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+%%%
+% Diff\'erentes représentations graphiques
+%%%
+\setKVdefault[TraceG]{Grille=false,Graduations=false,PasGradX=1,PasGradY=1,PasGrilleX=1,PasGrilleY=1,Xmin=-5.5,Xmax=5.5,Xstep=1,Ymin=-5.5,Ymax=5.5,Ystep=1,Bornea=-5.5,Borneb=5.5,LabelX={},LabelY={},LabelC=0.5,NomCourbe={},Origine={(5.5,5.5)},Fonction=false,Points=false,Invisible=false,CouleurPoint=red,CouleurTrace=black,Epaisseur=1,Relie=false,RelieSegment=false,Marque=dot,Code=false,Vide=false,NbPointsCourbe=100}%
+\defKV[TraceG]{Traces=\setKV[TraceG]{Code}}%
+
+\newcommand\TraceGraphique[2][]{%
+ \useKVdefault[TraceG]%
+ \setKV[TraceG]{#1}%
+ \ifboolKV[TraceG]{Fonction}{%
+ \MPTraceFonction[#1]{#2}%
+ }{%
+ \setKV[TraceG]{Xmin=0,Ymin=0}
+ \setKV[TraceG]{#1}%
+ \readlist*\ListePointsPlaces{#2}%
+ \newtoks\toklistepoint%
+ \foreachitem\compteur\in\ListePointsPlaces{\expandafter\Updatetoks\compteur\nil}%
+ \MPPlacePoint[#1]{\the\toklistepoint}
+ }%
+}%
+
+\newcommand\MPPlacePoint[2][]{%
+ \ifluatex
+ \mplibforcehmode
+ \begin{mplibcode}
+ xmin=\useKV[TraceG]{Xmin};
+ xmax=\useKV[TraceG]{Xmax};
+ ymin=\useKV[TraceG]{Ymin};
+ ymax=\useKV[TraceG]{Ymax};
+ pasx=\useKV[TraceG]{Xstep};
+ pasy=\useKV[TraceG]{Ystep};
+ x.u=1cm/\useKV[TraceG]{Xstep};
+ y.u=1cm/\useKV[TraceG]{Ystep};
+ grillex=\useKV[TraceG]{PasGrilleX};
+ grilley=\useKV[TraceG]{PasGrilleY};
+ pos=\useKV[TraceG]{LabelC};
+
+ marque_p:=str \useKV[TraceG]{Marque};
+ m_c:=m_c*2;
+
+ color colorpoint,colortrace;
+ colorpoint=\useKV[TraceG]{CouleurPoint};
+ colortrace=\useKV[TraceG]{CouleurTrace};
+ boolean Grille;
+ Grille=\useKV[TraceG]{Grille};
+
+ boolean Graduations;
+ Graduations=\useKV[TraceG]{Graduations};
+
+ boolean Relie;
+ Relie=\useKV[TraceG]{Relie};
+
+ boolean RelieSegment;
+ RelieSegment=\useKV[TraceG]{RelieSegment};
+
+ boolean Invisible;
+ Invisible=\useKV[TraceG]{Invisible};
+
+ pair Origine;
+ Origine=(0,0);
+
+ if Grille:
+ drawoptions(withcolor 0.75white);
+ for k=0 step grillex until (xmax-xmin):
+ trace (k*x.u,ypart(Origine))--(x.u*k,y.u*(ymax-ymin));
+ endfor;
+ for k=0 step grilley until (ymax-ymin):
+ trace (xpart(Origine),k*y.u)--(x.u*(xmax-xmin),y.u*k);
+ endfor;
+ drawoptions();
+ fi;
+
+ if Graduations:
+ for k=0 step grillex until (xmax-xmin):
+ trace ((0,-0.5mm)--(0,0.5mm)) shifted ((k*x.u,0) shifted Origine) withpen pencircle scaled1.25;
+ label.bot(TEX("\num{"&decimal(xmin+k)&"}"),(k*x.u,0) shifted Origine);
+ endfor;
+ label.ulft(TEX("\num{"&decimal(ymin)&"}"),(0,0) shifted Origine);
+ for k=grilley step grilley until (ymax-ymin):
+ trace ((-0.5mm,0)--(0.5mm,0)) shifted ((0,k*y.u) shifted Origine) withpen pencircle scaled1.25;
+ label.lft(TEX("\num{"&decimal(ymin+k)&"}"),(0,k*y.u) shifted Origine);
+ endfor;
+ fi;
+ drawoptions(withpen pencircle scaled1.5);
+ drawarrow Origine--(xpart(Origine),y.u*(ymax-ymin));
