So Here We Are

本文探讨了Linux内核的独特之处,包括其不采用传统libc库、内存保护机制的缺失等特点。虽然初看起来似乎难以驾驭,但文章鼓励读者深入了解并修改源代码,以克服初期的畏惧心理。
The kernel is indeed a unique and inimitable beast: No memory protection, no tried-and-true libc, a small statck, a huge source tree. The linux kernel plays by its own rules, running with the big boys and stopping just long enough to break the customs with which we are familiar. Despite this, however, the kernel is just a program. It is not very different from the usual, the accustomed, the status quo. Do not be afraid: Stand up to it, call it names, push it around.

Realizing that the kernel is not as daunting as first appearances might suggest is the first step on the road to having everything just make sense. To reach that utopia, however, you have to jump in, read the source, hack the source, and not be disheartened.

From: Linux kernel Development
Frame-independent movement If you run everything we have done so far, you will be able to move the circle, but it won't move uniformly. It will probably be very fast, because currently we have done the movement in a very naive way. Right now your computer will be running the update() function as fast as it can, which means it will probably call it a couple of hundreds of times each second, if not more. If we move the shape by one pixel for every frame, this can count up to several 100 pixels every second, making our little player fly all over the screen. You cannot just change the movement value to something lower, as it will only fix the problem for your computer. If you move to a slower or faster computer, the speed will change again. So how do we solve this? Well, let's look at the problem we are facing. We are having a problem because our movement is frame-dependent. We want to provide the speed in a way that changes depending on the time a frame takes. There is a simple formula you should remember from your old school days. It's the formula that goes: distance = speed * time. Now why is this relevant for us? Because with this formula we can calculate a relevant speed for every frame, so that the circle always travels exactly the distance we want it to travel over one second, no matter what computer we are sitting on. So let's modify the function to what we actually need to make this work. void Game::update(sf::Time deltaTime) { sf::Vector2f movement(0.f, 0.f); if (mIsMovingUp) movement.y -= PlayerSpeed; if (mIsMovingDown) movement.y += PlayerSpeed; if (mIsMovingLeft) movement.x -= PlayerSpeed; if (mIsMovingRight) movement.x += PlayerSpeed; mPlayer.move(movement * deltaTime.asSeconds()); } The major difference we have made here is that we now receive a time value every time we call the update. We calculate the distance we want to travel every frame, depending on how much time has elapsed. We call the time that has elapsed since the last frame delta time (or time step), and often abbreviate it as dt in the code. But how do we get this time? We are lucky because SFML provides the utilities for it.翻译
03-08
<think>嗯,用户问的是Frame-independent movement,也就是帧率无关的运动。我得先理解这个问题到底是怎么回事。根据提供的上下文,他们提到如果直接用每帧移动固定距离,会导致在不同性能的电脑上速度不一致,因为帧率不同。比如,高性能电脑每秒能跑几百帧,每帧移动1像素的话,每秒就能移动几百像素,而低性能电脑可能帧率低,移动速度就慢。这确实是个常见的问题。 那用户的需求应该是如何实现不管帧率高低,物体移动速度保持一致。解决方法应该是使用时间增量(delta time)来调整每帧的移动距离,也就是用“距离=速度×时间”的公式。用户提供的代码示例中,update函数接收一个deltaTime参数,然后用movement乘以deltaTime.asSeconds()。这里的关键是解释清楚delta time的作用,以及如何通过它来实现帧率无关的运动。 接下来,我需要确保自己正确理解delta time的计算方式。SFML提供了获取时间差的工具,比如sf::Clock和sf::Time,主循环中每次循环计算经过的时间,并将这个delta time传递给update函数。这样,每一帧的移动距离都是基于实际经过的时间,而不是固定的每帧移动量。 用户可能还需要了解为什么直接调整速度值不行,因为那样只是针对特定硬件的,换台电脑速度又会变。这时候需要强调帧率依赖的问题,以及如何通过时间增量来解耦运动速度与帧率的关系。 另外,用户提供的代码示例中的关键改动部分需要解释清楚,尤其是movement * deltaTime.asSeconds()这一行。这里是将每帧的移动向量乘以经过的时间(以秒为单位),从而使得移动距离与时间成正比,而不是帧数。 可能还需要提到,delta time通常指的是上一帧到当前帧的时间间隔,所以每一帧的更新都是基于这个时间间隔来计算应该移动的距离,这样无论帧率高还是低,每秒移动的总距离都是相同的,从而实现了速度的一致性。 总结一下,回答的结构应该包括问题描述、原因分析、解决方案、公式应用、代码示例解释,以及SFML中的具体实现方法。同时要确保用中文清晰解释这些概念,避免技术术语过于晦涩,让用户能够逐步理解帧率无关运动的原理和实现方式。</think>以下是关于"帧率无关运动(Frame-independent movement)"的详细解释: # 帧率依赖问题分析 $\boxed{\text{问题根源}}$ 当前代码中的运动是$\textcolor{red}{帧率依赖}$的(frame-dependent),即: $$移动距离 = 速度 \times 1帧$$ 这会导致在不同性能设备上出现速度差异。例如: - 高性能计算机:每秒500帧 → 500像素/秒 - 低性能计算机:每秒30帧 → 30像素/秒 # 解决方案原理 $\boxed{物理公式应用}$ 采用经典运动学公式: $$移动距离 = 速度 \times 时间$$ 这里引入$\textcolor{blue}{\Delta t}$(delta time)参数,表示两帧之间的时间差: $$每帧移动距离 = 速度 \times \Delta t$$ # SFML实现解析 ```cpp void Game::update(sf::Time deltaTime) { sf::Vector2f movement(0.f, 0.f); // 输入检测(假设PlayerSpeed=300像素/秒) if (mIsMovingUp) movement.y -= PlayerSpeed; // 每秒向上300像素 if (mIsMovingDown) movement.y += PlayerSpeed; if (mIsMovingLeft) movement.x -= PlayerSpeed; if (mIsMovingRight) movement.x += PlayerSpeed; // 关键计算:将速度转换为实际位移 mPlayer.move(movement * deltaTime.asSeconds()); } ``` # 技术要点说明 1. **$\Delta t$获取** SFML通过`sf::Clock`计时器自动计算: ```cpp sf::Clock clock; while (window.isOpen()) { sf::Time dt = clock.restart(); update(dt); } ``` 2. **单位一致性** - `PlayerSpeed`应以$\textcolor{green}{像素/秒}$为单位定义 - `deltaTime.asSeconds()`将时间转换为秒单位 - 两者相乘得到$\textcolor{green}{像素/帧}$的实际位移 3. **效果验证** 无论帧率如何变化: - 300像素/秒 × 0.02秒(50 FPS)= 6像素/帧 - 300像素/秒 × 0.016秒(60 FPS)= 4.8像素/帧 - 两种情况下每秒总位移保持300像素 # 优势总结 1. $\textcolor{blue}{硬件无关性}$:在不同性能设备上保持相同运动速度 2. $\textcolor{blue}{物理精确性}$:符合真实世界的运动规律 3. $\textcolor{blue}{代码可维护性}$:参数调整只需修改速度值,无需考虑帧率因素 建议在实际开发中始终采用这种帧率无关的运动实现方式,特别是在需要跨平台运行或物理模拟的场景中。
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