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+% tkz-tools-lua-math.tex
+% Copyright 2023 Alain Matthes
+% This work may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.3
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+% http://www.latex-project.org/lppl.txt
+% and version 1.3 or later is part of all distributions of LaTeX
+% version 2005/12/01 or later.
+% This work has the LPPL maintenance status “maintained”.
+% The Current Maintainer of this work is Alain Matthes.
+
+\def\fileversion{5.00c}
+\def\filedate{2023/01/23}
+\typeout{2023/01/23 5.00c tkz-tools-lua-math.tex}
+\makeatletter
+%<-------------------------------------------------------------------------->
+%<-------------------------------------------------------------------------->
+% Lengths
+%<-------------------------------------------------------------------------->
+%<-------------------------------------------------------------------------->
+\begin{luacode*}
+complex = {} -- global complex numbers registry
+M = {} -- the module
+local mt = {} --metatable for complex numbers
+setmetatable(_ENV, {__index = complex})
+ function new (r, i)
+ local cp = {}
+ cp = {r=r, i=i}
+ return setmetatable(cp,mt)
+ end
+ M.new = new -- add 'new' to the module
+ -- create constant 'i'
+ M.i = new(0, 1)
+
+ function M.add (c1, c2)
+ return new(c1.r + c2.r, c1.i + c2.i)
+ end
+
+ function M.sub (c1, c2)
+ return new(c1.r - c2.r, c1.i - c2.i)
+ end
+
+ function M.mul (c1, c2)
+ return new(c1.r*c2.r - c1.i*c2.i, c1.r*c2.i + c1.i*c2.r)
+ end
+
+ function M.inv (c)
+ local n = c.r^2 + c.i^2
+ return new(c.r/n, -c.i/n)
+ end
+
+ function M.div (c1, c2)
+ return M.mul(c1, M.inv(c2))
+ end
+
+ function M.re (c)
+ return new(c.r,0)
+ end
+
+ function M.im (c)
+ return new(c.i,0)
+ end
+
+ function M.mod (c)
+ local n = c.r^2 + c.i^2
+ return new(n,0)
+ end
+
+ function M.prinarg(c)
+ local arg
+ if c.r > 0 then
+ arg = math.atan(c.i/c.r)
+ elseif c.r < 0 and c.i >= 0 then
+ arg = math.atan(c.i/c.r) + math.pi
+ elseif c.r < 0 and c.i < 0 then
+ arg = math.atan(c.i/c.r) - math.pi
+ elseif c.r == 0 and c.i > 0 then
+ arg = math.pi / 2
+ elseif c.r == 0 and c.i < 0 then
+ arg = - math.pi / 2
+ else
+ error("Principal argument not defined.")
+ end
+ return arg
+ end
+
+ function M.op (...)
+ return ...
+ end
+
+ function M.tostring (c)
+ if c.i ==0 then
+ return string.format("%g", c.r)
+ elseif c.i> 0 and c.i==1 then
+ return string.format("%g+i", c.r)
+ elseif c.i> 0 and c.i~=1 then
+ return string.format("%g+%gi", c.r, c.i)
+ else
+ return string.format("%g%gi", c.r, c.i) --to avoid +-
+ end
+ end
+
+ --Setting Metatable operations.
+ mt.__add = M.add
+ mt.__mul = M.mul
+ mt.__sub = M.sub
+ mt.__tostring = M.tostring
+\end{luacode*}
+
+
+
+\begin{luacode*}
+ function normalize(angleA,angleB)
+ if angleA > 0 then
+ if angleA > angleB then
+ angleA = angleA - 360
+ end
+ else
+ if angleA > angleB then
+ angleB = angleB + 360
+ end
+ end
+ return angleA, angleB
+ end
+
+ function math.angle(x1, y1, x2, y2)
+ local a = math.deg(math.atan(y2 - y1, x2 - x1))
+ if a < 0 then
+ return a + 360
+ else
+ return a
+ end
+ end
+
+ function tkzop(...)
+ inf = math.huge
+ return ...
