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Diffstat (limited to 'graphics/pgf/contrib/tkz-grapheur/doc/tkz-grapheur-examples-integrals.tex')
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diff --git a/graphics/pgf/contrib/tkz-grapheur/doc/tkz-grapheur-examples-integrals.tex b/graphics/pgf/contrib/tkz-grapheur/doc/tkz-grapheur-examples-integrals.tex new file mode 100644 index 0000000000..068ba103eb --- /dev/null +++ b/graphics/pgf/contrib/tkz-grapheur/doc/tkz-grapheur-examples-integrals.tex @@ -0,0 +1,251 @@ +% !TeX TXS-program:compile = txs:///arara +% arara: pdflatex: {shell: yes, synctex: no, interaction: batchmode} + +\documentclass[a4paper,english,11pt]{article} +\usepackage[margin=1cm,includefoot]{geometry} +\usepackage[english]{tkz-grapheur} +\usepackage{tcolorbox} +\tcbuselibrary{skins,minted} +\usepackage{babel} + +\begin{document} + +\part*{Integrals examples} + +\section{Below cruve, by default} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Behind,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=ch]<h>{0.25*(x+2)^2+1} + \DrawIntegral% + [Colors=blue/cyan,Style=fill]% + {h(x)} %formula + {-5.25}{1.5} + \DrawCurve[Color=red]{h(x)} + \DrawAxisGrids[Above,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Behind interpolation curve} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstInterpol{(-6,4)(-2,-2)(3,3.5)}[\interpoA] + \DefineInterpoCurve[Name=interpotest,Tension=1.05]{\interpoA} + \DrawIntegral% + [NameInterpo=interpotest,Colors=blue/cyan,Style=fill,Type=itp,Tension=1.05]% + {\interpoA} %pointsinterpo + {-5.25}{1.5} + \DrawInterpoCurve[Color=red,Tension=1.05]{\interpoA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Behind cubic spline} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] + \DefineSplineCurve[Name=splinetest]{\lstsplineA}<\SplineTeal> + \DrawIntegral% + [NameSpline=\SplineTeal,Type=spl,Colors=blue/purple,Style=hatch]% + {splinetest} %namesplinecurve + {-5}{2} + \DrawSplineCurve[Color=teal]{\lstsplineA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between curves} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=ch]<h>{0.25*(x+2)^2-1} + \DefineCurve[Name=ck]<k>{-0.25*x+1} + \FindIntersections[Name=ITSC,Disp=false]{ch}{ck} + \DrawIntegral% + [Colors=olive/pink,Style=fill,Type=fct/fct,Bounds=node/abs]% + {h(x)}[k(x)] %formules + {(ITSC-1)}{1.5} + \DrawCurve[Color=red]{h(x)} + \DrawCurve[Color=blue]{k(x)} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between splines} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] + \DefineLstSpline{-6/-2/3§-2/4/0§3/-1/0}[\lstsplineB] + \DefineSplineCurve[Name=splinetestolive]{\lstsplineA}<\SplineOlive> + \DefineSplineCurve[Name=splinetestteal]{\lstsplineB}<\SplineTeal> + \FindIntersections[Name=ITT,Disp=false]{splinetestteal}{splinetestolive} + \DrawIntegral% + [NameSpline=\SplineTeal,NameSplineB=\SplineOlive,Type=spl/spl,Colors=blue/purple,Bounds=nodes]% + {splinetestolive} %Namecourbespline + [splinetestteal] %Namecourbespline + {(ITT-1)}{(ITT-2)} + \DrawSplineCurve[Color=teal]{\lstsplineA} + \DrawSplineCurve[Color=olive]{\lstsplineB} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between interpolations} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstInterpol{(-6,4)(-2,-2)(3,3.5)}[\interpoA] + \DefineInterpoCurve[Name=interpotest]{\interpoA} + \DefineLstInterpol{(-6,-2)(-1,4)(3,0)}[\interpoB] + \DefineInterpoCurve[Name=interpotesta]{\interpoB} + \DrawIntegral% + [NameInterpo=interpotesta,NameInterpoB=interpotest,Type=itp/itp,Colors=olive/pink]% + {\interpoB} %pointsinterpo + [\interpoA] %pointsinterpo + {-2}{1} + \DrawInterpoCurve[Color=red]{\interpoA} + \DrawInterpoCurve[Color=blue]{\interpoB} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Betweend