0.866\@ax \@by=0.500\@ay
 \@cx=\@bx \@cy=\@by
 \Dmul(\@bx,\@sx)\Dmul(\@by,\@sy)
 \Dmul(\@cx,\@sy)\Dmul(\@cy,\@sx)
 \Sub(\@ux,\@bx) \Sub(\@ux,\@by)
 \Sub(\@uy,\@cx) \Add(\@uy,\@cy)
 \Add(\@wx,\@bx) \Sub(\@wx,\@by)
 \Add(\@wy,\@cx) \Add(\@wy,\@cy)
 \@bx=0.000\@ax \@by=2.000\@ay
 \@cx=\@bx \@cy=\@by
 \Dmul(\@bx,\@sx)\Dmul(\@by,\@sy)
 \Dmul(\@cx,\@sy)\Dmul(\@cy,\@sx)
 \Add(\@vx,\@bx) \Sub(\@vx,\@by)
 \Add(\@vy,\@cx) \Add(\@vy,\@cy)
 \Rmoveto(\Np\@ux,\Np\@uy,2)
 \Rcurveto(#1)(\Np\@vx,\Np\@vy,1)(\Np\@wx,\Np\@wy,2)
 \Rcurveto(\@tb)(\Np\@vx,\Np\@vy,-1)(\Np\@ux,\Np\@uy,2)}

% -------------------------------------------------------------------------
% Draws a full circle with two rational quadratic Bezier curves.
%   \Circle(n)(x,y,radius)
% -------------------------------------------------------------------------
\gdef\Circle(#1)(#2,#3,#4){%
 \Set(\@tb,#1) \Mul(\@tb,2) 
 \Dset(\@ux,#2) \Dset(\@uy,#3)
 \Dset(\@vx,#2) \Dset(\@vy,#3)
 \Dset(\@wx,#2) \Dset(\@wy,#3)
 \Dset(\@ax,#4) \Dset(\@ay,#4) \Dset(\@az,#4)
 \@ax=0.866\@ax \@ay=0.500\@ay \@az=2.000\@az
 \Sub(\@ux,\@ax) \Add(\@wx,\@ax)
 \Sub(\@uy,\@ay) \Sub(\@vy,\@az) \Sub(\@wy,\@ay)
 \Rmoveto(\Np\@ux,\Np\@uy,2)
 \Rcurveto(#1)(\Np\@vx,\Np\@vy,1)(\Np\@wx,\Np\@wy,2)
 \Rcurveto(\@tb)(\Np\@vx,\Np\@vy,-1)(\Np\@ux,\Np\@uy,2)}

% -------------------------------------------------------------------------
% Draws a rectangle between two points, rotated at point x1,y1 by angle a
% in degree. \Rectangle(x1,y1)(x2,y2)(a)
% -------------------------------------------------------------------------
\gdef\Rectangle(#1,#2)(#3,#4)(#5){%
 \Dset(\@cx,#3) \Dset(\@cy,#4) \Dset(\@@U,#5)
 \@bx=\@cx \Dset(\@by,0) \Dset(\@dx,0) \@dy=\@cy
 \Rotpoint(#5)(\Np\@bx,\Np\@by)(\@ux,\@uy)
 \Rotpoint(#5)(\Np\@cx,\Np\@cy)(\@vx,\@vy)
 \Rotpoint(#5)(\Np\@dx,\Np\@dy)(\@wx,\@wy)
 \Dadd(\@ux,#1) \Dadd(\@uy,#2)
 \Dadd(\@vx,#1) \Dadd(\@vy,#2)
 \Dadd(\@wx,#1) \Dadd(\@wy,#2)
 \Polygon(#1,#2)(\Np\@ux,\Np\@uy)(\Np\@vx,\Np\@vy)(\Np\@wx,\Np\@wy)(#1,#2)}

