340 lines
14 KiB
Plaintext
340 lines
14 KiB
Plaintext
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// gm.asy - Un fourre-tout de fonctions (r<>centes ou anciennes) pour Asymptote.
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//
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// Derni<6E>re modification : 04/07/15 pour l'ajout d'une ancienne fonction cote3D(...)
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// propos<6F>e sur le forum le 10/04/10.
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import stats;
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import geometry;
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import graph;
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import three;
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///////////////////////////////////////////////////////////
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////////// STATISTIQUES
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///////////////////////////////////////////////////////////
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//
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// Remarque de f<>vrier 2012 : ce qui suit est amen<65> <20> disparaitre
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// Une extension gm_stats devrait voir le jour avant la fin 2012.
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// Tout sera r<><72>crit depuis une feuille blanche...
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// ... mais si cela peut d<>panner jusque l<>.
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//
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// Rappel de la histogramm d<>fini dans stats.asy :
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// void histogram(picture pic=currentpicture, real[] bins, real[] count,
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// real low=-infinity,
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// pen fillpen=nullpen, pen drawpen=nullpen, bool bars=false,
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// Label legend="", real markersize=legendmarkersize)
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// Une version perso (avec un e <20> la fin), plus adapt<70>e pour faire
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// des histogrammes pour un de math de lyc<79>e :
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void histogramme(picture pic=currentpicture,
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real[] tabxi, // les xi d<>finissants les classes
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real[] tabni, // les effectifs (ou fr<66>quence) par classe.
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bool bars=true,
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pen p1=lightgray,
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pen p2=.8bp+blue,
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string libellecaractere="Valeurs du caract\`ere",
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real minaxe=min(tabxi),
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real maxaxe=max(tabxi),
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real uniteaxe=(maxaxe-minaxe)/4,
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string libelleunite="",
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bool afficherUniteAire=true,
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bool valeurUniteAire=true,
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bool frequence=false,
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bool pourcent=false,
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real uniteaire=sum(tabni)/100){
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real uniteairetempo;
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if(frequence==false) uniteairetempo=uniteaire;
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if(frequence==true && pourcent==false) {
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if(uniteaire>=1) uniteaire=uniteaire/100;
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uniteairetempo=uniteaire*sum(tabni);
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}
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if(frequence==true && pourcent==true) {
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uniteairetempo=uniteaire*sum(tabni)/100;
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}
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// Une variable utile pour d<>terminer la plus petite amplitude :
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real largeurunite=abs(tabxi[1]-tabxi[0]);
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// ... et une autre pour le num<75>ro de classe correspondant :
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int iclasse=0;
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// Calcul des hauteurs (et de la plus petite amplitude de classe) :
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real[] tabhi;
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for(int i=0; i < tabni.length; ++i){
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tabhi[i]=tabni[i]/(tabxi[i+1]-tabxi[i]);
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if (largeurunite>abs(tabxi[i+1]-tabxi[i])) {
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largeurunite=abs(tabxi[i+1]-tabxi[i]);
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iclasse=i;
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}
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}
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// Hauteur du rectangle le plus haut pour placer l'unit<69> au dessus.
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real hauteurmaxi=max(tabhi);
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// Calcul de la hauteur <20> donner au rectangle unit<69> d'aire
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real hauteurunite=(uniteairetempo/tabni[iclasse])*tabhi[iclasse];
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int nbrlignes = ceil(hauteurmaxi/hauteurunite);
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for(int k=0; k<=nbrlignes; ++k){
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draw((minaxe,k*hauteurunite)--(maxaxe,k*hauteurunite),.5bp+gray);
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}
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for(int k=0; k<=((maxaxe-minaxe)/largeurunite); ++k){
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draw((minaxe+k*largeurunite,0)--(minaxe+k*largeurunite,nbrlignes*hauteurunite),.5bp+gray);
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}
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// Trac<61> de l'histogramme
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histogram(tabxi,tabhi,low=0,bars=bars,p1,p2);
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// Trac<61> de l'unit<69> d'aire et son <20>tiquette
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if(afficherUniteAire){
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filldraw(shift(truepoint(N+W))*box((0,0),(largeurunite,hauteurunite)),p1,p2);
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if(valeurUniteAire)
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label(libelleunite+(string) uniteaire+(pourcent==true ? "\%": ""),truepoint(N+W)+(largeurunite,-hauteurunite/2),E);
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}
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// Ajout de l'axe gradu<64>
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xaxis(libellecaractere, Bottom, minaxe,maxaxe,
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RightTicks(Label(currentpen+fontsize(6)),
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Step=uniteaxe),above=true);
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}
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/////// bam et multibam pour des diagrammes en boite.
