&p&作为一个纠结了很久是不是要读PhD的人，还有同样作为Graphics Professional，我来分享看法。&/p&&p&开始之前先推荐两个文档，比较客观给出了写了一些现状和评价：&/p&&p&Life after PhD, by Fredo Durand, MIT: &a href=&///?target=http%3A//people.csail.mit.edu/fredo/LifeAfterPhD.pdf& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&people.csail.mit.edu/fr&/span&&span class=&invisible&&edo/LifeAfterPhD.pdf&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&/p&&p&PhD Survival Guide, by Toshiya Hachisuka, 东京大学: &a href=&///?target=http%3A//www.ci.i.u-tokyo.ac.jp/%7Ehachisuka/survival.pdf& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&ci.i.u-tokyo.ac.jp/~hac&/span&&span class=&invisible&&hisuka/survival.pdf&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&/p&&br&&p&鉴于很多人可能懒得点，我就大概的在这总结一下。。&/p&&p&首先General的来说，PhD的几种出路：&/p&&p&&b&教职&/b&：&/p&&p&优点是非常灵活的工作节奏，主要职责是教书，做科研，带学生。会面对一些需要筹钱和对自己Lab的基本管理。拿到tenure以后变成铁饭碗。缺点是教职的市场非常competitive，相信在中国和美国都一样。周围认识的PhD师兄真正走这条路成功的凤毛菱角，而且常常也意味着需要蹲当post doc若干时间。。Graphics方向的当上faculty的中国人我所知道的有&a href=&///?target=http%3A//www.cs.columbia.edu/%7Ecxz/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Changxi Zheng's Homepage&i class=&icon-external&&&/i&&/a&和&a href=&///?target=http%3A//web.cse.ohio-state.edu/%7Ewhmin/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Huamin Wang&i class=&icon-external&&&/i&&/a&。后者还是我老板的学生。我都不personally认识他们，但是圈子里口耳相传这些也是传说级别了。&/p&&p&&b&研究科学家&/b&:&/p&&p&似乎这东西美国才有，就是研究员。和faculty一样也要筹钱带学生做research。但是不能教书，工作没有tenure稳定而且筹钱的压力也更大。但是毕竟还在学术圈，有机会转成faculty。&/p&&p&&b&工业界的研究机构&/b&：&/p&&p&如MSR,Intel Research, NVIDIA Research，Adobe等。不需要教书和筹集资金。而且要是发牛逼paper也有机会再回学术圈。但是做起研究来比较难找到好的grad student，通常都是招的summer intern。还有同样的，研究的职位也相对竞争非常激烈。&/p&&p&&b&工业界&/b&：&/p&&p&优点是钱多，而且也许不那么忙（在美国的话）。但是不能教书，工作没有那么灵活，而且一旦离开学术圈很难再回去。&/p&&p&&b&创业&/b&：&/p&&p&没什么说的，大家都懂，例如百度李彦宏。&/p&&br&&p&说完了General的PhD，再聊聊Graphics这个方向。&/p&&p&作为多年的graphics enthusiast，记得当年本科毕业的时候在招聘会上就被各种令郎满目的“招Java”，“招Php”，“招前端”等给亮瞎了眼。似乎自己的存在感被抹杀了，当时找了个最和图形有关系的实习居然是腾讯的某2D网页游戏的策划（跑题了- -）。&/p&&p&其他方向我不是特别了解，但graphics的学术圈和工业界focus的重点脱节其实蛮严重的。举个简单的例子就是&b&Animation&/b&现在是Graphics非常热的一个研究方向。非常math and physics intense，也有点偏robotics（例如&a href=&///?target=http%3A//www.cc.gatech.edu/%7Ejtan34/project/learningBicycleStunts.html& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Learning Bicycle Stunts&i class=&icon-external&&&/i&&/a&，转一个大牛师兄的paper）。