+end
+
+function tkzround(nb, ND)
+ local p = 10^(ND or 0)
+ return math.floor(nb * p + 0.5) / p
+end
+\end{luacode*}
+
+\newcommand\cpxNew[2]{%
+\directlua{complex[\luastringN{#1}] = M.new(#2)}}
+\newcommand\cpxPrint[1]{%
+\directlua{tex.sprint(tostring(complex[\luastringN{#1}]))}}
+\newcommand\cpxAdd[3]{%
+\directlua{complex[\luastringN{#1}]%
+ =M.add(complex[\luastringN{#2}],complex[\luastringN{#3}])}}
+
+
+\def\tkz@Dec#1{%
+ \directlua{tex.print(string.format('\@percentchar.6f',#1))}
+ }
+\def\tkz@Op#1{\directlua{tex.sprint(tostring(tkzop(#1)))}}
+\def\tkz@Log#1{\directlua{tex.sprint(math.log(#1))}}
+\def\tkz@Exp#1{\directlua{tex.sprint(math.exp(#1))}}
+\def\tkz@Sqrt#1{\directlua{tex.sprint(math.sqrt(#1))}}
+\def\tkz@Abs#1{\directlua{tex.sprint(math.abs(#1))}}
+\def\tkz@Pi{\directlua{tex.sprint(math.pi)}}
+\def\tkz@Cos#1{\directlua{tex.sprint(math.cos(#1))}}
+\def\tkz@Sin#1{\directlua{tex.sprint(tostring(math.sin(#1)))}}
+\def\tkz@Tan#1{\directlua{tex.sprint(math.tan(#1))}}
+\def\tkz@Rad#1{\directlua{tex.sprint(math.rad(#1))}}
+\def\tkz@Acos#1{\directlua{tex.sprint(math.acos(#1))}}
+\def\tkz@Asin#1{\directlua{tex.sprint(math.asin(#1))}}
+\def\tkz@Atan#1{\directlua{tex.sprint(math.atan(#1))}}
+\def\tkz@Round#1#2{\directlua{tex.sprint(tostring(tkzround(#1,#2)))}}
+\def\tkz@Angle#1#2#3#4{\directlua{tex.sprint(math.angle(#1,#2,#3,#4))}}
+\def\tkz@Ceil#1{\directlua{tex.sprint(math.ceil(#1))}}
+\def\tkz@Floor#1{\directlua{tex.sprint(math.floor(#1))}}
+\def\tkz@Huge{\directlua{tex.sprint(math.huge)}}
+\def\tkz@Max#1{\directlua{tex.sprint(math.max(#1))}}
+\def\tkz@Min#1{\directlua{tex.sprint(math.min(#1))}}
+\def\tkz@Random#1{\directlua{tex.sprint(math.random(#1))}}
+\def\tkz@veclen#1#2{%
+ \directlua{%
+ tex.print(string.format('\@percentchar.6f',math.sqrt((#1)^2+(#2)^2)))%
+ }%
+}
+\let\tkzSqrt\tkz@Sqrt
+\let\tkzPi\tkz@Pi
+\let\tkzExp\tkz@Exp
+\let\tkzLog\tkz@Log
+\let\tkzSin\tkz@Sin
+\let\tkzCos\tkz@Cos
+% \tkzpointnormalised#
+% tkzCalcLength
+% \tkzGetLength
+% \tkzpttocm
+% \tkzcmtopt
+% \tkzFindSlope
+% option xfp
+
+% \tkzpointnormalised normalise un point A-->A' tq ||v(OA')=1||
+% équivalent de \pgfpointnormalised avec fp
+% example
+% \tkzpointnormalised{%
+% \pgfpointdiff{\pgfpointanchor{A}{center}}
+% {\pgfpointanchor{B}{center}}}
+
+% or
+% \pgf@x=1 cm
+% \pgf@y=12 cm
+% \tkzpointnormalised{}
+%<--------------------------------------------------------------------------
+\def\tkzpointnormalised#1{%
+\pgf@process{#1}%
+\pgf@xa=\pgf@x%
+\pgf@ya=\pgf@y%
