// Graphique pour les Sciences, avec barres d'erreur
import graph;

size(8cm,6cm);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(f,df,red);
draw(graph(f),"L\'egende",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

legendmargin=5;
attach(legend(),point(N),5N);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

// Graphique pour les Sciences, avec barres d'erreur
import graph;

size(8cm,6cm,IgnoreAspect);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(f,df,red);
draw(graph(f),"L\'egende",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

legendmargin=5;
attach(legend(),point(S),30S);

// Graphique pour les Sciences, avec barres d'erreur
import graph;

size(8cm,6cm,IgnoreAspect);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(f,df,red);
draw(graph(f),"L\'egende",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

scale(true);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

legendmargin=5;
attach(legend(),point(S),30S);

// Graphique pour les Sciences, avec barres d'erreur
import graph;

size(8cm,6cm);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(f,df,red);
draw(graph(f),"L\'egende",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

scale(true);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

legendmargin=5;
attach(legend(),point(S),30S);

// Graphique pour les Sciences, avec barres d'erreur
import graph;

size(8cm,6cm);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(f,df,red);
draw(graph(f),"L\'egende",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

scale(true);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);

legendmargin=5;
pair p1=point(S), p2=truepoint(S);
attach(legend(red),(p1.x,p2.y),10S);
attach(legend(blue),p2,10S);

// Graphique pour les Sciences, avec barres d'erreur
import graph;

picture pic;
real xsize=8cm, ysize=6cm;
size(pic,xsize,ysize,IgnoreAspect);

pair[] f={(5,4),(40,10),(50,20),(90,40)};
pair[] df={(0,0),(2,0),(5,7),(0,5)};

errorbars(pic,f,df,red);
draw(pic,graph(pic,f),"legend",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

scale(pic,true);

xaxis(pic,"$x$",BottomTop,LeftTicks);
yaxis(pic,"$y$",LeftRight,RightTicks);
legendmargin=5;
add(pic,legend(pic),point(pic,NW),20SE,UnFill);

picture pic2;
size(pic2,xsize,ysize,IgnoreAspect);

frame mark;
filldraw(mark,scale(0.8mm)*polygon(6),green,green);
draw(mark,scale(0.8mm)*cross(6),blue);

draw(pic2,graph(pic2,f),marker(mark,markuniform(5)));

scale(pic2,true);

xaxis(pic2,"$x$",BottomTop,LeftTicks);
yaxis(pic2,"$y$",LeftRight,RightTicks);

xequals(pic2,60.0,green+Dotted);
yequals(pic2,25.0,green+Dotted);

add(pic.fit(),(0,0),N);
add(pic2.fit(),(0,-.5cm),S);

import geometry;
size(7.5cm,0);

// Affichage du repère par défaut (O,vec{i},vec_{j})
show(defaultcoordsys);

real a=5, b=4, theta=-27, poids=3;
ellipse el = ellipse(origin, a, b);
arc     ar = arc(el,(0,-b),(a,0),CCW);
path p = (0,-b-1)--ar--(a+1,0)--(a+1,-b-1)--cycle;
point pO = (0,0), pM=angpoint(ar,90+theta);
abscissa abscM = nodabscissa(el,pM);
real     timeM = abscM.x;
vector utangM = -dir(el,timeM), 
       unormM = rotate(90)*utangM,
       vpoids=(0,-poids),
       vreactionN = -dot(vpoids,unormM)*unormM,
       vfrottement = -dot(vpoids,utangM)*utangM;

filldraw(p,lightgray,blue);
draw(pO--pM,dashed);
markangle("$\theta$",1.5cm,pM,origin,(1,0));

// Affichage d'un nouveau repère (M,vec{u_{\theta}},vec_{u_{r}})
coordsys R=cartesiansystem(pM,i=utangM,j=unormM);
show("$M$", "$\vec{u_{\theta}}$", "$\vec{u_{r}}$", R, xpen=invisible);

// Affichage des trois vecteurs dans le repère R
point RpM=changecoordsys(R, pM);
show(Label("$\vec{f}$",EndPoint),RpM+vfrottement);
show(Label("$\vec{R}$",EndPoint),RpM+vreactionN);
show(Label("$\vec{P}$",EndPoint),RpM+vpoids);

import geometry;
size(7.5cm,0);

// Affichage du repère par défaut (O,vec{i},vec_{j})
show(defaultcoordsys);

real a=5, b=4, theta=-70, poids=3;
ellipse el = ellipse(origin, a, b);
arc     ar = arc(el,(0,-b),(a,0),CCW);
path p = (0,-b-1)--ar--(a+1,0)--(a+1,-b-1)--cycle;
point pO = (0,0), pM=angpoint(ar,90+theta);
abscissa abscM = nodabscissa(el,pM);
real     timeM = abscM.x;
vector utangM = -dir(el,timeM), 
       unormM = rotate(90)*utangM,
       vpoids=(0,-poids),
       vreactionN = -dot(vpoids,unormM)*unormM,
       vfrottement = -dot(vpoids,utangM)*utangM;

filldraw(p,lightgray,blue);
draw(pO--pM,dashed);
markangle("$\theta$",1.5cm,pM,origin,(1,0));

