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+% tkz-tools-eu-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-eu-math.tex}
+\makeatletter
+%<-------------------------------------------------------------------------->
+% \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}%
+\edef\tkz@den{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+\edef\tkz@coordx{\fpeval{\pgf@x/\tkz@den}}
+\edef\tkz@coordx{\fpeval{round(\tkz@coordx,5)}}
+\edef\tkz@coordy{\fpeval{\pgf@y/\tkz@den}}
+\edef\tkz@coordy{\fpeval{round(\tkz@coordy,5)}}
+\pgf@x = \tkz@coordx pt
+\pgf@y = \tkz@coordy pt
+}
+%<-------------------------------------------------------------------------->
+% 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){%
+%\pgfkeys{tkzcalclen/.cd, cm = true}
+\pgfqkeys{/tkzcalclen}{#1}%
+\begingroup
+\tkz@@CalcLength(#2,#3){tkzLengthResult}
+\iftkzLengthIncm
+ \pgfmathparse{\tkzLengthResult pt/1cm}
+ \edef\tkz@xfpMathLen{\fpeval{round(\pgfmathresult,6)}}
+ \global\let\tkzLengthResult\tkz@xfpMathLen
+\fi
+\endgroup
+}%
+\def\tkz@@CalcLength(#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\tkz@@CalcLengthcm(#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/28.45274,6)}}
+\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
+ \pgfmathparse{#1/1cm}
+ \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}}
+ \global\let\tkz@mathresult\tkz@mathresult
+ \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}%
+\endgroup
+}%
+%<-------------------------------------------------------------------------->
+% \tkzcmtopt passage de cm   pt mul par 28.45274
+%<--------------------------------------------------------------------------
+\def\tkzcmtopt(#1)#2{%
+\begingroup
+ \pgfmathparse{#1*1cm}
+ \edef\tkz@mathresult{\fpeval{round(\pgfmathresult,5)}}
+ \global\let\tkz@mathresult\tkz@mathresult
+ \global\expandafter\edef\csname #2\endcsname{\tkz@mathresult}%
+\endgroup
+}%
+
+% Schrodinger's cat idea 03/01/20
+\tikzset{veclen/.code={%
+\pgfmathdeclarefunction*{veclen}{2}{%
+\begingroup%
+ \pgfmath@x##1pt\relax%
+ \pgfmath@y##2pt\relax%
+ \edef\tkz@xfpMathLen{\fpeval{sqrt((\pgf@x)^2+(\pgf@y)^2)}}
+ \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}}%
+\tkz@ax\pgf@x%
+\tkz@ay\pgf@y%
+\pgfextractx{\pgf@x}{\pgfpointanchor{#2}{center}}%
+\pgfextracty{\pgf@y}{\pgfpointanchor{#2}{center}}
+\tkz@bx\pgf@x%
+\tkz@by\pgf@y%
+\pgfextractx{\pgf@x}{\pgfpointanchor{#3}{center}}%
+\pgfextracty{\pgf@y}{\pgfpointanchor{#3}{center}}%
+\tkz@cx\pgf@x%
+\tkz@cy\pgf@y%
+\edef\tkz@@dotprod{\fpeval{round(((\tkz@bx-\tkz@ax)*(\tkz@cx-\tkz@ax)+(\tkz@by-\tkz@ay)*(\tkz@cy-\tkz@ay))/(809.55841),5)}}
+\global\let\tkzMathResult\tkz@@dotprod
+\endgroup}
+%<---------------------------------------------------------–>
+ \def\tkzGetResult#1{%
+ \global\expandafter\edef\csname #1\endcsname{\tkzMathResult}}
+%<---------------------------------------------------------–>
+% #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{\fpeval{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{\fpeval{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{\fpeval{round(\tkz@om*\tkz@om -\tkz@ra*\tkz@ra,5)}}
+\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{\fpeval{\tkz@d-(\tkz@ra+\tkz@rb)}}
+\edef\tkzMathResultb{\fpeval{abs(\tkz@d-(\tkz@ra+\tkz@rb))}}
+\edef\tkzMathResultc{\fpeval{abs(\tkz@d-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
+}
+\def\tkzmathrotatepointaround#1#2#3{%
+ \pgf@process{%
+ \pgf@process{#1}%
+ \pgf@xc=\pgf@x%
+ \pgf@yc=\pgf@y%
+ \pgf@process{#2}%
+ \pgf@xa\pgf@x%
+ \pgf@ya\pgf@y%
+ \pgf@xb\pgf@x%
+ \pgf@yb\pgf@y%
+ \pgf@x=\pgf@xc%
+ \pgf@y=\pgf@yc%
+ \advance\pgf@x-\pgf@xa%
+ \advance\pgf@y-\pgf@ya%
+ \pgfmathsetmacro\angle{#3}%
+ \mathSin{\mathRad{\angle}}%
+ \let\sineangle\pgfmathresult%
+ \mathCos{\mathRad{\angle}}%
+ \let\cosineangle\pgfmathresult%
+ \pgf@xa\cosineangle\pgf@x%
+ \advance\pgf@xa-\sineangle\pgf@y%
+ \pgf@ya\sineangle\pgf@x%
+ \advance\pgf@ya\cosineangle\pgf@y%
+ \pgf@x\pgf@xb%
+ \pgf@y\pgf@yb%
+ \advance\pgf@x\pgf@xa%
+ \advance\pgf@y\pgf@ya%
+ }%
+}
+\makeatother
+\endinput \ No newline at end of file