这一类技术在无论游戏或者是电影应用的普及程度几乎为零，并且短期内我不太相信这种局面能改变。&/p&&p&另一个大方向是&b&Simulation&/b&（例如&a href=&///?target=http%3A//physbam.stanford.edu/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&PhysBAM&i class=&icon-external&&&/i&&/a&，特别炫的网页），也是我个人研究的方向之一，能用code写出各种炫酷的效果实在是神奇。但是现实就是，搞这个东西的出路也许只有教职和少数例如Adobe，Autodesk的研究机构和特效公司例如Weta，ILM等。&/p&&p&再甚至&b&Rendering&/b&，在美国（中国就不说了，几乎完全没有这方面的机会）绝大多数研究相信还是基于光线追踪的离线渲染，如何更高校的采样更复杂的场景。而业界需要的rendering绝大多数岗位都是游戏公司。而游戏里用的渲染技术更多是hack，不需要大量的人去做这个事情。业界更注重从系统的角度使artist和engineer能更高效的工作和输出结果。哪怕是电影特效界的渲染器，如renderman，也都并不一定都是完全基于物理的渲染，他们同样需要从系统的角度使得他们的制作流水线更加高效，控制成本等（&a href=&///?target=http%3A///featured/the-state-of-rendering-part-2/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&The State of Rendering&i class=&icon-external&&&/i&&/a& 一个概括业界主流渲染器的文章）。而且其实学术圈这两三年光线追踪的各种牛逼算法目前其实基本上所有创新都来自于欧洲那群学校，美国只要cornell能和他们拼拼了。但我毕竟没有在游戏公司呆过，这方面Zynga的工程师 &a class=&member_mention& href=&///people/baaf84c2fc30cd& data-editable=&true& data-hash=&baaf84c2fc30cd& data-title=&@庞博& data-hovercard=&p$b$baaf84c2fc30cd&&@庞博&/a& 应该更有资格发言。哪怕看起来完全对口的公司，NVIDIA，其实绝大部分岗位都是和graphics没有半毛钱关系的。我现在有幸在NV做Rendering的部门，之前在也在Architecture部门实习过还是可以很负责的说这个话的。当然PhD毕业去NV Research还是能做很多有意思的事情的，感觉NV真的把所有graphics人都招了。。&/p&&p&当然例外也是有的， CMU PhD &a class=&member_mention& href=&///people/661caec93ce39338cd42& data-editable=&true& data-hash=&661caec93ce39338cd42& data-title=&@Yong He& data-hovercard=&p$b$661caec93ce39338cd42&&@Yong He&/a& 的research就是从从系统的角度去做业界直接需要的graphics问题，但他是我认识唯一一个这样的人。。&/p&&p&还有一些其他方向，geometry，3d printing等，我不是特别了解就不评价了。。但总之和其他研究大数据的打个电话能去google弄相关的东西比有些差别。&/p&&br&&p&不知不觉好像写成吐槽文了。其实绝对不是的。Graphics的确是最有魅力最浪漫的一个CS branch。而且有太多可以自己钻研的空间，从头到尾写一个（非常快的）渲染器，甚至自己的引擎等也非常锻炼整体coding的能力,各种有趣的物理、数学、统计学更是有研究不完的问题（&a href=&///?target=http%3A//www.ci.i.u-tokyo.ac.jp/%7Ehachisuka/mcqmc2014.pdf& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&ci.i.u-tokyo.ac.jp/~hac&/span&&span class=&invisible&&hisuka/mcqmc2014.pdf&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&）。而且回到主题，能当一个好的PhD唯一应该有的动机，和能成功坚持动力就应该是对于你所做事情本身的热爱！也许这个方向机会不如那些去google，fb的多，但是另一个角度也说明最后坚持下来做的人都是真正爱他的，拔尖的人，不是么？这些人肯定有机会闯出一番天地啊！&/p&&br&&p&不要太过花时间去在意这些大家对你说的“以后可能的出路”，去大胆的做自己爱的事情，你会收获快乐和成长，你会走出你自己的路。我很自豪我热爱Graphics！最后..我引用一些steve jobs在stanford演讲说过的话作为这冗长文的结束吧.
