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đź”—graph-fig022

Figure graph 022 Generated with Asymptote

Show graph/fig0230.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Graph.asy
Tags : #Graph | #Function (drawing) | #Fraction | #Label | #Tex/latex features | #Struct

import graph;
unitsize(x=1cm,y=2cm);

struct rational
{
  int p;
  int q;
  real ep=1/10^5;
};

rational operator init() {return new rational;}

rational rational(real x, real ep=1/10^5)
{
  rational orat;
  int q=1;
  while (abs(round(q*x)-q*x)>ep)
    {
      ++q;
    }
  orat.p=round(q*x);
  orat.q=q;
  orat.ep=ep;
  return orat;
}

int pgcd(int a, int b)
{
  int a_=abs(a), b_=abs(b), r=a_;
  if (b_>a_) {a_=b_; b_=r; r=a_;}
  while (r>0)
    {
      r=a_%b_;
      a_=b_;
      b_=r;
    }
  return a_;
}

string texfrac(int p, int q,
               string factor="",
               bool signin=false, bool factorin=true,
               bool displaystyle=false,
               bool zero=true)
{
  if (p==0) return (zero ? "$0$" : "");
  string disp= displaystyle ? "$\displaystyle " : "$";
  int pgcd=pgcd(p,q);
  int num= round(p/pgcd), den= round(q/pgcd);
  string nums;
  if (num==1)
    if (factor=="" || (!factorin && (den !=1))) nums="1"; else nums="";
  else
    if (num==-1)
      if (factor=="" || (!factorin && (den !=1))) nums="-1"; else nums="-";
    else nums= (string) num;
  if (den==1) return "$" + nums + factor + "$";
  else
    {
      string dens= (den==1) ? "" : (string) den;
      if (signin || num>0)
        if (factorin)
          return disp + "\frac{" + nums + factor + "}{" + (string) dens + "}$";
        else
          return disp + "\frac{" + nums + "}{" + (string) dens + "}"+ factor + "$";
      else
        {
          if (num==-1)
            if (factor=="" || !factorin) nums="1"; else nums="";
          else nums=(string)(abs(num));
        if (factorin)
          return disp + "-\frac{" + nums + factor + "}{" + (string) dens + "}$";
        else
          return disp + "-\frac{" + nums + "}{" + (string) dens + "}"+ factor + "$";
        }
    }
}

string texfrac(rational x,
               string factor="",
               bool signin=false, bool factorin=true,
               bool displaystyle=false,
               bool zero=true)
{
  return texfrac(x.p, x.q, factor, signin, factorin, displaystyle, zero);
}

ticklabel labelfrac(real ep=1/10^5, real factor=1.0,
                    string symbol="",
                    bool signin=false, bool symbolin=true,
                    bool displaystyle=false,
                    bool zero=true)
{
  return new string(real x)
    {
      return texfrac(rational(x/factor), symbol, signin, symbolin, displaystyle, zero);
    };
}

ticklabel labelfrac=labelfrac();

xlimits( -2pi, 2pi);
ylimits( -1, 1);

yaxis("y",LeftRight , Ticks(labelfrac,Step=.5,step=.25, ptick=grey, extend=true));

xaxis("$\theta$",BottomTop, Ticks(labelfrac(factor=pi,symbol="\pi",symbolin=false),
                           Step=pi/2, step=pi/4, ptick=grey, extend=true));

draw(graph(new real(real x){return sin(x);},-2pi,2pi));
draw(graph(new real(real x){return cos(x);},-2pi,2pi), .8red);

đź”—graph-fig023

Figure graph 023 Generated with Asymptote

Show graph/fig0240.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 2D | Graph.asy
Tags : #Graph | #Function (drawing) | #Fraction | #Label | #Tex/latex features | #Struct

import graph;

