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% tkz-obj-eu-circles.tex
% Copyright 2020 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{3.02c}
\def\filedate{2020/01/24}
\typeout{2020/01/24 3.02c 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@numc{0}
\pgfkeys{/tkzcircle/.cd,
through/.code = \def\tkz@numc{0},
radius/.code = \def\tkz@numc{0},
diameter/.code = \def\tkz@numc{1},
circum/.code = \def\tkz@numc{2},
in/.code = \def\tkz@numc{3},
ex/.code = \def\tkz@numc{4},
euler/.code = \def\tkz@numc{5},
nine/.code = \def\tkz@numc{5},
apollonius/.code = \def\tkz@numc{6},
orthogonal from/.code args = {#1}{\def\tkz@ptfrom{#1}
\def\tkz@numc{7}},
orthogonal through/.code args = {#1 and #2}{\def\tkz@ptone{#1}
\def\tkz@pttwo{#2}
\def\tkz@numc{8}},
spieker/.code = \def\tkz@numc{9},
K/.code = \def\tkz@koeff{#1},
K = 1,
through
}
\def\tkzDefCircle{\pgfutil@ifnextchar[{\tkz@DefCircle}{\tkz@DefCircle[]}}
\def\tkz@DefCircle[#1](#2){%
\begingroup
\pgfqkeys{/tkzcircle}{#1}
\ifcase\tkz@numc%
\tkzDefCircleThrough(#2)%
\or% 1
\tkzDefCircleD(#2)
\or% 2
\tkzDefCircumCircle(#2)
\or% 3
\tkzDefInCircle(#2)
\or% 4
\tkzDefExCircle(#2)
\or% 5
\tkzDefEulerCircle(#2)
\or% 6
\tkzDefApolloniusCircle(#2)
\or% 7
\tkzDefOrthogonalCircle(#2,\tkz@ptfrom)
\or% 8
\tkzDefOrthoThroughCircle(#2,\tkz@ptone,\tkz@pttwo)
\or% 9
\tkzDefSpiekerCircle(#2)
\fi
\endgroup
}
%<--------------------------------------------------------------------------–>
% Circum Circle
%<--------------------------------------------------------------------------–>
\def\tkzDefCircumCircle(#1,#2,#3){%
\begingroup
\tkzCircumCenter(#1,#2,#3)
\tkzCalcLength(#1,tkzPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
% In(scribe) Circle
%<--------------------------------------------------------------------------–>
\def\tkzDefInCircle(#1,#2,#3){%
\begingroup
\tkzInCenter(#1,#2,#3)
\pgfnodealias{tkz@incenter}{tkzPointResult}
\tkzUProjection(#1,#3)(tkz@incenter)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\tkzCalcLength(tkzPointResult,tkz@incenter)
\pgfnodealias{tkzPointResult}{tkz@incenter}
\pgfnodealias{tkzFirstPointResult}{tkz@incenter}
\endgroup
}
%<--------------------------------------------------------------------------–>
% Ex(scribe) Circle
%<--------------------------------------------------------------------------–>
\def\tkzDefExCircle(#1,#2,#3){%
\begingroup
\tkzExCenter(#1,#2,#3)
\pgfnodealias{tkz@excenter}{tkzPointResult}
\tkzUProjection(#1,#3)(tkz@excenter)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\tkzCalcLength(tkzPointResult,tkz@excenter)% for tkzGetLength
\pgfnodealias{tkzPointResult}{tkz@excenter}
\pgfnodealias{tkzFirstPointResult}{tkz@excenter}
\endgroup
}
%<--------------------------------------------------------------------------–>
% Radius Ex Circle
%<--------------------------------------------------------------------------–>
\def\tkzDefExRadius(#1,#2,#3){%
\begingroup
\tkzExCenter(#1,#2,#3)
\tkzUProjection(#1,#3)(tkzPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
% The nine-point circle, also called Euler's circle or the Feuerbach circle
% best way Ma,Mb,Mc circum center 2020
%<--------------------------------------------------------------------------–>
\def\tkzDefEulerCircle(#1,#2,#3){%
\begingroup
\tkzDefMidPoint(#1,#2) \pgfnodealias{tkz@e1}{tkzPointResult}
\tkzDefMidPoint(#2,#3) \pgfnodealias{tkz@e2}{tkzPointResult}
\tkzDefMidPoint(#1,#3) \pgfnodealias{tkz@e3}{tkzPointResult}
\tkzCircumCenter(tkz@e1,tkz@e2,tkz@e3)
\tkzCalcLength(tkzPointResult,tkz@e1)