&You've got to find what you love. And that is as ture for works as
it is for lovers. Your works is gonna fill a large part of your lives. And the
only way to truely satisfy is to do what you believe is great work. And the only
way to do great work is to love what you do. If you haven't found it yet, keep
looking, don't settle. You'll know when you find it.&&/p&&p&
还有..&/p&&p&
&Time is limited, so don't waste it living someelse's lives. Dont be
trapped by dogma, which is living with the results of other people's thinking.
Dont let noise of others' opinion drown out your inner voice. And most
important, have the courage to follow your heart and intuition. They somehow
already know what you truly want. Everything else is secondary.&&/p&&br&&p&补充一下，&/p&&p&看到许多朋友的评论说弄图形吃力不讨好，冷门等。似乎这文章起到了反效果。。&/p&&p&我想说的是上面写的东西只是说明，图形学术圈的人做的事情和工业界的大多数岗位不一样（学术界会更先进，但是解决方案也没有那么健壮和相对工业界多年的积累，相信其他方向也一样但是可能分化相对小些）。例如做Simulation的人去了Apple，估计就去弄图形API，或者OS的渲染，但是要是去了Weta Digital估计还是有机会继续simulation的，只是后者的岗位相对少。&/p&&p&&b&但我不是想说图形业界衰败了，没有工作职位！&/b&楼下的朋友们总结了那么多公司我就不重复了，对于那些岗位来说有图形背景童鞋的竞争力肯定比没有的大许多。而且总的来说游戏行业和电影行业都是非常庞大的，无论是桌面还是手机需要很多的图形从业者。苹果不是还新出了个Metal么。&a href=&///?target=http%3A//pbrt.org/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Physically Based Rendering: From Theory to Implementation&i class=&icon-external&&&/i&&/a& 的作者现在还在Google做神秘的事情呢。而且作为博士你的老板也会有各种业界的联系让你有很大机会能继续你的研究。&/p&
作为一个纠结了很久是不是要读PhD的人，还有同样作为Graphics Professional，我来分享看法。开始之前先推荐两个文档，比较客观给出了写了一些现状和评价：Life after PhD, by Fredo Durand, MIT: PhD Survival Guide, by Toshiya Hachi…
感谢邀请。这个话题太大了，我本人了解的就并不全面，研究的更只是其中一个很小的分支。不过我可以尽量尝试着讲一下。&br&计算机图形学各个领域的目标或许不同，但最终的形式都是渲染(即绘制)在二维的显示设备上的图像。下面是一个简单（可能并不完全）的分类：&br&计算机图形学-领域及分支：&br&1 绘制&br&
1.1 真实感绘制(非实时)&br&
1.1.1 光线追踪(Ray-tracing)&br&
1.1.2 全局光照(Global Illumination)&br&
......&br&
1.2 实时绘制&br&
1.2.1 Shading(BRDF, Programmable Shading等)&br&
1.2.2 纹理(Texture Synthesis, 反走样, 采样等)&br&
1.2.3 阴影和环境光照(Ambient Occlusion, Shadow Volume等)&br&
1.2.4 基于图像的算法(HDR, Depth of Field, Motion Blur等)&br&
1.2.5 光照算法(PRT, 球面谐波(Spherical Harmonic)等)&br&
......&br&2 建模&br&
2.1 曲面/曲线(Bézier曲线, B样条(B-Spline), 细分曲面(Subdivision Surface/Tessellation))&br&
2.2 网格(Mesh)及形变(Morphing)&br&
2.3 模型修复及重建(计算机视觉交叉方向)&br&
......&br&3 物理模拟&br&
3.1 刚体碰撞模拟&br&
3.2 流体模拟(烟 火 水)&br&
3.3 柔体模拟(布料 头发 皮肤 橡胶等)&br&
......&br&4 动画&br&
4.1 关键帧技术(keyframe)&br&
4.2 基于物理的动画(Human motion capture, character animation等)&br&
......&br&5 科学计算可视化&br&
5.1 标量场可视化(Isosurface和体绘制 Raycasting等)&br&
5.2 矢量场可视化(Flow visualization等)&br&
5.3 信息可视化(如Social-Network Link Graph等)&br&
......&br&6 延展和相关领域&br&
6.1 图形硬件和GPU Computing(利用GPU进行普适的并行计算)&br&
6.2 计算摄影学Computational Photography(图像处理和图形学的结合)&br&
6.3 计算机视觉Computer Vision(是计算机图形学的逆向学科 如何从二维图像和视频中提取三维空间信息和内容理解)&br&
6.4 大规模数据分析(大规模数据的可视化及物理模拟 如天气 洋流 社交网络信息等)&br&
6.5 游戏引擎(是实时绘制+建模+物理模拟+动画的集合体)&br&
6.6 电影动画及特效(是真实感绘制+建模+物理模拟+动画+计算机视觉等的集合体)&br&
6.7 编译器及编程模型(GPU Shading Language语言设计及并行编程模型)&br&
