// Project P1a
// Implement the following functions as suggested (do not use f7 to implement them)

// constant speed in [0,1]
float f1(float t) {return(t);} 

// constant acceleration in [0,0.5], then constant deceleration (Hint: solve second degree equation for the accelration value)
float f2(float t) {
    if (t <= .5)
      return(4*.5*t*t);  // replace this with your own
    else
      return(-.5 + 2*t - .5 * 4 * (t-.5) * (t-.5));
  } 
 
// more dynamic than f2: more acceleration at first and breaks later (Hint: use cos)
float f3(float t) {
  return(-(cos(3*t)/2.0 - .5));
  } 

// heavy car: slow start then breaks hard (Hint: use cos power or rational function)
float f4(float t) {
  return(pow(cos(t-1),9));
  } 

// wind up first and overshoot a bit (Hint: use cubic Bezier)
// bezier equation from wikipedia.org (http://en.wikipedia.org/wiki/B%C3%A9zier_curve)
float f5(float t) {
   float p0=0,
         p1=-.2,
         p2=.5,
         p3=1,
         b;
         float oneminust = (1-t);
          b = p0 * oneminust*oneminust*oneminust +
             3 * p1 * t *oneminust*oneminust +
             3 * p2 * t*t * oneminust +
             p3 * t*t*t;

   return(b);  }

// start with high speed, then slows down (Hint: use cubic with different values)
float f6(float t) {
   float p0=0,
         p1=.8,
         p2=.9,
         p3=1,
         b;
         float oneminust = (1-t);
          b = p0 * oneminust*oneminust*oneminust +
             3 * p1 * t *oneminust*oneminust +
             3 * p2 * t*t * oneminust +
             p3 * t*t*t;

   return(b);    }