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authorNorbert Preining <norbert@preining.info>2020-01-25 03:01:31 +0000
committerNorbert Preining <norbert@preining.info>2020-01-25 03:01:31 +0000
commit75672286990bb55c7b46277f845d14eafcf2ba61 (patch)
tree29456eb5880d5a2629b2ae329423c9ceaaaf6887 /macros/latex/contrib/tkz/tkz-euclide/latex/tkz-obj-eu-points.tex
parente1192611f0655a1ccaff0dff2f53c7c65fa5db07 (diff)
CTAN sync 202001250301
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+% 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 \ No newline at end of file