function and spline} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=ch]<h>{-0.25*(x+2)^2+3.5} + \DefineLstSpline{-6/4/-2§-5/2/-2§-4/0/-2§-2/-2/0§1/2/2§3/3.5/0.5}[\lstsplineA] + \DefineSplineCurve[Name=splineblue]{\lstsplineA}<\Splineblue> + \DrawIntegral% + [NameSplineB=\Splineblue,Type=fct/spl,Colors=olive/pink]% + {h(x)} %formule + [splineblue] %Namecourbespline + {-3}{0} + \DrawCurve[Color=red]{h(x)} + \DrawSplineCurve[Color=blue]{\lstsplineA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between spline and function} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=ch]<h>{0.25*(x+2)^2-2} + \DefineLstSpline{-6/4/2§-5/-2/-2§-4/0/2§-2/2/0§1/-2/-2§3/3.5/-0.5}[\lstsplineA] + \DefineSplineCurve[Name=splineblue]{\lstsplineA}<\Splineblue> + \DrawIntegral% + [NameSpline=\Splineblue,Type=spl/fct,Colors=olive/pink]% + {splineblue} %Namecourbespline + [h(x)] %formule + {-3}{-1} + \DrawCurve[Color=red]{h(x)} + \DrawSplineCurve[Color=blue]{\lstsplineA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between function and interpo} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=cm]<m>{-0.25*(x+2)^2+4} + \DefineLstInterpol{(-6,4)(-5,-2)(-2,1)(1,-2)(3,3)}[\interpoB] + \DefineInterpoCurve[Name=interpotestb]{\interpoB} + \DrawIntegral% + [NameInterpoB=interpotestb,Type=fct/itp,Colors=olive/pink]% + {m(x)} %formule + [\interpoB] %pointsinterpo + {-4}{1} + \DrawCurve[Color=red]{m(x)} + \DrawInterpoCurve[Color=blue]{\interpoB} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between interpo and function} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineCurve[Name=courbeQ]<q>{0.25*(x+2)^2-2.5} + \DefineLstInterpol{(-6,-2)(-5,4)(-2,-1)(1,2)(3,-2)}[\interpoA] + \DefineInterpoCurve[Name=interpotest]{\interpoA} + \FindIntersections[Name=FGH,Disp]{interpotest}{courbeQ} + \DrawIntegral% + [NameInterpo=interpotest,Type=itp/fct,Colors=olive/pink,Bounds=nodes]% + {\interpoA} %pointsinterpo + [q(x)] %formule + {(FGH-1)}{(FGH-2)} + \DrawCurve[Color=red]{q(x)} + \DrawInterpoCurve[Color=blue]{\interpoA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between spline and interpo} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstSpline{-6/-2/2§-3/4/0§3/-2/0}[\lstsplineA] + \DefineSplineCurve[Name=splinered]{\lstsplineA}<\Splinered> + \DefineLstInterpol{(-6,4)(-5,-2)(-2,1)(1,-2)(3,3)}[\interpoB] + \DefineInterpoCurve[Name=interpotestb]{\interpoB} + \DrawIntegral% + [NameInterpoB=interpotestb,NameSpline=\Splinered,Type=spl/itp,Colors=olive/pink]% + {splinered} %Namecourbespline + [\interpoB] %pointsinterpo + {-4}{-2} + \DrawSplineCurve[Color=red]{\lstsplineA} + \DrawInterpoCurve[Color=blue]{\interpoB} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\section{Between interpo and spline} + +\begin{tcblisting}{listing engine=minted,minted language=latex,colframe=lightgray,colback=lightgray!5} +\begin{GraphTikz}% + [x=0.8cm,y=1cm,Xmin=-7,Xmax=4,Ymin=-3,Ymax=5] + \DrawAxisGrids[Grads=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} + \DefineLstSpline{-6/4/-2§-3/-2.25/0§3/3/0}[\lstsplineB] + \DefineSplineCurve[Name=splineblue]{\lstsplineB}<\Splineblue> + \DefineLstInterpol{(-6,-2)(-5,4)(-2,-1)(1,2)(3,-2.5)}[\interpoA] + \DefineInterpoCurve[Name=interpotest]{\interpoA} + \FindIntersections[Name=UIO,Disp]{interpotest}{splineblue} + \DrawIntegral% + [NameInterpo=interpotest,NameSplineB=\Splineblue,Type=itp/spl,Colors=olive/pink,Bounds=nodes]% + {\interpoA} %pointsinterpo + [splineblue] %Namecourbespline + {(UIO-1)}{(UIO-2)} + \DrawSplineCurve[Color=blue]{\lstsplineB} + \DrawInterpoCurve[Color=red]{\interpoA} + \DrawAxisGrids[Grid=false,Enlarge=2.5mm]{-7,-6,...,4}{-3,-2,...,5} +\end{GraphTikz} +\end{tcblisting} + +\end{document}
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