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 );
integrate (perviousState, t, accumulator);

render( state );
}

----
sorry it's split into two parts

Black is centertile, used to determine gravity.
White is the active area for effects and triggering.
Green/Red is the bounding box, green when free, red when solid.