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% tkz-obj-eu-circles.tex
% Copyright 2022 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{4.22c}
\def\filedate{2022/07/28}
\typeout{2022/07/28 4.22c tkz-obj-eu-circles.tex}
\makeatletter
%<--------------------------------------------------------------------------–>
% tkzCircle center and one point
%<--------------------------------------------------------------------------–>
% attention radius circle is defined by center and a point on the circle
% R defined by center and the value of the radius
% no need to define a circle with R tikz uses this method.
% through instead of radius
\def\tkz@numcby{0}
\pgfkeys{/tkzDefCircleBy/.cd,
translation/.code args = {from #1 to #2} { \def\tkz@numcby{0}
\def\tkzfrom{#1}
\def\tkzto{#2}},
homothety/.code args = {center #1 ratio #2}{ \def\tkz@numcby{1}
\def\tkzcenter{#1}
\def\tkzratio{#2}},
reflection/.code args = {over #1--#2}{ \def\tkz@numcby{2}
\def\tkzdeb{#1}
\def\tkzfin{#2}},
symmetry/.code args = {center #1}{ \def\tkz@numcby{3}
\def\tkzcenter{#1}},
rotation/.code args = {center #1 angle #2}{ \def\tkz@numcby{4}
\def\tkzcenter{#1}
\def\tkzangle{#2}},
inversion/.code args={center #1 through #2}{ \def\tkz@numcby{5}
\def\tkzcenter{#1}
\def\tkzpoint{#2}},
inversion negative/.code args = {center #1 through #2}{\def\tkz@numcby{6}
\def\tkzcenter{#1}
\def\tkzpoint{#2}}
}
\def\tkzDefCircleBy{\pgfutil@ifnextchar[{\tkz@DefCircleBy}{\tkz@DefCircleBy[]}}
\def\tkz@DefCircleBy[#1](#2){%
\begingroup
\pgfqkeys{/tkzDefCircleBy}{#1}
\ifcase\tkz@numcby%
\tkzDefCircleTranslation(#2)%
\or% 1
\tkzDefCircleHomothety(#2)
\or% 2
\tkzDefCircleReflection(#2)
\or% 3
\tkzDefCircleSymmetry(#2)
\or% 4
\tkzDefCircleRotation(#2)
\or% 5
\tkzDefInversionCircle(#2,\tkzcenter,\tkzpoint)
\or% 6
\tkzDefInversionNegativeCircle(#2,\tkzcenter,\tkzpoint)
\fi
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefCircleTranslation(#1,#2){%
\begingroup
\tkzUTranslation(\tkzfrom,\tkzto)(#1)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUTranslation(\tkzfrom,\tkzto)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefCircleHomothety(#1,#2){%
\begingroup
\tkzUHomo(\tkzcenter,\tkzratio)(#1)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUHomo(\tkzcenter,\tkzratio)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefCircleReflection(#1,#2){%
\begingroup
\tkzUSymOrth(\tkzdeb,\tkzfin)(#1)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUSymOrth(\tkzdeb,\tkzfin)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefCircleSymmetry(#1,#2){%
\begingroup
\tkzUCSym(\tkzcenter)(#1)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUCSym(\tkzcenter)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefCircleRotation(#1,#2){%
\begingroup
\tkzURotateAngle(\tkzcenter,\tkzangle)(#1)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzURotateAngle(\tkzcenter,\tkzangle)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
% #3,#4 cercle d'inversion centre #3. through #4
% Si le cercle passe par le pôle l'image est une droite
\def\tkzDefInversionCircle(#1,#2,#3,#4){%
\begingroup
\tkz@@CalcLengthcm(#1,#2){tkz@lna}%
\tkz@@CalcLengthcm(#1,#3){tkz@lnb}%
\gdef\tkzMathResult{\fpeval{round(abs(\tkz@lnb - \tkz@lna),6)}}
\ifdim\tkzMathResult pt < 1 pt\relax%
\tkzURotateAngle(#1,-90)(#2)
\pgfnodealias{tkz@a}{tkzPointResult}
\tkzUInversePoint(#3,#4)(tkz@a)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUInversePoint(#3,#4)(#2)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\else
\tkzURotateAngle(#1,90)(#2)
\pgfnodealias{tkz@a}{tkzPointResult}
\tkzURotateAngle(#1,-90)(#2)
\pgfnodealias{tkz@b}{tkzPointResult}
\tkzUInversePoint(#3,#4)(tkz@a)
\pgfnodealias{tkz@p1}{tkzPointResult}
\tkzUInversePoint(#3,#4)(tkz@b)
\pgfnodealias{tkz@p2}{tkzPointResult}
\tkzUInversePoint(#3,#4)(#2)
\pgfnodealias{tkz@p3}{tkzPointResult}
\tkzDefCircle[circum](tkz@p3,tkz@p1,tkz@p2)
\fi
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefInversionNegativeCircle(#1,#2,#3,#4){%
\begingroup
\tkzDefInversionCircle(#1,#2,#3,#4)
\tkzUCSym(\tkzcenter)(tkzFirstPointResult)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkzUCSym(\tkzcenter)(tkzSecondPointResult)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\endgroup
}
%<--------------------------------------------------------------------------–>
% End Def Circle
%<--------------------------------------------------------------------------–>
\makeatother
\endinput
|