// public real xunit=1cm,yunit=1cm;

void graphicrules(picture pic=currentpicture, string prefix=defaultfilename, real unit=1cm,
                  real xunit=unit != 0 ? unit : 0,
                  real yunit=unit != 0 ? unit : 0,
                  real xmin, real xmax, real ymin, real ymax)
{
  xlimits(xmin, xmax);
  ylimits(ymin, ymax);
  unitsize(x=xunit, y=yunit);
}

struct rational
{
  int p;
  int q;
  real ep=1/10^5;
};

rational operator init() {return new rational;}

rational rational(real x, real ep=1/10^5)
{
  rational orat;
  int q=1;
  while (abs(round(q*x)-q*x)>ep)
    {
      ++q;
    }
  orat.p=round(q*x);
  orat.q=q;
  orat.ep=ep;
  return orat;
}

int pgcd(int a, int b)
{
  int a_=abs(a), b_=abs(b), r=a_;
  if (b_>a_) {a_=b_; b_=r; r=a_;}
  while (r>0)
    {
      r=a_%b_;
      a_=b_;
      b_=r;
    }
  return a_;
}

string texfrac(int p, int q,
               string factor="",
               bool signin=false, bool factorin=true,
               bool displaystyle=false,
               bool zero=true)
{
  if (p==0) return (zero ? "$0$" : "");
  string disp= displaystyle ? "$\displaystyle " : "$";
  int pgcd=pgcd(p,q);
  int num= round(p/pgcd), den= round(q/pgcd);
  string nums;
  if (num==1)
    if (factor=="" || (!factorin && (den !=1))) nums="1"; else nums="";
  else
    if (num==-1)
      if (factor=="" || (!factorin && (den !=1))) nums="-1"; else nums="-";
    else nums= (string) num;
  if (den==1) return "$" + nums + factor + "$";
  else
    {
      string dens= (den==1) ? "" : (string) den;
      if (signin || num>0)
        if (factorin)
          return disp + "\frac{" + nums + factor + "}{" + (string) dens + "}$";
        else
          return disp + "\frac{" + nums + "}{" + (string) dens + "}"+ factor + "$";
      else
        {
          if (num==-1)
            if (factor=="" || !factorin) nums="1"; else nums="";
          else nums=(string)(abs(num));
          if (factorin)
            return disp + "-\frac{" + nums + factor + "}{" + (string) dens + "}$";
          else
            return disp + "-\frac{" + nums + "}{" + (string) dens + "}"+ factor + "$";
        }
    }
}

string texfrac(rational x,
               string factor="",
               bool signin=false, bool factorin=true,
               bool displaystyle=false,
               bool zero=true)
{
  return texfrac(x.p, x.q, factor, signin, factorin, displaystyle, zero);
}

ticklabel labelfrac(real ep=1/10^5, real factor=1.0,
                    string symbol="",
                    bool signin=false, bool symbolin=true,
                    bool displaystyle=false,
                    bool zero=true)
{
  return new string(real x)
    {
      return texfrac(rational(x/factor), symbol, signin, symbolin, displaystyle, zero);
    };
}

ticklabel labelfrac=labelfrac();

void grid(picture pic=currentpicture,
          real xmin=pic.userMin().x, real xmax=pic.userMax().x,
          real ymin=pic.userMin().y, real ymax=pic.userMax().y,
          real xStep=1, real xstep=.5,
          real yStep=1, real ystep=.5,
          pen pTick=nullpen, pen ptick=grey, bool above=true)
{
  xaxis(pic, BottomTop, xmin, xmax, Ticks("%",extend=true,Step=xStep,step=xstep,pTick=pTick,ptick=ptick), above=above);
  yaxis(pic, LeftRight, ymin, ymax, Ticks("%",extend=true,Step=yStep,step=ystep,pTick=pTick,ptick=ptick), above=above);
}

void cartesianaxis(picture pic=currentpicture,
                   Label Lx=Label("$x$",align=S),
                   Label Ly=Label("$y$",align=W),
                   real xmin=pic.userMin().x, real xmax=pic.userMax().x,
                   real ymin=pic.userMin().y, real ymax=pic.userMax().y,
                   real extrawidth=1, real extraheight=extrawidth,
                   pen p=currentpen,
                   ticks xticks=Ticks("%",pTick=nullpen, ptick=grey),
                   ticks yticks=Ticks("%",pTick=nullpen, ptick=grey),
                   bool above=true,
                   arrowbar arrow=Arrow)
{
  extraheight= cm*extraheight/(2*pic.yunitsize);
  extrawidth = cm*extrawidth/(2*pic.xunitsize);
  yequals(pic, Lx, 0, xmin-extrawidth, xmax+extrawidth, p, above, arrow=arrow);
  yequals(pic, 0, xmin, xmax, p, xticks, above);
  xequals(pic, Ly, 0, ymin-extraheight, ymax+extraheight, p, above, arrow=arrow);
  xequals(pic, 0, ymin, ymax, p, yticks, above);
}

