28 Aug 2007

## Asymptote using graph.asy – fig0240

 (Compiled with Asymptote version 1.84svn-r4619)

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);



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