Distance approximation from velocity, friction and fps

distance.py

def get_distance_from_velocity_loop(self, vel, fri, dt=1 / 60.):
    # original algo from tito
    dist = 0
    it = 0
    while abs(vel) > .5:
        it += 1
        vel -= vel * fri
        dist += vel * dt
    return dist

def get_distance_from_velocity_math(self, vel, fri, dt=1 / 60.):
    # adapted from inclement (https://gist.github.com/inclement/4e004c4efb5c154fc4790ca11290a68f)
    direction = -1 if vel < 0 else 1
    vel = abs(vel)
    fri = fri / dt
    time_taken = -1 * log(0.5 / vel) / fri
    distance_travelled = (
        -1 * vel / fri * exp(-1 * fri * time_taken)
        + vel / fri)
    return distance_travelled * direction

def get_distance_from_velocity_geom(self, vel, fri, dt=1 / 60.):
    # from arndt (https://stackoverflow.com/questions/49494658/mathematically-sum-a-sequence)
    k = 1 - fri
    r = k / (1 - k)
    return r * vel * (1 / dt)