% -------------------------------------------------------------------------
% Draws a triangle between three points, rotated at point x1,y1 by angle a
% in degree. \Triangle(x1,y1)(x2,y2)(x3,y3)(a)
% -------------------------------------------------------------------------
\gdef\Triangle(#1,#2)(#3,#4)(#5,#6)(#7){%
 \Dset(\@bx,#3) \Dsub(\@bx,#1)
 \Dset(\@by,#4) \Dsub(\@by,#2)
 \Dset(\@cx,#5) \Dsub(\@cx,#1)
 \Dset(\@cy,#6) \Dsub(\@cy,#2)
 \Rotpoint(#7)(\Np\@bx,\Np\@by)(\@ux,\@uy)
 \Rotpoint(#7)(\Np\@cx,\Np\@cy)(\@vx,\@vy)
 \Dadd(\@ux,#1) \Dadd(\@uy,#2)
 \Dadd(\@vx,#1) \Dadd(\@vy,#2)
 \Polygon(#1,#2)(\Np\@ux,\Np\@uy)(\Np\@vx,\Np\@vy)(#1,#2)}

% -------------------------------------------------------------------------
% Draws a equilateral polygon with radius r and n vertices. It is rotated
% around the center x,y by an angle a in degree. The first (unrotated)
% point is r,0. \Epolygon(n)(x,y)(r,a)
% -------------------------------------------------------------------------
\gdef\Epolygon(#1)(#2,#3)(#4,#5){%
 \Rotpoint(#5)(#4,0)(\@vx,\@vy)
 \Dadd(\@vx,#2) \Dadd(\@vy,#3)
 \@ch=0
 \Moveto(\Np\@vx,\Np\@vy)
 \@whilenum{\@ch<#1}\do{\Add(\@ch,1)
  \Dset(\@ax,6.2832) \Div(\@ax,#1) \Mul(\@ax,\@ch)
  \Cos(\Np\@ax,\@vx) \Dmul(\@vx,#4pt)
  \Sin(\Np\@ax,\@vy) \Dmul(\@vy,#4pt)
  \Rotpoint(#5)(\Np\@vx,\Np\@vy)(\@vx,\@vy)
  \Dadd(\@vx,#2) \Dadd(\@vy,#3)
  \Lineto(\Np\@vx,\Np\@vy)}}

% -------------------------------------------------------------------------
% Draws a sector of a circle with center xm,ym, radius r, direction a and
% angle b in degree with n segments. \Sector(n)(xm,ym)(a,b)(r)
% -------------------------------------------------------------------------
\gdef\Sector(#1)(#2,#3)(#4,#5)(#6){%
 \Dset(\@ax,#4) \Dset(\@bx,#5) \Dset(\@rx,#6) \@ch=0
 \Rad(#4,\@sx) \Cos(\Np\@sx,\@sx) \Dmul(\@sx,\@rx)
 \Rad(#4,\@sy) \Sin(\Np\@sy,\@sy) \Dmul(\@sy,\@rx)
 \Dadd(\@sx,#2) \Dadd(\@sy,#3)
 \Line(#2,#3)(\Np\@sx,\Np\@sy)
 \@whilenum{\@ch<#1}\do{\Add(\@ch,1)
  \Dset(\@dx,#5) \Div(\@dx,#1) \Mul(\@dx,\@ch) \Dadd(\@dx,#4)
  \Rad(\Np\@dx,\@sx) \Cos(\Np\@sx,\@sx) \Dmul(\@sx,\@rx)
  \Rad(\Np\@dx,\@sy) \Sin(\Np\@sy,\@sy) \Dmul(\@sy,\@rx)
  \Dadd(\@sx,#2) \Dadd(\@sy,#3) \Lineto(\Np\@sx,\Np\@sy)} \Lineto(#2,#3)}

% -------------------------------------------------------------------------
% These draw a circular arc (or a circular vector) with center xm,ym,
% radius r, direction a and angle b in degree with n segments. Both use
% \@Arc. \Arc(n)(xm,ym)(a,b)(r) \Varc(n)(xm,ym)(a,b)(r)
% -------------------------------------------------------------------------
\gdef\Arc(#1)(#2,#3)(#4,#5)(#6){\@Arc(#1)(#2,#3)(#4,#5)(#6,0)}
\gdef\Varc(#1)(#2,#3)(#4,#5)(#6){\@Arc(#1)(#2,#3)(#4,#5)(#6,1)}

