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%%%
% Fraction Nombre
%%%
\newtoks\tokFractionNombrePerso%
\def\UpdatetoksFN#1\nil{\addtotok\tokFractionNombrePerso{"#1",}}%
\setKVdefault[ClesFN]{Unite=5cm,Aire=false,Solution=false,Quadrillage=false,PasQuad=5mm,HautQuad=3,LargQuad=8,Vide=false,Creation=false,Couleur=blue,UniteAire=1x1}%
\defKV[ClesFN]{Perso=\setKV[ClesFN]{Creation}\xdef\PfCFooCheminFN{#1}}%
\NewDocumentCommand\FractionNombre{om}{%
\useKVdefault[ClesFN]%
\setKV[ClesFN]{#1}%
\tokFractionNombrePerso{}%
\ifboolKV[ClesFN]{Creation}{%
\setsepchar{,}\ignoreemptyitems%
\readlist*\PfCListeDeplacements{\PfCFooCheminFN}%
\foreachitem\compteur\in\PfCListeDeplacements{\expandafter\UpdatetoksFN\compteur\nil}%
}{}%
\StrCut{#2}{/}\PfCNumA\PfCNumB%
\ifboolKV[ClesFN]{Aire}{%
\StrCut{\useKV[ClesFN]{UniteAire}}{x}\PfCAirex\PfCAirey%
\ifboolKV[ClesFN]{Creation}{%
\BuildFractionNombreAirePerso{\PfCNumA}{\PfCNumB}{\PfCAirex}{\PfCAirey}{\the\tokFractionNombrePerso}%
}{%
\BuildFractionNombreAire{\PfCNumA}{\PfCNumB}{\PfCAirex}{\PfCAirey}%
}%
}{%
\ifboolKV[ClesFN]{Quadrillage}{%
\BuildFractionNombreQuadrillage{\PfCNumA}{\PfCNumB}{\the\tokFractionNombrePerso}%
}{%
\BuildFractionNombreSegment{\PfCNumA}{\PfCNumB}%
}%
}%
}%
\NewDocumentCommand\BuildFractionNombreAirePerso{mmmmm}{%
\ifluatex%
\mplibforcehmode%
\begin{mplibcode}
vardef LireMotif(text t)=
lmotif=0;
hmotif=0;
for p_=t:
hmotif:=hmotif+1;
if lmotif<(length p_):
lmotif:=length p_;
fi;
endfor;
enddef;
%
vardef PlacerMotif(text t)=
ChoixLigneD=hmotif+ceiling(uniformdeviate(HautQuad-1-hmotif));
ChoixColonneD=ceiling(uniformdeviate(LargQuad-#3-1-lmotif));
Colonne:=ChoixColonneD;
Ligne=ChoixLigneD;
for p_=t:
Colonne:=ChoixColonneD;
for k=0 upto ((length p_)-1):
if (substring(k,k+1) of p_)="x":
fill ((unitsquare scaled 5mm) shifted (5mm*(Colonne-1,Ligne-1))) withcolor LightSteelBlue;
fi;
Colonne:=Colonne+1;
endfor;
Ligne:=Ligne-1;
endfor;
enddef;
%
PasQuad=\useKV[ClesFN]{PasQuad};
HautQuad=\useKV[ClesFN]{HautQuad};
LargQuad=\useKV[ClesFN]{LargQuad};
pair A,B,C,D,U[];
A=(0,0);
B-A=PasQuad*(LargQuad,0);
C-B=PasQuad*(0,HautQuad);
D-C=A-B;
% l'unité
U0=C;
U1-U0=#3*PasQuad*(-1,0);
U3-U0=#4*PasQuad*(0,-1);
U2-U3=U1-U0;
%
LireMotif(#5);
PlacerMotif(#5);
% Tracage
fill polygone(U0,U1,U2,U3) withcolor 0.7white;
label.top(TEX("\textbf{1 ua}"),iso(U1,U0));
%Le quadrillage