void labeloij(picture pic=currentpicture,
              Label Lo=Label("$O$",NoFill),
              Label Li=Label("$\vec{\imath}$",NoFill),
              Label Lj=Label("$\vec{\jmath}$",NoFill),
              pair diro=SW, pair diri=S, pair dirj=W,
              pen p=scale(2)*currentpen,
              filltype filltype=NoFill, arrowbar arrow=Arrow(2mm))
{
  if (Lo.filltype==NoFill) Lo.filltype=filltype;
  if (Li.filltype==NoFill) Li.filltype=filltype;
  if (Lj.filltype==NoFill) Lj.filltype=filltype;
  labelx(pic, Lo, 0, diro, p);
  draw(pic, Li, (0,0)--(1,0), diri, p, arrow);
  draw(pic, Lj, (0,0)--(0,1), dirj, p, arrow);
  dot(pic, (0,0), dotsize(p)+p);
}

void labeloIJ(picture pic=currentpicture,
              Label Lo=Label("$O$",NoFill),
              Label LI=Label("$I$",NoFill),
              Label LJ=Label("$J$",NoFill),
              pair diro=SW, pair dirI=S, pair dirJ=W,
              pen p=currentpen,
              filltype filltype=NoFill, arrowbar arrow=Arrow)
{
  if (Lo.filltype==NoFill) Lo.filltype=filltype;
  if (LI.filltype==NoFill) LI.filltype=filltype;
  if (LJ.filltype==NoFill) LJ.filltype=filltype;
  labelx(pic, LI, 1, dirI, p);
  labely(pic, LJ, 1, dirJ, p);
  labelx(pic, Lo, 0, diro, p);
  dot(pic, (0,0), dotsize(p)+p);
}

graphicrules(xunit=1cm, yunit=3cm,
             xmin=-2pi, xmax=2pi, ymin=-1, ymax=1);
grid(xStep=pi/2, xstep=pi/4, yStep=.5, ystep=.25);
cartesianaxis(xticks=Ticks(Label(UnFill),labelfrac(factor=pi,symbol="\pi",symbolin=true, zero=false),Step=pi/2, step=pi/4, ptick=grey),
              yticks=Ticks(Label(UnFill),labelfrac(zero=false),Step=.5,step=.25, ptick=grey), arrow=None);
dot("$O$",(0,0),2SW);

đź”—randomwalk-fig002

Figure randomwalk 002 Generated with Asymptote

Show randomwalk/fig0020.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Surveys | Random Walk (3D)
Tags : #Random | #Struct

import three;
settings.render=0;

// The available directions of steps
triple[] dirs={X,-X,Y,-Y,Z,-Z};
dirs.cyclic=true;

struct walk
{
  triple[] nodes;
  pen[] p;
}

// Comput the nodes of the path
walk randWalk(real Srnd(), int n, pen[] p={currentpen})
{
  p.cyclic=true;
  walk ow;
  triple pos=O, tpos;
  for (int i=0; i < n; ++i) {
    int R=round(Srnd());
    tpos=pos+dirs[R];
    ow.nodes.push(tpos);
    ow.p.push(p[R]);
    pos=tpos;
  }
  return ow;
}

walk randWalk(int Srnd(), int n, pen[] p={currentpen})
{
  real R(){ return Srnd();}
  return randWalk(R,n,p);
}

