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Diffstat (limited to 'Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex')
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diff --git a/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex new file mode 100644 index 00000000000..62600426e73 --- /dev/null +++ b/Master/texmf-dist/tex/latex/tkz-euclide/tkz-obj-eu-points.tex @@ -0,0 +1,465 @@ +% tkz-obj-eu-points.tex +% Copyright 2011 by Alain Matthes +% This file may be distributed and/or modified +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Public License. +\def\fileversion{3.01c} +\def\filedate{2020/01/23} +\typeout{2020/01/23 3.01c tkz-obj-eu-points.tex} +\makeatletter +%add ExCenter +%<--------------------------------------------------------------------------–> +% Specific points +%<--------------------------------------------------------------------------–> +% barycentre +%<--------------------------------------------------------------------------–> +\def\tkzDefBarycentricPoint(#1){% +\begingroup + \path[coordinate] (barycentric cs:#1) coordinate (tkzPointResult); +\endgroup +} +\let\tkzDefBCPoint\tkzDefBarycentricPoint + +\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 +} +%<--------------------------------------------------------------------------–> +% Internal Similitude center +% Two circles have two similitude centers namely the internal center of similitude Si and the external similitude center Se. +%<--------------------------------------------------------------------------–> +\def\tkzDefIntSimilitudeCenter(#1,#2)(#3,#4){% +\begingroup + \path[coordinate](barycentric cs:#1=#4,#3=#2)coordinate (tkzPointResult); +\endgroup +} +\let\tkzIntSimilitudeCenter\tkzDefIntSimilitudeCenter +%<--------------------------------------------------------------------------–> +% External Similitude center +%<--------------------------------------------------------------------------–> +\def\tkzDefExtSimilitudeCenter(#1,#2)(#3,#4){% +\begingroup + \path[coordinate](barycentric cs:#1=-#4,#3=#2) coordinate(tkzPointResult); +\endgroup +} +\let\tkzExtSimilitudeCenter\tkzDefExtSimilitudeCenter +%<--------------------------------------------------------------------------–> +% triangle center +%<--------------------------------------------------------------------------–> + +\def\tkz@numtc{0} +\pgfkeys{/tkzDefTriangleCenter/.cd, + ortho/.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){% H orthocentre +\begingroup + \tkzUProjection(#1,#2)(#3) + \pgfnodealias{ort@pta}{tkzPointResult} + \tkzUProjection(#1,#3)(#2) + \pgfnodealias{ort@ptb}{tkzPointResult} + \tkzInterLL(#2,ort@ptb)(#3,ort@pta) +\endgroup +} +\let\tkzDefOrthoCenter\tkzOrthoCenter +%<--------------------------------------------------------------------------–> +% GravityCenter +%<--------------------------------------------------------------------------–> +% \def\tkzCentroid(#1,#2,#3){% +% \begingroup +% \path[coordinate](barycentric cs:#1=1,#2=1,#3=1)coordinate (tkzPointResult); +% \endgroup +% } +\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% + \advance\tkz@cx by\tkz@ax\relax% + \advance\tkz@cy by\tkz@ay\relax% + \advance\tkz@cx by\tkz@bx\relax% + \advance\tkz@cy by\tkz@by\relax% + \divide\tkz@cx by3\relax% + \divide\tkz@cy by3\relax + \pgfcoordinate{tkzPointResult}{\pgfqpoint{\tkz@cx}{\tkz@cy}} + %\path[coordinate](barycentric cs:#1=1,#2=1,#3=1)coordinate (tkzPointResult); +\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 +\def\tkzNagelCenter(#1,#2,#3){% +\begingroup +\pgfinterruptboundingbox + \tkzInCenter(#1,#2,#3) + \pgfnodealias{tkz@ptin}{tkzPointResult} + \tkzCentroid(#1,#2,#3) + \pgfnodealias{tkz@cen}{tkzPointResult} + \tkz@VecCoLinear(tkz@ptin,tkz@cen,tkz@ptin) +\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 +} + + +\makeatother +\endinput
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