\endgroup
}
\let\tkzDefNinePointsCircle\tkzEulerCircle%
\let\tkzFeuerBachCircle\tkzEulerCircle%
\def\tkzDefEulerRadius(#1,#2,#3){%
\begingroup
\tkzEulerCenter(#1,#2,#3)
\pgfnodealias{eur@pta}{tkzPointResult}
\tkzDefMidPoint(#1,#2)
\tkzCalcLength(eur@pta,tkzPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
% Apollonius circle
%<--------------------------------------------------------------------------–>
\def\tkzDefApolloniusCircle(#1,#2){%
\begingroup
\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)
\tkzCalcLength(tkzPointResult,tkzFirstPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
% Apollonius radius
%<--------------------------------------------------------------------------–>
\pgfkeys{/tkzapor/.cd,
K/.code = \def\tkz@koeff{#1},% apollonius
K = 1
}
\def\tkzDefApolloniusRadius{\pgfutil@ifnextchar[{%
\tkz@DefApolloniusRadius}{\tkz@DefApolloniusRadius[]}}
\def\tkz@DefApolloniusRadius[#1](#2,#3){%
\begingroup
\pgfqkeys{/tkzapor}{#1}
\tkz@VecK[\tkz@koeff/(1+\tkz@koeff)](#2,#3)
\pgfnodealias{apo@pta}{tkzPointResult}
\tkz@VecK[\tkz@koeff/(\tkz@koeff-1)](#2,#3)
\pgfnodealias{apo@ptb}{tkzPointResult}
\tkzDefMidPoint(apo@pta,apo@ptb)
\tkzCalcLength(tkzPointResult,apo@pta)
\endgroup
}
%<--------------------------------------------------------------------------–>
% Apollonius point
%<--------------------------------------------------------------------------–>
\pgfkeys{/tkzapop/.cd,
K/.code = \def\tkz@koeff{#1},% apollonius
K = 1
}
\def\tkzDefApolloniusPoint{\pgfutil@ifnextchar[{\tkz@DefApolloniusPoint}{\tkz@DefApolloniusPoint[]}}
\def\tkz@DefApolloniusPoint[#1](#2,#3){%
\begingroup
\pgfqkeys{/tkzapop}{#1}
\tkzDefBarycentricPoint(#2=1,#3=\tkz@koeff)
\endgroup
}
%<--------------------------------------------------------------------------–>
% Apollonius center
%<--------------------------------------------------------------------------–>
\pgfkeys{/tkzapoc/.cd,
K/.code = \def\tkz@koeff{#1},% apollonius
K = 1
}
\def\tkzApolloniusCenter{\pgfutil@ifnextchar[{\tkz@ApolloniusCenter}{\tkz@ApolloniusCenter[]}}
\def\tkz@ApolloniusCenter[#1](#2,#3){%
\begingroup
\pgfqkeys{/tkzapoc}{#1}
\tkz@VecK[\tkz@koeff/(1+\tkz@koeff)](#2,#3)
\pgfnodealias{tkzFirstPointResult}{tkzPointResult}
\tkz@VecK[\tkz@koeff/(\tkz@koeff-1)](#2,#3)
\pgfnodealias{tkzSecondPointResult}{tkzPointResult}
\tkzDefMidPoint(tkzFirstPointResult,tkzSecondPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefOrthogonalCircle(#1,#2,#3){%
\begingroup
\tkzTgtFromP(#1,#2)(#3)
\tkzCalcLength[cm](#1,tkzFirstPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
\def\tkzDefOrthoThroughCircle(#1,#2,#3,#4){%
\begingroup
\tkzCalcLength[cm](#1,#3)\tkzGetLength{tkz@lnb}%
\edef\tkz@lnc{\fpeval{1/\tkz@lnb}}
\tkzVecKNorm[\tkz@lnc](#1,#3)
\pgfnodealias{tkz@PointResult}{tkzPointResult}
\tkzCircumCenter(tkz@PointResult,#3,#4)
\tkzCalcLength(tkzPointResult,#3)
\endgroup
}
%<--------------------------------------------------------------------------–>
% Spieker Circle
%<--------------------------------------------------------------------------–>
\def\tkzDefSpiekerCircle(#1,#2,#3){%
\begingroup
\tkzSpiekerCenter(#1,#2,#3)
\pgfnodealias{tkz@spka}{tkzPointResult}
\tkzDefMidPoint(#1,#2)
\tkzUProjection(#1,#2)(tkzPointResult)
\tkzCalcLength(tkz@spka,tkzPointResult)
\endgroup
}
%<--------------------------------------------------------------------------–>
% End Def Circle
%<--------------------------------------------------------------------------–>
\makeatother
\endinput
|
