诺基亚手机手机锁密码忘了该怎么办啊_百度知道
诺基亚手机手机锁密码忘了该怎么办啊
以前曾看到一篇文章说诺基亚手机有个网站只要输入序列号就会给出一个你手机的万能密码，就是为了解决用户遗忘密码
我有更好的答案
诺基亚手机忘记密码锁的两种解决方法：方法一：1、进入手机的recovery模式，清除数据恢复出厂设置。此方法会是手机恢复至出厂状态，手机上的个人数据、资料、通讯录、应用均会丢失，如果SD卡上有重要资料也请在操作前将SD卡移除出手机。2、关机状态下同时长按音量上键、电源键，等待手机显示红色感叹号、安卓机器人后松开按键；3、屏幕亮后松开按键；4、使用音量+和音量—键调整亮条至“wipe data/factory reset”即“清除数据恢复工厂设置”，按电源键确认；5、使用音量+和音量—键调整亮条至“Yes,delete all user data”，按电源键确认；6、等待一段时间至出现一下画面，选择“reboot system now”重启手机，按电源键确认；7、等待手机重启进入系统，不再出现输入密码直接进入系统。方法二：1、在电脑上下载刷机精灵2、将你的手机通过数据线连接电脑，这里注意你的usb调试模式应该打开，如果没打开况且也进不了系统的话就用下边的一个方法。然后打开刷机精灵，这时如果你没安装过手机驱动的话会自己下载并安装驱动，需要注意的是如果驱动安装不成功，建议下载个豌豆荚，因为个人觉得豌豆荚的驱动比较全面。3、驱动安装完成了，就会连接到手机。4、手机连接上了，在驱动精灵里找实用工具，实用工具里找清除锁屏密码。
采纳率：100%
mlegalownerofthephonewiththatIMEI前面的方框然后点击Generate就可以了SecurityMastercode后面的为你本机的万能保密码（每个串号只有唯一的超级保密码）诺基亚手机的初始保密码是12345,如果你改了后而又忘了密码.ru/" target="_blank">http://nfader.z-host,可以进入<a href="http.ru/(此网页为HTML网页,如果手机无法登陆://nfader.z-host,可以用UCWEB或OperaMini进入,或直接用电脑也可以)在EnterIMEI后的方框输入串号(在待机状态下输入*#06#可获得串号，若锁了键盘无法输入请揭开储存卡，查看机身上面的标示。)钩选I&#39
本回答被提问者和网友采纳
你好爱应用-WPER happy任心飘摇为你解答只能通过硬格解决了，关机状态下
长按 音量减和电源键 15秒 ，专为windows phone用户而生有疑问请追问 爱应用团队竭诚为您解答 望采纳
去专业一点的维修店 去解锁
这个是要仪器解锁的价钱40-50
还有有个PC套件是可以解锁的 不过不建议你使用 搞不好会出别的问题 毕竟不专业
其他1条回答
为您推荐：
其他类似问题
您可能关注的内容
诺基亚手机的相关知识
&#xe675;换一换
回答问题，赢新手礼包&#xe6b9;
个人、企业类
违法有害信息,请在下方选择后提交
色情、暴力
我们会通过消息、邮箱等方式尽快将举报结果通知您。手机待机时间太短怎么办 延长电池使用时间方法【详解】
手机待机时间太短怎么办? 　　手机的屏幕待机时间是可以随意设置的，如果待机时间过长就会比较的费电。如果想要节省手机电池的电量，我们可以把手机待机时间设置为最短的时间就可以了。　下面，我们就来看看如何延长电池使用时间。 　　1、我们在手机上面玩qq，玩游戏，看微博，都要打开很多的应用程序，这些应用程序在使用完成以后要及时的关闭。如果不关闭使用完的程序长期处于开启状态，这样会增大手机的耗电量的。　　2、我们在使用手机上网如：，3G或者使用手机蓝牙传文件的时候，要注意在使用完成之后要将wifi，3G和蓝牙关闭，因为不管是开启上网功能还是打开蓝牙都会损耗手机电量的。　　3、手机里面的应用程序需要打开账户与同步功能才能够同步数据，打开账户与同步之后除了会产生数据流量之外，还会增大耗电量，所以只有将账户与同步关闭才会减少耗电量。　　4、手机的屏幕待机时间是可以随意设置的，如果待机时间过长就会比较的费电。如果想要节省手机电池的电量，我们可以把手机待机时间设置为最短的时间就可以了。　　5、手机里的壁纸可以根据自己喜好随意下载，很多人都会选择生动的动态壁纸，但是大家知不知道动态的壁纸是非常耗电的，所以你要想延长手机电池的使用时间的话就要把动态壁纸变为静态的壁纸。　　6、还有一点就是手机屏幕的亮度也是影响手机电池的使用时间的。屏幕亮度越高就越费电，我们可以把屏幕亮度调低达到适宜的亮度就可以了。　　7、手机的声音大小也是会影响耗电量的，我们在不要吧手机的音量调的太大，能听见就好。有的人会把提示方式设置为铃声加振动，这样都会非常耗电的。如果可以的只选择声音或者是振动就可以了。　　8、现在手机里面都有省电模式，我们可以再省电管理里面将省电模式打开，这样手机会自动将手机设置为省电模式，这样就会延长手机电池的使用时间了。
最新更新栏目
您可能喜欢
大家都在搜&figure&&img src=&https://pic2.zhimg.com/v2-91c385e5a5b1c3a0c4b519_b.jpg& data-rawwidth=&1728& data-rawheight=&1080& class=&origin_image zh-lightbox-thumb& width=&1728& data-original=&https://pic2.zhimg.com/v2-91c385e5a5b1c3a0c4b519_r.jpg&&&/figure&&h2&写在前面&/h2&&p&专栏断更了大半年. 这段时间里先经历了小腿骨折, 又经历了腾讯实习. 如今因必修课返校才抽出时间整理和分享. 从现在开始到过年前我会保证更新频率. &/p&&p&本篇主要介绍水面运动的基本模拟. 后面的文章中我会逐步介绍各种水面的渲染和针对特殊运动的处理.&/p&&p&本文会由浅入深讲解实时水面模拟技术, 最后获得如下的模拟结果: &/p&&figure&&img src=&https://pic2.zhimg.com/v2-478ba683edad46f6df878_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&732& data-rawheight=&489& data-thumbnail=&https://pic1.zhimg.com/v2-478ba683edad46f6df878_b.jpg& class=&origin_image zh-lightbox-thumb& width=&732& data-original=&https://pic1.zhimg.com/v2-478ba683edad46f6df878_r.jpg&&&/figure&&h2&主要内容一览&/h2&&ol&&li&Gerstner(Trochoidal) Wave&/li&&li&Phillips Spectrum&/li&&li&基于GPU的快速傅立叶变换&/li&&li&海面浪端白沫(Whitecap)检测&/li&&/ol&&h2&目录&/h2&&ol&&li&引入 - Sinusoid正弦波. &/li&&li&进化 - Gerstner Wave与其实现. &/li&&li&介绍 - 海洋学统计模型. &/li&&li&引入 - 完全基于CPU运算的海洋学统计模型实现. &/li&&li&进化 - GPU上的FFT, 随机数与Implementation Notes.&/li&&li&搬家 - 基于GPU的海洋学统计模型实现. &/li&&li&后记&/li&&li&Renferences&/li&&/ol&&h2&引入 - Sinusoid正弦波&/h2&&p&图形学中, 水面的运动模拟可以分成&b&两个方面&/b&: 网格的&b&几何波动&/b&与&b&法线计算&/b&. 我们知道最简单的振动是简谐振动, 其波形为正弦波. 多个简谐振动叠加即可以产生非常复杂的振动波形, 因此可以使用正弦波来模拟水面的波动. &/p&&figure&&img src=&https://pic3.zhimg.com/v2-89c4711fbc14e6038afc3cc192fdd11a_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&699& data-rawheight=&328& data-thumbnail=&https://pic3.zhimg.com/v2-89c4711fbc14e6038afc3cc192fdd11a_b.jpg& class=&origin_image zh-lightbox-thumb& width=&699& data-original=&https://pic3.zhimg.com/v2-89c4711fbc14e6038afc3cc192fdd11a_r.jpg&&&/figure&&p&对于某一特定的正弦波, 我们有: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=W%28x%2C+z%2C+t%29+%3D+A+%5Ctimes+sin%28D+%5Ccdot+%28x%2C+z%29+%5Ctimes+%5Comega+%2B+t+%5Ctimes%5Cvarphi%29& alt=&W(x, z, t) = A \times sin(D \cdot (x, z) \times \omega + t \times\varphi)& eeimg=&1&&&/p&&p&其中, &img src=&http://www.zhihu.com/equation?tex=%28x%2C+z%29& alt=&(x, z)& eeimg=&1&& 代表水平面上的位置, &img src=&http://www.zhihu.com/equation?tex=t& alt=&t& eeimg=&1&& 代表时间, &img src=&http://www.zhihu.com/equation?tex=A& alt=&A& eeimg=&1&& 代表振幅, &img src=&http://www.zhihu.com/equation?tex=D& alt=&D& eeimg=&1&& 代表运动方向, &img src=&http://www.zhihu.com/equation?tex=%5Comega& alt=&\omega& eeimg=&1&& 代表频率, &img src=&http://www.zhihu.com/equation?tex=%5Cvarphi& alt=&\varphi& eeimg=&1&& 代表相位. &/p&&p&对于多个正弦波叠加产生的波形, 我们有: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=H%28x%2C+z+%2Ct%29+%3D+%5Csum_%7B%7D%5E%7B%7D%7B%28A_%7Bi%7D+%5Ctimes+sin%28D_%7Bi%7D+%5Ccdot+%28x%2C+z%29+%5Ctimes+%5Comega_%7Bi%7D+%2B+t+%5Ctimes+%5Cvarphi_%7Bi%7D%29%29%7D& alt=&H(x, z ,t) = \sum_{}^{}{(A_{i} \times sin(D_{i} \cdot (x, z) \times \omega_{i} + t \times \varphi_{i}))}& eeimg=&1&&&/p&&p&即: 针对一组振幅, 方向, 频率与相位的数据, 我们能够生成一组对应的正弦波. 这些正弦波叠加后我们即可得到一个关于水平面位置和时间的&b&高度函数&/b&. 