void drawWalk(walk walk)
{
  triple camera=currentprojection.camera;
  if(currentprojection.infinity)
    camera *= max(abs(minbound(walk.nodes)),abs(maxbound(walk.nodes)));
  real[][] depth;
  for(int i=0; i < walk.nodes.length-1; ++i) {
    real d=abs(camera-0.5*(walk.nodes[i]+walk.nodes[i+1]));
    depth.push(new real[] {d,i});
  }
  depth=sort(depth);
  triple M=walk.nodes[round(depth[0][1])];
  triple m=walk.nodes[round(depth[depth.length-1][1]+1)];
  // Draw from farthest to nearest
  while(depth.length > 0) {
    real[] a=depth.pop();
    int i=round(a[1]);
    // dot(walk.nodes[i],walk.p[i]);
    draw(walk.nodes[i]--walk.nodes[i+1],abs(walk.nodes[i]-m)/abs(M-m)*(walk.p[i]+walk.p[i+1]));
  }
}


size(18cm);
currentprojection=orthographic((0.5,0.5,1));

drawWalk(randWalk(rand,50000,new pen[]{red, blue, green, yellow, purple}));
shipout(bbox(3mm,Fill));

đź”—various-fig003

Figure various 003 Generated with Asymptote

Show various/fig0300.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Miscellaneous
Tags : #Struct

// On définit ce qu'est l'objet 'rectangle'
// On peut comparer ça à la définition d'une voiture:
// elle a des propriètés: la couleur, le nombre de portes...
// elle a aussi des actions (ou méthodes en info): ouvrir la porte, tourner le volant, avancer...
struct rectangle
{
  pair A,B,C,D; // Ce sont des propriétés (au sens informatique): ses sommets.
  path path(){return A--B--C--D--cycle;} // Ceci est une action du rectangle (renvoyer le chemin du rectangle)
};

// Le constructeur de l'objet (une action qui renvoie l'objet).
// Chaque fois que l'on va définir une variable 'X' de type 'rectangle'
// c'est le retour de l'action rectangle.init qui est affecté à X.
rectangle operator init() {return new rectangle;}

// La fonction rectangle  qui prend en argument le coin inférieur gauche
// et le coin supérieur droit retourne un rectangle.
// On notera comment l'on récupére une propriété ou une action d'un
// objet grâce au '.' en écrivant objet.propriété ou
// objet.action(les_paramètres).
rectangle rectangle(pair gb, pair dh)
{
  rectangle retour;
  retour.A=(dh.x,gb.y);
  retour.B=dh;
  retour.C=(gb.x,dh.y);
  retour.D=gb;
  return retour;
}

// On peut alors définir tous les opérateurs que l'on veut sur les
// rectangles.
// par exemple la multiplication d'un réal par un rectangle (x*rectangle):
rectangle operator *(real x, rectangle rectangle)
{
  rectangle retour;
  retour.A=rectangle.A+x*(rectangle.B-rectangle.A);
  retour.B=rectangle.B+x*(rectangle.C-rectangle.B);
  retour.C=rectangle.C+x*(rectangle.D-rectangle.C);
  retour.D=rectangle.D+x*(rectangle.A-rectangle.D);
  return retour;
}

// Ici, cette opération est commutative (rectangle*x=x*rectangle):
rectangle operator *(rectangle rectangle,real x){return x*rectangle;}

// On dit ici comment "Asymptote" doit convertir, si besoin est, un type 'rectangle'
// en 'path' puis en 'path[]' (tableau de 'path').
path operator cast(rectangle rectangle){return rectangle.path();}
path[] operator cast(rectangle rectangle){return rectangle.path();}
//Par exemple, dans le code:
/*
  rectangle SQ=rectangle((0,0), (1,1));
  draw(SQ);
*/
// 'draw' attend un type 'path' donc 'SQ' sera automatiquement converti.


// Maintenant on peut travailler avec cette structure
size(10cm);
rectangle SQ=rectangle((0,0), (1,1));
pen [] col= new pen[]{gray,yellow};

int nb=10;
for (int i=0; i<nb; ++i) {
  filldraw(SQ,col[i%2]);
  SQ=.25*SQ;
 }

This page was generated by the Asymptote Exemples Builder
Last modified the 2025-04-20 12:26:19
©2011 Philippe Ivaldi

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