如何使时间独立于FPS？

Question

I have a program which runs the tick() method every frame. I want an object to fall according to a set gravity constant, so I created a Ball object which will update its position to the position on the previous frame minus the y velocity. The y velocity will decrease by the gravity constant each tick. But the fall is far too rapid because the ticks do not directly translate to seconds. I think I'm missing some basic math but I'm juggling so many variables I can't see what it is.

EDIT: Added code

@Override
public void run(){
    init();

    long lastTime=System.nanoTime(), timer=System.currentTimeMillis();
    final double ticks=60.0;
    double ns=1000000000/ticks, delta=0;
    int updates=0, frames=0;

    while(running){
        long now=System.nanoTime();
        delta+=(now-lastTime)/ns;
        lastTime=now;

        if(delta>=1){
            tick();
            updates++;
            delta--;
        }

        render();
        frames++;

        if((System.currentTimeMillis()-timer)>1000){
             timer+=1000;
             System.out.println(updates+" ticks, FPS "+frames);
             frame.setTitle("Ball -- "+SCALEWIDTH+"x"+SCALEHEIGHT+" at "+frames+" FPS");
             updates=0;
             frames=0;
        }
    }
    stop();
}

Answer 1

For each update frame, you will need to compute the time in seconds between now and the previous update. This will need to be a float or double since it will likely be a fraction of a second. To do this, you get the current time in milliseconds or nanoseconds, subtract the previous time, and convert to seconds.

You can then use a process called numerical integration to compute the new position and velocity. This means finding an approximation to the equations of motion by computing the position and velocity in the current frame based on computations from the previous frame and the time between them. This looks something like:

position += velocity * dt;
velocity += acceleration * dt;

where dt is the time between frames in seconds. This particular method for integrating position and velocity is called the Euler Method . This method is easy and it might work just fine for your application, but it starts to become inaccurate over time when velocity or acceleration is not constant. This is because the values being calculated are an approximation to a curve.

If you need more accuracy, you will want to look into other integration methods like Verlet or Runge-Kutta .