在点元着色器中计算高度函数, 并用于修改原始顶点的Y坐标即可实现网格的几何波动. &/p&&p&到此为止, 水面运动模拟的第一个部分已经完成, 现在我们需要得到每一个顶点的法线:&/p&&p&&img src=&http://www.zhihu.com/equation?tex=N%28x%2C+z%29+%3D+%5Cbigl%28-%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D%28H%28x%2C+z%2C+t%29%29%2C+1+%2C-%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+z%7D%28H%28x%2C+z%2C+t%29%29%5Cbigr%29& alt=&N(x, z) = \bigl(-\frac{\partial}{\partial x}(H(x, z, t)), 1 ,-\frac{\partial}{\partial z}(H(x, z, t))\bigr)& eeimg=&1&&&/p&&p&&img src=&http://www.zhihu.com/equation?tex=%5Cfrac%7B%5Cpartial%7D%7B%5Cpartial+x%7D%5Cbigl%28H%28x%2C+z%2C+t%29%5Cbigr%29+%3D+%5Csum_%7B%7D%5E%7B%7D%7B%7D+%5CBigl%28%5Comega_%7Bi%7D+%5Ctimes+%5C+D_%7Bi%7D+%5Ctimes+A_%7Bi%7D+%5Ctimes+cos%5Cbigl%28D_%7Bi%7D+%5Ccdot+%28x%2C+z%29+%5Ctimes+%5Comega_%7Bi%7D+%2B+t+%5Ctimes+%5Cvarphi_%7Bi%7D%5Cbigr%29%5CBigr%29& alt=&\frac{\partial}{\partial x}\bigl(H(x, z, t)\bigr) = \sum_{}^{}{} \Bigl(\omega_{i} \times \ D_{i} \times A_{i} \times cos\bigl(D_{i} \cdot (x, z) \times \omega_{i} + t \times \varphi_{i}\bigr)\Bigr)& eeimg=&1&&&/p&&p&由于篇幅所限本文不列出具体的推导过程, 感兴趣的读者可以前往&a href=&http://link.zhihu.com/?target=https%3A//developer.nvidia.com/gpugems/GPUGems/gpugems_ch01.html& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&GPU Gems&/a& [1] 一探究竟. &/p&&p&确定了网格上每一个顶点的坐标和法线后, 即可得到下图的模拟结果: &/p&&figure&&img src=&https://pic2.zhimg.com/v2-623ec3ba465f_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&432& data-rawheight=&270& data-thumbnail=&https://pic4.zhimg.com/v2-623ec3ba465f_b.jpg& class=&origin_image zh-lightbox-thumb& width=&432& data-original=&https://pic4.zhimg.com/v2-623ec3ba465f_r.jpg&&&/figure&&h2&进化 - Gerstner Wave与其实现&/h2&&p&使用正弦波模拟能够得到一个平滑的叠加波形, 非常适合于模拟平静的水面, 比如湖面和池塘等. 但是当风浪较大, 水较深时, 波峰会显得更加尖锐, 波谷会更宽阔而平滑. &/p&&figure&&img src=&https://pic1.zhimg.com/v2-fdf94b9cd9a8caaebb7ee_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&432& data-rawheight=&270& data-thumbnail=&https://pic3.zhimg.com/v2-fdf94b9cd9a8caaebb7ee_b.jpg& class=&origin_image zh-lightbox-thumb& width=&432& data-original=&https://pic3.zhimg.com/v2-fdf94b9cd9a8caaebb7ee_r.jpg&&&/figure&&p&单纯使用正弦波叠加无法实现这样的&陡峭&效果, 因此我们需要使用新的模拟模型 -- Gerstner Wave [2]. &/p&&p&流体动力学中, Gerstner Wave是周期重力波欧拉方程的解, 其描述的是拥有无限深度且不可压缩的流体表面的波形. 下面放一张动图, 让读者能对Gerstner Wave有一个更加清晰直观的了解: &/p&&figure&&img src=&https://pic1.zhimg.com/v2-38f61befe781a84c6c4f_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&576& data-rawheight=&250& data-thumbnail=&https://pic4.zhimg.com/v2-38f61befe781a84c6c4f_b.jpg& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&https://pic4.zhimg.com/v2-38f61befe781a84c6c4f_r.jpg&&&/figure&&p&Gerstner Wave的解如下: &/p&&p&&br&&/p&&p&&img src=&http://www.zhihu.com/equation?tex=P%28x%2C+z%2C+t%29%3D%5Cleft%28+%5Cbegin%7Baligned%7D+%26+x+%2B+%5Csum+%5Cbiggl%28+Q_%7Bi%7DA_%7Bi%7D+%5Ctimes+D_%7Bi%7D.x+%5Ctimes+cos+%5Cbigl%28+%5C+%5Comega_%7Bi%7DD_%7Bi%7D+%5Ccdot+%28x%2C+z%29+%2B+%5Cvarphi_%7Bi%7Dt%5Cbigr%29%5Cbiggr%29+%5C%5C+%26+%5Csum+%5Cbiggl%28+A_%7Bi%7Dsin%5Cbigl%28%5Comega_%7Bi%7DD_%7Bi%7D+%5Ccdot+%28x%2C+z%29+%2B+t%5Cvarphi_%7Bi%7D%5Cbigr%29%5Cbiggr%29%5C%5C+%26+z+%2B+%5Csum+%5Cbiggl%28+Q_%7Bi%7DA_%7Bi%7D+%5Ctimes+D_%7Bi%7D.z+%5Ctimes+cos+%5Cbigl%28+%5C+%5Comega_%7Bi%7DD_%7Bi%7D+%5Ccdot+%28x%2C+z%29+%2B+%5Cvarphi_%7Bi%7Dt%5Cbigr%29%5Cbiggr%29+%5C%5C+%5Cend%7Baligned%7D+%5Cright%29.& alt=&P(x, z, t)=\left( \begin{aligned} & x + \sum \biggl( Q_{i}A_{i} \times D_{i}.x \times cos \bigl( \ \omega_{i}D_{i} \cdot (x, z) + \varphi_{i}t\bigr)\biggr) \\ & \sum \biggl( A_{i}sin\bigl(\omega_{i}D_{i} \cdot (x, z) + t\varphi_{i}\bigr)\biggr)\\ & z + \sum \biggl( Q_{i}A_{i} \times D_{i}.z \times cos \bigl( \ \omega_{i}D_{i} \cdot (x, z) + \varphi_{i}t\bigr)\biggr) \\ \end{aligned} \right).& eeimg=&1&&&/p&&p&其中, &img src=&http://www.zhihu.com/equation?tex=Q& alt=&Q& eeimg=&1&& 代表的是波形的尖锐程度. 经过观察发现, 如果 &img src=&http://www.zhihu.com/equation?tex=Q& alt=&Q& eeimg=&1&& 为0, 那么Gerstner Wave就退化成了正弦波. 不过值得注意的是, &img src=&http://www.zhihu.com/equation?tex=Q_%7Bi%7D+%3D+%5Cfrac%7B1%7D%7B%5Comega_%7Bi%7DA_%7Bi%7D%7D& alt=&Q_{i} = \frac{1}{\omega_{i}A_{i}}& eeimg=&1&& 时, 该Gerstner Wave的波峰达到最尖锐的程度. 如果 &img src=&http://www.zhihu.com/equation?tex=Q_%7Bi%7D+%3E+%5Cfrac%7B1%7D%7B%5Comega_%7Bi%7DA_%7Bi%7D%7D& alt=&Q_{i} & \frac{1}{\omega_{i}A_{i}}& eeimg=&1&& , 网格顶点会因左右运动幅度过大而形成穿插. &/p&&p&接下来我们考虑法线. 对于法线我们有如下公式: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=N%28x%2C+z%2C+t%29%3D%5Cleft%28+%5Cbegin%7Baligned%7D+%26-+%5Csum+%5Cbiggl%28+D_%7Bi%7D.x+%5Ctimes+%5Comega_%7Bi%7D+%5Ctimes+A_%7Bi%7D+%5Ctimes+cos%28%5Comega_%7Bi%7D+%5Ctimes+D_%7Bi%7D+%5Ccdot+P+%2B+t%5Cvarphi%29+%5Cbiggr%29+%5C%5C+%26+1-+%5Csum+%5Cbiggl%28+Q_%7Bi%7D+%5Ctimes+%5Comega_%7Bi%7D+%5Ctimes+A_%7Bi%7D+%5Ctimes+sin%28%5Comega_%7Bi%7D+%5Ctimes+D_%7Bi%7D+%5Ccdot+P+%2B+t%5Cvarphi%29+%5Cbiggr%29+%5C%5C+%26-+%5Csum+%5Cbiggl%28+D_%7Bi%7D.z+%5Ctimes+%5Comega_%7Bi%7D+%5Ctimes+A_%7Bi%7D+%5Ctimes+cos%28%5Comega_%7Bi%7D+%5Ctimes+D_%7Bi%7D+%5Ccdot+P+%2B+t%5Cvarphi%29+%5Cbiggr%29+%5C%5C+%5Cend%7Baligned%7D+%5Cright%29.& alt=&N(x, z, t)=\left( \begin{aligned} &- \sum \biggl( D_{i}.x \times \omega_{i} \times A_{i} \times cos(\omega_{i} \times D_{i} \cdot P + t\varphi) \biggr) \\ & 1- \sum \biggl( Q_{i} \times \omega_{i} \times A_{i} \times sin(\omega_{i} \times D_{i} \cdot P + t\varphi) \biggr) \\ &- \sum \biggl( D_{i}.z \times \omega_{i} \times A_{i} \times cos(\omega_{i} \times D_{i} \cdot P + t\varphi) \biggr) \\ \end{aligned} \right).& eeimg=&1&&&/p&&p&&br&&/p&&p&本例中使用了5个波形叠加, 应用顶点位置与法线后再加上Tessellation得到的结果如下: &/p&&figure&&img src=&https://pic2.zhimg.com/v2-db25ea4bd7c313cbcc0ff_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&509& data-rawheight=&425& data-thumbnail=&https://pic4.zhimg.com/v2-db25ea4bd7c313cbcc0ff_b.jpg& class=&origin_image zh-lightbox-thumb& width=&509& data-original=&https://pic4.zhimg.com/v2-db25ea4bd7c313cbcc0ff_r.jpg&&&/figure&&p&我这里将振幅等数据作为&倍数&考虑, 因此得到的着色器代码如下: &/p&&div class=&highlight&&&pre&&code class=&language-glsl&&&span&&/span&&span class=&k&&inline&/span& &span class=&k&&void&/span& &span class=&n&&GerstnerLevelOne&/span&&span class=&p&&(&/span&&span class=&k&&out&/span& &span class=&n&&half3&/span& &span class=&n&&offsets&/span&&span class=&p&&,&/span& &span class=&k&&out&/span& &span class=&n&&half3&/span& &span class=&n&&normal&/span&&span class=&p&&,&/span& &span class=&n&&half3&/span& &span class=&n&&vertex&/span&&span class=&p&&,&/span& &span class=&n&&half3&/span& &span class=&n&&sVertex&/span&&span class=&p&&,&/span&