+\edef\tkz@temp@xa{\strip@pt\pgf@xa}%
+\edef\tkz@temp@ya{\strip@pt\pgf@ya}%
+\edef\tkz@den{\tkz@veclen{\tkz@temp@xa}{\tkz@temp@ya}}
+\edef\tkz@coordx{\tkz@Op{\tkz@temp@xa/\tkz@den}}
+\edef\tkz@coordx{\tkz@Dec{\tkz@Round{\tkz@coordx}{5}}}
+\edef\tkz@coordy{\tkz@Op{\tkz@temp@ya/\tkz@den}}
+\edef\tkz@coordy{\tkz@Dec{\tkz@Round{\tkz@coordy}{5}}}
+\pgf@x = \tkz@coordx pt
+\pgf@y = \tkz@coordy pt
+}
+%\def\tkz@Dec#1{\directlua{tex.print(string.format('\@percentchar.12f',#1))}}
+%<-------------------------------------------------------------------------->
+% restaure and save length
+\def\tkz@save@length{\global\let\tkz@temp@length\tkzLengthResult}%
+\def\tkz@restore@length{\global\let\tkzLengthResult\tkz@temp@length }%
+%<-------------------------------------------------------------------------->
+% \tkzCalcLength Distance entre deux points en pt ou en cm avec xfp
+% \veclen mais avec fp
+% option cm le résultat est en cm sinon en pt with cm=false
+%<-------------------------------------------------------------------------->
+\pgfkeys{tkzcalclen/.cd,
+ cm/.is if = tkzLengthIncm,
+ cm/.default = true,
+ cm = true}
+
+\def\tkzCalcLength{\pgfutil@ifnextchar[{\tkz@CalcLength}{\tkz@CalcLength[]}}
+\def\tkz@CalcLength[#1](#2,#3){%
+\pgfqkeys{/tkzcalclen}{#1}%
+\begingroup
+\tkz@@CalcLength(#2,#3){tkzLengthResult}
+\iftkzLengthIncm
+ \edef\tkz@xfpMathLen{\tkz@Dec{\tkz@Round{\tkzLengthResult/28.45274}{6}}}
+ \global\let\tkzLengthResult\tkz@xfpMathLen
+\fi
+\endgroup
+}%
+
+\def\tkz@@CalcLength(#1,#2)#3{%
+\pgfpointdiff{\pgfpointanchor{#1}{center}}%
+ {\pgfpointanchor{#2}{center}}%
+\edef\tkz@xa{\strip@pt\pgf@x}%
+\edef\tkz@ya{\strip@pt\pgf@y}%
+\edef\tkz@xfpMathLen{\tkz@veclen{\tkz@xa}{\tkz@ya}}
+\global\expandafter\edef\csname #3\endcsname{\tkz@xfpMathLen}
+}
+
+\def\tkz@@CalcLengthcm(#1,#2)#3{%
+\pgfpointdiff{\pgfpointanchor{#1}{center}}%
+ {\pgfpointanchor{#2}{center}}%
+\edef\tkz@xa{\strip@pt\pgf@x}%
+\edef\tkz@ya{\strip@pt\pgf@y}%
+\edef\tkz@xfpMathLen{\tkz@veclen{\tkz@xa}{\tkz@ya}}
+\edef\tkz@xfpMathLen{\tkz@Dec{\tkz@Round{\tkz@xfpMathLen/28.45274}{6}}}
+\global\expandafter\edef\csname #3\endcsname{\tkz@xfpMathLen}
+}
+\def\tkz@@CalcLengthb(#1,#2)#3{%
+\pgfpointdiff{\pgfpointanchor{#1}{center}}%
+ {\pgfpointanchor{#2}{center}}%
+\edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+\edef\tkz@xfpMathLen{\fpeval{round(\tkz@xfpMathLen,6)}}
+\global\expandafter\edef\csname #3\endcsname{\tkz@xfpMathLen}
+}
+%<-------------------------------------------------------------------------->
