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+% =========================================================================
+% 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'.