+ drawarrow Origine--((xmax-xmin)*x.u,ypart(Origine));
+ drawoptions();
+
+ % On relie éventuellement les points
+ if Relie:
+ pair N[];
+ nbpoint=0;
+ for p_=#2:
+ nbpoint:=nbpoint+1;
+ N[nbpoint]=(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin));
+ endfor;
+ draw N[1] for k=2 upto nbpoint:
+ ..N[k]
+ endfor withcolor colortrace;
+ fi;
+ if RelieSegment:
+ pair N[];
+ nbpoint=0;
+ for p_=#2:
+ nbpoint:=nbpoint+1;
+ N[nbpoint]=(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin));
+ endfor;
+ draw N[1] for k=2 upto nbpoint:
+ --N[k]
+ endfor withcolor colortrace;
+ fi;
+
+ % On place les points
+ if Invisible=false:
+ drawoptions(withcolor colorpoint);
+ for p_=#2:
+ if marque_p="dot":
+ dotlabel("",(x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin)));
+ elseif marque_p="croix":
+ pointe((x.u*(xpart(p_)-xmin),y.u*(ypart(p_)-ymin)));
+ fi;
+ endfor;
+ drawoptions();
+ fi;
+ %on labelise les axes
+ label.urt(btex \useKV[TraceG]{LabelX} etex,(x.u*(xmax-xmin),ypart(Origine)));
+ label.urt(btex \useKV[TraceG]{LabelY} etex,(xpart(Origine),y.u*(ymax-ymin)));
+ \end{mplibcode}
+ \else
+ \mpxcommands{%
+ \usepackage{ProfCollege}
+ \setKV[TraceG]{#1}
+ }
+ \begin{mpost}[mpsettings={xmin=\useKV[TraceG]{Xmin};xmax=\useKV[TraceG]{Xmax};ymin=\useKV[TraceG]{Ymin};ymax=\useKV[TraceG]{Ymax};pasx=\useKV[TraceG]{Xstep};pasy=\useKV[TraceG]{Ystep};xu=1cm/\useKV[TraceG]{Xstep};yu=1cm/\useKV[TraceG]{Ystep};grillex=\useKV[TraceG]{PasGrilleX};grilley=\useKV[TraceG]{PasGrilleY};pos=\useKV[TraceG]{LabelC};color colorpoint,colortrace;colorpoint=\useKV[TraceG]{CouleurPoint};colortrace=\useKV[TraceG]{CouleurTrace};boolean Grille;Grille=\useKV[TraceG]{Grille};boolean Graduations;Graduations=\useKV[TraceG]{Graduations};boolean Relie;Relie=\useKV[TraceG]{Relie};boolean RelieSegment;RelieSegment=\useKV[TraceG]{RelieSegment};boolean Invisible;Invisible=\useKV[TraceG]{Invisible};}]
+ pair Origine;
+ Origine=(0,0);
+
+ if Grille:
+ drawoptions(withcolor 0.75white);
+ for k=0 step grillex until (xmax-xmin):
+ trace (k*xu,ypart(Origine))--(xu*k,yu*(ymax-ymin));
+ endfor;
+ for k=0 step grilley until (ymax-ymin):
+ trace (xpart(Origine),k*yu)--(xu*(xmax-xmin),yu*k);
+ endfor;
+ drawoptions();
+ fi;
+
+ if Graduations:
+ for k=0 step grillex until (xmax-xmin):
+ trace ((0,-0.5mm)--(0,0.5mm)) shifted ((k*xu,0) shifted Origine) withpen pencircle scaled1.25;
+ label.bot(LATEX("\num{"&decimal(xmin+k)&"}"),(k*xu,0) shifted Origine);
+ endfor;
+ label.ulft(LATEX("\num{"&decimal(ymin)&"}"),(0,0) shifted Origine);
+ for k=grilley step grilley until (ymax-ymin):
+ trace ((-0.5mm,0)--(0.5mm,0)) shifted ((0,k*yu) shifted Origine) withpen pencircle scaled1.25;
+ label.lft(LATEX("\num{"&decimal(ymin+k)&"}"),(0,k*yu) shifted Origine);
+ endfor;
+ fi;
+ drawoptions(withpen pencircle scaled1.5);
+ drawarrow Origine--(xpart(Origine),yu*(ymax-ymin));