% -------------------------------------------------------------------------
% Helper macro that draws a circular arc (t=0) or vector (t=1).
% It is called by \Arc and \Varc. \@Arc(n)(xm,ym)(a,b)(r,t)
% -------------------------------------------------------------------------
\gdef\@Arc(#1)(#2,#3)(#4,#5)(#6,#7){%
 \Dset(\@ax,#4) \Dset(\@bx,#5) \Dset(\@rx,#6) \@ch=0
 \Rad(#4,\@vx) \Cos(\Np\@vx,\@vx) \Dmul(\@vx,\@rx)
 \Rad(#4,\@vy) \Sin(\Np\@vy,\@vy) \Dmul(\@vy,\@rx)
 \Dadd(\@vx,#2) \Dadd(\@vy,#3)
 \@whilenum{\@ch<#1}\do{\Add(\@ch,1) \@ux=\@vx \@uy=\@vy
  \Dset(\@dx,#5) \Div(\@dx,#1) \Mul(\@dx,\@ch) \Dadd(\@dx,#4)
  \Rad(\Np\@dx,\@vx) \Cos(\Np\@vx,\@vx) \Dmul(\@vx,\@rx)
  \Rad(\Np\@dx,\@vy) \Sin(\Np\@vy,\@vy) \Dmul(\@vy,\@rx)
  \Dadd(\@vx,#2) \Dadd(\@vy,#3)
  \ifnum#7=0 \Polygon(\Np\@ux,\Np\@uy)(\Np\@vx,\Np\@vy) \else
   \ifnum\@ch<#1 \Polygon(\Np\@ux,\Np\@uy)(\Np\@vx,\Np\@vy) \else
    {\Vpolygon(\Np\@ux,\Np\@uy)(\Np\@vx,\Np\@vy) \Stroke} \fi \fi}}

% -------------------------------------------------------------------------
% Draws a circular arc with center xm,ym, radius r, direction a and angle b
% with n segments. The incoming direction goes from the current point. The
% last point x2, y2 gives the outgoing direcion. Lines from the current
% point and to the end point are also drawn. \Arcto(n)(x1,y1)(x2,y2)(r)
% -------------------------------------------------------------------------
\gdef\Arcto(#1)(#2,#3)(#4,#5)(#6){%
 \Dset(\@yx,#2) \Dset(\@yy,#3)
 \Dset(\@zx,#4) \Dset(\@zy,#5) \Dset(\@rx,#6)
 \Direc(#2,#3)(\Np\@xx,\Np\@xy)(\@ax)
 \Direc(#2,#3)(\Np\@zx,\Np\@zy)(\@ay)
 \Len(\Np\@yx,\Np\@yy)(\Np\@xx,\Np\@xy)(\@dx)
 \Len(\Np\@yx,\Np\@yy)(\Np\@zx,\Np\@zy)(\@dy)
 \Len(\Np\@xx,\Np\@xy)(\Np\@zx,\Np\@zy)(\@dz)
 \Cos(\Np\@ay,\@ex) \Dmul(\@ex,\@dx) \Add(\@ex,\@xx)
 \Add(\@ex,\@yx) \@ex=0.5\@ex
 \Sin(\Np\@ay,\@ey) \Dmul(\@ey,\@dx) \Add(\@ey,\@xy)
 \Add(\@ey,\@yy) \@ey=0.5\@ey
 \Direc(\Np\@yx,\Np\@yy)(\Np\@ex,\Np\@ey)(\@az)
 \@cy=2.0\@dx \Dmul(\@cy,\@dy)
 \Dmul(\@dx,\@dx) \Dmul(\@dy,\@dy) \Dmul(\@dz,\@dz)
 \Add(\@dx,\@dy) \Sub(\@dx,\@dz) \Ddiv(\@dx,\@cy)
 \Acos(\Np\@dx,\@cx) \@cy=0.5\@cx
 \Dset(\@@U,1.5708) \Sub(\@@U,\@cy)
 \Tan(\Np\@@U,\@dx) \Dmul(\@dx,\@rx) \Cos(\Np\@@U,\@@U)
 \Cos(\Np\@ax,\@ux) \Dmul(\@ux,\@dx) \Add(\@ux,\@yx)
 \Sin(\Np\@ax,\@uy) \Dmul(\@uy,\@dx) \Add(\@uy,\@yy)
 \Cos(\Np\@ay,\@vx) \Dmul(\@vx,\@dx) \Add(\@vx,\@yx)
 \Sin(\Np\@ay,\@vy) \Dmul(\@vy,\@dx) \Add(\@vy,\@yy)
 \Polygon(\Np\@xx,\Np\@xy)(\Np\@ux,\Np\@uy) \Stroke
 \Rcurve(#1)(\Np\@ux,\Np\@uy,1)(#2,#3,\Np\@@U)(\Np\@vx,\Np\@vy,1)
 \Lineto(#4,#5) \Stroke}