// Affichage d'un nouveau repère (M,vec{u_{\theta}},vec_{u_{r}})
coordsys R=cartesiansystem(pM,i=utangM,j=unormM);
show("$M$", "$\vec{u_{\theta}}$", "$\vec{u_{r}}$", R, xpen=invisible);

// Affichage des trois vecteurs dans le repère R
point RpM=changecoordsys(R, pM);
show(Label("$\vec{f}$",EndPoint),RpM+vfrottement);
show(Label("$\vec{R}$",EndPoint),RpM+vreactionN);
show(Label("$\vec{P}$",EndPoint),RpM+vpoids);

import graph3;
import palette;

size(8cm,0);
currentprojection=perspective(camera=(5,2,8),up=Y);

pen[] couleur={paleblue,white};

real c=1; // demi-distance focale
int  n=4; // nombre d'hyperboloïdes
real vx=2,
     vy=vx; 

for(int i=0; i<n; ++i){
  real d=(i+1)*c/(n+1);
  real a=sqrt(c^2-d^2);
  real f(pair z) {return d*sqrt(abs(z)^2/a^2+1);}
  surface s=surface(f,(-vx,-vy),(vx,vy),4,4,Spline);
  draw(s,couleur[i%couleur.length]);
  draw(rotate(180,X)*s,couleur[i%couleur.length]);

  real x(real t) {return 2;}
  real y(real t) {return t;}
  real z(real t) {return d*sqrt(1+(t^2+vx^2)/a^2);}
  path3 p=graph(x,y,z,-vy,vy,operator ..);
  draw(p^^rotate(180,X)*p,red);
}
path3 pl0=(vx,vy,0)--(vx,-vy,0)--(-vx,-vy,0)--(-vx,vy,0)--cycle;
draw(surface(pl0),white);
draw((vx,-vy,0)--(vx,vy,0),orange);

dot((0,0,c),red);
dot((0,0,-c),red);

path3 pl=(0,vy+1,1.8vx)--(0,vy+1,-1.8vx)
          --(0,-vy-1,-1.8vx)--(0,-vy-1,1.8vx)--cycle;
surface plan=surface(pl);                 
draw(plan,lightgrey,.8blue);
draw(shift(vx,0,0)*plan,lightgrey+opacity(.8),.8blue);

limits((-vx-2,-vy-2,-vx),(vx+2,vy+2,vx+3));
xaxis3("$x$",Arrow3);
yaxis3("$y$",Arrow3);

shipout(bbox(2mm,Fill(white)));

import graph3;
import palette;

size(8cm);
currentprojection=perspective(camera=(5,4,-5),up=Y);
currentlight=nolight;

pen[] couleur={orange,red};

real c=1; // demi-distance focale
int  n=4; // nombre d'hyperboloïdes
real vx=1.5,
     vy=vx; 

for(int i=0; i<n; ++i){
  real d=(i+1)*c/(n+1);
  real a=sqrt(c^2-d^2);
  real f(pair z) {return d*sqrt(abs(z)^2/a^2+1);}
  surface s=surface(f,(0,-vy),(vx,vy),4,4,Spline);
  draw(s,couleur[i%couleur.length]);
  draw(rotate(180,X)*s,couleur[i%couleur.length]);

  real x(real t) {return vx;}
  real y(real t) {return t;}
  real z(real t) {return d*sqrt(1+(t^2+vx^2)/a^2);}
  path3 p=graph(x,y,z,-vy,vy,operator ..);
  draw(p^^rotate(180,X)*p,blue);
}
path3 pl0=(vx,vy,0)--(vx,-vy,0)--(0,-vy,0)--(0,vy,0)--cycle;
draw(surface(pl0),red);
draw((vx,-vy,0)--(vx,vy,0),blue);

dot((0,0,c),red);
dot((0,0,-c),red);

path3 pl=(0,vy,1.8vx)--(0,vy,-1.8vx)
          --(0,-vy,-1.8vx)--(0,-vy,1.8vx)--cycle;
surface plan=surface(pl);                 
draw(plan,grey);
draw(shift(vx,0,0)*plan,lightgrey+opacity(.8),.8blue);

limits((-.5vx,-1.5vy,-vx),(1.5vx,1.3vy,vx));
xaxis3("$x$",Arrow3);
yaxis3("$y$",Arrow3);