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void bam(real[] xi, real h=1, real dh=0, bool lab=true, real Step=1){
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xi=sort(xi);
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real n=xi.length;
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real xmin=min(xi),
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q1= (floor(.25*n)==.25*n) ? xi[floor(.25*n)-1] : xi[floor(.25*n)],
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me= (n%2==0) ? (xi[floor(n/2)-1]+xi[floor(n/2)])/2 : xi[floor((n+1)/2)-1],
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q3= (floor(.75*n)==.75*n) ? xi[floor(.75*n)-1] : xi[floor(.75*n)],
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xmax=max(xi);
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xaxis(xmin,xmax,Ticks(Step=Step,Size=2));
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draw(box((q1,1+dh),(q3,1+dh+h)));
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draw((me,1+dh)--(me,1+dh+h));
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real hm=(1+dh+1+dh+h)/2;
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draw((xmin,hm)--(q1,hm)^^(q3,hm)--(xmax,hm));
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draw((xmin,hm-.1)--(xmin,hm+.1)^^(xmax,hm-.1)--(xmax,hm+.1));
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draw((xmin,0)--(xmin,hm)^^(q1,0)--(q1,hm)^^(me,0)--(me,hm)^^(q3,0)--(q3,hm)
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^^(xmax,0)--(xmax,hm),linetype("4 4"));
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if(lab){
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label("$X_{min}$",(xmin,hm),S,UnFill());
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label("$Q_1$",(q1,hm-h/2),S,UnFill());
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label("$M$",(me,hm-h/2),S,UnFill());
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label("$Q_3$",(q3,hm-h/2),S,UnFill());
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label("$X_{max}$",(xmax,hm),S,UnFill());
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}
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}
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picture bam0(real[] xi, real larg=1,
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bool comment_b=false,
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bool titre_b =false,
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Label titre_l ="",
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pair titre_pos=max(xi),
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align titre_dir=NoAlign,
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pen stylo=currentpen, pen backgr=nullpen
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){
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picture pic;
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xi=sort(xi);
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real n=xi.length;
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real xmin=min(xi),
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q1= (floor(.25*n)==.25*n) ? xi[floor(.25*n)-1] : xi[floor(.25*n)],
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me= (n%2==0) ? (xi[floor(n/2)-1]+xi[floor(n/2)])/2 : xi[floor((n+1)/2)-1],
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q3= (floor(.75*n)==.75*n) ? xi[floor(.75*n)-1] : xi[floor(.75*n)],
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xmax=max(xi);
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filldraw(pic,box((q1,-larg/2),(q3,larg/2)),backgr,stylo);
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draw(pic,(me,-larg/2)--(me,larg/2),stylo);
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draw(pic,(xmin,0)--(q1,0)^^(q3,0)--(xmax,0),stylo);
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draw(pic,(xmin,-.1)--(xmin,.1)^^(xmax,-.1)--(xmax,.1),stylo);
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if(titre_b) label(pic,titre_l,titre_pos,titre_dir);
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if(comment_b){
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label(pic,"$X_{min}$",(xmin,0),S,UnFill());
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label(pic,"$Q_1$",(q1,-larg/2),S,UnFill());
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label(pic,"$M$",(me,-larg/2),S,UnFill());
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label(pic,"$Q_3$",(q3,-larg/2),S,UnFill());
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label(pic,"$X_{max}$",(xmax,0),S,UnFill());
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}
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return pic;
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}
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void multibam(picture pic=currentpicture,
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real[][] ij,
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real[] larg =new real[],
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real[] esp =new real[],
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bool tit_b =false,
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Label[] tit =new Label[],
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align[] tit_d =new align[],
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pen[] sty =new pen[],
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pen[] bkg =new pen[],
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real Step=0, real step=0, real xmargin=0,
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bool vertical=false,
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bool twoaxis=false){
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picture pict;
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int n=ij.length;
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if(larg.length==0)larg.push(1);
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if(esp.length==0) esp.push(.5);
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while(larg.length<n) larg.push(larg[larg.length-1]);
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while(esp.length<n+1)esp.push(esp[esp.length-1]);
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while(tit.length<n) tit.push("");
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while(tit_d.length<n) tit_d.push((vertical)?plain.W:plain.E);
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while(sty.length<n) sty.push(currentpen);
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while(bkg.length<n) bkg.push(nullpen);
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real[] espa=new real[n+1];
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for(int k=0; k<n; ++k){
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espa[k]=((k!=0)?espa[k-1]+larg[k-1]/2:0)+esp[k]+larg[k]/2;
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add(pict,shift(0,espa[k])*bam0(
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ij[k],
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larg = larg[k],