+ drawarrow Origine--((xmax-xmin)*xu,ypart(Origine));
+ drawoptions();
+
+ % On relie éventuellement les points
+ if Relie:
+ pair N[];
+ nbpoint=0;
+ for p_=#2:
+ nbpoint:=nbpoint+1;
+ N[nbpoint]=(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin));
+ endfor;
+ draw N[1] for k=2 upto nbpoint:
+ ..N[k]
+ endfor withcolor colortrace;
+ fi;
+ if RelieSegment:
+ pair N[];
+ nbpoint=0;
+ for p_=#2:
+ nbpoint:=nbpoint+1;
+ N[nbpoint]=(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin));
+ endfor;
+ draw N[1] for k=2 upto nbpoint:
+ --N[k]
+ endfor withcolor colortrace;
+ fi;
+
+ % On place les points
+ if Invisible=false:
+ drawoptions(withcolor colorpoint);
+ for p_=#2:
+ dotlabel("",(xu*(xpart(p_)-xmin),yu*(ypart(p_)-ymin)));
+ endfor;
+ drawoptions();
+ fi;
+ %on labelise les axes
+ label.urt(btex \unexpanded{\useKV[TraceG]{LabelX}} etex,(xu*(xmax-xmin),ypart(Origine)));
+ label.urt(btex \unexpanded{\useKV[TraceG]{LabelY}} etex,(xpart(Origine),yu*(ymax-ymin)));
+ \end{mpost}
+ \fi
+}
+
+\newcommand\MPTraceFonction[2][]{%
+ \ifluatex
+ \mplibforcehmode
+ \begin{mplibcode}
+ borneinf=\useKV[TraceG]{Bornea};
+ bornesup=\useKV[TraceG]{Borneb};
+ nbpointsCourbe:=\useKV[TraceG]{NbPointsCourbe};
+ xmin=\useKV[TraceG]{Xmin};
+ xmax=\useKV[TraceG]{Xmax};
+ ymin=\useKV[TraceG]{Ymin};
+ ymax=\useKV[TraceG]{Ymax};
+ pasx=\useKV[TraceG]{Xstep};
+ pasy=\useKV[TraceG]{Ystep};
+ x.u=1cm/\useKV[TraceG]{Xstep};
+ y.u=1cm/\useKV[TraceG]{Ystep};
+ grillex=\useKV[TraceG]{PasGrilleX};
+ grilley=\useKV[TraceG]{PasGrilleY};
+ gradx=\useKV[TraceG]{PasGradX};
+ grady=\useKV[TraceG]{PasGradY};
+ pos=\useKV[TraceG]{LabelC};
+ Epaisseur:=\useKV[TraceG]{Epaisseur};
+
+ color colortrace;
+ colortrace=\useKV[TraceG]{CouleurTrace};
+
+ pair Origine;
+ Origine=(xmin,ymin)+\useKV[TraceG]{Origine};
+
+ boolean Grille,Vide;
+ Grille=\useKV[TraceG]{Grille};
+ Vide=\useKV[TraceG]{Vide};
+
+ boolean Graduations;
+ Graduations=\useKV[TraceG]{Graduations};
+
+ vardef sin(expr t) = sind(c*t) enddef;
+
+ vardef cos(expr t) = cosd(c*t) enddef;
+
+ vardef tan(expr t) = sin(t)/cos(t) enddef;
+
+ vardef exp(expr t) = e**t enddef;
+
+ vardef ch(expr x)=(exp(x)+exp(-x))/2 enddef;
+
+ vardef sh(expr x)=(exp(x)-exp(-x))/2 enddef;
+
+ vardef ln(expr t) = mlog(t)/256 enddef;
+
+ vardef arcsin(expr x)=%Définition mathématique en radian
+ pi*angle((sqrt(1-x**2),x))/180
+ enddef;
+
+ vardef arccos(expr x)=%Définition mathématique en radian
+ pi*angle((x,sqrt(1-x**2)))/180
+ enddef;
+
+ def enplace=
+ xscaled x.u yscaled y.u shifted (Origine*cm)
+ enddef;
+
+ vardef placepoint(expr q,r)=
+ (q,r) enplace
+ enddef;
+
+ path Cb[];
+
+ vardef courbe[](expr a,b,nb)(text texte)=
+ path Courbe;
+ for i:=0 upto nb :
+ x@[i]:=(a+i*(b-a)/nb);
+ x:=x@[i];
+ y@[i]:=texte;
+ endfor ;
+ Cb@:=(x@.0*x.u,y@.0*y.u)
+ for i:=1 upto nb :
