Framerate Difficulty Problem about fifty-bird HOT 5 OPEN

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@coltonoscopy what would be the recommendation when it comes to 60+ FPS? It's quite unplayable at 144 :)

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@snekbaev Limit dt with some min_dt: https://github.com/games50/fifty-bird/pull/15/files

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@sharifmarat can't recall the details now, but I think the suggested approach wasn't good enough. I remember reading some article about fixing the frame rate issues using different methods and pros and cons of each. One of the better ones was to use the accumulator approach. I think I've implemented some variation of that

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A few years late to the party, but I didn't see this mentioned anywhere, so FWIW I'll explain why you experienced this issue and share a fix for it. Hopefully it will help future students:

**tl;dr: ** Pull Request #21 will fix this issue.

We'll start by discussing basic physics (probably mandatory knowledge for game developers anyway):
Our bird's location is defined by x and y values. The units of these values are pixels.
The speed, dy, is given in units of pixels / second (so, for example, if our bird has speed of dy = 20, it means it will pass 20 pixels every second).
Now we get to the gravity. Gravity is just acceleration towards the positive direction of the y-axis. Acceleration measures the degree in which the speed changes (so, for example, if gravity is 20, it means the bird's speed is increased by 20 pixels / second every second),
so if the speed's units are pixels / second, the acceleration units are pixels / second / second or pixels / second ^ 2.

now, when we calculate the bird's speed this is done correctly, we take the gravity and multiply it by the elapsed time, dt, giving us the speed:

The mess starts when we try and add this speed to the bird's y position:

To demonstrate how this affects users who run on a frame rate which is not 60 fps, let's consider two users, user A and user B.
User A runs the game on 60fps (dt of every frame is 1 / 60 = 0.01666). User B runs the game on 120fps (dt of every frame is 1 / 120 = 0.008333).
Now, let's check the bird's y position after 0.2 seconds (so 12 frames for user A and 24 frames for user B), by running this simple code (written in python for my convenience :) ):

GRAVITY = 20  # As defined in fifty-bird
def simulate_frames(num_frames: str, dt: float) -> float:
    y = 136  # As defined in fifty-bird
    dy = 0  # Starting y speed is 0
    for i in range(num_frames):
        dy += GRAVITY * dt
        y += dy
    return y

print(simulate_frames(num_frames=6, dt=1 / 60))  # User A
print(simulate_frames(num_frames=12, dt=1 / 120))  # User B

Running the above code prints:

>>> print(simulate_frames(num_frames=12, dt=1 / 60))  # User A
162.0
>>> print(simulate_frames(num_frames=24, dt=1 / 120))  # User B
186.0

so over the same timeframe, user A saw the bird move 26 pixels, and user B saw it moving 50 pixels, almost twice as much!

How can we fix this?
simply comply to the laws of physics, and multiply the speed by dt before adding it to the bird's y position:

function Bird:update(dt)
    self.dy = self.dy + GRAVITY * dt

    if love.keyboard.wasPressed('space') or love.mouse.wasPressed(1) then
        self.dy = -5
        sounds['jump']:play()
    end

    self.y = self.y + self.dy * dt
end

However, this will cause the bird to move much slower, and we will need to set new values.
There is no right answer here, but from playing around with different values I put it as GRAVITY = 750 and dy = -200 for jumping, that seemed similar enough to what's shown in the lecture's video.

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