% -------------------------------------------------------------------------
% Draws a vector from point x1,y1 to point x2,y2. \Vect(x1,y1)(x2,y2)
% -------------------------------------------------------------------------
\gdef\Vect(#1,#2)(#3,#4){%
 \Dset(\@ux,#1) \Dset(\@uy,#2)
 \Len(\Np\@ux,\Np\@uy)(#3,#4)(\@tx)
 \Direc(\Np\@ux,\Np\@uy)(#3,#4)(\@ty)
 \@cd=0 \Deg(\Np\@ty,\@ty)
 \@dx=\@tx \Dsub(\@dx,0.20) \Dset(\@dy,0.05)
 \@ex=\@dx \@ey=-\@dy
 \Rotpoint(\Np\@ty)(\Np\@dx,\Np\@dy)(\@dx,\@dy)
 \Rotpoint(\Np\@ty)(\Np\@ex,\Np\@ey)(\@ex,\@ey)
 \Add(\@dx,\@ux) \Add(\@dy,\@uy)
 \Add(\@ex,\@ux) \Add(\@ey,\@uy)
 \Polygon(\Np\@ux,\Np\@uy)(#3,#4)(\Np\@dx,\Np\@dy)(\Np\@ex,\Np\@ey)(#3,#4)
 \Sfill}

% -------------------------------------------------------------------------
% Draws a vector from the current point to point x1,y1. \Vecto(x1,y1)
% -------------------------------------------------------------------------
\gdef\Vecto(#1,#2){\Vect(\Np\@xx,\Np\@xy)(#1,#2)}

% -------------------------------------------------------------------------
% Computes the function value of a polynom (dregree <= 3) at x and stores
% the result in y. \Fpoly(x,y)
% -------------------------------------------------------------------------
\gdef\Fpoly(#1,#2){#2=\@ax
 \Dmul(#2,#1) \Add(#2,\@bx)
 \Dmul(#2,#1) \Add(#2,\@cx)
 \Dmul(#2,#1) \Add(#2,\@dx)}

% -------------------------------------------------------------------------
% Computes the first derivative of a polynom (degree <= 3) at x and stores
% the result in y. \Dpoly(x,y)
% -------------------------------------------------------------------------
\gdef\Dpoly(#1,#2){#2=\@ax
 \Dmul(#2,#1) \Mul(#2,3)
 \Add(#2,\@bx) \Add(#2,\@bx)
 \Dmul(#2,#1) \Add(#2,\@cx)}

% -------------------------------------------------------------------------
% Draws a polynom y=ax^3+bx^2+cx+d from x1 to x2 with a cubic bezier curve.
% All coefficients may be zero. So you can draw lines, parabolas and cubics.
% \Polynom(x1,x2)(a,b,c,d)
% -------------------------------------------------------------------------
\gdef\Polynom(#1,#2)(#3,#4,#5,#6){%
 \Dset(\@sx,#1) \Dset(\@vx,#2)
 \Dset(\@ax,#3) \Dset(\@bx,#4)
 \Dset(\@cx,#5) \Dset(\@dx,#6)
 \@zx=\@vx \Sub(\@zx,\@sx)
 \Div(\@zx,3)
 \@tx=\@sx \Add(\@tx,\@zx)
 \@ux=\@vx \Sub(\@ux,\@zx)
 \Dpoly(\@sx,\@wx) \Dmul(\@wx,\@zx)
 \Dpoly(\@vx,\@wy) \Dmul(\@wy,\@zx)
 \Fpoly(\@sx,\@sy) \Fpoly(\@vx,\@vy)
 \@ty=\@sy \Add(\@ty,\@wx)
 \@uy=\@vy \Sub(\@uy,\@wy)
 \Moveto(\Np\@sx,\Np\@sy)
 \Bezier(\Np\@tx,\Np\@ty,\Np\@ux,\Np\@uy,\Np\@vx,\Np\@vy)}

