// Author : Philippe Ivaldi // http://www.piprime.fr/ // 2006/11/10 import animation; import graph; 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); A.add(); 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); A.add(); restore(); } A.movie(0,10);