/*<asyxml>syracuse</asyxml>*/
// From an idea posted by Fabrice Couvreur
import geometry_dev;
import animate;
settings.tex="pdflatex";
settings.outformat="pdf";

point A=(0,0), B=(8,0), C=(8,10);
unitsize(5cm/B.x,5cm/C.y);
animation Anim,Anim1;
path locus;

triangle t=triangle(A,B,C);
transform proj=projection(t.BC);
draw(t,linewidth(bp));
label(t);
segment s=segment(t.AB);
line l1 =line(t.BC);

int n=50; // Points number of the locus
real a=0, step=1/(n-1);
for (int i=0; i < n; ++i) {
  save(); // Geometry part
  point M=point(s,a);
  line l2=parallel(M,l1);
  point Np=intersectionpoint(l2,t.AC);
  point P=proj*Np;
  dot("$M$",M,S,0.8*red);
  dot("$P$",P,E,0.8*red);
  dot("$N$",Np,W,0.8*red);
  fill(M--Np--P--B--cycle,0.8*red);
  perpendicularmark(t.BC,t.BA);
  Anim.add(); // Anim contain only the geometry part
  restore();
  // Graph part
  picture gph; // picture of the graph
  unitsize(gph,5cm/B.x,4cm/C.y); // units for the graph
  show(gph,currentcoordsys);
  point Sp=(a*abs(B-A),abs(M-B)*abs(M-Np));
  locus=locus..Sp;
  draw(gph,locus, bp+0.8*red);
  Anim1.add(gph); // Anim1 contain only the graph part
  a += step;
}

Anim1.export(); // make all Anim1 pictures to the same size.
Anim1.purge();

for (int i=0; i < Anim.pictures.length; ++i) {
  // draw axis on all pictures of Anim1
  draw(Anim1.pictures[i],Label("$x$",align=S,position=EndPoint),hline,Arrow);
  draw(Anim1.pictures[i],Label("$y$",align=W,position=EndPoint),vline,Arrow);
  // add each graph to the corresponding geometric picture
  add(Anim.pictures[i],Anim1.pictures[i].fit(),1.25*B);
}

Anim.movie();