+ ..(x@[i]*x.u,y@[i]*y.u)
+ endfor;
+ Cb@:=Cb@ shifted (Origine*cm);
+ Courbe=Cb@;
+ Courbe
+ enddef;
+
+ if Grille:
+ drawoptions(withcolor 0.75white);
+ for k=xpart(Origine) step grillex until xmax:
+ trace u*(k,ymin)--u*(k,ymax);
+ endfor;
+ for k=xpart(Origine) step -grillex until xmin:
+ trace u*(k,ymin)--u*(k,ymax);
+ endfor;
+ for k=ypart(Origine) step grilley until ymax:
+ trace u*(xmin,k)--u*(xmax,k);
+ endfor;
+ for k=ypart(Origine) step -grilley until ymin:
+ trace u*(xmin,k)--u*(xmax,k);
+ endfor;
+ drawoptions();
+ fi;
+ if Graduations:
+ for k=gradx step gradx until bornesup:%xmax*gradx/grillex:
+ dotlabel.bot(TEX("\num{"&decimal(k)&"}"),(k*x.u+xpart(Origine*cm),ypart(Origine*cm)));
+ endfor;
+ for k=-gradx step -gradx until borneinf:%xmin*gradx/grillex:
+ dotlabel.bot(TEX("\num{"&decimal(k)&"}"),(k*x.u+xpart(Origine*cm),ypart(Origine*cm)));
+ endfor;
+ for k=grady step grady until ymax*grady/grilley:
+ dotlabel.lft(TEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*y.u+ypart(Origine*cm)));
+ endfor;
+ for k=-grady step -grady until ymin*grady/grilley:
+ dotlabel.lft(TEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*y.u+ypart(Origine*cm)));
+ endfor;
+ fi;
+
+ drawoptions(withpen pencircle scaled(1));
+ drawarrow (u*(0,ymin)--u*(0,ymax)) shifted (u*(xpart(Origine),0));
+ drawarrow (u*(xmin,0)--u*(xmax,0)) shifted (u*(0,ypart(Origine)));
+ label.llft(btex 0 etex,u*Origine);
+ drawoptions();
+ if Vide:
+ else:
+ draw courbe1(borneinf,bornesup,nbpointsCourbe)(#2) withpen (pencircle scaled Epaisseur) withcolor colortrace;
+ % labelisation
+ numeric t;
+ t=pos*length Cb1;
+ pair PT,Tangente;
+ PT:=point (pos*length Cb1) of Cb1;
+ Tangente:=unitvector(direction t of Cb1);
+ label(TEX("\useKV[TraceG]{NomCourbe}") rotated angle(Tangente),PT+2mm*(Tangente rotated 90));
+ % fin labelisation
+ clip currentpicture to polygone(u*(xmin,ymin),u*(xmax,ymin),u*(xmax,ymax),u*(xmin,ymax));
+ label.rt(btex \useKV[TraceG]{LabelX} etex,u*(xmax,ypart(Origine)));
+ label.top(btex \useKV[TraceG]{LabelY} etex,u*(xpart(Origine),ymax));
+ if \useKV[TraceG]{Code}:
+ \useKV[TraceG]{Traces}
+ fi;
+ fi;
+ \end{mplibcode}
+ \else
+ \mpxcommands{%
+ \usepackage{ProfCollege}
+ \setKV[TraceG]{#1}
+ }
+ \begin{mpost}[mpsettings={borneinf=\useKV[TraceG]{Bornea};bornesup=\useKV[TraceG]{Borneb};nbpointsCourbe:=\useKV[TraceG]{NbPointsCourbe};xmin=\useKV[TraceG]{Xmin};xmax=\useKV[TraceG]{Xmax};ymin=\useKV[TraceG]{Ymin};ymax=\useKV[TraceG]{Ymax};pasx=\useKV[TraceG]{Xstep};pasy=\useKV[TraceG]{Ystep};xu=1cm/\useKV[TraceG]{Xstep};yu=1cm/\useKV[TraceG]{Ystep};grillex=\useKV[TraceG]{PasGrilleX};grilley=\useKV[TraceG]{PasGrilleY};pos=\useKV[TraceG]{LabelC};Epaisseur=\useKV[TraceG]{Epaisseur}; color colortrace;colortrace=\useKV[TraceG]{CouleurTrace};boolean Grille,Vide;Grille=\useKV[TraceG]{Grille};Vide=\useKV[TraceG]{Vide};boolean Graduations;Graduations=\useKV[TraceG]{Graduations};
