float tolerance = 10;

void myActions() { // actions to be executed at each frame
    scribe("DEREK TATUM mod of [Jarek Rossignac's edge / edge intersection (general position)]");         // prints text at top of the graphic window (see TAB UI), line 0
    if ((mousePressed)&&(!keyPressed)) dragPoint();    // while mouse pressed moves the selected point by mouse displacement (in TAB polygon)
    fill(black);              // set fill color to black (for writing text in the windows)
    strokeWeight(3);          // set stroke width to 3
    stroke(green);             // set current color to blue
    pt A=P[0]; A.show(2); A.showLabel("A");  // Assign variable point A to P[0], show it as a disk of radius 4, write its label "A" next to it
    pt B=P[1]; B.show(2); B.showLabel("B"); 
    pt C=P[2]; C.show(2); C.showLabel("C");     
    A.to(B);                                // draw a line from A to B in current color (see TAB geo2D, end of class pt)
    B.to(C); 
    C.to(A); 
    stroke(blue);
    pt D=P[3]; D.show(2); D.showLabel("D");
    pt E=P[4]; E.show(2); E.showLabel("E");
    D.to(E);
    stroke(orange);
    //showEdgeEdgeIntersection(A,B,C,D,E);      // WHERE THE ACTUAL INTERSECTION IS COMPUTED AND DISPLAYED (see below)
    fill(black);     
    int count = 0;
    //pt P, Q;
    pt P = P(0,0);
    pt Q = P(0,0);
/////////////////////////////////////
    if (edgesCross(A,B,D,E)) {
      P = computeIntersectionPoint(A,B,D,E);
      stroke(orange);
      P.show(2);
      count++;
    }
    if (edgesCross(B,C,D,E)) {
      if (count==1){
        Q = computeIntersectionPoint(B,C,D,E);
        stroke(orange);
        Q.show(2);
      }
      else {
        P = computeIntersectionPoint(B,C,D,E);
        stroke(orange);
        P.show(2);
      }
      count++;
    }
    if (edgesCross(C,A,D,E)) {
      if (count==1){
        Q = computeIntersectionPoint(C,A,D,E);
        stroke(orange);
        Q.show(2);
      }
      else {
        P = computeIntersectionPoint(C,A,D,E);
        stroke(orange);
        P.show(2);
      }
      count++;
    }
    
//////////////////////////    
    if(count==0){
      if (PinT(A,B,C,D)&&PinT(A,B,C,E)){
        stroke(red);
        D.to(E);
        D.show(2);
        E.show(2);
        //line(D.x,D.y,E.x,E.y);
      }
    }//DONE with count==0
/////////////////////////////////////
    if (count==1){
       stroke(red);
       if (PinT(A,B,C,D)){
          D.to(P);
          D.show(2);
        }
       if (PinT(A,B,C,E)){
          E.to(P);
          E.show(2);
        }
    }//DONE with count==1
///////////////////////////////////
    if (count==2){
      stroke(red);
      P.to(Q);
    }//DONE with count==2
    toleranceImplementation(A,B,C,D,E,P,Q);
    };
///////////////////////////////////////////
void toleranceImplementation(pt A, pt B, pt C, pt D, pt E, pt P, pt Q) { // show intersection point between two edges if it exists
  if (PinE(A,B,P)||PinE(A,C,P)||PinE(B,C,P)) {
    stroke(orange);
    P.show(4);
  }
  if (PinE(A,B,Q)||PinE(A,C,Q)||PinE(B,C,Q)) {
    stroke(orange);
    Q.show(4);
  }
  
  if (PinE(A,B,D)||PinE(A,C,D)||PinE(B,C,D)) {
    stroke(cyan);
    D.show(4);
  }
  if (PinE(A,B,E)||PinE(A,C,E)||PinE(B,C,E)) {
    stroke(cyan);
    E.show(4);
  }    
    
}

//from slide 25 of geometry2D.ppt
pt computeIntersectionPoint(pt A, pt B, pt D, pt E) {  // compute intersection point P (between edges AB and DE)
  pt S = A.clone();  // = new pt(A.x, A.y);
  vec T = V(A,B);
  vec QS = V(D,A);
  vec N = R(V(D,E));
  float t = -(dot(QS,N))/dot(T,N);
   //pt makeTranslatedBy(float s, vec V) {return(new pt(x + s*V.x, y + s*V.y));}; 
  pt P = S.makeTranslatedBy(t,T);
  return P;
}
boolean ordered(pt A, pt B, pt C){return (0<dot(V(A,B),V(A,C))) && (dot(V(A,B),V(A,C))<dot(V(A,C),V(A,C))); }  // tests whether B falls between A and C
boolean right1(pt A,pt B,pt C) {return (dot(R(V(A,B)),V(A,C))>0); }
boolean edgesCross(pt A, pt B, pt C, pt D) {return (dot(U(R(V(A,B))),V(A,C))>0 != dot(U(R(V(A,B))),V(A,D))>0) // tests whether two edges cross
                                                && (dot(U(R(V(C,D))),V(C,A))>0 != dot(U(R(V(C,D))),V(C,B))>0) ; }   
//boolean MYedgesCross(pt A, pt B, pt C, pt D, pt E) {return (dot(U(R(V(A,B))),V(A,D))>0 != dot(U(R(V(A,B))),V(A,E))>0) // tests whether two edges cross
                                               // && (dot(U(R(V(D,E))),V(D,A))>0 != dot(U(R(V(D,E))),V(D,B))>0) ; }
boolean PinT(pt A,pt B,pt C,pt P) {return (right1(A,B,P)== right1(B,C,P)) && (right1(A,B,P)== right1(C,A,P)) ;}
boolean PinE(pt A,pt B,pt C) {  // is C on AB?
  vec U=V(A,B);
  return (
(abs(dot(R(U.makeUnit()),V(A,C))) < tolerance) &&  //makeUnit normalizes U
(0 < dot(V(A,B),V(A,C))) &&
(dot(V(A,B),V(A,C)) < dot(V(A,B),V(A,B)))
) 
; }
///
/*
boolean PinEOLD(pt A,pt B,pt C) {  // is C on AB?
  return (
dot(R(V(A,B)),V(A,C))==0&& 
(0 < dot(V(A,B),V(A,C))) &&
(dot(V(A,B),V(A,C)) < dot(V(A,B),V(A,B)))
) 
; }
*/
//boolean edgesCross(pt A, pt B, pt C, pt D) {return (dot(U(R(V(A,B))),V(A,C))>0 != dot(U(R(V(A,B))),V(A,D))>0) // tests whether two edges cross
                                                //&& (dot(U(R(V(C,D))),V(C,A))>0 != dot(U(R(V(C,D))),V(C,B))>0) ; }                                                
  //boolean edgesCross(pt A, pt B, pt C, pt D, pt E) {return true;}