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titre_b = false,
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titre_l = tit[k],
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titre_dir = tit_d[k],
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stylo = sty[k],
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backgr = bkg[k])
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);
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}
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espa[n]=espa[n-1]+larg[n-1]/2+esp[n];
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if(vertical){
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add(pic,reflect(Oy)*rotate(90)*pict);
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addMargins(pic,0,xmargin);
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xlimits(pic,0,espa[n]);
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ylimits(pic,min(ij)-xmargin,max(ij)+xmargin);
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yaxis(pic,BottomTop,
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Ticks("%",Step=Step,step=step,extend=true,.2bp+dashed));
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yaxis(pic,Left,Ticks(Step=Step,step=step,Size=2,size=1,pTick=.7bp+blue,ptick=black));
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if(twoaxis) yaxis(pic,Right,Ticks(Step=Step,step=step,Size=2,size=1,pTick=.7bp+blue,ptick=black));
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if(tit_b) for(int k=0; k<n; ++k)
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label(pic,tit[k],(espa[k],min(ij)-xmargin),plain.S);
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} else {
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add(pic,pict);
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addMargins(pic,xmargin);
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ylimits(pic,0,espa[n]);
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xlimits(pic,min(ij)-xmargin,max(ij)+xmargin);
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xaxis(pic,LeftRight,
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Ticks("%",Step=Step,step=step,extend=true,.2bp+dashed));
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xaxis(pic,Bottom,Ticks(Step=Step,step=step,Size=2,size=1,pTick=.7bp+blue,ptick=black));
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if(twoaxis) xaxis(pic,Top,Ticks(Step=Step,step=step,Size=2,size=1,pTick=.7bp+blue,ptick=black));
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if(tit_b) for(int k=0; k<n; ++k)
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label(pic,tit[k],(max(ij)+xmargin,espa[k]),plain.E);
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}
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}
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void diabandes(real X, real Y,
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real ymin, real ymax, real ystep,
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real tickwidth, string yformat,
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Label LX, Label LY, Label[] LLX,
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real[] height,
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pen p=nullpen){
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draw((0,0)--(0,Y),EndArrow);
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draw((0,0)--(X,0),EndArrow);
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label(LX,(X,0),plain.SE,fontsize(9));
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label(LY,(0,Y),plain.N,fontsize(9));
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real yscale=Y/(ymax+ystep);
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for(real y=ymin; y<ymax; y+=ystep) {
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draw((-tickwidth,yscale*y)--(0,yscale*y));
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label(format(yformat,y),(-tickwidth,yscale*y),plain.W,fontsize(9));
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}
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int n=LLX.length;
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real xscale=X/(2*n+2);
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for(int i=0;i<n;++i) {
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real x=xscale*(2*i+1);
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path P=(x,0)--(x,height[i]*yscale)--(x+xscale,height[i]*yscale)--(x+xscale,0)--cycle;
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fill(P,p);
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draw(P);
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label(LLX[i],(x+xscale/2),plain.S,fontsize(10));
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}
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for(int i=0;i<n;++i)
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draw((0,height[i]*yscale)--(X,height[i]*yscale),dashed);
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}
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//////////////////////////////////////////////////////////////////
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/// TRACER UNE COURBE AVEC V.I.
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//////////////////////////////////////////////////////////////////
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guide[] graphgm(picture pic=currentpicture, real f(real), real a, real b,
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int n=ngraph, real T(real)=identity,
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bool3 cond(real), interpolate join=operator --)
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{
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if(T == identity)
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return graph(join,cond)(new pair(real x) {
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return (x,pic.scale.y.T(f(pic.scale.x.Tinv(x))));},
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pic.scale.x.T(a),pic.scale.x.T(b),n);
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else
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return graph(join,cond)(new pair(real x) {
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return Scale(pic,(T(x),f(T(x))));},
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a,b,n);
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}
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//////////////////////////////////////////////////////////////////
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/// SIMILITUDES
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/// - simili_Ckphi(point C, real k, real phi)
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/// si sont connus : centre, rapport et angle
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/// - simili_ABCD(point A, point B, point C, point D)
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/// si sont connues les images C et D de deux points A et B.
