15. 翻译，dt，FPS

3.11，翻译了 arkanoid 教程，做一下昨天剩的题。

delta time

11.0 之前 variable dt

function love.run()
	if love.math then love.math.setRandomSeed(os.time()) end
	if love.load then love.load(arg) end
	if love.timer then love.timer.step() end

	local dt = 0

	while true do
		if love.event then
			love.event.pump()
			for name, a,b,c,d,e,f in love.event.poll() do
				if name == "quit" then
					if not love.quit or not love.quit() then
						return a
					end
				end
				love.handlers[name](a,b,c,d,e,f)
			end
		end

		-- 真实耗时多少就传多少
		if love.timer then
			love.timer.step()
			dt = love.timer.getDelta()
		end
		if love.update then love.update(dt) end

		if love.graphics and love.graphics.isActive() then
			love.graphics.clear(love.graphics.getBackgroundColor())
			love.graphics.origin()
			if love.draw then love.draw() end
			love.graphics.present()
		end

		if love.timer then love.timer.sleep(0.001) end
	end
end

11.0 之后 variable dt

function love.run()
	if love.load then love.load(love.arg.parseGameArguments(arg), arg) end
	if love.timer then love.timer.step() end

	local dt = 0

	return function()
		if love.event then
			love.event.pump()
			for name, a,b,c,d,e,f in love.event.poll() do
				if name == "quit" then
					if not love.quit or not love.quit() then
						return a or 0
					end
				end
				love.handlers[name](a,b,c,d,e,f)
			end
		end

		-- dt 可变，物理容易不稳定
		if love.timer then dt = love.timer.step() end
		if love.update then love.update(dt) end

		if love.graphics and love.graphics.isActive() then
			love.graphics.origin()
			love.graphics.clear(love.graphics.getBackgroundColor())
			if love.draw then love.draw() end
			love.graphics.present()
		end

		if love.timer then love.timer.sleep(0.001) end
	end
end

fixed dt

function love.run()
	if love.load then love.load(love.arg.parseGameArguments(arg), arg) end
	if love.timer then love.timer.step() end

	local dt = 1/60

	return function()
		if love.event then
			love.event.pump()
			for name, a,b,c,d,e,f in love.event.poll() do
				if name == "quit" then
					if not love.quit or not love.quit() then
						return a or 0
					end
				end
				love.handlers[name](a,b,c,d,e,f)
			end
		end

		-- 不管真实耗时多少，每帧都传 1/60
		if love.update then love.update(dt) end

		if love.graphics and love.graphics.isActive() then
			love.graphics.origin()
			love.graphics.clear(love.graphics.getBackgroundColor())
			if love.draw then love.draw() end
			love.graphics.present()
		end

		if love.timer then love.timer.sleep(0.001) end
	end
end

semi-fixed timestep

function love.run()
	if love.load then love.load(love.arg.parseGameArguments(arg), arg) end
	if love.timer then love.timer.step() end

	local dt = 0
  	local upper_dt = 1/60

	return function()
		if love.event then
			love.event.pump()
			for name, a,b,c,d,e,f in love.event.poll() do
				if name == "quit" then
					if not love.quit or not love.quit() then
						return a or 0
					end
				end
				love.handlers[name](a,b,c,d,e,f)
			end
		end

		if love.timer then dt = love.timer.step() end
		-- 真实耗时大的就切片处理，单次传入的 dt 过大会进入死亡循环
		while dt > 0 do
			local current_dt = math.min(dt, upper_dt)
			if love.update then love.update(current_dt) end
			dt = dt - current_dt
		end

		if love.graphics and love.graphics.isActive() then
			love.graphics.origin()
			love.graphics.clear(love.graphics.getBackgroundColor())
			if love.draw then love.draw() end
			love.graphics.present()
		end

		if love.timer then love.timer.sleep(0.001) end
	end
end

free the physics

function love.run()
	if love.load then love.load(love.arg.parseGameArguments(arg), arg) end
	if love.timer then love.timer.step() end

	local dt = 0
	local fixed_dt = 1/60
	local accumulator = 0

	return function()
		if love.event then
			love.event.pump()
			for name, a,b,c,d,e,f in love.event.poll() do
				if name == "quit" then
					if not love.quit or not love.quit() then
						return a or 0
					end
				end
				love.handlers[name](a,b,c,d,e,f)
			end
		end

    	if love.timer then dt = love.timer.step() end
		accumulator = accumulator + dt
		-- 累计一个固定步长再跑一次物理更新
		while accumulator >= fixed_dt do
			if love.update then love.update(fixed_dt) end
			accumulator = accumulator - fixed_dt
		end

		if love.graphics and love.graphics.isActive() then
			love.graphics.origin()
			love.graphics.clear(love.graphics.getBackgroundColor())
			if love.draw then love.draw() end
			love.graphics.present()
		end

		if love.timer then love.timer.sleep(0.001) end
	end
end

Balatro dt

function love.run()
    if love.load then love.load(love.arg.parseGameArguments(arg), arg) end
    if love.timer then love.timer.step() end

    local dt = 0
    local dt_smooth = 1 / 100
    local run_time = 0

    return function()
        run_time = love.timer.getTime()
        if love.event and G and G.CONTROLLER then
            love.event.pump()
            local _n, _a, _b, _c, _d, _e, _f, touched
            for name, a, b, c, d, e, f in love.event.poll() do
                if name == "quit" then
                    if not love.quit or not love.quit() then
                        return a or 0
                    end
                end
                if name == 'touchpressed' then
                    touched = true
                elseif name == 'mousepressed' then
                    _n, _a, _b, _c, _d, _e, _f = name, a, b, c, d, e, f
                else
                    love.handlers[name](a, b, c, d, e, f)
                end
            end
            if _n then
                love.handlers['mousepressed'](_a, _b, _c, touched)
            end
        end

        if love.timer then dt = love.timer.step() end
		-- 给可变 dt 做一个指数平滑，并且给了一个 dt 上限 0.1
        dt_smooth = math.min(0.8 * dt_smooth + 0.2 * dt, 0.1)
        if love.update then love.update(dt_smooth) end

        if love.graphics and love.graphics.isActive() then
            if love.draw then love.draw() end
            love.graphics.present()
        end

		-- 这一帧实际花了多少时间，上限为 0.1
        run_time = math.min(love.timer.getTime() - run_time, 0.1)
		-- 帧率上限 500 FPS
        G.FPS_CAP = G.FPS_CAP or 500
		-- 这一帧跑的太快就 sleep 一下补足时间
        if run_time < 1/G.FPS_CAP then
			love.timer.sleep(1/G.FPS_CAP - run_time)
		end
    end
end

指数平滑

$$smooth=\alpha \cdot new+(1-\alpha )\cdot old$$

真实帧率一直是稳定的 100FPS 的话，dt 就是 0.01，某一帧突然卡顿 dt 跳到 0.1：

0.01 → 0.01
0.01 → 0.01
0.1  → 0.8*0.01  + 0.2*0.1  = 0.028
0.01 → 0.8*0.028 + 0.2*0.01 = 0.024
0.01 → 0.8*0.024 + 0.2*0.01 = 0.021
...