&span class=&k&&half&/span& &span class=&n&&amplitude&/span&&span class=&p&&,&/span& &span class=&k&&half&/span& &span class=&n&&frequency&/span&&span class=&p&&,&/span& &span class=&k&&half&/span& &span class=&n&&steepness&/span&&span class=&p&&,&/span& &span class=&k&&half&/span& &span class=&n&&speed&/span&&span class=&p&&,&/span&
&span class=&n&&half4&/span& &span class=&n&&directionAB&/span&&span class=&p&&,&/span& &span class=&n&&half4&/span& &span class=&n&&directionCD&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&half3&/span& &span class=&n&&offs&/span& &span class=&o&&=&/span& &span class=&mo&&0&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span&&span class=&p&&(&/span&&span class=&k&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mo&&0&/span&&span class=&p&&;&/span&&span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&mi&&5&/span&&span class=&p&&;&/span&&span class=&n&&i&/span&&span class=&o&&++&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&offs&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&o&&+=&/span& &span class=&n&&steepness&/span& &span class=&o&&*&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&steeps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&x&/span& &span class=&o&&*&/span& &span class=&n&&cos&/span&&span class=&p&&(&/span&&span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&sVertex&/span&&span class=&p&&.&/span&&span class=&n&&xz&/span&&span class=&p&&,&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&])&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&n&&offs&/span&&span class=&p&&.&/span&&span class=&n&&z&/span& &span class=&o&&+=&/span& &span class=&n&&steepness&/span& &span class=&o&&*&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&steeps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&y&/span& &span class=&o&&*&/span& &span class=&n&&cos&/span&&span class=&p&&(&/span&&span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&sVertex&/span&&span class=&p&&.&/span&&span class=&n&&xz&/span&&span class=&p&&,&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&])&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&n&&offs&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&o&&+=&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&sin&/span&&span class=&p&&(&/span&&span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&sVertex&/span&&span class=&p&&.&/span&&span class=&n&&xz&/span&&span class=&p&&,&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&xy&/span&&span class=&p&&)&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&n&&offsets&/span& &span class=&o&&=&/span& &span class=&n&&offs&/span&&span class=&p&&;&/span&
&span class=&n&&normal&/span& &span class=&o&&=&/span& &span class=&n&&half3&/span&&span class=&p&&(&/span&&span class=&mo&&0&/span&&span class=&p&&,&/span& &span class=&mi&&1&/span&&span class=&p&&,&/span& &span class=&mo&&0&/span&&span class=&p&&);&/span&
&span class=&k&&for&/span&&span class=&p&&(&/span&&span class=&k&&int&/span& &span class=&n&&i&/span& &span class=&o&&=&/span& &span class=&mo&&0&/span&&span class=&p&&;&/span&&span class=&n&&i&/span& &span class=&o&&&&/span& &span class=&mi&&5&/span&&span class=&p&&;&/span&&span class=&n&&i&/span&&span class=&o&&++&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&normal&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&o&&-=&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&x&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&cos&/span&&span class=&p&&(&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&offs&/span&&span class=&p&&,&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&])&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&n&&normal&/span&&span class=&p&&.&/span&&span class=&n&&z&/span& &span class=&o&&-=&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&y&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&cos&/span&&span class=&p&&(&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&offs&/span&&span class=&p&&,&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&])&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&n&&normal&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&o&&-=&/span& &span class=&n&&steepness&/span& &span class=&o&&*&/span& &span class=&n&&steeps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amps&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&amplitude&/span& &span class=&o&&*&/span& &span class=&n&&sin&/span&&span class=&p&&(&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&offs&/span&&span class=&p&&,&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&dir&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&])&/span& &span class=&o&&+&/span& &span class=&n&&speeds&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&frequency&/span& &span class=&o&&*&/span& &span class=&n&&fs&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&]&/span& &span class=&o&&*&/span& &span class=&n&&_Time&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&&p&Gerstner Wave在游戏中比较常用. 网络上&a href=&http://link.zhihu.com/?target=https%3A//80.lv/articles/tutorial-ocean-shader-with-gerstner-waves/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&有一个UE4的实现教程&/a& [3], 写得非常好, 大家可以参考一下. &/p&&p&Gerstner Wave还有一个变种 --- Skewed Trochoidal Wave, 可以用来模拟涌向岸边的潮水. 