% -------------------------------------------------------------------------
% Draws the tangent of a polynom y=ax^3+bx^2+cx+d at abszissa x from x1
% to x2 and marks the touching point. \Tangent(x)(x1,x2)(a,b,c,d)
% -------------------------------------------------------------------------
\gdef\Tangent(#1)(#2,#3)(#4,#5,#6,#7){%
 \Dset(\@xx,#1)
 \Dset(\@sx,#2) \Dset(\@tx,#3)
 \Dset(\@ax,#4) \Dset(\@bx,#5)
 \Dset(\@cx,#6) \Dset(\@dx,#7)
 \Fpoly(\@xx,\@xy) \Dpoly(\@xx,\@wx)
 \@sy=\@wx \@ty=\@wx
 \Dmul(\@sy,\@sx) \Dmul(\@ty,\@tx)
 \Add(\@sy,\@xy) \Add(\@ty,\@xy)
 \Dmul(\@wx,\@xx)
 \Sub(\@sy,\@wx) \Sub(\@ty,\@wx)
 \Line(\Np\@sx,\Np\@sy)(\Np\@tx,\Np\@ty)
 \Stroke
 \Point(1)(#1,\Np\@xy)}

% -------------------------------------------------------------------------
% Draws a sequence of line segments. You have to provide m points
% with m=i+1 (i=1,2,..).  \Polygon(x1,y1)(x2,y2)...(xm,ym)
% -------------------------------------------------------------------------
\gdef\Polygon{\@ifnextchar ({\@polygon}{\@ck=0}}
 \gdef\@polygon(#1,#2){\@ifnextchar ({\@pdraw(#1,#2)}{\@ck=0}}
 \gdef\@pdraw(#1,#2)(#3,#4){\ifnum\@ck=0 \@ck=1 \Moveto(#1,#2) \fi
  \Lineto(#3,#4) \Polygon(#3,#4)}

% -------------------------------------------------------------------------
% Draws a sequence of vector segments. You have to provide m points
% with m=i+1 (i=1,2,..).  \Vpolygon(x1,y1)(x2,y2)...(xm,ym)
% -------------------------------------------------------------------------
\gdef\Vpolygon{\@ifnextchar ({\@Vdraw}{\relax}}
 \gdef\@Vdraw(#1,#2){\@ifnextchar ({\@Vcoord(#1,#2)}{\relax}}
 \gdef\@Vcoord(#1,#2)(#3,#4){\Vect(#1,#2)(#3,#4) \Vpolygon(#3,#4)}

% -------------------------------------------------------------------------
% Draws a sequence of quadratic bezier curves.
% You have to provide m points with m=2*i+1 (i=1,2,..).
%     \Quadratic(x1,y1)(x2,y2)(x3,y3)...(xm,ym)
% -------------------------------------------------------------------------
\gdef\Quadratic{\@ifnextchar ({\@Qdraw}{\relax}}
\gdef\@Qdraw(#1,#2){\@ifnextchar ({\@Qcoord(#1,#2)}{\relax}}
\gdef\@Qcoord(#1,#2)(#3,#4)(#5,#6){%
 \Dset(\@ax,#1) \Dset(\@ay,#2)
 \Dset(\@bx,#3) \Dset(\@by,#4)
 \Dset(\@cx,#5) \Dset(\@cy,#6)
 \Mul(\@bx,2)   \Mul(\@by,2)
 \Add(\@ax,\@bx)\Div(\@ax,3)
 \Add(\@ay,\@by)\Div(\@ay,3)
 \Add(\@cx,\@bx)\Div(\@cx,3)
 \Add(\@cy,\@by)\Div(\@cy,3)
 \Moveto(#1,#2) \Bezier(\Np\@ax,\Np\@ay,\Np\@cx,\Np\@cy,#5,#6)
 \Quadratic(#5,#6)}

% -------------------------------------------------------------------------
% Draws a sequence of n cubic bezier curves.
% You have to provide m points with m=3*i+1 (i=1,2,..).
%     \Cubic(x1,y1)(x2,y2)(x3,y3)(x4,y4)...(xm,ym)
% -------------------------------------------------------------------------
\gdef\Cubic{\@ifnextchar ({\@Cdraw}{\relax}}
\gdef\@Cdraw(#1,#2){\@ifnextchar ({\@Ccoord(#1,#2)}{\relax}}
\gdef\@Ccoord(#1,#2)(#3,#4)(#5,#6)(#7,#8){%
 \Moveto(#1,#2) \Bezier(#3,#4,#5,#6,#7,#8)
 \Cubic(#7,#8)}

