Fixed timestep loop in C++

Question

I am trying to implement a fixed timestep loop so that the game refreshes at a constant rate. I found a great article at http://gafferongames.com/game-physics/fix-your-timestep/ but am having trouble translating that into my own 2d engine.

The specific place I am referring to is the function in the last part "The Final Touch" which is what most people recommend. This is his function:

double t = 0.0;
    const double dt = 0.01;

    double currentTime = hires_time_in_seconds();
    double accumulator = 0.0;

    State previous;
    State current;

    while ( !quit )
    {
         double newTime = time();
         double frameTime = newTime - currentTime;
         if ( frameTime > 0.25 )
              frameTime = 0.25;   // note: max frame time to avoid spiral of death
         currentTime = newTime;

         accumulator += frameTime;

         while ( accumulator >= dt )
         {
              previousState = currentState;
              integrate( currentState, t, dt );
              t += dt;
              accumulator -= dt;
         }

         const double alpha = accumulator / dt;

         State state = currentState*alpha + previousState * ( 1.0 - alpha );

         render( state );
    }

For myself, I am just moving a player across the screen keeping track of an x and y location as well as velocity rather than doing calculus integration. **I am confused as to what I would apply to the updating of the player's location (dt or t?). Can someone break this down and explain it further?

The second part is the interpolation which I understand as the formula provided makes sense and I could simply interpolate between the current and previous x, y player positions.

Also, I realize I need to get a more accurate timer.

Answer 1

If you can get at least microsecond accuracy, try this:

long int start = 0, end = 0;
double delta = 0;
double ns = 1000000.0 / 60.0; // Syncs updates at 60 per second (59 - 61)
while (!quit) {
    start = timeAsMicro();
    delta+=(double)(start - end) / ns;
    end = start;

    while (delta >= 1.0) {
       doUpdates();
       delta-=1.0;
    }
}

Answer 2

See: http://en.wikipedia.org/wiki/Integral & http://en.wikipedia.org/wiki/Numerical_integration

The function is a numerical technique (2nd link) for approximating the integral function (1st link).

Answer 3

You should review your high school physics. Simply put velocity is change in distance over change in time(dxdt), acceleration is change in velocity over change in time(dvdt) If you know dxdt you can get the distance by integrating it w/ respect to t, if you know dvdt you can get the velocity by integrating it with respect to t. Obviously this is a very simple explanation, but there are tons of references out there with more details if you so desire.