其原理可以在&a href=&http://link.zhihu.com/?target=http%3A//outerra.blogspot.com/2011/02/ocean-rendering.html& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&这里&/a&了解(似乎需要梯子). &/p&&figure&&img src=&https://pic3.zhimg.com/v2-afb2cff50ffa_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&640& data-rawheight=&157& class=&origin_image zh-lightbox-thumb& width=&640& data-original=&https://pic3.zhimg.com/v2-afb2cff50ffa_r.jpg&&&/figure&&h2&介绍 - 海洋学统计模型&/h2&&p&海洋科学中并不使用Gerstner Wave作为海面模拟方案, 而是使用基于&b&经验&/b&推导出的&b&统计学模型&/b& [4]: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=h%28x%2C+t%29+%3D%5Csum_%7Bk%7D%5Ctilde%7Bh%7D%28k%2C+t%29exp%28ik+%5Ccdot+x%29& alt=&h(x, t) =\sum_{k}\tilde{h}(k, t)exp(ik \cdot x)& eeimg=&1&&&/p&&p&&img src=&http://www.zhihu.com/equation?tex=k+%3D+%282%5Cpi+n+%2F+L_%7Bx%7D%2C+2%5Cpi+m+%2F+L_%7Bz%7D%29& alt=&k = (2\pi n / L_{x}, 2\pi m / L_{z})& eeimg=&1&&&/p&&p&其中, &img src=&http://www.zhihu.com/equation?tex=n%2C+m& alt=&n, m& eeimg=&1&& 可以理解为网格中每一个顶点的横向和纵向索引, 而求解高度函数 &img src=&http://www.zhihu.com/equation?tex=h& alt=&h& eeimg=&1&& 只需要对 &img src=&http://www.zhihu.com/equation?tex=%5Ctilde%7Bh%7D%28k%2C+t%29& alt=&\tilde{h}(k, t)& eeimg=&1&& 做傅立叶变换即可. &img src=&http://www.zhihu.com/equation?tex=%5Ctilde%7Bh%7D%28k%2C+t%29& alt=&\tilde{h}(k, t)& eeimg=&1&& 定义如下: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=%5Ctilde%7Bh%7D%28k%2C+t%29+%3D+%5Ctilde%7Bh%7D_%7B0%7Dexp%5C%7Bi%5Comega%28k%29t%5C%7D+%2B+%5Ctilde%7Bh%7D_%7B0%7D%5E%7B%2A%7Dexp%5C%7B-i%5Comega%28k%29t%5C%7D& alt=&\tilde{h}(k, t) = \tilde{h}_{0}exp\{i\omega(k)t\} + \tilde{h}_{0}^{*}exp\{-i\omega(k)t\}& eeimg=&1&&&/p&&p&&img src=&http://www.zhihu.com/equation?tex=%5Ctilde%7Bh%7D_%7B0%7D%28k%29+%3D+%28%5Cxi_%7Br%7D+%2B+i%5Cxi_%7Bi%7D%29%5Csqrt%7BP%28k%29+%2F+2%7D& alt=&\tilde{h}_{0}(k) = (\xi_{r} + i\xi_{i})\sqrt{P(k) / 2}& eeimg=&1&&&/p&&p&&img src=&http://www.zhihu.com/equation?tex=%5Comega%5E%7B2%7D%28k%29+%3D+gk%281+%2B+k%5E%7B2%7DL%5E%7B2%7D%29& alt=&\omega^{2}(k) = gk(1 + k^{2}L^{2})& eeimg=&1&&&/p&&p&其中, &img src=&http://www.zhihu.com/equation?tex=%5Cxi_%7Br%7D& alt=&\xi_{r}& eeimg=&1&& 和 &img src=&http://www.zhihu.com/equation?tex=%5Cxi_%7Bi%7D& alt=&\xi_{i}& eeimg=&1&& 是0-1之间的随机数, 不同分布形式的随机数会导致不同的海洋模拟结果; &img src=&http://www.zhihu.com/equation?tex=P%28k%29& alt=&P(k)& eeimg=&1&& 是初始频谱, 本篇文章中我们使用Phillips频谱: &/p&&p&&img src=&http://www.zhihu.com/equation?tex=P_%7Bh%7D%28k%29+%3D+A+%5Cfrac%7Bexp%5Cbigl%28+-1+%2F+%28kL%29%5E%7B2%7D+%5Cbigr%29%7D%7Bk%5E%7B4%7D%7D%7C%5Cbar%7Bk%7D+%5Ccdot+%5Cbar%7B%5Comega%7D%7C%5E%7B2%7D& alt=&P_{h}(k) = A \frac{exp\bigl( -1 / (kL)^{2} \bigr)}{k^{4}}|\bar{k} \cdot \bar{\omega}|^{2}& eeimg=&1&&&/p&&p&另外, Dupuy [5]等人提出可以利用&b&雅可比行列式&/b&来求得每一个顶点的运动撕扯程度. 对于撕扯程度较大的位置更容易产生&b&白沫&/b&:&/p&&figure&&img src=&https://pic2.zhimg.com/v2-2cab501515edcaf_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&550& data-rawheight=&106& class=&origin_image zh-lightbox-thumb& width=&550& data-original=&https://pic2.zhimg.com/v2-2cab501515edcaf_r.jpg&&&/figure&&h2&引入 - 完全基于CPU运算的海洋学统计模型实现&/h2&&p&对于绝大多数人来说, 看到这么多公式内心都是崩溃的(比方说我), 更别提直接实现出来. 考虑到我们之前说过的, &b&水面运动模拟要得到的无非是两组数据: 水面网格的几何波动和法线方向&/b&. 对于前者, 相当于是一组&b&顶点坐标数据&/b&; 对于后者, 相当于是一组&b&向量数据&/b&. 想到这里, 我们不妨先在CPU上实现一下海洋学统计模型, 将结果直接写入Attribute中, 再交给显卡渲染. 显然这种做法的&b&效率&/b&非常之&b&低&/b&, 但是有助于我们&b&理解&/b&. &/p&&p&做法的原理很简单: 先生成初始频谱, 然后每一帧根据当前的散布函数计算当前帧频谱, 最后做傅立叶变换即可得到数据. 让我们不要考虑性能, 不要考虑代码质量, 简单粗暴地写一个来验证下想法: &/p&&div class=&highlight&&&pre&&code class=&language-csharp&&&span&&/span&&span class=&cp&&#region MonoBehaviours&/span&
&span class=&k&&private&/span& &span class=&k&&void&/span& &span class=&nf&&Update&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&n&&timer&/span& &span class=&p&&+=&/span& &span class=&n&&Time&/span&&span class=&p&&.&/span&&span class=&n&&deltaTime&/span& &span class=&p&&/&/span& &span class=&n&&tDivision&/span&&span class=&p&&;&/span&
&span class=&n&&EvaluateWaves&/span&&span class=&p&&(&/span&&span class=&n&&timer&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&k&&private&/span& &span class=&k&&void&/span& &span class=&nf&&Awake&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&n&&filter&/span& &span class=&p&&=&/span& &span class=&n&&GetComponent&/span&&span class=&p&&&&/span&&span class=&n&&MeshFilter&/span&&span class=&p&&&();&/span&
&span class=&n&&mesh&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Mesh&/span&&span class=&p&&();&/span&
&span class=&n&&filter&/span&&span class=&p&&.&/span&&span class=&n&&mesh&/span& &span class=&p&&=&/span& &span class=&n&&mesh&/span&&span class=&p&&;&/span&
&span class=&n&&SetParams&/span&&span class=&p&&();&/span&
&span class=&n&&GenerateMesh&/span&&span class=&p&&();&/span&
&span class=&p&&}&/span&
&span class=&cp&&#endregion&/span&
&/code&&/pre&&/div&&p&&br&&/p&&div class=&highlight&&&pre&&code class=&language-csharp&&&span&&/span&&span class=&k&&private&/span& &span class=&k&&void&/span& &span class=&nf&&SetParams&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&n&&vertices&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&n&&indices&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&kt&&int&/span&&span class=&p&&[(&/span&&span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span& &span class=&p&&*&/span& &span class=&m&&6&/span&&span class=&p&&];&/span&
&span class=&n&&normals&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&n&&vertConj&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&n&&verttilde&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&n&&vertMeow&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&&span class=&c1&&//Meow ~ &/span&
&span class=&n&&uvs&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&p&&}&/span&
&span class=&k&&private&/span& &span class=&k&&void&/span& &span class=&nf&&GenerateMesh&/span&&span class=&p&&()&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&indiceCount&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span&
&span class=&kt&&int&/span& &span class=&n&&halfResolution&/span& &span class=&p&&=&/span& &span class=&n&&resolution&/span& &span class=&p&&/&/span& &span class=&m&&2&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&i&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&kt&&float&/span& &span class=&n&&horizontalPosition&/span& &span class=&p&&=&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&-&/span& &span class=&n&&halfResolution&/span&&span class=&p&&)&/span& &span class=&p&&*&/span& &span class=&n&&unitWidth&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&j&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&currentIdx&/span& &span class=&p&&=&/span& &span class=&n&&i&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span&&span class=&p&&)&/span& &span class=&p&&+&/span& &span class=&n&&j&/span&&span class=&p&&;&/span&