% -------------------------------------------------------------------------
% This is the general macro for drawing integral bezier curves. It draws
% bezier curves of degree 1..7. The degree depends on the number of
% coordinates. If \@ce is zero, the curve is drawn, depending on the
% counter \@ci. If \@ce is not zero, the coordinates are read until no
% more open cordinates are found. \Curveto needs \Moveto in front to
% draw from the current point.
%     \Curve(n)(x0,y0)...,   \Curveto(n)(x1,y1)...
% -------------------------------------------------------------------------
\gdef\Curve{\@cg=0\@ce=1\@ifnextchar ({\@Draw}{\@Draw(0)}}
\gdef\Curveto{\@cg=0\@ce=0\@ifnextchar ({\@Draw}{\@Draw(0)}}

\gdef\@Draw(#1){\@ifnextchar ({\@Coord(#1)}{%
 \@ci=0  \ifcase\@cf\or\@Acurve\or
 \@Bcurve\or\@Ccurve\or\@Dcurve\or
 \@Ecurve\or\@Fcurve\or\@Gcurve\fi}}

\gdef\@Coord(#1)(#2,#3){%
 \ifnum#1=0
  \Add(\@cf,1)  \Euclid(#2,#3)
 \else
  \@cf=0 \@ca=#1
  \@cb=\@ca \Add(\@cb,1)
  \ifnum\@ce=1
   \Dset(\@ax,#2)\Dset(\@ay,#3)
   \Moveto(\Np\@ax,\Np\@ay)
  \else
   \Add(\@cf,1)
   \@ax=\@xx \@ay=\@xy
   \Dset(\@bx,#2)\Dset(\@by,#3)
  \fi\fi \Curve(0)}

% -------------------------------------------------------------------------
% This sets the points in euclidean (affine) coordinate space
% -------------------------------------------------------------------------
\gdef\Euclid(#1,#2){%
 \ifcase\@cf\or
  \Dset(\@bx,#1)\Dset(\@by,#2)\or
  \Dset(\@cx,#1)\Dset(\@cy,#2)\or
  \Dset(\@dx,#1)\Dset(\@dy,#2)\or
  \Dset(\@ex,#1)\Dset(\@ey,#2)\or
  \Dset(\@fx,#1)\Dset(\@fy,#2)\or
  \Dset(\@gx,#1)\Dset(\@gy,#2)\or
  \Dset(\@hx,#1)\Dset(\@hy,#2)\fi}

% -------------------------------------------------------------------------
% This is the general macro to draw rational bezier curves. It draws
% bezier curves of degree 1..7. The degree depends on the number of
% coordinates. If \@ce is zero, the curve is drawn, depending on the
% counter \@ci. If \@ci is not zero, the coordinates are read until no
% more open cordinates are found. \Rcurveto needs \Rmoveto in front to
% draw from the current point.
%      \Rcurve(n)(x0,y0,z0)...,   \Rcurveto(n)(x1,y1,z1)...
% -------------------------------------------------------------------------
\gdef\Rcurve{\@cg=1\@ce=1\@ifnextchar ({\@Rdraw}{\@Rdraw(0)}}
\gdef\Rcurveto{\@cg=1\@ce=0\@ifnextchar ({\@Rdraw}{\@Rdraw(0)}}

\gdef\@Rdraw(#1){\@ifnextchar ({\@Rcoord(#1)}{%
 \@ci=0  \ifcase\@cf\or\@Acurve\or
 \@Bcurve\or\@Ccurve\or\@Dcurve\or
 \@Ecurve\or\@Fcurve\or\@Gcurve\fi}}

\gdef\@Rcoord(#1)(#2,#3,#4){%
 \ifnum#1=0
  \Add(\@cf,1)  \Homogen(#2,#3,#4)
 \else
  \@cf=0 \@ca=#1
  \@cb=\@ca \Add(\@cb,1)
  \ifnum\@ce=1
   \Dset(\@ax,#2)\Dset(\@ay,#3)\Dset(\@az,#4)
   \Rmoveto(\Np\@ax,\Np\@ay,\Np\@az)
   \Dmul(\@ax,\@az)\Dmul(\@ay,\@az)
  \else
   \Add(\@cf,1)
   \@ax=\@xx \@ay=\@xy \@az=\@xz
   \Dmul(\@ax,\@az)\Dmul(\@ay,\@az)
   \Dset(\@bx,#2)\Dset(\@by,#3)\Dset(\@bz,#4)
   \Dmul(\@bx,\@bz)\Dmul(\@by,\@bz)
  \fi\fi \Rcurve(0)}