trace polygone(A,B,C,D);
for k=1 upto LargQuad-1:
trace (k/LargQuad)[A,B]--(k/LargQuad)[D,C];
endfor;
for k=1 upto HautQuad-1:
trace (k/HautQuad)[A,D]--(k/HautQuad)[B,C];
endfor;
\end{mplibcode}
\fi%
}%
\NewDocumentCommand\BuildFractionNombreAire{mmmm}{%
\ifluatex%
\mplibforcehmode%
\begin{mplibcode}
boolean Impossible[][];
%
vardef InitialisationZone=
for k=-1 upto HautQuad+1:
for l=-1 upto LargQuad+1:
Impossible[k][l]=true;
endfor;
endfor;
for k=1 upto HautQuad-1:
for l=1 upto LargQuad-#3-1:
Impossible[k][l]:=false;
endfor;
endfor;
enddef;
%
vardef RAZZone=
pair PileChemin[];
indiceChemin:=0;
enddef;
%
def PushChemin(expr tt)=
if indiceChemin<1:
PileChemin[1]:=tt;
indiceChemin:=1;
else:
PileChemin[indiceChemin+1]:=tt;
indiceChemin:=indiceChemin+1;
fi;
enddef;
%
def PopChemin=
currentpicture:=nullpicture;
RAZZone;
for k=-1 upto HautQuad:
for l=-1 upto LargQuad:
Impossible[k][l]:=true;
endfor;
endfor;
for k=1 upto HautQuad-1:
for l=1 upto LargQuad-#3-1:
Impossible[k][l]:=false;
endfor;
endfor;
%Redemarrage
nbcaseschoisies:=1;
PushChemin((ChoixLigneD,ChoixColonneD));
fill ((unitsquare scaled 5mm) shifted (5mm*(ChoixColonneD-1,ChoixLigneD-1))) withcolor LightSteelBlue;
Impossible[ChoixLigneD][ChoixColonneD]:=true;
VoisinDispo(ChoixLigneD,ChoixColonneD);
enddef;
%
%Pile des cases voisines de la case parcourue
pair PileVoisin[];
numeric indiceVoisin;
indiceVoisin=0;
%
vardef RAZPileVoisin=
indiceVoisin:=0;
enddef;
%
def PushVoisin(expr tt)=
if indiceVoisin<1:
PileVoisin[1]:=tt;
indiceVoisin:=1;
else:
PileVoisin[indiceVoisin+1]:=tt;
indiceVoisin:=indiceVoisin+1;
fi;
enddef;
%
vardef VoisinDispo(expr la,lo)=
RAZPileVoisin;
numeric nbvoisin;
nbvoisin=0;
if Impossible[la+1][lo]=false:
nbvoisin:=nbvoisin+1;
PushVoisin((la+1,lo));
fi;
if Impossible[la-1][lo]=false:
nbvoisin:=nbvoisin+1;
PushVoisin((la-1,lo));
fi;
if Impossible[la][lo+1]=false:
nbvoisin:=nbvoisin+1;
PushVoisin((la,lo+1));
fi;
if Impossible[la][lo-1]=false:
nbvoisin:=nbvoisin+1;
PushVoisin((la,lo-1));
fi;
enddef;
%
PasQuad=\useKV[ClesFN]{PasQuad};
HautQuad=\useKV[ClesFN]{HautQuad};
LargQuad=\useKV[ClesFN]{LargQuad};
pair A,B,C,D,U[];
A=(0,0);
B-A=PasQuad*(LargQuad,0);
C-B=PasQuad*(0,HautQuad);
D-C=A-B;
% l'unité
U0=C;
U1-U0=#3*PasQuad*(-1,0);
U3-U0=#4*PasQuad*(0,-1);
U2-U3=U1-U0;
% Le nombres total de cases à colorier
NbTotalCasesAColorier=((#1*#3*#4)/#2);
