% TeXdraw toolbox macros, useful for extended TeXdraw commands
% $Id: txdtools.tex 1.11 2019/04/18 TeXdraw-v2r3 $
% Copyright (C) 1991-2019 Peter Kabal
% This work is licensed under the Creative Commons Attribution (CC-BY)
% License, any version. To view the licenses, visit
% creativecommons.org/licenses/by or send a letter to
% Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
% Peter Kabal
% Department of Electrical & Computer Engineering
% McGill University
% peter dot kabal at mcgill dot ca
%
http://www-mmsp.ece.mcgill.ca/MMSP/Documents/Software/
% ===============================================================
% These macros use temporary count registers defined by TeXdraw
% \t@counta \t@pixa
% \t@countb \t@pixb
% \t@countc \t@pixc
% \t@pixd
\chardef\catamp=\the\catcode`\@
\catcode`\@=11
% ===== Real arithmetic
% Real addition
% #1 - summand
% #2 - summand
% #3 - macro name to capture the real result
\def\realadd #1#2#3{\dimen0=#1pt
\dimen2=#2pt
\advance \dimen0 by \dimen2
\edef #3{\expandafter\c@lean\the\dimen0}}
% Real division
% #1 - numerator
% #2 - denominator (divisor)
% #3 - macro name to capture the real result
\def\realdiv #1#2#3{\dimen0=#1pt
\t@counta=\dimen0
\dimen0=#2pt
\t@countb=\dimen0
\intdiv \t@counta \t@countb #3}
% ===== Integer arithmetic
% Length of the hypotenuse
% Find the length of a vector, lenhyp = sqrt(dx*dx + dy*dy)
% #1 - integer value, dx
% #2 - integer value, dy
% #3 - count register to capture the integer value
\def\lenhyp #1#2#3{\t@counta=#1%
\multiply \t@counta by \t@counta
\t@countb=#2%
\multiply \t@countb by \t@countb
\advance \t@counta by \t@countb
\sqrtnum \t@counta #3}
% Square root of an integer
% Newton-Raphson iteration to find the square root, integer argument
% Let the current estimate of the square root of x be b(k).
% Form an error function, e(k)=b(k)*b(k)-x. Follow the gradient of the
% error to calculate the next guess,
%
% e(k) - 0 d e(k) b(k) + x/b(k)
% ---------- = ------ = 2*b(k) ==> b(k+1) = -------------
% b(k)-b(k+1) d b(k) 2
%
% Note this iteration does not work for x=0, since the guess is then b(k)=0.
% Rename the count registers to have more suggestive names
\let\bk=\t@counta
\let\bn=\t@countb
\let\xval=\t@countc
\def\sqrtnum #1#2{\xval=#1%
\bk=\xval
\loop
\bn=\xval
\divide \bn by \bk
\advance \bn by \bk
\advance \bn by 1 % rounding
\divide \bn by 2
\ifnum \bn < \bk
\bk=\bn
\repeat
#2=\bn}
% ===== Coordinate macros
% Return the coordinates of the current position
% #1 - macro name to capture the x-coordinate
% #2 - macro name to capture the y-coordinate
\def\currentpos #1#2{\t@pixa=\x@pix
\advance \t@pixa by -\x@segoffpix
\pixtocoord \t@pixa #1
\t@pixa=\y@pix
\advance \t@pixa by -\y@segoffpix
\pixtocoord \t@pixa #2}
% Length of a vector
% Find the length of the vector between coordinate (#1 #2) and
% coordiante (#3 #4). The length is expressed relative to the
% current scaling.
% (#1 #2) - vector start coordinates
% (#3 #4) - vector end coordinates
% #5 - macro name to receive the length
\def\vectlen (#1 #2)(#3 #4)#5{\getpos (#1 #2)\x@arga\y@arga
\getpos (#3 #4)\x@argb\y@argb
\coordtopix \x@arga \t@pixa
\coordtopix \x@argb \t@pixb
\advance \t@pixb by -\t@pixa
\coordtopix \y@arga \t@pixc
\coordtopix \y@argb \t@pixd
\advance \t@pixd by -\t@pixc
\lenhyp \t@pixb \t@pixd \t@pixc
\pixtocoord \t@pixc #5}
% Cossine and sine
% Find the cosine and sine of the angle of a vector directed from
% the coordinate (#1 #2) to the coordinate (#3 #4).
% (#1 #2) - start coordinates
% (#3 #4) - end coordinates
% #5 - macro name to receive the cosine of the angle
% #6 - macro name to receive the sine of the angle
\def\cossin (#1 #2)(#3 #4)#5#6{\getpos (#1 #2)\x@arga\y@arga
\getpos (#3 #4)\x@argb\y@argb
\coordtopix \x@arga \t@pixa
\coordtopix \x@argb \t@pixb
\advance \t@pixb by -\t@pixa
\coordtopix \y@arga \t@pixc
\coordtopix \y@argb \t@pixd
\advance \t@pixd by -\t@pixc
\lenhyp \t@pixb \t@pixd \t@pixc
\intdiv \t@pixb\t@pixc #5%
\intdiv \t@pixd\t@pixc #6}
\catcode`\@=\catamp