&span class=&kt&&float&/span& &span class=&n&&verticalPosition&/span& &span class=&p&&=&/span& &span class=&p&&(&/span&&span class=&n&&j&/span& &span class=&p&&-&/span& &span class=&n&&halfResolution&/span&&span class=&p&&)&/span& &span class=&p&&*&/span& &span class=&n&&unitWidth&/span&&span class=&p&&;&/span&
&span class=&n&&vertices&/span&&span class=&p&&[&/span&&span class=&n&&currentIdx&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&(&/span&&span class=&n&&horizontalPosition&/span& &span class=&p&&+&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&%&/span& &span class=&m&&2&/span& &span class=&p&&==&/span& &span class=&m&&0&/span&&span class=&p&&?&/span& &span class=&n&&unitWidth&/span& &span class=&p&&/&/span& &span class=&m&&2f&/span& &span class=&p&&:&/span& &span class=&m&&0f&/span&&span class=&p&&),&/span& &span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&n&&verticalPosition&/span& &span class=&p&&+&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&%&/span& &span class=&m&&2&/span& &span class=&p&&==&/span& &span class=&m&&0&/span&&span class=&p&&?&/span& &span class=&n&&unitWidth&/span& &span class=&p&&/&/span& &span class=&m&&2f&/span& &span class=&p&&:&/span& &span class=&m&&0f&/span&&span class=&p&&));&/span&
&span class=&n&&normals&/span&&span class=&p&&[&/span&&span class=&n&&currentIdx&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&(&/span&&span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&1f&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&);&/span&
&span class=&n&&verttilde&/span&&span class=&p&&[&/span&&span class=&n&&currentIdx&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&n&&htilde0&/span&&span class=&p&&(&/span&&span class=&n&&i&/span&&span class=&p&&,&/span& &span class=&n&&j&/span&&span class=&p&&);&/span&
&span class=&n&&Vector2&/span& &span class=&n&&temp&/span& &span class=&p&&=&/span& &span class=&n&&htilde0&/span&&span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&n&&i&/span&&span class=&p&&,&/span& &span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&n&&j&/span&&span class=&p&&);&/span&
&span class=&n&&vertConj&/span&&span class=&p&&[&/span&&span class=&n&&currentIdx&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&p&&-&/span&&span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&n&&uvs&/span&&span class=&p&&[&/span&&span class=&n&&currentIdx&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&*&/span& &span class=&m&&1.0f&/span& &span class=&p&&/&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&),&/span& &span class=&n&&j&/span& &span class=&p&&*&/span& &span class=&m&&1.0f&/span& &span class=&p&&/&/span& &span class=&p&&(&/span&&span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&));&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&j&/span& &span class=&p&&==&/span& &span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span&
&span class=&k&&continue&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&!=&/span& &span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span&&span class=&p&&;&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span& &span class=&p&&+&/span& &span class=&m&&1&/span&&span class=&p&&;&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span& &span class=&p&&+&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&!=&/span& &span class=&m&&0&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span&&span class=&p&&;&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span& &span class=&p&&-&/span& &span class=&n&&resolution&/span& &span class=&p&&+&/span& &span class=&m&&1&/span&&span class=&p&&;&/span&
&span class=&n&&indices&/span&&span class=&p&&[&/span&&span class=&n&&indiceCount&/span&&span class=&p&&++]&/span& &span class=&p&&=&/span& &span class=&n&&currentIdx&/span& &span class=&p&&+&/span& &span class=&m&&1&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&vertices&/span& &span class=&p&&=&/span& &span class=&n&&vertices&/span&&span class=&p&&;&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&SetIndices&/span&&span class=&p&&(&/span&&span class=&n&&indices&/span&&span class=&p&&,&/span& &span class=&n&&MeshTopology&/span&&span class=&p&&.&/span&&span class=&n&&Triangles&/span&&span class=&p&&,&/span& &span class=&m&&0&/span&&span class=&p&&);&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&normals&/span& &span class=&p&&=&/span& &span class=&n&&normals&/span&&span class=&p&&;&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&uv&/span& &span class=&p&&=&/span& &span class=&n&&uvs&/span&&span class=&p&&;&/span&
&span class=&n&&filter&/span&&span class=&p&&.&/span&&span class=&n&&mesh&/span& &span class=&p&&=&/span& &span class=&n&&mesh&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&&p&&br&&/p&&div class=&highlight&&&pre&&code class=&language-csharp&&&span&&/span&&span class=&k&&private&/span& &span class=&n&&Vector3&/span& &span class=&nf&&Displacement&/span&&span class=&p&&(&/span&&span class=&n&&Vector2&/span& &span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&kt&&float&/span& &span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&k&&out&/span& &span class=&n&&Vector3&/span& &span class=&n&&nor&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&Vector2&/span& &span class=&n&&h&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&);&/span&
&span class=&n&&Vector2&/span& &span class=&n&&d&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&);&/span&