+ pair Origine;
+ Origine=(xmin,ymin)+\useKV[TraceG]{Origine};}]
+
+ vardef sin(expr t) = sind(c*t) enddef;
+
+ vardef cos(expr t) = cosd(c*t) enddef;
+
+ vardef tan(expr t) = sin(t)/cos(t) enddef;
+
+ vardef exp(expr t) = e**t enddef;
+
+ vardef ch(expr x)=(exp(x)+exp(-x))/2 enddef;
+
+ vardef sh(expr x)=(exp(x)-exp(-x))/2 enddef;
+
+ vardef ln(expr t) = mlog(t)/256 enddef;
+
+ vardef arcsin(expr x)=%Définition mathématique en radian
+ pi*angle((sqrt(1-x**2),x))/180
+ enddef;
+
+ vardef arccos(expr x)=%Définition mathématique en radian
+ pi*angle((x,sqrt(1-x**2)))/180
+ enddef;
+
+ path Cb[];
+
+ vardef courbe[](expr a,b,nb)(text texte)=
+ path Courbe;
+ for i:=0 upto nb :
+ x@[i]:=(a+i*(b-a)/nb);
+ x:=x@[i];
+ y@[i]:=texte;
+ endfor ;
+ Cb@:=(x@.0*xu,y@.0*yu)
+ for i:=1 upto nb :
+ ..(x@[i]*xu,y@[i]*yu)
+ endfor;
+ Cb@:=Cb@ shifted (Origine*cm);
+ Courbe=Cb@;
+ Courbe
+ enddef;
+
+ if Grille:
+ drawoptions(withcolor 0.75white);
+ for k=xpart(Origine) step grillex until xmax:
+ trace u*(k,ymin)--u*(k,ymax);
+ endfor;
+ for k=xpart(Origine) step -grillex until xmin:
+ trace u*(k,ymin)--u*(k,ymax);
+ endfor;
+ for k=ypart(Origine) step grilley until ymax:
+ trace u*(xmin,k)--u*(xmax,k);
+ endfor;
+ for k=ypart(Origine) step -grilley until ymin:
+ trace u*(xmin,k)--u*(xmax,k);
+ endfor;
+ drawoptions();
+ fi;
+ if Graduations:
+ for k=1 upto xmax/grillex:
+ dotlabel.bot(LATEX("\num{"&decimal(k)&"}"),(k*xu+xpart(Origine*cm),ypart(Origine*cm)));
+ endfor;
+ for k=-1 downto xmin/grillex:
+ dotlabel.bot(LATEX("\num{"&decimal(k)&"}"),(k*xu+xpart(Origine*cm),ypart(Origine*cm)));
+ endfor;
+ for k=1 upto ymax/grilley:
+ dotlabel.lft(LATEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*yu+ypart(Origine*cm)));
+ endfor;
+ for k=-1 downto ymin/grilley:
+ dotlabel.lft(LATEX("\num{"&decimal(k)&"}"),(xpart(Origine*cm),k*yu+ypart(Origine*cm)));
+ endfor;
+ fi;
+ drawoptions(withpen pencircle scaled1.5);
+ drawarrow (u*(0,ymin)--u*(0,ymax)) shifted (u*(xpart(Origine),0));
+ drawarrow (u*(xmin,0)--u*(xmax,0)) shifted (u*(0,ypart(Origine)));
+ drawoptions();
+ if Vide:
+ else:
+ draw courbe1(borneinf,bornesup,nbpointsCourbe)(#2) withpen (pencircle scaled Epaisseur) withcolor colortrace;
+% % labelisation
+ numeric t;
+ t=pos*length Cb1;
+ pair PT,Tangente;
+ PT:=point (pos*length Cb1) of Cb1;
+ Tangente:=unitvector(direction t of Cb1);
+ label(btex \noexpand\useKV[TraceG]{NomCourbe} etex rotated angle(Tangente),PT+2mm*(Tangente rotated 90));
+% % fin labelisation
+ clip currentpicture to polygone(u*(xmin,ymin),u*(xmax,ymin),u*(xmax,ymax),u*(xmin,ymax));
+ label.rt(btex \useKV[TraceG]{LabelX} etex,u*(xmax,ypart(Origine)));
+ label.top(btex \useKV[TraceG]{LabelY} etex,u*(xpart(Origine),ymax));
+ fi;
+ \end{mpost}
+ \fi
+}% \ No newline at end of file