+\def\tkzGetLength#1{%
+\global\expandafter\edef\csname #1\endcsname{\tkzLengthResult}}
+%<-------------------------------------------------------------------------->
+% \tkzpttocm passage de pt   cm div par 28.45274
+%<-------------------------------------------------------------------------->
+\def\tkzpttocm(#1)#2{%
+\begingroup
+ \edef\tkz@mathresult{\tkz@Round{#1/28.45274}{6}}
+ \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}%
+\endgroup
+}%
+%<-------------------------------------------------------------------------->
+% \tkzcmtopt passage de cm   pt mul par 28.45274
+%<--------------------------------------------------------------------------
+\def\tkzcmtopt(#1)#2{%
+\begingroup
+ \edef\tkz@mathresult{\tkz@Round{#1*28.45274}{6}}
+ \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}%
+\endgroup
+}%
+%<---------------------------------------------------------–>
+ \def\tkzGetResult#1{%
+ \global\expandafter\edef\csname #1\endcsname{\tkzMathResult}}
+%<---------------------------------------------------------–>
+% Schrodinger's cat idea 03/01/20
+\tikzset{veclen/.code={%
+\pgfmathdeclarefunction*{veclen}{2}{%
+\begingroup%
+ \pgfmath@x##1pt\relax%
+ \pgfmath@y##2pt\relax%
+ \pgf@xa=\pgf@x%
+ \pgf@ya=\pgf@y%
+ \edef\tkz@temp@xa{\strip@pt\pgf@xa}%
+ \edef\tkz@temp@ya{\strip@pt\pgf@ya}%
+ \edef\tkz@xfpMathLen{\tkz@veclen{\tkz@temp@xa}{\tkz@temp@ya}}%
+ \pgfmath@returnone\tkz@xfpMathLen pt%
+\endgroup%
+}}}%
+%<---------------------------------------------------------–>
+\def\tkzSwapPoints(#1,#2){
+ \pgfnodealias{tkzPointTmp}{#2}
+ \pgfnodealias{#2}{#1}
+ \pgfnodealias{#1}{tkzPointTmp}}
+%<---------------------------------------------------------–>
+\def\tkzPermute(#1,#2,#3){
+ \tkzURotateWithNodes(#1,#3,#2)(#3) \tkzGetPoint{tkzpt}
+ \tkzURotateWithNodes(#1,#2,#3)(#2) \tkzGetPoint{#2}
+ \tkzSwapPoints(tkzpt,#3)
+}
+%<---------------------------------------------------------–>
+\def\tkzDotProduct(#1,#2,#3){%
+\begingroup
+\pgfextractx{\pgf@x}{\pgfpointanchor{#1}{center}}%
+\pgfextracty{\pgf@y}{\pgfpointanchor{#1}{center}}%
+\edef\tkzax{\strip@pt\pgf@x}%
+\edef\tkzay{\strip@pt\pgf@y}%
+\pgfextractx{\pgf@x}{\pgfpointanchor{#2}{center}}%
+\pgfextracty{\pgf@y}{\pgfpointanchor{#2}{center}}%
+\edef\tkzbx{\strip@pt\pgf@x}%
+\edef\tkzby{\strip@pt\pgf@y}%
+\pgfextractx{\pgf@x}{\pgfpointanchor{#3}{center}}%
+\pgfextracty{\pgf@y}{\pgfpointanchor{#3}{center}}%
+\edef\tkzcx{\strip@pt\pgf@x}%
+\edef\tkzcy{\strip@pt\pgf@y}%
