22 Nov 2007

## Animation with Asymptote – fig0100

Category: Animation,Asymptote

 (Compiled with Asymptote version 1.86svn-r4626)
Movie flash (swf)
This animation is available in the Syracuse web site.
```
import animation;
import graph;

settings.tex="pdflatex";
settings.outformat="pdf";

unitsize(x=2cm,y=1.5cm);

typedef real realfcn(real);

real lambda=4;
real T=2;
real [] k=new real[3];
real [] w=new real[3];
k[0]=2pi/lambda;
w[0]=2pi/T;
real dk=-.5;
k[1]=k[0]-dk;
k[2]=k[0]+dk;
real dw=1;
w[1]=w[0]-dw;
w[2]=w[0]+dw;

real vp=w[1]/k[1];
real vg=dw/dk;

realfcn F(real x) {
return new real(real t) {
return cos(k[1]*x-w[1]*t)+cos(k[2]*x-w[2]*t);
};
};

realfcn G(real x) {
return new real(real t) {
return 2*cos(0.5*(k[2]-k[1])*x+0.5*(w[1]-w[2])*t);
};
};

realfcn operator -(realfcn f) {return new real(real t) {return -f(t);};};

animation A;

real tmax=abs(2pi/dk);
real xmax=abs(2pi/dw);

pen envelope=0.8*blue;
pen fillpen=lightgrey;

int n=50;
real step=tmax/(n-1);
for(int i=0; i < n; ++i) {
save();
real t=i*step;
real a=xmax*t/tmax-xmax/pi;
real b=xmax*t/tmax;
path f=graph(F(t),a,b);
path g=graph(G(t),a,b);
path h=graph(-G(t),a,b);
fill(buildcycle(reverse(f),g),fillpen);
draw(f);
draw(g,envelope);
draw(h,envelope);
restore();
}

for(int i=0; i < n; ++i) {
save();
real t=i*step;
real a=-xmax/pi;
real b=xmax;
path f=graph(F(t),a,b);
path g=graph(G(t),a,b);
path h=graph(-G(t),a,b);
path B=box((-xmax/pi,-2),(xmax,2));
fill(buildcycle(reverse(f),g,B),fillpen);
fill(buildcycle(f,g,reverse(B)),fillpen);
draw(f);
draw(g,envelope);
draw(h,envelope);