&span class=&n&&Vector3&/span& &span class=&n&&n&/span& &span class=&p&&=&/span& &span class=&n&&Vector3&/span&&span class=&p&&.&/span&&span class=&n&&zero&/span&&span class=&p&&;&/span&
&span class=&n&&Vector2&/span& &span class=&n&&c&/span&&span class=&p&&,&/span& &span class=&n&&htilde_c&/span&&span class=&p&&,&/span& &span class=&n&&k&/span&&span class=&p&&;&/span&
&span class=&kt&&float&/span& &span class=&n&&kx&/span&&span class=&p&&,&/span& &span class=&n&&kz&/span&&span class=&p&&,&/span& &span class=&n&&k_length&/span&&span class=&p&&,&/span& &span class=&n&&kDotX&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&i&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&n&&kx&/span& &span class=&p&&=&/span& &span class=&m&&2&/span& &span class=&p&&*&/span& &span class=&n&&PI&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&-&/span& &span class=&n&&resolution&/span& &span class=&p&&/&/span& &span class=&m&&2.0f&/span&&span class=&p&&)&/span& &span class=&p&&/&/span& &span class=&n&&length&/span&&span class=&p&&;&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&j&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&n&&kz&/span& &span class=&p&&=&/span& &span class=&m&&2&/span& &span class=&p&&*&/span& &span class=&n&&PI&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&j&/span& &span class=&p&&-&/span& &span class=&n&&resolution&/span& &span class=&p&&/&/span& &span class=&m&&2.0f&/span&&span class=&p&&)&/span& &span class=&p&&/&/span& &span class=&n&&length&/span&&span class=&p&&;&/span&
&span class=&n&&k&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&kx&/span&&span class=&p&&,&/span& &span class=&n&&kz&/span&&span class=&p&&);&/span&
&span class=&n&&k_length&/span& &span class=&p&&=&/span& &span class=&n&&k&/span&&span class=&p&&.&/span&&span class=&n&&magnitude&/span&&span class=&p&&;&/span&
&span class=&n&&kDotX&/span& &span class=&p&&=&/span& &span class=&n&&Vector2&/span&&span class=&p&&.&/span&&span class=&n&&Dot&/span&&span class=&p&&(&/span&&span class=&n&&k&/span&&span class=&p&&,&/span& &span class=&n&&x&/span&&span class=&p&&);&/span&
&span class=&n&&c&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Cos&/span&&span class=&p&&(&/span&&span class=&n&&kDotX&/span&&span class=&p&&),&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Sin&/span&&span class=&p&&(&/span&&span class=&n&&kDotX&/span&&span class=&p&&));&/span&
&span class=&n&&Vector2&/span& &span class=&n&&temp&/span& &span class=&p&&=&/span& &span class=&n&&htilde&/span&&span class=&p&&(&/span&&span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&n&&i&/span&&span class=&p&&,&/span& &span class=&n&&j&/span&&span class=&p&&);&/span&
&span class=&n&&htilde_c&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&p&&*&/span& &span class=&n&&c&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&p&&-&/span& &span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&p&&*&/span& &span class=&n&&c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span& &span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&p&&*&/span& &span class=&n&&c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&p&&+&/span& &span class=&n&&temp&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&p&&*&/span& &span class=&n&&c&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&);&/span&
&span class=&n&&h&/span& &span class=&p&&+=&/span& &span class=&n&&htilde_c&/span&&span class=&p&&;&/span&
&span class=&n&&n&/span& &span class=&p&&+=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&(-&/span&&span class=&n&&kx&/span& &span class=&p&&*&/span& &span class=&n&&htilde_c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&p&&-&/span&&span class=&n&&kz&/span& &span class=&p&&*&/span& &span class=&n&&htilde_c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&k_length&/span& &span class=&p&&&&/span& &span class=&n&&EPSILON&/span&&span class=&p&&)&/span&
&span class=&k&&continue&/span&&span class=&p&&;&/span&
&span class=&n&&d&/span& &span class=&p&&+=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&kx&/span& &span class=&p&&/&/span& &span class=&n&&k_length&/span& &span class=&p&&*&/span& &span class=&n&&htilde_c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span& &span class=&p&&-&/span&&span class=&n&&kz&/span& &span class=&p&&/&/span& &span class=&n&&k_length&/span& &span class=&p&&*&/span& &span class=&n&&htilde_c&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&n&&nor&/span& &span class=&p&&=&/span& &span class=&n&&Vector3&/span&&span class=&p&&.&/span&&span class=&n&&Normalize&/span&&span class=&p&&(&/span&&span class=&n&&Vector3&/span&&span class=&p&&.&/span&&span class=&n&&up&/span& &span class=&p&&-&/span& &span class=&n&&n&/span&&span class=&p&&);&/span&
&span class=&k&&return&/span& &span class=&k&&new&/span& &span class=&nf&&Vector3&/span&&span class=&p&&(&/span&&span class=&n&&d&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&h&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&d&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&&p&&br&&/p&&div class=&highlight&&&pre&&code class=&language-csharp&&&span&&/span&&span class=&k&&private&/span& &span class=&k&&void&/span& &span class=&nf&&EvaluateWaves&/span&&span class=&p&&(&/span&&span class=&kt&&float&/span& &span class=&n&&t&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&hds&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&i&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&j&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&index&/span& &span class=&p&&=&/span& &span class=&n&&i&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span& &span class=&p&&+&/span& &span class=&n&&j&/span&&span class=&p&&;&/span&