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//////////////////////////////////////////////////////////////////
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transform simili_Ckphi(point C, real k, real phi){
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return rotate(phi,C)*scale(k,C);
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}
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transform simili_ABCD(point A, point B, point C, point D){
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point a=(D-C)/(B-A), b=C-a*A, centre=b/(1-a);
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real rapport=abs(a), angle=degrees(a);
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return simili_Ckphi(centre,rapport,angle);
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}
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//////////////////////////////////////////////////////////////////
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///
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/// 3D : le nom des fonctions parlent d'elles-m<>me.
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///
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//////////////////////////////////////////////////////////////////
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projection cavaliereX(real k=.5, real angle=45)
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{
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transform3 t={{-k*Cos(angle),1,0,0},
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{-k*Sin(angle),0,1,0},
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{1,0,0,-1},
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{0,0,0,1}};
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return projection((1,Cos(angle)^2,1-Cos(angle)^2),normal=(1,0,0),
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new transformation(triple,triple,triple) { return transformation(t);});
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}
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projection cavaliereX=cavaliereX();
|
|||
|
|
projection cavaliereYZ=cavaliereX();
|
|||
|
|
|
|||
|
|
projection cavaliereY(real k=.5, real angle=45)
|
|||
|
|
{
|
|||
|
|
transform3 t={{1,k*Cos(angle),0,0},
|
|||
|
|
{0,k*Sin(angle),1,0},
|
|||
|
|
{0,-1,0,-1},
|
|||
|
|
{0,0,0,1}};
|
|||
|
|
return projection((Cos(angle)^2,-1,1-Cos(angle)^2),normal=(0,-1,0),
|
|||
|
|
new transformation(triple,triple,triple) { return transformation(t);});
|
|||
|
|
}
|
|||
|
|
projection cavaliereY=cavaliereY();
|
|||
|
|
projection cavaliereXZ=cavaliereY();
|
|||
|
|
|
|||
|
|
projection cavaliereZ(real k=.5, real angle=45)
|
|||
|
|
{
|
|||
|
|
transform3 t={{1,0,-k*Cos(angle),0},
|
|||
|
|
{0,1,-k*Sin(angle),0},
|
|||
|
|
{0,0,1,-1},
|
|||
|
|
{0,0,0,1}};
|
|||
|
|
return projection((Cos(angle)^2,1-Cos(angle)^2,1),up=(0,1,0),normal=(0,0,1),
|
|||
|
|
new transformation(triple,triple,triple) { return transformation(t);});
|
|||
|
|
}
|
|||
|
|
projection cavaliereZ=cavaliereZ();
|
|||
|
|
projection cavaliereXY=cavaliereZ();
|
|||
|
|
|
|||
|
|
|
|||
|
|
//////////////////////////////////////////////////////////////////
|
|||
|
|
///////
|
|||
|
|
/////// Inspir<69>e par la d<>finition de la fonction distance(...)
|
|||
|
|
/////// que l'on trouve dans l'extension geometry,
|
|||
|
|
/////// une fonction qui permet d'indiquer une distance entre deux triples :
|
|||
|
|
///////
|
|||
|
|
//////////////////////////////////////////////////////////////////
|
|||
|
|
|
|||
|
|
void cote3D(picture pic=currentpicture, Label L="", triple A, triple B,
|
|||
|
|
triple v=O, real offset=1cm,
|
|||
|
|
pen p=currentpen, pen joinpen=dotted, arrowbar3 arrow=Arrows3){
|
|||
|
|
triple A=A, B=B, vAB=B-A;
|
|||
|
|
path3 g=A--B;
|
|||
|
|
if(v==O) v=(abs(vAB.x)>abs(vAB.y))? ((abs(vAB.y)>abs(vAB.z))?Z:Y) : ((abs(vAB.x)>abs(vAB.z))?Z:X);
|
|||
|
|
transform3 Tp=shift(offset*v);
|
|||
|
|
pic.add(new void(picture f, transform3 t) {
|
|||
|
|
picture opic;
|
|||
|
|
path3 G=Tp*t*g;
|
|||
|
|
Label L=L.copy();
|
|||
|
|
draw(opic,L,G,p,arrow);
|
|||
|
|
triple Ap=t*A, Bp=t*B;
|
|||
|
|
draw(opic,(Ap--Tp*Ap)^^(Bp--Tp*Bp), joinpen);
|
|||
|
|
add(f,opic);
|
|||
|
|
}, true);
|
|||
|
|
}
|