+\edef\tkz@tmp{\tkz@Dec{\tkz@Round{((\tkzbx-(\tkzax))*(\tkzcx-(\tkzax))+(\tkzby-(\tkzay))*(\tkzcy-(\tkzay)))/809.55841}{6}}}
+\global\let\tkzMathResult\tkz@tmp
+\endgroup
+}
+
+% #1,#2 and #3 aligned
+\def\tkzIsLinear(#1,#2,#3){%
+\begingroup
+\tkz@@CalcLengthcm(#1,#2){tkz@la}
+\tkz@@CalcLengthcm(#1,#3){tkz@lb}
+\tkzDotProduct(#1,#2,#3)
+\edef\tkzResult{\tkz@Dec{\tkz@Abs{\tkzMathResult}-(\tkz@la)*(\tkz@lb)}}
+\ifdim \tkzResult pt < 0.01 pt\relax%
+\global\tkzLineartrue
+\else
+\global\tkzLinearfalse
+\fi
+\endgroup
+}
+%<---------------------------------------------------------–>
+% syntax : vec(#2,#1) ortho vec(#3,#1)
+\def\tkzIsOrtho(#1,#2,#3){%
+\begingroup
+\tkzDotProduct(#1,#2,#3)
+\edef\tkzResult{\tkz@Dec{\tkz@Abs{\tkzMathResult}}}
+\ifdim \tkzResult pt < 1 pt\relax%
+\global\tkzOrthotrue
+\else
+\global\tkzOrthofalse
+\fi
+\endgroup
+}
+%<---------------------------------------------------------–>
+% \tkzPowerCircle(M)(O,A) --> OM^2-OA^2
+\def\tkzPowerCircle(#1)(#2,#3){%
+\begingroup
+\tkz@@CalcLengthcm(#2,#3){tkz@ra}
+\tkz@@CalcLengthcm(#1,#2){tkz@om}
+\gdef\tkzMathResult{\tkz@Dec{(\tkz@om)^2-(\tkz@ra)^2}}
+\endgroup
+}
+%<---------------------------------------------------------–>
+\def\tkzDefRadicalAxis(#1,#2)(#3,#4){%
+\begingroup
+\tkz@@CalcLengthcm(#1,#3){tkz@d}
+\tkz@@CalcLengthcm(#1,#2){tkz@ra}
+\tkz@@CalcLengthcm(#3,#4){tkz@rb}
+\edef\tkzMathResult{\tkz@Dec{\tkz@d-(\tkz@ra+\tkz@rb)}}
+\edef\tkzMathResultb{\tkz@Dec{\tkz@Abs{(\tkz@d-(\tkz@ra+\tkz@rb))}}}
+\edef\tkzMathResultc{\tkz@Dec{\tkz@Abs{\tkz@d-\tkz@Abs{(\tkz@ra-(\tkz@rb))}}}}
+\ifdim \tkzMathResultc pt < 0.1 pt\relax%
+ \tkzURotateAngle(#2,90)(#3) \tkzGetPoint{tkzFirstPointResult}
+ \tkzURotateAngle(#2,-90)(#3) \tkzGetPoint{tkzSecondPointResult}
+\else
+\ifdim \tkzMathResultb pt < 0.1 pt\relax%
+ \tkzURotateAngle(#2,90)(#3) \tkzGetPoint{tkzFirstPointResult}
+ \tkzURotateAngle(#2,-90)(#3) \tkzGetPoint{tkzSecondPointResult}
+ \else
+\ifdim \tkzMathResult pt > 1 pt\relax%
+ \tkzURotateAngle(#1,60)(#3) \tkzGetPoint{tkz@aux}
+ \tkzInterCC(#1,#2)(tkz@aux,#1) \tkzGetPoints{tkz@pta}{tkz@ptb}
+ \tkzInterCC(#3,#4)(tkz@aux,#1) \tkzGetPoints{tkz@ptc}{tkz@ptd}
+ \tkzInterLL(tkz@pta,tkz@ptb)(tkz@ptc,tkz@ptd) \tkzGetPoint{tkz@pta}
+ \tkzUProjection(#1,#3)(tkz@pta) \tkzGetPoint{tkz@ptb}
+ \pgfnodealias{tkzSecondPointResult}{tkz@ptb}
+ \pgfnodealias{tkzFirstPointResult}{tkz@pta}
+\else
+\tkzInterCCR(#1,\tkz@ra)(#3,\tkz@rb){tkzFirstPointResult}{tkzSecondPointResult}
+\fi
+\fi
+\fi
+\endgroup
+}
+
+\makeatother
+\endinput \ No newline at end of file