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diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-spc.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-spc.tex new file mode 100644 index 00000000000..9ed94b26e08 --- /dev/null +++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-lua-points-spc.tex @@ -0,0 +1,695 @@ +% tkz-obj-lua-points.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-obj-lua-points.tex} +\makeatletter +%add ExCenter +%<--------------------------------------------------------------------------–> +% Specific points +%<--------------------------------------------------------------------------–> +% barycentre +%<--------------------------------------------------------------------------–> +\def\tkzDefBarycentricPoint(#1){% +\begingroup + \path[coordinate] (barycentric cs:#1) coordinate (tkzPointResult); +\endgroup +} +\let\tkzDefBCPoint\tkzDefBarycentricPoint + +\def\tkzDefBarycentricPointTwo(#1,#2,#3,#4){% +\begingroup +\pgfextractx{\pgf@x}{\pgfpointanchor{#1}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#1}{center}} +\tkz@ax\pgf@x % +\tkz@ay\pgf@y % +\edef\tkzcax{\strip@pt\tkz@ax}% +\edef\tkzcay{\strip@pt\tkz@ay}% +\pgfextractx{\pgf@x}{\pgfpointanchor{#3}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#4}{center}} +\tkz@bx\pgf@x % +\tkz@by\pgf@y % +\edef\tkzcbx{\strip@pt\tkz@bx}% +\edef\tkzcby{\strip@pt\tkz@by}% +\edef\tkztpmx{\tkz@Dec{(\tkzcax*(#2) + \tkzcbx*(#4))/(#2 + #4 )}} +\edef\tkztpmy{\tkz@Dec{(\tkzcay*(#2) + \tkzcby*(#2))/(#2 + #4 )}} +\pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkztpmx pt}{\tkztpmy pt}} +\endgroup +} + +% \def\tkzDefCentroid(#1){% +% \begingroup +% \xdef\tkz@arg{} +% \foreach \X in {#1} +% {% +% \ifx\tkzutil@empty\tkz@arg% +% \xdef\tkz@arg{\X=1} +% \else +% \xdef\tkz@arg{\tkz@arg,\X=1} +% \fi +% } +% \path[coordinate] (barycentric cs:\tkz@arg) coordinate (tkzPointResult); +% \endgroup +% } + +%<--------------------------------------------------------------------------–> +% milieu de deux points +%<--------------------------------------------------------------------------–> +% possible \coordinate (#3) at ($(#1)!0.5!(#2)$); +%<--------------------------------------------------------------------------–> +% \def\tkzDefMidPoint(#1,#2){% +% \begingroup +% \path (#1) -- (#2) coordinate[pos=.5](tkzPointResult); +% \endgroup +% } +\def\tkzDefMidPoint(#1,#2){% +\begingroup + \pgf@process{\pgfpointanchor{#1}{center}}% + \tkz@ax\pgf@x% + \tkz@ay\pgf@y% + \pgf@process{\pgfpointanchor{#2}{center}}% + \tkz@bx\pgf@x% + \tkz@by\pgf@y% + \advance\tkz@bx by\tkz@ax\relax% + \advance\tkz@by by\tkz@ay\relax% + \divide\tkz@bx by2\relax% + \divide\tkz@by by2\relax + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkz@bx}{\tkz@by}} +\endgroup +} +\def\tkz@DefMidPoint(#1,#2,#3,#4){% +\begingroup + \tkz@ax#1% + \tkz@ay#2% + \tkz@bx#3% + \tkz@by#4% + \advance\tkz@bx by\tkz@ax\relax% + \advance\tkz@by by\tkz@ay\relax% + \divide\tkz@bx by2\relax% + \divide\tkz@by by2\relax + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkz@bx}{\tkz@by}} +\endgroup +} + +%<--------------------------------------------------------------------------–> +\def\tkz@simicenter{0} +\pgfkeys{/tkzsimicenter/.cd, + ext/.code = \def\tkz@simicenter{0}, + int/.code = \def\tkz@simicenter{1}, + ext +}% + +\def\tkzDefSimilitudeCenter{\pgfutil@ifnextchar[{\tkz@DefSimilitudeCenter}% + {\tkz@DefSimilitudeCenter[]}} +\def\tkz@DefSimilitudeCenter[#1](#2,#3)(#4,#5){% +\pgfqkeys{/tkzsimicenter}{#1} +\begingroup +\ifcase\tkz@simicenter% + \tkzDefExtSimilitudeCenter[#1](#2,#3)(#4,#5) + \or% 1 + \tkzDefIntSimilitudeCenter[#1](#2,#3)(#4,#5) +\fi +\endgroup +} +%<--------------------------------------------------------------------------–> +% Internal Similitude center +% Two circles have two similitude centers namely the internal center of +% similitude Si and the external similitude center Se. +%<--------------------------------------------------------------------------–> +\def\tkz@numhomo{0} +\pgfkeys{ +/tkzSimilitudeCenter/.cd, + node/.code = \def\tkz@numhomo{0}, + R/.code = \def\tkz@numhomo{1}, + node, + /tkzSimilitudeCenter/.unknown/.code = {\let\searchname=\pgfkeyscurrentname + \pgfkeysalso{\searchname/.try=#1, /tikz/\searchname/.retry=#1}} +} +\def\tkzDefIntSimilitudeCenter{\pgfutil@ifnextchar[{\tkz@DefIntSimilitudeCenter}{\tkz@DefIntSimilitudeCenter[]}} +\def\tkz@DefIntSimilitudeCenter[#1](#2,#3)(#4,#5){% +\begingroup +\pgfqkeys{/tkzSimilitudeCenter}{#1} +\ifcase\tkz@numhomo% + \tkz@@CalcLengthcm(#2,#3){tkz@rt}% + \tkz@@CalcLengthcm(#4,#5){tkz@rf}% + \or% 1 + \def\tkz@rt{#3}% + \def\tkz@rf{#5}% +\fi +\pgfinterruptboundingbox +\pgfextractx{\pgf@x}{\pgfpointanchor{#2}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#2}{center}} +\tkz@ax\pgf@x % +\tkz@ay\pgf@y % +\edef\tkzcax{\strip@pt\tkz@ax}% +\edef\tkzcay{\strip@pt\tkz@ay}% +\pgfextractx{\pgf@x}{\pgfpointanchor{#4}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#4}{center}} +\tkz@bx\pgf@x % +\tkz@by\pgf@y % +\edef\tkzcbx{\strip@pt\tkz@bx}% +\edef\tkzcby{\strip@pt\tkz@by}% +\edef\tkztpmx{\tkz@Dec{(\tkzcax*\tkz@rf + \tkzcbx*\tkz@rt)/(\tkz@rf + \tkz@rt )}} +\edef\tkztpmy{\tkz@Dec{(\tkzcay*\tkz@rf + \tkzcby*\tkz@rt)/(\tkz@rf + \tkz@rt )}} + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkztpmx pt}{\tkztpmy pt}} +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefIntHomotheticCenter\tkzDefIntSimilitudeCenter +%<--------------------------------------------------------------------------–> +% External Similitude center +%<--------------------------------------------------------------------------–> +\def\tkzDefExtSimilitudeCenter{\pgfutil@ifnextchar[{\tkz@DefExtSimilitudeCenter}{% +\tkz@DefExtSimilitudeCenter[]}} + +\def\tkz@DefExtSimilitudeCenter[#1](#2,#3)(#4,#5){% +\begingroup +\pgfqkeys{/tkzSimilitudeCenter}{#1} +\ifcase\tkz@numhomo% + \tkz@@CalcLengthcm(#2,#3){tkz@rt}% + \tkz@@CalcLengthcm(#4,#5){tkz@rf}% + \or% 1 + \def\tkz@rt{#3}% + \def\tkz@rf{#5}% +\fi +\pgfinterruptboundingbox +\pgfextractx{\pgf@x}{\pgfpointanchor{#2}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#2}{center}} +\tkz@ax\pgf@x % +\tkz@ay\pgf@y % +\edef\tkzcax{\strip@pt\tkz@ax}% +\edef\tkzcay{\strip@pt\tkz@ay}% +\pgfextractx{\pgf@x}{\pgfpointanchor{#4}{center}} +\pgfextracty{\pgf@y}{\pgfpointanchor{#4}{center}} +\tkz@bx\pgf@x % +\tkz@by\pgf@y % +\edef\tkzcbx{\strip@pt\tkz@bx}% +\edef\tkzcby{\strip@pt\tkz@by}% +\edef\tkztpmx{\tkz@Dec{(\tkzcax*(-\tkz@rf) + \tkzcbx*\tkz@rt)/(\tkz@rt - (\tkz@rf))}} +\edef\tkztpmy{\tkz@Dec{(\tkzcay*(-\tkz@rf) + \tkzcby*\tkz@rt)/(\tkz@rt - (\tkz@rf))}} + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkztpmx pt}{\tkztpmy pt}} + \endpgfinterruptboundingbox +\endgroup +} + +\let\tkzDefExtHomotheticCenter\tkzDefExtSimilitudeCenter +%<--------------------------------------------------------------------------–> +% Harmonic Division +%<--------------------------------------------------------------------------–> +% A , B , C ,D CA/CB = DA/DB +%<--------------------------------------------------------------------------–> +\def\tkz@numdha{0} +\pgfkeys{/tkzharmonic/.cd, + ext/.code = \def\tkz@numdha{0}, + int/.code = \def\tkz@numdha{1}, + both/.code = \def\tkz@numdha{2}, + both, +}% + +\def\tkzDivHarmonic{\pgfutil@ifnextchar[{\tkz@DivHarmonic}{\tkz@DivHarmonic[]}} +\def\tkz@DivHarmonic[#1](#2){% +\begingroup +\pgfqkeys{/tkzharmonic}{#1} + \ifcase\tkz@numdha% + \tkzDefDivHarmonicExt(#2) + \or% + \tkzDefDivHarmonicInt(#2) + \or% + \tkzDefDivHarmonicBoth(#2) + \fi +\endgroup +} + +\def\tkzDefDivHarmonicExt(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox + \tkz@VecKOrth[](#1,#2) \tkzGetPoint{tkz@px} + \tkzDefMidPoint(tkz@px,#2) \tkzGetPoint{tkz@py} + \tkzInterLL(tkz@px,#3)(#1,tkz@py) \tkzGetPoint{tkz@pz} + \tkzInterLL(#2,tkz@pz)(#1,tkz@px) \tkzGetPoint{tkz@px} + \tkzInterLL(tkz@py,tkz@px)(#1,#2) \tkzGetPoint{tkzPointResult} +\endpgfinterruptboundingbox +\endgroup +} + +\def\tkzDefDivHarmonicInt(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox + \tkz@VecKOrth[1](#1,#2) \tkzGetPoint{tkz@px} + \tkzDefMidPoint(tkz@px,#2) \tkzGetPoint{tkz@py} + \tkzInterLL(tkz@py,#3)(#1,tkz@px) \tkzGetPoint{tkz@pz} + \tkzInterLL(#2,tkz@pz)(#1,tkz@py) \tkzGetPoint{tkz@py} + \tkzInterLL(tkz@py,tkz@px)(#1,#2) \tkzGetPoint{tkzPointResult} +\endpgfinterruptboundingbox +\endgroup +} + +\def\tkzDefDivHarmonicBoth(#1,#2,#3){% +\begingroup +\edef\tkz@k{\fpeval{#3}} + \path[coordinate] (barycentric cs:#1=1,#2={\tkz@k}) coordinate (tkzFirstPointResult); + \path[coordinate] (barycentric cs:#1=1,#2={-\tkz@k}) coordinate (tkzSecondPointResult); +\endgroup +} + +\let\tkzDefHarmonic\tkzDivHarmonic +%<--------------------------------------------------------------------------–> +% golden ratio +%<--------------------------------------------------------------------------–> +\def\tkzDefGoldenRatio(#1,#2){% +\begingroup +\tkzDefPointWith[linear,K=\tkzInvPhi](#1,#2) +\endgroup +} +%<--------------------------------------------------------------------------–> +% triangle