% -------------------------------------------------------------------------
% For rational bezier curves, this adds a weight component to the points
% and multiplies the components by the weights. Now, we can treat the
% curve as integral bezier curve with 3 components (homogen coordinates)
% px=px*w, py=py*w, pz=w. \Homogen(px,py,w)
% -------------------------------------------------------------------------
\gdef\Homogen(#1,#2,#3){%
 \ifcase\@cf\or
  \Dset(\@bx,#1)\Dset(\@by,#2)\Dset(\@bz,#3)\Dmul(\@bx,\@bz)\Dmul(\@by,\@bz)
 \or
  \Dset(\@cx,#1)\Dset(\@cy,#2)\Dset(\@cz,#3)\Dmul(\@cx,\@cz)\Dmul(\@cy,\@cz)
 \or
  \Dset(\@dx,#1)\Dset(\@dy,#2)\Dset(\@dz,#3)\Dmul(\@dx,\@dz)\Dmul(\@dy,\@dz)
 \or
  \Dset(\@ex,#1)\Dset(\@ey,#2)\Dset(\@ez,#3)\Dmul(\@ex,\@ez)\Dmul(\@ey,\@ez)
 \or
  \Dset(\@fx,#1)\Dset(\@fy,#2)\Dset(\@fz,#3)\Dmul(\@fx,\@fz)\Dmul(\@fy,\@fz)
 \or
  \Dset(\@gx,#1)\Dset(\@gy,#2)\Dset(\@gz,#3)\Dmul(\@gx,\@gz)\Dmul(\@gy,\@gz)
 \or
  \Dset(\@hx,#1)\Dset(\@hy,#2)\Dset(\@hz,#3)\Dmul(\@hx,\@hz)\Dmul(\@hy,\@hz)
 \fi}

% -------------------------------------------------------------------------
% For rational bezier curves, this projects homogeneous coordinates into
% affine space by dividing each component through the interpolated weight
% if pz=0 px=py=0 else px=px/pz, py=py/pz. \Affine
% -------------------------------------------------------------------------
\gdef\Affine{%
 \ifdim\@zz=\z@ \Dset(\@zx,0) \Dset(\@zy,0)
 \else \Ddiv(\@zx,\@zz) \Ddiv(\@zy,\@zz)\fi}

% -------------------------------------------------------------------------
% Linear interpolation between two coordinates. We have to take care, not
% to change the contents of #1 and #2, because these are fixed bezier
% coordinates. The interpolation value is returned in register #3.
% b0=a0+i*(a1-a0)/n
% -------------------------------------------------------------------------
\gdef\@One(#1,#2,#3){#3=#2
 \Sub(#3,#1) \Mul(#3,\@ci)
 \Div(#3,\@ca) \Add(#3,#1)}

% -------------------------------------------------------------------------
% Two degree interpolation between three coordinates.
% c0=b0+i*(b1-b0)/n, c1=b1+i*(b2-b1)/n, c=c0+i*(c1-c0)/n
% -------------------------------------------------------------------------
\gdef\@Two(#1,#2,#3,#4){%
 \@One(#1,#2,\@sx)
 \@One(#2,#3,\@sy)
 \@One(\@sx,\@sy,#4)}

% -------------------------------------------------------------------------
% Three degree interpolation between four coordinates.
% d0=c0+i*(c1-c0)/n, d1=c1+i*(c2-c1)/n, d=d0+i*(d1-d0)/n
% -------------------------------------------------------------------------
\gdef\@Three(#1,#2,#3,#4,#5){%
 \@Two(#1,#2,#3,\@tx)
 \@Two(#2,#3,#4,\@ty)
 \@One(\@tx,\@ty,#5)}

% -------------------------------------------------------------------------
% Four degree interpolation between five coordinates.
% e0=d0+i*(d1-d0)/n, e1=d1+i*(d2-d1)/n, e=e0+i*(e1-e0)/n
% -------------------------------------------------------------------------
\gdef\@Four(#1,#2,#3,#4,#5,#6){%
 \@Three(#1,#2,#3,#4,\@ux)
 \@Three(#2,#3,#4,#5,\@uy)
 \@One(\@ux,\@uy,#6)}

