class car {              // cars
 float h=30, w=100;                       // car dimensions
// float h=15, w=30;                       // car dimensions
//  float h=30, w=70;                       // car dimensions
  color col=color(20,60,30,30);             // color of car
  pt B=new pt(0,0), F=new pt(w,0);         // front and back points (centers of disks)
  float speed = 1;                        // speed of car (user adjusted)
  float a=0.0;                             // angle of car orientation wrt I vector
  boolean picked = false;                  // true if car being dragged
  boolean pickedSpeed = false;             // true if speed being adjusted
  car() {};
  car (float px, float py, float pa, color pc) 
      {B.x=px; B.y=py; 
      a=pa; a=roll(a);
      col=pc; 
      F.x=px+w; F.y=py; F.turnAround(B,-a);}     // creation
  car clone () {return(new car (B.x,B.y,a,col));}     // creation       
  void setFrom (car C) 
      {B.x=C.B.x; B.y=C.B.y; 
      a=C.a; 
      col=C.col; 
      F.x=B.x+w; F.y=B.y; F.turnAround(B,-a);
      }     // creation
 
   void paint() {pushMatrix(); translate(B.x,B.y); rotate(a);              // paints car
      noStroke(); fill(col);  ellipse(0,0,h,h); 
      beginShape(); vertex(0,h/2); vertex(w,0); vertex(0,-h/2); endShape(CLOSE);
      popMatrix(); }    
  
  boolean selected() {boolean pic = F.vecTo(mouse()).norm()<w/5; picked=pic; return(pic); }  // returns true and sets picked if mouse-clicked on car
  
  void write() {println("Car: a="+a); print(". B="); B.write(); print(". F="); F.write(); }

  void track() {    // drag the picked car to follow mouse
    pt M=mouse();   
    vec FB = F.vecTo(B); float fb = FB.norm(); vec MB = M.vecTo(B); float mb = MB.norm();
    if (mb<0.0001) {F.setTo(M); B.addVec(FB); } else {F.setTo(M); M.addScaledVec(fb/mb,MB); B.setTo(M); };
    a=angle(I,B.vecTo(F)); 
    }
 
   
 void paintDots() {if (!picked) { F.show(20); }; }; // paints disk in the car front

 vec velocity() {vec BF=B.vecTo(F); BF.unit(); return(BF); };

 void interpolateLinear (car P, float s, car Q) {// performs linear interpolation
    B.interpolate(P.B,s,Q.B);
    a=P.a+s*(Q.a-P.a); 
    F.turnAround(B,-a);
    P.B.showLineTo(Q.B);
    } 

 void interpolateTwist (car P, float s, car Q) {  // Interpolation through pure rotation
     vec U = P.velocity(); U.unit();
     vec V = Q.velocity(); V.unit();
     float b=angle(U,V);
     b=roll(Q.a-P.a); 
     pt M = midPt(P.B,Q.B);   
     float d=P.B.disTo(Q.B);
     float h = 0; if (abs(b)>=0.0001) h=d/2/tan(b/2); 
     vec W = P.B.vecTo(Q.B); W.unit();
     vec L = W.left();   L.mul(h);
     M.addVec(L);  // fill(0); M.show(6);
     L.back();  L.unit(); 
     if (abs(h)>=0.0001) h=d/2/tan(b/2); L.mul(abs(h+sq(d)/4/h)); 
     pt N = M.make(); N.addVec(L);  
     pt O = new pt(width/2,height/2);
     B.setTo(P.B);
     B.turnAround(M,-s*b);
     a=P.a+s*b; a=roll(a);
     F.turnAround(B,a);
     } 

 void interpolateBezier (car P, float s, car Q) { // performs bezier interpolation
     pt P1=P.B.make(); pt P2=P1.make();  P2.addVec(P.velocity()); 
     pt P4=Q.B.make();  pt P3=P4.make();  P3.subVec(Q.velocity()); 
     stroke(50,60,40); beginShape(); P1.vert(); P2.vert(); P3.vert(); P4.vert(); endShape();
     stroke(20,60,40); bezier(P1.x, P1.y, P2.x, P2.y, P3.x, P3.y, P4.x, P4.y);
     B.setTo(bezier(P1,P2,P3,P4,s));  
     a=bezierAngle(P1,P2,P3,P4,s); 
     F.turnAround(B,-a);
     } 
     
  }     
  
 void drawTwist (car P, car Q) {  // Interpolation through pure rotation
     vec U = P.velocity(); U.unit();
     vec V = Q.velocity(); V.unit();
     float b=angle(U,V);
     b=roll(Q.a-P.a);
     pt M = midPt(P.B,Q.B);   
     float d=P.B.disTo(Q.B);
    float h = 0; if (abs(b)>=0.0001) h = d/2/tan(b/2);
     vec W = P.B.vecTo(Q.B); W.unit();
     vec L = W.left();   L.mul(h);
     M.addVec(L);  
     L.back();  L.unit(); 
     if (abs(h)>0.001) L.mul(abs(h+sq(d)/4/h)); 
     pt N = M.make(); N.addVec(L); drawArc(P.B,N,Q.B,2); 
     } 

 car interpolate (car P, float s, car Q) {  // Interpolation through pure rotation
     vec U = P.velocity(); U.unit();
     vec V = Q.velocity(); V.unit();
     float b=angle(U,V);
     b=roll(Q.a-P.a);
     pt M = midPt(P.B,Q.B);   
     float d=P.B.disTo(Q.B);
     float h = d/2/tan(b/2);
     vec W = P.B.vecTo(Q.B); W.unit();
     vec L = W.left();   L.mul(h);
     M.addVec(L);  // fill(0); M.show(6);
     L.back();  L.unit(); 
     L.mul(abs(h+sq(d)/4/h)); 
     pt N = M.make(); N.addVec(L); // stroke(0); drawArc(P.B,N,Q.B,5); 
     pt O = new pt(width/2,height/2);
     car K = new car(0,0,0,derived);
     K.B.setTo(P.B);
     K.B.turnAround(M,-s*b);
     K.a=P.a+s*b; K.a=roll(K.a);
     K.F.turnAround(K.B,K.a);
     return(K);
     }