%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% Correction to PiCTeX 1.1 9/21/87 %
% by Andreas Schrell, Wuppertal, FRG, 9/30/91 %
% %
% The bug forces wrong height and position of the %
% vertical \betweenarrows - structure if the %
% coordinate difference is negative. %
% You can search for ERROR in this file. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\catcode`!=11
\global
\def\betweenarrows #1#2 from #3 #4 to #5 #6 {%
\!xloc=\!M{#3}\!xunit \!xxloc=\!M{#5}\!xunit%
\!yloc=\!M{#4}\!yunit \!yyloc=\!M{#6}\!yunit%
\!dxpos=\!xxloc \advance\!dxpos by -\!xloc
\!dypos=\!yyloc \advance\!dypos by -\!yloc
\advance\!xloc .5\!dxpos
\advance\!yloc .5\!dypos
%
\let\!MBA=\!M% ** save current coord\dimen mode
\!setdimenmode% ** express locations in dimens
\ifdim\!dypos=\!zpt
\ifdim\!dxpos<\!zpt \!dxpos=-\!dxpos \fi
\put {\!lrarrows{\!dxpos}{#1}}#2{} at {\!xloc} {\!yloc}
\else
\ifdim\!dxpos=\!zpt
% \ifdim\!dypos<\!zpt \!dypos=-\!zpt \fi
% ^^^^^ ERROR!
\ifdim\!dypos<\!zpt \!dypos=-\!dypos \fi
% ^^^^^^^ CORRECTION!
\put {\!udarrows{\!dypos}{#1}}#2{} at {\!xloc} {\!yloc}
\fi
\fi
\let\!M=\!MBA% ** restore previous c/d mode
\ignorespaces}
% correction added by Robin Fairbairns (
[email protected]) 1999/09/14
\def\!qjoin (#1,#2) (#3,#4){%
\advance\!intervalno by 1
\!ifcoordmode
\edef\!xmidpt{#1}\edef\!ymidpt{#2}%
\else
\!dimenA=#1\relax \edef\!xmidpt{\the\!dimenA}%
% \!dimenA=#2\relax \edef\!xmidpt{\the\!dimenA}% WRONG
% ^^^^^^^^
\!dimenA=#2\relax \edef\!ymidpt{\the\!dimenA}%
% ^^^^^^^^
\fi
\!xM=\!M{#1}\!xunit \!yM=\!M{#2}\!yunit \!rotateaboutpivot\!xM\!yM
\!xE=\!M{#3}\!xunit \!yE=\!M{#4}\!yunit \!rotateaboutpivot\!xE\!yE
%
% ** Find coefficients for x(t)=a_x + b_x*t + c_x*t**2
\!dimenA=\!xM \advance \!dimenA by -\!xS% ** dimA = I = xM - xS
\!dimenB=\!xE \advance \!dimenB by -\!xM% ** dimB = II = xE-xM
\!xB=3\!dimenA \advance \!xB by -\!dimenB% ** b=3I-II
\!xC=2\!dimenB \advance \!xC by -2\!dimenA% ** c=2(II-I)
%
% ** Find coefficients for y(t)=y_x + b_y*t + c_y*t**2
\!dimenA=\!yM \advance \!dimenA by -\!yS%
\!dimenB=\!yE \advance \!dimenB by -\!yM%
\!yB=3\!dimenA \advance \!yB by -\!dimenB%
\!yC=2\!dimenB \advance \!yC by -2\!dimenA%
%
% ** Use Simpson's rule to calculate arc length over [0,1/2]:
% ** arc length = 1/2[1/6 f(0) + 4/6 f(1/4) + 1/6 f(1/2)]
% ** with f(t) = sqrt(x'(t)**2 + y'(t)**2).
\!xprime=\!xB \!yprime=\!yB% ** x'(t) = b + 2ct
\!dxprime=.5\!xC \!dyprime=.5\!yC% ** dt=1/4 ==> dx'(t) = c/2
\!getf \!midarclength=\!dimenA
\!getf \advance \!midarclength by 4\!dimenA
\!getf \advance \!midarclength by \!dimenA
\divide \!midarclength by 12
%
% ** Get arc length over [0,1].
\!arclength=\!dimenA
\!getf \advance \!arclength by 4\!dimenA
\!getf \advance \!arclength by \!dimenA
\divide \!arclength by 12% ** Now have arc length over [1/2,1]
\advance \!arclength by \!midarclength
\global\advance \totalarclength by \!arclength
%
%
% ** Check to see if there's anything to plot in this interval
\ifdim\!distacross>\!arclength
\advance \!distacross by -\!arclength% ** nothing
%
\else
\!initinverseinterp% ** initialize for inverse interpolation on arc length
\loop\ifdim\!distacross<\!arclength% ** loop over points on arc
\!inverseinterp% ** find t such that arc length[0,t] = distacross,
% ** using inverse quadratic interpolation
% ** now evaluate x(t)=(c*t + b)*t + a
\!xpos=\!t\!xC \advance\!xpos by \!xB
\!xpos=\!t\!xpos \advance \!xpos by \!xS
% ** evaluate y(t)
\!ypos=\!t\!yC \advance\!ypos by \!yB
\!ypos=\!t\!ypos \advance \!ypos by \!yS
\!plotifinbounds% ** plot point if in bounds
\advance\!distacross \plotsymbolspacing%** advance arc length for next pt
\!advancedashing% ** see "linear"
\repeat
%
\advance \!distacross by -\!arclength% ** prepare for next interval
\fi
%
\!xS=\!xE% ** shift ending points to starting points
\!yS=\!yE
\ignorespaces}
}
\endinput
