按时间正确缩放模拟

Question

I have a small sample simulation, think of it like tossing a ball into the air. I want to be able to 'speed up' the simulation, so it will complete in a fewer # of loops, but the 'ball' will still go just as high in the air as if it is at normal speed (1.0f).

Right now, the simulation completes in a fewer # of iterations, but the coordinates of the ball are either too high or too low. What's wrong here?

static void Test()
{
    float scale = 2.0f;
    float mom = 100 * scale;
    float grav = 0.01f * scale;
    float pos = 0.0f;

    int i;
    for (i = 0; i < 10000; i++)
    {
        if (i == (int)(5000 / scale)) // Random sampling of a point in time
            printf("Pos is %f\n", pos);

        mom -= grav;
        pos += mom;
    }
}

Answer 1

Is 'scale' the variable you are trying to use to change the time-step size?

If so, it should affect how mom and pos are updated. So you might start by replacing

mom -= grav;
pos += mom;

with

mom -= grav*scale;
pos += mom*scale;

Maybe this bit of pseudocode helps..

const float timestep = 0.01; // this is how much time passes every iteration
                             // if it is too high, your simulation
                             // may be inaccurate! If it is too low, 
                             // your simulation will run unnecessarily
                             // slow!

float x=0; //this is a variable that changes over time during your sim.
float t=0.0; // this is the current time in your simulation

for(t=0;t<length_of_simulation;t+=timestep) {
    x += [[insert how x changes here]] * timestep;
}