center +%<--------------------------------------------------------------------------–> + +\def\tkz@numtc{0} +\pgfkeys{/tkzDefTriangleCenter/.cd, + ortho/.code = \def\tkz@numtc{0}, + orthic/.code = \def\tkz@numtc{0}, + centroid/.code = \def\tkz@numtc{1}, + median/.code = \def\tkz@numtc{1}, + circum/.code = \def\tkz@numtc{2}, + in/.code = \def\tkz@numtc{3}, + ex/.code = \def\tkz@numtc{4}, + euler/.code = \def\tkz@numtc{5}, + symmedian/.code = \def\tkz@numtc{6}, + lemoine/.code = \def\tkz@numtc{6}, + grebe/.code = \def\tkz@numtc{6}, + spieker/.code = \def\tkz@numtc{7}, + gergonne/.code = \def\tkz@numtc{8}, + nagel/.code = \def\tkz@numtc{9}, + mittenpunkt/.code = \def\tkz@numtc{10}, + feuerbach/.code = \def\tkz@numtc{11}, + circum +} +\def\tkzDefTriangleCenter{\pgfutil@ifnextchar[{\tkz@DefTriangleCenter}{\tkz@DefTriangleCenter[]}} +\def\tkz@DefTriangleCenter[#1](#2){% +\begingroup +\pgfqkeys{/tkzDefTriangleCenter}{#1} +\ifcase\tkz@numtc% + \tkzOrthoCenter(#2) + \or% 1 + \tkzCentroid(#2) + \or% 2 + \tkzCircumCenter(#2) + \or% 3 + \tkzInCenter(#2) + \or% 4 + \tkzExCenter(#2) + \or% 5 + \tkzEulerCenter(#2) + \or% 6 + \tkzSymmedianCenter(#2) + \or% 7 + \tkzSpiekerCenter(#2) + \or% 8 + \tkzGergonneCenter(#2) + \or%9 + \tkzNagelCenter(#2) + \or%10 + \tkzMittenpunktCenter(#2) + \or%11 + \tkzFeuerbachCenter(#2) + \fi +\endgroup +} +%<--------------------------------------------------------------------------–> +% OrthoCenter +%<--------------------------------------------------------------------------–> +\def\tkzOrthoCenter(#1,#2,#3){% +\begingroup + \pgfinterruptboundingbox + \tkzUProjection(#1,#2)(#3) + \pgfnodealias{ort@pta}{tkzPointResult} + \tkzUProjection(#1,#3)(#2) + \pgfnodealias{ort@ptb}{tkzPointResult} + \tkzInterLL(#2,ort@ptb)(#3,ort@pta) + \endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefOrthoCenter\tkzOrthoCenter +%<--------------------------------------------------------------------------–> +% GravityCenter modif 3.03 +%<--------------------------------------------------------------------------–> +\def\tkzCentroid(#1,#2,#3){% +\begingroup + \pgf@process{\pgfpointanchor{#1}{center}}% + \tkz@ax\pgf@x% + \tkz@ay\pgf@y% + \pgf@process{\pgfpointanchor{#2}{center}}% + \tkz@bx\pgf@x% + \tkz@by\pgf@y% + \pgf@process{\pgfpointanchor{#3}{center}}% + \tkz@cx\pgf@x% + \tkz@cy\pgf@y% + \edef\tkzcax{\strip@pt\tkz@ax}% + \edef\tkzcay{\strip@pt\tkz@ay}% + \edef\tkzcbx{\strip@pt\tkz@bx}% + \edef\tkzcby{\strip@pt\tkz@by}% + \edef\tkzccx{\strip@pt\tkz@cx}% + \edef\tkzccy{\strip@pt\tkz@cy}% + \edef\tkztpmx{\tkz@Dec{(\tkzcax + \tkzcbx + \tkzccx)/3}} + \edef\tkztpmy{\tkz@Dec{(\tkzcay + \tkzcby + \tkzccy)/3}} + \pgfinterruptboundingbox + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkztpmx pt}{\tkztpmy pt}} + \endpgfinterruptboundingbox +\endgroup +} +\let\tkzBaryCenter\tkzCentroid + +%<--------------------------------------------------------------------------–> +% CircumCenter +%<--------------------------------------------------------------------------–> +\def\tkzCircumCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox + \tkzDefMediatorLine(#1,#2) + \pgf@process{\pgfpointanchor{tkzFirstPointResult}{center}}% + \tkz@ax\pgf@x% + \tkz@ay\pgf@y% + \pgf@process{\pgfpointanchor{tkzSecondPointResult}{center}}% + \tkz@bx\pgf@x% + \tkz@by\pgf@y% + \tkzDefMediatorLine(#1,#3) + \pgf@process{\pgfpointanchor{tkzFirstPointResult}{center}}% + \tkz@cx\pgf@x% + \tkz@cy\pgf@y% + \pgf@process{\pgfpointanchor{tkzSecondPointResult}{center}}% + \tkz@dx\pgf@x% + \tkz@dy\pgf@y% +\tkzInterLLxy(\tkz@ax,\tkz@ay,\tkz@bx,\tkz@by)(\tkz@cx,\tkz@cy,\tkz@dx,\tkz@dy)% +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefCircumCenter\tkzCircumCenter +%<--------------------------------------------------------------------------–> +% InCenter +%<--------------------------------------------------------------------------–> +\def\tkzInCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzDefBisectorLine(#3,#1,#2) +\pgf@process{\pgfpointanchor{tkzPointResult}{center}}% +\tkz@bx\pgf@x% +\tkz@by\pgf@y% +\tkzDefBisectorLine(#3,#2,#1) +\pgf@process{\pgfpointanchor{tkzPointResult}{center}}% +\tkz@dx\pgf@x% +\tkz@dy\pgf@y% +\pgf@process{\pgfpointanchor{#1}{center}}% +\tkz@ax\pgf@x% +\tkz@ay\pgf@y% +\pgf@process{\pgfpointanchor{#2}{center}}% +\tkz@cx\pgf@x% +\tkz@cy\pgf@y% +\tkzInterLLxy(\tkz@ax,\tkz@ay,\tkz@bx,\tkz@by)(\tkz@cx,\tkz@cy,\tkz@dx,\tkz@dy)% +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefInCenter\tkzInCenter +%<--------------------------------------------------------------------------–> +% ExCenter +%<--------------------------------------------------------------------------–> +\def\tkzExCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzDefBisectorOutLine(#2,#1,#3) +\pgf@process{\pgfpointanchor{tkzPointResult}{center}}% +\tkz@bx\pgf@x% +\tkz@by\pgf@y% +\tkzDefBisectorOutLine(#2,#3,#1) +\pgf@process{\pgfpointanchor{tkzPointResult}{center}}% +\tkz@dx\pgf@x% +\tkz@dy\pgf@y% +\pgf@process{\pgfpointanchor{#1}{center}}% +\tkz@ax\pgf@x% +\tkz@ay\pgf@y% +\pgf@process{\pgfpointanchor{#3}{center}}% +\tkz@cx\pgf@x% +\tkz@cy\pgf@y% +\tkzInterLLxy(\tkz@ax,\tkz@ay,\tkz@bx,\tkz@by)(\tkz@cx,\tkz@cy,\tkz@dx,\tkz@dy)% +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefExCenter\tkzExCenter +%<--------------------------------------------------------------------------–> +% EulerCenter neuf points +%<--------------------------------------------------------------------------–> +\def\tkzEulerCenter(#1,#2,#3){% +% mileu de orthocentre et centre cercle circonscrit +% passe par les midpoints par les pieds des hauteurs +\begingroup +\pgfinterruptboundingbox +\tkzDefMidPoint(#1,#2) +\pgfnodealias{eu@mic}{tkzPointResult} +\tkzDefMidPoint(#1,#3) +\pgfnodealias{eu@mib}{tkzPointResult} +\tkzDefMidPoint(#2,#3) +\pgfnodealias{eu@mia}{tkzPointResult} +\tkzCircumCenter(eu@mia,eu@mib,eu@mic) +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzNinePointCenter\tkzEulerCenter +\let\tkzDefEulerCenter\tkzEulerCenter +%<--------------------------------------------------------------------------–> +%Symmedian center Lemoine point Grebe point K +%<--------------------------------------------------------------------------–> +\def\tkzSymmedianCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzDefMidPoint(#2,#3) +\pgfnodealias{eu@mic}{tkzPointResult} +\tkzDefMidPoint(#1,#3) +\pgfnodealias{eu@mib}{tkzPointResult} +\tkzUProjection(#2,#3)(#1) +\pgfnodealias{ort@pta}{tkzPointResult} +\tkzDefMidPoint(#1,ort@pta) +\pgfnodealias{eu@mid}{tkzPointResult} +\tkzUProjection(#1,#3)(#2) +\pgfnodealias{ort@ptb}{tkzPointResult} +\tkzDefMidPoint(#2,ort@ptb) +\pgfnodealias{eu@mie}{tkzPointResult} +\tkzInterLL(eu@mic,eu@mid)(eu@mib,eu@mie) +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzLemoinePoint\tkzSymmedianCenter +\let\tkzGrebePoint\tkzSymmedianCenter +\let\tkzDefLemoinePoint\tkzLemoinePoint +%<--------------------------------------------------------------------------–> +% Spieker center +%<--------------------------------------------------------------------------–> +\def\tkzSpiekerCenter(#1,#2,#3){% +\begingroup +% we need to get the midpoints +\pgfcoordinate{tkz@m3}{% + \pgfpointscale{0.5}{% + \pgfpointadd{\pgfpointanchor{#1}{center}}% + {\pgfpointanchor{#2}{center}}}}% +\pgfcoordinate{tkz@m2}{% + \pgfpointscale{0.5}{% + \pgfpointadd{\pgfpointanchor{#1}{center}}% + {\pgfpointanchor{#3}{center}}}}% +\pgfcoordinate{tkz@m1}{% + \pgfpointscale{0.5}{% + \pgfpointadd{\pgfpointanchor{#2}{center}}% + {\pgfpointanchor{#3}{center}}}}% +\tkzInCenter(tkz@m1,tkz@m2,tkz@m3) +\endgroup +} +\let\tkzDefSpiekerCenter\tkzSpiekerCenter +%<--------------------------------------------------------------------------–> +% Gergonne center Ge +%<--------------------------------------------------------------------------–> +\def\tkzGergonneCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzInCenter(#1,#2,#3) +\pgfnodealias{tkz@ptin}{tkzPointResult} +\tkzUProjection(#2,#3)(tkz@ptin) +\pgfnodealias{tkz@oca}{tkzPointResult} +\tkzUProjection(#1,#3)(tkz@ptin) +\pgfnodealias{tkz@ocb}{tkzPointResult} +\tkzInterLL(#1,tkz@oca)(#2,tkz@ocb) +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefGergonneCenter\tkzGergonneCenter +%<--------------------------------------------------------------------------–> +% Nagel center Na +%<--------------------------------------------------------------------------–> +% INa = 3 IG. Nagel point % correction 02/02/20 +\def\tkzNagelCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzDefExcentralTriangle(#1,#2,#3){tkz@a,tkz@b,tkz@c} +\tkzUProjection(#2,#3)(tkz@a) +\pgfnodealias{tkz@tgta}{tkzPointResult} +\tkzUProjection(#1,#2)(tkz@c) +\pgfnodealias{tkz@tgtc}{tkzPointResult} +\tkzInterLL(#1,tkz@tgta)(#3,tkz@tgtc) +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefNagelCenter\tkzNagelCenter +%<--------------------------------------------------------------------------–> +% Mittenpunkt +%<--------------------------------------------------------------------------–> +\def\tkzMittenpunktCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzExCenter(#2,#3,#1) +\pgfnodealias{tkz@a}{tkzPointResult} +\tkzExCenter(#3,#1,#2) +\pgfnodealias{tkz@b}{tkzPointResult} +\pgfcoordinate{tkz@ma}{% +\pgfpointscale{0.5}{% +\pgfpointadd{\pgfpointanchor{#1}{center}}{\pgfpointanchor{#2}{center}}}}% +\pgfcoordinate{tkz@mb}{% +\pgfpointscale{0.5}{% +\pgfpointadd{\pgfpointanchor{#2}{center}}{\pgfpointanchor{#3}{center}}}}% +\tkzInterLL(tkz@a,tkz@ma)(tkz@b,tkz@mb) +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefMittenpunktCenter\tkzMittenpunktCenter +\let\tkzDefMiddlespoint\tkzMittenpunktCenter +%<--------------------------------------------------------------------------–> +% Feuerbach point +%<--------------------------------------------------------------------------–> +\def\tkzFeuerbachCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox +\tkzEulerCenter(#1,#2,#3) +\pgfnodealias{tkz@euler}{tkzPointResult} +\tkzInCenter(#1,#2,#3) +\pgfnodealias{tkz@in}{tkzPointResult} +\tkzUProjection(#2,#3)(tkzPointResult) +\tkzInterLC(tkz@in,tkz@euler)(tkz@in,tkzPointResult)\tkzGetFirstPoint{tkz@fe} +\tkzRenamePoint(tkz@fe){tkzPointResult} +\endpgfinterruptboundingbox +\endgroup +} +\let\tkzDefFeuerbachCenter\tkzFeuerbachCenter +%<--------------------------------------------------------------------------–> +% Orthogonal center +%<--------------------------------------------------------------------------–> +\def\tkzOrthogonalCenter(#1,#2){% +\begingroup +\pgfinterruptboundingbox +\tkz@VecK[\tkz@koeff/(1+\tkz@koeff)](#1,#2) +\pgfnodealias{tkzFirstPointResult}{tkzPointResult} +\tkz@VecK[\tkz@koeff/(\tkz@koeff-1)](#1,#2) +\pgfnodealias{tkzSecondPointResult}{tkzPointResult} +\tkzDefMidPoint(tkzFirstPointResult,tkzSecondPointResult) +\endpgfinterruptboundingbox +\endgroup +} +%<--------------------------------------------------------------------------–> +% End Triangle center +%<--------------------------------------------------------------------------–> +%<--------------------------------------------------------------------------–> +% Projection center of excircles +%<--------------------------------------------------------------------------–> +\def\tkzDefProjExcenter{\pgfutil@ifnextchar[{% + \tkz@DefProjExcenter}{% + \tkz@DefProjExcenter[]} + } +\def\tkz@DefProjExcenter[#1](#2,#3,#4)(#5)#6{ +\begingroup + \SetUpPTTR{#1} + \foreach \name [count=\i] in {#5} {% + \global\expandafter\edef\csname tkz@pt\i\endcsname{\name} + } + \foreach \name [count=\i] in {#6} {% + \global\expandafter\edef\csname tkz@ppt\i\endcsname{\name} + } +\tkzDefPointBy[projection=onto #3--#4 ](\tkz@pttr@name \csname tkz@pt1\endcsname) +\pgfnodealias{\csname tkz@ppt1\endcsname\csname tkz@pt1\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #3--#4 ](\tkz@pttr@name \csname tkz@pt2\endcsname) +\pgfnodealias{\csname tkz@ppt1\endcsname\csname tkz@pt2\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #3--#4 ](\tkz@pttr@name \csname tkz@pt3\endcsname) +\pgfnodealias{\csname tkz@ppt1\endcsname\csname tkz@pt3\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #2--#4 ](\tkz@pttr@name \csname tkz@pt1\endcsname) +\pgfnodealias{\csname tkz@ppt2\endcsname\csname tkz@pt1\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #2--#4 ](\tkz@pttr@name \csname tkz@pt2\endcsname) +\pgfnodealias{\csname tkz@ppt2\endcsname\csname tkz@pt2\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #2--#4 ](\tkz@pttr@name \csname tkz@pt3\endcsname) +\pgfnodealias{\csname tkz@ppt2\endcsname\csname tkz@pt3\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #3--#2 ](\tkz@pttr@name \csname tkz@pt1\endcsname) +\pgfnodealias{\csname tkz@ppt3\endcsname\csname tkz@pt1\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #3--#2 ](\tkz@pttr@name \csname tkz@pt2\endcsname) +\pgfnodealias{\csname tkz@ppt3\endcsname\csname tkz@pt2\endcsname}{tkzPointResult} +\tkzDefPointBy[projection=onto #3--#2 ](\tkz@pttr@name \csname tkz@pt3\endcsname) +\pgfnodealias{\csname tkz@ppt3\endcsname\csname tkz@pt3\endcsname}{tkzPointResult} +\endgroup +} +%<--------------------------------------------------------------------------–> +% Point on circle +%<--------------------------------------------------------------------------–> +\def\tkz@numptcirc{0} +\pgfkeys{/tkzptcircle/.cd, +through/.code args = {center #1 angle #2 point #3} { \def\tkz@center{#1}% + \def\tkz@angle{#2}% + \def\tkz@through{#3}% + \def\tkz@numptcirc{0}}, +R/.code args = {center #1 angle #2 radius #3} { \def\tkz@center{#1}% + \def\tkz@angle{#2}% + \def\tkz@radius{#3}% + \def\tkz@numptcirc{1}}, +through in rad/.code args = {center #1 angle #2 point #3} { \def\tkz@center{#1}% + \def\tkz@angle{#2}% + \def\tkz@through{#3}% + \def\tkz@numptcirc{2}}, +R in rad/.code args = {center #1 angle #2 radius #3} { \def\tkz@center{#1}% + \def\tkz@angle{#2}% + \def\tkz@radius{#3}% + \def\tkz@numptcirc{3}} +} + +\def\tkzDefPointOnCircle{\pgfutil@ifnextchar[{\tkz@DefPointOnCircle}{% + \tkz@DefPointOnCircle[]}} +\def\tkz@DefPointOnCircle[#1]{% +\begingroup +\pgfqkeys{/tkzptcircle}{#1} + \ifcase\tkz@numptcirc% + \tkz@@CalcLengthcm(\tkz@center,\tkz@through){tkz@radius} + \or% 1 + \relax% + \or% 2 + \pgfmathparse{\tkz@angle\space r} + \let\tkz@angle\pgfmathresult + \tkz@@CalcLengthcm(\tkz@center,\tkz@through){tkz@radius} + \or% 3 + \pgfmathparse{\tkz@angle\space r} + \let\tkz@angle\pgfmathresult +\fi +\path (\tkz@center) --++(\tkz@angle:\tkz@radius) coordinate(tkzPointResult); +\endgroup +} +%<--------------------------------------------------------------------------–> +% Point on line +%<--------------------------------------------------------------------------–> +\def\tkzDefPointOnLine{\pgfutil@ifnextchar[{\tkz@DefPointOnLine}{\tkz@DefPointOnLine[]}} +\def\tkz@DefPointOnLine[#1](#2,#3){% +\begingroup +\path (#2) to [#1] coordinate (tkzPointResult) (#3); +\endgroup +} + +\makeatother +\endinput
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