boolean showVertexIds=false, showVertices=false;
 boolean showLinear=false, showSpiral=true, showCircles=false, animate=false, showFrames=true;
float tt=0;
 void myActions() { // actions to be executed at each frame
   if ((mousePressed)&&(!keyPressed)) editPolygon(); // edit points
    if ((mousePressed)&&(mouse().isInWindow())&&(keyPressed)) {
         if (key=='z') scaleBy(1.- d(screenCenter(),Mouse()) / d(screenCenter(),Pmouse()) );
         if (key=='r') rotateBy( angle( V(screenCenter(),Mouse()) , V(screenCenter(),Pmouse()) ) );
         if (key=='t') translateBy(MouseDrag());
         }
    pt A=P[0]; pt B=P[1]; pt C=P[2]; pt D=P[3]; pt E=P[4];
    EDGE AB=E(A,B);  EDGE DE=E(D,E);
    pt c=AB.grab(C); pt F=P[5]; F.setTo(DE.put(c)); 
    fill(black); A.showLabel("A");  B.showLabel("B");  C.showLabel("C");  D.showLabel("D"); E.showLabel("E"); noFill();
    strokeWeight(1); stroke(dgreen); B.to(C); C.to(A); stroke(dblue); E.to(F); F.to(D); 
    strokeWeight(3); stroke(dgreen); AB.show(); stroke(dblue); DE.show(); strokeWeight(1);  
    if(showFrames) {
     float dt=0.1;
     if(showLinear) {stroke(magenta);  for(float t=0; t<=1; t+=dt) {EDGE PQ=Slinear(AB,t,DE); PQ.show(c);};};
      if(showSpiral) {stroke(red);   for(float t=0; t<=1.01; t+=dt) {EDGE PQ=Sspiral(AB,t,DE); PQ.show(c);};};
      };
    if(animate) {strokeWeight(2);
      tt+=0.01; if(tt>1) tt=0;
      if(showLinear) {stroke(magenta);  EDGE PQ=Slinear(AB,tt,DE); PQ.show(c);};
      if(showSpiral) {stroke(red);   EDGE PQ=Sspiral(AB,tt,DE); PQ.show(c);};
      strokeWeight(1);};
    String S="File: P"+Format0(fn,2)+" out of "+Format0(maxfn,2)+". Using"; 
    if (showLinear) S=S+" linear"; if (showLinear&&showSpiral) S=S+" and "; if (showSpiral) S=S+" spiral"; 
    scribe(S);                
    };

EDGE E(pt A, pt B) {return new EDGE(A,B); }
class EDGE {
  pt A=P(); pt B=P();
  vec Vec() {return V(A,B);}
  float n2() {return dot(V(A,B),V(A,B));}
  float n() {return d(A,B);}
  EDGE(pt P, pt Q) {A.setTo(P); B.setTo(Q);};
  void show() {A.show(2); A.to(B);}
  void show(pt c) {pt C=put(c); A.show(2); A.to(B); B.to(C); C.to(A);}
  pt grab(pt C) {return P(dot(V(A,C),V(A,B))/n2(),dot(V(A,C),R(V(A,B)))/n2() );}
  pt put(pt C) {return S(S(A,C.x,V(A,B)),C.y,R(V(A,B))); }
  }
EDGE Slinear(EDGE E0, float t, EDGE E1) {return E(S(E0.A,t,E1.A),S(E0.B,t,E1.B));}
EDGE Sspiral(EDGE E0, float t, EDGE E1) {
   float a = a(E0.Vec(),E1.Vec());
   float s = E1.n() / E0.n();
   pt C1=circleCenterForAngle(E0.A,E1.A,a); float r1=d(C1,E0.A); 
   pt C2=circleCenterForAngle(E0.B,E1.B,a); float r2=d(C2,E0.B); 
   pt Gr = CCr(C1,r1,C2,r2); 
   pt Gl = CCl(C1,r1,C2,r2); 
   pt G=Gl;  if (abs(s-d(Gr,E1.A)/d(Gr,E0.A))<abs(s-d(Gl,E1.A)/d(Gl,E0.A))) G=Gr;
   pt M = S(G,1+t*(s-1),R(E0.A,t*a,G)); 
   pt N = S(G,1+t*(s-1),R(E0.B,t*a,G));  
   if (showCircles) {stroke(orange); C1.show(r1); C2.show(r2);G.show(2); stroke(red);}
  return E(M,N);
  }

pt circleCenterForAngle(pt A, pt B, float a) {                   // computes center of the circle of points C such that angle(A,C,B)=a
   pt M = M(A,B); float d=d(A,B)/2; float h=d*tan(PI/2.-a); vec V=R(S(h,U(V(A,B))));  return S(M,V); }

pt CCl(pt C1, float r1, pt C2, float r2) { // computes  the intersection of two circles that is on the left of (C1,C2)
   float d=d(C1,C2);
   float d1=(sq(r1)-sq(r2)+sq(d))/(d*2);
   float h=sqrt(sq(r1)-sq(d1));
   return T(T(C1,d1,C2),-h,R(V(C1,C2)));}
   
pt CCr(pt C1, float r1, pt C2, float r2) { // computes  the intersection of two circles that is on the right of (C1,C2)
   float d=d(C1,C2);
   float d1=(sq(r1)-sq(r2)+sq(d))/(d*2);
   float h=sqrt(sq(r1)-sq(d1));
   return T(T(C1,d1,C2),h,R(V(C1,C2)));}