&span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&n&&vertices&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&];&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&i&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&j&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&index&/span& &span class=&p&&=&/span& &span class=&n&&i&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span& &span class=&p&&+&/span& &span class=&n&&j&/span&&span class=&p&&;&/span&
&span class=&n&&Vector3&/span& &span class=&n&&nor&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector3&/span&&span class=&p&&(&/span&&span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&);&/span&
&span class=&n&&Vector3&/span& &span class=&n&&hd&/span& &span class=&p&&=&/span& &span class=&n&&Displacement&/span&&span class=&p&&(&/span&&span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&z&/span&&span class=&p&&),&/span& &span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&k&&out&/span& &span class=&n&&nor&/span&&span class=&p&&);&/span&
&span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&y&/span& &span class=&p&&=&/span& &span class=&n&&hd&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&;&/span&
&span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&z&/span& &span class=&p&&=&/span& &span class=&n&&vertices&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&z&/span& &span class=&p&&-&/span& &span class=&n&&hd&/span&&span class=&p&&.&/span&&span class=&n&&z&/span& &span class=&p&&*&/span& &span class=&n&&choppiness&/span&&span class=&p&&;&/span&
&span class=&n&&vertMeow&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&x&/span& &span class=&p&&=&/span& &span class=&n&&vertices&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&x&/span& &span class=&p&&-&/span& &span class=&n&&hd&/span&&span class=&p&&.&/span&&span class=&n&&x&/span& &span class=&p&&*&/span& &span class=&n&&choppiness&/span&&span class=&p&&;&/span&
&span class=&n&&normals&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&n&&nor&/span&&span class=&p&&;&/span&
&span class=&n&&hds&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&hd&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&hd&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&n&&Color&/span&&span class=&p&&[]&/span& &span class=&n&&colors&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Color&/span&&span class=&p&&[&/span&&span class=&n&&resolution&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span&&span class=&p&&];&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&i&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&i&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&i&/span&&span class=&p&&++)&/span&&span class=&c1&&//写得并不正确,&/span&
&span class=&p&&{&/span&
&span class=&k&&for&/span& &span class=&p&&(&/span&&span class=&kt&&int&/span& &span class=&n&&j&/span& &span class=&p&&=&/span& &span class=&m&&0&/span&&span class=&p&&;&/span& &span class=&n&&j&/span& &span class=&p&&&&/span& &span class=&n&&resolution&/span&&span class=&p&&;&/span& &span class=&n&&j&/span&&span class=&p&&++)&/span&
&span class=&p&&{&/span&
&span class=&kt&&int&/span& &span class=&n&&index&/span& &span class=&p&&=&/span& &span class=&n&&i&/span& &span class=&p&&*&/span& &span class=&n&&resolution&/span& &span class=&p&&+&/span& &span class=&n&&j&/span&&span class=&p&&;&/span&
&span class=&n&&Vector2&/span& &span class=&n&&dDdx&/span& &span class=&p&&=&/span& &span class=&n&&Vector2&/span&&span class=&p&&.&/span&&span class=&n&&zero&/span&&span class=&p&&;&/span&
&span class=&n&&Vector2&/span& &span class=&n&&dDdy&/span& &span class=&p&&=&/span& &span class=&n&&Vector2&/span&&span class=&p&&.&/span&&span class=&n&&zero&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&i&/span& &span class=&p&&!=&/span& &span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&dDdx&/span& &span class=&p&&=&/span& &span class=&m&&0.5f&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&hds&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&-&/span& &span class=&n&&hds&/span&&span class=&p&&[&/span&&span class=&n&&index&/span& &span class=&p&&+&/span& &span class=&n&&resolution&/span&&span class=&p&&]);&/span&
&span class=&p&&}&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&j&/span& &span class=&p&&!=&/span& &span class=&n&&resolution&/span& &span class=&p&&-&/span& &span class=&m&&1&/span&&span class=&p&&)&/span&
&span class=&p&&{&/span&
&span class=&n&&dDdy&/span& &span class=&p&&=&/span& &span class=&m&&0.5f&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&n&&hds&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&-&/span& &span class=&n&&hds&/span&&span class=&p&&[&/span&&span class=&n&&index&/span& &span class=&p&&+&/span& &span class=&m&&1&/span&&span class=&p&&]);&/span&
&span class=&p&&}&/span&
&span class=&kt&&float&/span& &span class=&n&&jacobian&/span& &span class=&p&&=&/span& &span class=&p&&(&/span&&span class=&m&&1&/span& &span class=&p&&+&/span& &span class=&n&&dDdx&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&)&/span& &span class=&p&&*&/span& &span class=&p&&(&/span&&span class=&m&&1&/span& &span class=&p&&+&/span& &span class=&n&&dDdy&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&)&/span& &span class=&p&&-&/span& &span class=&n&&dDdx&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&p&&*&/span& &span class=&n&&dDdy&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&;&/span&
&span class=&n&&Vector2&/span& &span class=&n&&noise&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Vector2&/span&&span class=&p&&(&/span&&span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Abs&/span&&span class=&p&&(&/span&&span class=&n&&normals&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&x&/span&&span class=&p&&),&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Abs&/span&&span class=&p&&(&/span&&span class=&n&&normals&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&].&/span&&span class=&n&&z&/span&&span class=&p&&))&/span& &span class=&p&&*&/span& &span class=&m&&0.3f&/span&&span class=&p&&;&/span&