NbTotalCasesRestantes=HautQuad*(LargQuad-#3-1);
%
InitialisationZone;
RAZZone;
%
ChoixLigneD=ceiling(uniformdeviate(HautQuad-1));
ChoixColonneD=ceiling(uniformdeviate(LargQuad-#3-1));
%
PushChemin((ChoixLigneD,ChoixColonneD));
nbcaseschoisies=1;
fill ((unitsquare scaled 5mm) shifted (5mm*(ChoixColonneD-1,ChoixLigneD-1))) withcolor LightSteelBlue;
Impossible[ChoixLigneD][ChoixColonneD]:=true;
VoisinDispo(ChoixLigneD,ChoixColonneD);
% Le "parcours"
forever: exitif nbcaseschoisies>NbTotalCasesAColorier-1;
nb:=ceiling(uniformdeviate(nbvoisin));
if nb>0:
for k=1 upto nbvoisin:
Impossible[xpart(PileVoisin[nb])][ypart(PileVoisin[nb])]:=true;
endfor;
PushChemin((xpart(PileVoisin[nb]),ypart(PileVoisin[nb])));
nbcaseschoisies:=nbcaseschoisies+1;
fill ((unitsquare scaled 5mm) shifted (5mm*(ypart(PileVoisin[nb])-1,xpart(PileVoisin[nb])-1))) withcolor LightSteelBlue;
VoisinDispo(xpart(PileChemin[indiceChemin]),ypart(PileChemin[indiceChemin]));
else:
PopChemin;
fi;
endfor;
% Tracage
fill polygone(U0,U1,U2,U3) withcolor 0.7white;
label.top(TEX("\textbf{1 ua}"),iso(U1,U0));
%Le quadrillage
trace polygone(A,B,C,D);
for k=1 upto LargQuad-1:
trace (k/LargQuad)[A,B]--(k/LargQuad)[D,C];
endfor;
for k=1 upto HautQuad-1:
trace (k/HautQuad)[A,D]--(k/HautQuad)[B,C];
endfor;
\end{mplibcode}
\fi
}%
\NewDocumentCommand\BuildFractionNombreSegment{mm}{%
\ifluatex%
\mplibforcehmode%
\begin{mplibcode}
Unite:=\useKV[ClesFN]{Unite};
boolean Solution,Vide;
Solution=\useKV[ClesFN]{Solution};
Vide=\useKV[ClesFN]{Vide};
color CoulFN;
CoulFN=\useKV[ClesFN]{Couleur};
Num:=#1;
Pas:=#2;
pair A,B,C,D;
A=(0,0);
B=Unite*(1,0);
if Num>Pas:
C=((Num+1)/Pas)[A,B];
Total=Num+1;
else:
C=B;
Total=Pas;
fi;
D=(Num/Pas)[A,B];
trace segment(A,C);
for k=0 upto Total:
trace ((0,-1mm)--(0,1mm)) shifted ((k/Pas)[A,B]);
endfor;
trace cotationmil(A,B,5mm,15,TEX("1 ul"));
if Solution:
draw (A--D) withpen pencircle scaled 2 withcolor CoulFN;
trace cotationmil(A,D,-5mm,25,TEX("$?=\dfrac{"&decimal(#1)&"}{"&decimal(#2)&"}$~ul"));
else:
if Vide:
else:
trace cotationmil(A,D,-5mm,25,TEX("$?=\dots$~ul"));
fi;
fi;
\end{mplibcode}
\fi%
}%
\NewDocumentCommand\BuildFractionNombreQuadrillage{mmm}{%
\ifluatex%
\mplibforcehmode%
\begin{mplibcode}
Unite:=#2;%\useKV[ClesFN]{Unite};%en carreaux
HautQuad:=\useKV[ClesFN]{HautQuad};
Largeur:=Unite;%en carreaux