% -------------------------------------------------------------------------
% Five degree interpolation between six coordinates.
% f0=e0+i*(e1-e0)/n, f1=e1+i*(e2-e1)/n, f=f0+i*(f1-f0)/n
% -------------------------------------------------------------------------
\gdef\@Five(#1,#2,#3,#4,#5,#6,#7){%
 \@Four(#1,#2,#3,#4,#5,\@vx)
 \@Four(#2,#3,#4,#5,#6,\@vy)
 \@One(\@vx,\@vy,#7)}

% -------------------------------------------------------------------------
% Six degree interpolation between seven coordinates.
% g0=f0+i*(f1-f0)/n, g1=f1+i*(f2-f1)/n, g=g0+i*(g1-g0)/n
% -------------------------------------------------------------------------
\gdef\@Six(#1,#2,#3,#4,#5,#6,#7,#8){%
 \@Five(#1,#2,#3,#4,#5,#6,\@wx)
 \@Five(#2,#3,#4,#5,#6,#7,\@wy)
 \@One(\@wx,\@wy,#8)}

% -------------------------------------------------------------------------
% Seven degree interpolation between eight coordinates.
% h0=g0+i*(g1-g0)/n, h1=g1+i*(g2-g1)/n, h=h0+i*(h1-h0)/n
% -------------------------------------------------------------------------
\gdef\@Seven(#1,#2,#3,#4,#5,#6,#7,#8,#9){%
 \@Six(#1,#2,#3,#4,#5,#6,#7,\@yx)
 \@Six(#2,#3,#4,#5,#6,#7,#8,\@yy)
 \@One(\@yx,\@yy,#9)}

% -------------------------------------------------------------------------
% Draws a one degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Acurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@One(\@ax,\@bx,\@zx)
  \@One(\@ay,\@by,\@zy)
  \ifnum\@cg=1
   \@One(\@az,\@bz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a two degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Bcurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Two(\@ax,\@bx,\@cx,\@zx)
  \@Two(\@ay,\@by,\@cy,\@zy)
  \ifnum\@cg=1
   \@Two(\@az,\@bz,\@cz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a three degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Ccurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Three(\@ax,\@bx,\@cx,\@dx,\@zx)
  \@Three(\@ay,\@by,\@cy,\@dy,\@zy)
  \ifnum\@cg=1
   \@Three(\@az,\@bz,\@cz,\@dz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a four degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Dcurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Four(\@ax,\@bx,\@cx,\@dx,\@ex,\@zx)
  \@Four(\@ay,\@by,\@cy,\@dy,\@ey,\@zy)
  \ifnum\@cg=1
   \@Four(\@az,\@bz,\@cz,\@dz,\@ez,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a five degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Ecurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Five(\@ax,\@bx,\@cx,\@dx,\@ex,\@fx,\@zx)
  \@Five(\@ay,\@by,\@cy,\@dy,\@ey,\@fy,\@zy)
  \ifnum\@cg=1
   \@Five(\@az,\@bz,\@cz,\@dz,\@ez,\@fz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a six degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Fcurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Six(\@ax,\@bx,\@cx,\@dx,\@ex,\@fx,\@gx,\@zx)
  \@Six(\@ay,\@by,\@cy,\@dy,\@ey,\@fy,\@gy,\@zy)
  \ifnum\@cg=1
   \@Six(\@az,\@bz,\@cz,\@dz,\@ez,\@fz,\@gz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
% Draws a seven degree bezier curve (integral or rational).
% -------------------------------------------------------------------------
\gdef\@Gcurve{%
 \@whilenum{\@ci<\@cb}\do{%
  \@Seven(\@ax,\@bx,\@cx,\@dx,\@ex,\@fx,\@gx,\@hx,\@zx)
  \@Seven(\@ay,\@by,\@cy,\@dy,\@ey,\@fy,\@gy,\@hy,\@zy)
  \ifnum\@cg=1
   \@Seven(\@az,\@bz,\@cz,\@dz,\@ez,\@fz,\@gz,\@hz,\@zz)\Affine\fi
  \Lineto(\Np\@zx,\Np\@zy) \Add(\@ci,1)}}

% -------------------------------------------------------------------------
\endinput

%% End of file `lapdf.sty'.