&span class=&kt&&float&/span& &span class=&n&&turb&/span& &span class=&p&&=&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Max&/span&&span class=&p&&(&/span&&span class=&m&&1f&/span& &span class=&p&&-&/span& &span class=&n&&jacobian&/span& &span class=&p&&+&/span& &span class=&n&&noise&/span&&span class=&p&&.&/span&&span class=&n&&magnitude&/span&&span class=&p&&,&/span& &span class=&m&&0f&/span&&span class=&p&&);&/span&
&span class=&kt&&float&/span& &span class=&n&&xx&/span& &span class=&p&&=&/span& &span class=&m&&1f&/span& &span class=&p&&+&/span& &span class=&m&&3f&/span& &span class=&p&&*&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&SmoothStep&/span&&span class=&p&&(&/span&&span class=&m&&1.2f&/span&&span class=&p&&,&/span& &span class=&m&&1.8f&/span&&span class=&p&&,&/span& &span class=&n&&turb&/span&&span class=&p&&);&/span&
&span class=&n&&xx&/span& &span class=&p&&=&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&Min&/span&&span class=&p&&(&/span&&span class=&n&&turb&/span&&span class=&p&&,&/span& &span class=&m&&1.0f&/span&&span class=&p&&);&/span&
&span class=&n&&xx&/span& &span class=&p&&=&/span& &span class=&n&&Mathf&/span&&span class=&p&&.&/span&&span class=&n&&SmoothStep&/span&&span class=&p&&(&/span&&span class=&m&&0f&/span&&span class=&p&&,&/span& &span class=&m&&1f&/span&&span class=&p&&,&/span& &span class=&n&&turb&/span&&span class=&p&&);&/span&
&span class=&n&&colors&/span&&span class=&p&&[&/span&&span class=&n&&index&/span&&span class=&p&&]&/span& &span class=&p&&=&/span& &span class=&k&&new&/span& &span class=&n&&Color&/span&&span class=&p&&(&/span&&span class=&n&&xx&/span&&span class=&p&&,&/span& &span class=&n&&xx&/span&&span class=&p&&,&/span& &span class=&n&&xx&/span&&span class=&p&&,&/span& &span class=&n&&xx&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&p&&}&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&vertices&/span& &span class=&p&&=&/span& &span class=&n&&vertMeow&/span&&span class=&p&&;&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&normals&/span& &span class=&p&&=&/span& &span class=&n&&normals&/span&&span class=&p&&;&/span&
&span class=&n&&mesh&/span&&span class=&p&&.&/span&&span class=&n&&colors&/span& &span class=&p&&=&/span& &span class=&n&&colors&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&/code&&/pre&&/div&&p&&br&&/p&&p&以上代码完全没有经过任何优化, 甚至连DFT都使用了暴力方式进行求解, 相当于把公式直白地翻译了一遍(换句话说, 这要是还看不懂就可以 ... 额). 这段代码运行起来, 在我的i7-7700HQ上可以支持高达18*18的水面(笑, 再大一点就跑不满60FPS了): &/p&&figure&&img src=&https://pic2.zhimg.com/v2-9219c35cfcc11be8bc29c94d80ac20d7_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&475& data-rawheight=&422& data-thumbnail=&https://pic4.zhimg.com/v2-9219c35cfcc11be8bc29c94d80ac20d7_b.jpg& class=&origin_image zh-lightbox-thumb& width=&475& data-original=&https://pic4.zhimg.com/v2-9219c35cfcc11be8bc29c94d80ac20d7_r.jpg&&&/figure&&p&关于统计学模型在CPU上的实现, &a href=&http://link.zhihu.com/?target=https%3A//www.keithlantz.net/2011/10/ocean-simulation-part-one-using-the-discrete-fourier-transform/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&这篇博客&/a&写得不错 [6]. 虽然里面有些公式用错了, 但是有很大的参考价值. &/p&&p&嗯, 看起来我们的理论没有问题. 那么现在要做的就是给暴力的运算提提速, 搬个家! &/p&&h2&进化 - GPU上的FFT, 随机数与Implementation Notes&/h2&&p&说到FFT, 我们马上就能想到的是Cooley-Tukey [6]的蝶形变换, 能将n方级别的DIT优化到nlogn级别. Cooley-Tukey的FFT求解方式是可以放到GPU上实现的, 但是基于GPU的FFT中有一种叫Stockham Formulation [7]的做法. 下图是两个做法的比较: &/p&&figure&&img src=&https://pic1.zhimg.com/v2-a00ecbca83e58_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&547& data-rawheight=&293& class=&origin_image zh-lightbox-thumb& width=&547& data-original=&https://pic1.zhimg.com/v2-a00ecbca83e58_r.jpg&&&/figure&&p&如今很多GPU上的FFT实现方式都是基于Stockham FFT的, 比如&a href=&http://link.zhihu.com/?target=https%3A//github.com/Themaister/GLFFT& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&GLFFT&/a&. 关于各种FFT求解方式的横向比较可以&a href=&http://link.zhihu.com/?target=http%3A//users.ece.cmu.edu/%7Efranzf/papers/fft-enc11.pdf& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&参考这里&/a& [8]. &/p&&p&Stockham FFT的伪代码如下: &/p&&figure&&img src=&https://pic1.zhimg.com/v2-8b6acfab14fca8a9f9e0efa82dbcea5c_b.jpg& data-caption=&& data-size=&normal& data-rawwidth=&634& data-rawheight=&358& class=&origin_image zh-lightbox-thumb& width=&634& data-original=&https://pic1.zhimg.com/v2-8b6acfab14fca8a9f9e0efa82dbcea5c_r.jpg&&&/figure&&p&我的实现中把横向和纵向写到了一起, 通过Shader开关来控制. 代码如下: &/p&&div class=&highlight&&&pre&&code class=&language-glsl&&&span&&/span&&span class=&n&&Shader&/span& &span class=&err&&&&/span&&span class=&n&&Hidden&/span&&span class=&o&&/&/span&&span class=&n&&Mistral&/span& &span class=&n&&Water&/span&&span class=&o&&/&/span&&span class=&n&&Helper&/span&&span class=&o&&/&/span&&span class=&n&&Vertex&/span&&span class=&o&&/&/span&&span class=&n&&Stockham&/span&&span class=&err&&&&/span&
&span class=&p&&{&/span&
&span class=&n&&Properties&/span&
&span class=&p&&{&/span&
&span class=&n&&_Input&/span& &span class=&p&&(&/span&&span class=&err&&&&/span&&span class=&n&&Input&/span& &span class=&n&&Sampler&/span&&span class=&err&&&&/span&&span class=&p&&,&/span& &span class=&mi&&2&/span&&span class=&n&&D&/span&&span class=&p&&)&/span& &span class=&o&&=&/span& &span class=&err&&&&/span&&span class=&n&&black&/span&&span class=&err&&&&/span& &span class=&p&&{}&/span&
&span class=&n&&_TransformSize&/span& &span class=&p&&(&/span&&span class=&err&&&&/span&&span class=&n&&Transform&/span& &span class=&n&&Size&/span&&span class=&err&&&&/span&&span class=&p&&,&/span& &span class=&n&&Float&/span&&span class=&p&&)&/span& &span class=&o&&=&/span& &span class=&mi&&256&/span&
&span class=&n&&_SubTransformSize&/span& &span class=&p&&(&/span&&span class=&err&&&&/span&&span class=&n&&Log&/span& &span class=&n&&Size&/span&&span class=&err&&