boolean Solution,Vide,Creation;
Solution=\useKV[ClesFN]{Solution};
Vide=\useKV[ClesFN]{Vide};
Creation=\useKV[ClesFN]{Creation};
color CoulFN;
CoulFN=\useKV[ClesFN]{Couleur};
Num:=#1;
Pas:=#2;
PasQuad:=\useKV[ClesFN]{PasQuad};
pair A,B,C,D;
A=(0,0);
B=(((#1 div #2)+1)*Unite+1)*PasQuad*(1,0);
C-B=(0,HautQuad*PasQuad);
D-C=A-B;
trace polygone(A,B,C,D);
TotalLargeur=(((#1 div #2)+1)*Unite+1);
for k=1 upto TotalLargeur-1:
trace (k/TotalLargeur)[A,B]--(k/TotalLargeur)[D,C];
endfor;
for k=1 upto HautQuad-1:
trace (k/HautQuad)[A,D]--(k/HautQuad)[B,C];
endfor;
% Macro pour le chemin perso
vardef RemplirChemin(text t)=
nbpoints:=0;
% On compte le dénivelé
denivele=0;
denivmax:=0;
denivmin:=0;
for p_=t:
if p_="+":
denivmax:=denivmax+1;
elseif p_="-":
denivmin:=denivmin-1;
fi;
endfor;
depart:=-(denivmin)+floor(uniformdeviate(HautQuad-2-abs(denivmax-abs(denivmin))));
ch[0]=PasQuad*(0,depart);
for p_=t:
nbpoints:=nbpoints+1;
if p_=">":
ch[nbpoints]=ch[nbpoints-1]+PasQuad*(1,0);
elseif p_="<":
ch[nbpoints]=ch[nbpoints-1]+PasQuad*(-1,0);
elseif p_="+":
ch[nbpoints]=ch[nbpoints-1]+PasQuad*(0,1);
elseif p_="-":
ch[nbpoints]=ch[nbpoints-1]+PasQuad*(0,-1);
fi;
endfor;
enddef;
% On choisit le départ.
pair ch[];
numeric xe[],ye[];
if Creation:
RemplirChemin(#3);
else:
depart:=floor(uniformdeviate(HautQuad-1));
ch[0]=PasQuad*(0,depart);
xe0=0;
ye0=depart;
for k=1 upto #1:
if (k mod 2)=1:
ch[k]-ch[k-1]=PasQuad*(1,0);
xe[k]=xe[k-1]+1;
ye[k]=ye[k-1];
else:
if ye[k-1]=0:
alea:=uniformdeviate(2);
if alea<1:
ch[k]-ch[k-1]=PasQuad*(0,1);
xe[k]=xe[k-1];
ye[k]=ye[k-1]+1;
else:
ch[k]-ch[k-1]=PasQuad*(1,0);
xe[k]=xe[k-1]+1;
ye[k]=ye[k-1];
fi;
elseif ye[k-1]=2:
alea:=uniformdeviate(2);
if alea<1:
ch[k]-ch[k-1]=PasQuad*(0,-1);
xe[k]=xe[k-1];
ye[k]=ye[k-1]-1;
else:
ch[k]-ch[k-1]=PasQuad*(1,0);
xe[k]=xe[k-1]+1;
ye[k]=ye[k-1];
fi;
else:
alea:=uniformdeviate(3);
if alea<1:
ch[k]-ch[k-1]=PasQuad*(0,1);
xe[k]=xe[k-1];
ye[k]=ye[k-1]+1;
elseif alea<2:
ch[k]-ch[k-1]=PasQuad*(1,0);
xe[k]=xe[k-1]+1;
ye[k]=ye[k-1];
else:
ch[k]-ch[k-1]=PasQuad*(0,-1);
xe[k]=xe[k-1];
ye[k]=ye[k-1]-1;
fi;
fi;
fi;
endfor;
fi;
if Vide=false:
trace ch[0] for k=1 upto #1:--ch[k] endfor withpen pencircle scaled 2 withcolor CoulFN;
fi;
trace cotationmil(D,(D+#2*(PasQuad,0)),5mm,15,TEX("1 ul"));
trace segment(D,D+#2*(PasQuad,0)) withpen pencircle scaled 1.5;
\end{mplibcode}
\fi
}%
|