public double ComputeTimeToReach(double x, double acceleration)
{
var lastKnown = KnownPositions.Last(p => p.X <= x);
var sol = ResolveSecondOrderEq(0.5 * acceleration, lastKnown.Speed, lastKnown.X - x);
return(sol.Single(s => s >= 0));
}
public MyCar()
{
KnownPositions.Add(new Position
{
Time = 0,
Speed = 0,
X = 0
});
}
public Position ComputePositionAtTime(double t, double acceleration)
{
var lastKnown = KnownPositions.Last(x => x.Time <= t);
var elapsedTime = t - lastKnown.Time;
return(new Position
{
Time = t,
Speed = lastKnown.Speed + elapsedTime * acceleration,
X = lastKnown.X + lastKnown.Speed * elapsedTime + 0.5 * acceleration * elapsedTime * elapsedTime,
});
}
public double ComputeTimeToReach(double x)
{
var previousPosition = KnownPositions.Last(p => p.X <= x);
var nextPosition = KnownPositions.First(p => p.X >= x);
var dx = nextPosition.X - previousPosition.X;
var dt = nextPosition.Time - previousPosition.Time;
if (dx == 0)
{
return(previousPosition.Time);
}
return(previousPosition.Time + (x - previousPosition.X) * dt / dx);
}
public Position ComputePositionAtTime(double t)
{
var exactPosition = KnownPositions.SingleOrDefault(x => Math.Abs(x.Time - t) <= double.Epsilon);
if (exactPosition != null)
{
return(exactPosition);
}
var previousPosition = KnownPositions.Last(x => x.Time <= t);
var nextPosition = KnownPositions.First(x => x.Time >= t);
var speed = (nextPosition.X - previousPosition.X) / (nextPosition.Time - previousPosition.Time);
return(new Position
{
Time = t,
Speed = speed,
X = previousPosition.X + speed * (t - previousPosition.Time),
});
}