......&br&参考资料：&br&[1] Real-Time Rendering, Third Edition&br&[2] Physical-based Rendering, Second Edition&br&[2] The Visualization Hand Book&br&这个分类一定还不够完全，欢迎各位同仁指出不完备之处。不过提问者可以通过上面的表大概了解图形学的研究内容。至于未来的发展趋势，我个人从事的图形硬件和并行计算我认为是一个很有前景的方向。另外几乎在每个我所列出的领域内都有迷人而艰难的未解决的问题。在图灵奖历次获奖者中，和计算机图形学唯一相关的就是图形学之父Ivan Sutherland。所以说，计算机图形学是一个相当年轻的学科，会有很光明的发展前途。我会在下面列出一些曾经帮助过我的参考资料和一些领域的教授页面/软件资源以 1)供提问者进一步获取信息 2)展示图形学的迷人之处：&br&&br&[1] 一篇极好的介绍球面谐波的教程：&a href=&///?target=http%3A//www.cs.columbia.edu/%7Ecs4162/slides/spherical-harmonic-lighting.pdf& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&cs.columbia.edu/~cs4162&/span&&span class=&invisible&&/slides/spherical-harmonic-lighting.pdf&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[2] Gatech教授Karen Liu 主要研究动画技术：&a href=&///?target=http%3A//www.cc.gatech.edu/%7Ekarenliu/Home.html& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&cc.gatech.edu/~karenliu&/span&&span class=&invisible&&/Home.html&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[3] TAMU教授Jin-xiang Chai 动画技术：&a href=&///?target=http%3A//faculty.cs.tamu.edu/jchai/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&faculty.cs.tamu.edu/jch&/span&&span class=&invisible&&ai/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[4] Cornell教授Doug L. James 物理模拟：&a href=&///?target=http%3A//www.cs.cornell.edu/%7Edjames/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&cs.cornell.edu/~djames/&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[5] Stanford教授Ron Fedkiw 物理模拟：&a href=&///?target=http%3A//physbam.stanford.edu/%7Efedkiw/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&physbam.stanford.edu/~f&/span&&span class=&invisible&&edkiw/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[6] 物理模拟的一篇Siggraph课程：&a href=&///?target=http%3A///realtimephysics/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&/re&/span&&span class=&invisible&&altimephysics/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[7] 微软的Hugues Hoppe 模型+纹理：&a href=&///?target=http%3A///en-us/um/people/hoppe/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&/&/span&&span class=&invisible&&en-us/um/people/hoppe/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[8] Caltech应用几何实验室：&a href=&///?target=http%3A//www.geometry.caltech.edu/geo.html& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&geometry.caltech.edu/ge&/span&&span class=&invisible&&o.html&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[9] 浙江大学GAPS实验室：&a href=&///?target=http%3A//www.gaps-zju.org/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&gaps-zju.org/&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[10] 清华大学胡事民教授实验室： &a href=&///?target=http%3A//cg.cs./& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&cg.cs./&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[11] 中科院深先所陈宝权教授： &a href=&///?target=http%3A//web./%7Ebaoquan/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&web./~baoquan&/span&&span class=&invisible&&/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[12] UC Davis教授John Owens(我的导师:-)，GPU Computing：&a href=&///?target=http%3A//www.ece.ucdavis.edu/%7Ejowens/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&ece.ucdavis.edu/~jowens&/span&&span class=&invisible&&/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[13] GPU Gems 1/2/3: &a href=&///?target=http%3A///content/gpu-gems-part-i-natural-effects& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&/co&/span&&span class=&invisible&&ntent/gpu-gems-part-i-natural-effects&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &a href=&///?target=http%3A///node/17& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&/no&/span&&span class=&invisible&&de/17&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &a href=&///?target=http%3A///content/gpu-gems-3& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&/co&/span&&span class=&invisible&&ntent/gpu-gems-3&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[14] Pixar的Renderman页面： &a href=&///?target=https%3A///& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&https://&/span&&span class=&visible&&/&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[15] 国内最好的开源游戏引擎(作者是MSRA的龚敏敏)： &a href=&///?target=http%3A//www.klayge.org/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&klayge.org/&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[16] 最适宜学习引擎结构的游戏引擎OGRE： &a href=&///?target=http%3A//www.ogre3d.org/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&ogre3d.org/&/span&&span class=&invisible&&&/span&&i class=&icon-external&&&/i&&/a&&br&[17] 个人认为最好的开源的基于物理的真实感绘制引擎LuxRender: &a href=&///?target=http%3A//www.luxrender.net/en_GB/index& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&luxrender.net/en_GB/ind&/span&&span class=&invisible&&ex&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[18] 图形学界最无私的奉献者Ke-sen Huang的主页，包含历次重要图形学会议所有可公开下载论文及资料链接 向他致敬： &a href=&///?target=http%3A///& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&&/span&&span class=&invisible&&/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &br&&br&另外，上面提到的三本教材也值得一读。希望提问者能享受图形学的学习，尽快找到研究方向并作出好的成果。个人认为在拥有数据挖掘背景的前提下，提问者可以尝试在大规模数据分析和可视化或计算机视觉领域寻找感兴趣的方向，我个人有如下推荐：&br&[1] 社交网络分析 &a href=&///?target=http%3A//en.wikipedia.org/wiki/Social_network_analysis& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&en.wikipedia.org/wiki/S&/span&&span class=&invisible&&ocial_network_analysis&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&&br&[2] 基于海量网络照片的三维模型重建&br&&a href=&///?target=http%3A//www.cs.cornell.edu/%7Esnavely/courses/phototour_im2gps/index.html& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://www.&/span&&span class=&visible&&cs.cornell.edu/~snavely&/span&&span class=&invisible&&/courses/phototour_im2gps/index.html&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &br&&a href=&///?target=http%3A//phototour.cs.washington.edu/& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&phototour.cs.washington.edu&/span&&span class=&invisible&&/&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &br&photosynth是微软的一个项目，看看埃菲尔铁塔的例子：&a href=&///?target=http%3A//photosynth.net/view.aspx%3Fcid%3Dbe06fae6-bda7-4e91-aea3-d214fb4508e7& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&photosynth.net/view.asp&/span&&span class=&invisible&&x?cid=be06fae6-bda7-4e91-aea3-d214fb4508e7&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &br&[3] 胡事民老师的一个非常聪明的项目，Sketch2photo：&br&&a href=&///?target=http%3A//cg.cs./montage/main.htm& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&cg.cs./m&/span&&span class=&invisible&&ontage/main.htm&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a& &br&&br&希望能给你一些灵感。
感谢邀请。这个话题太大了，我本人了解的就并不全面，研究的更只是其中一个很小的分支。不过我可以尽量尝试着讲一下。 计算机图形学各个领域的目标或许不同，但最终的形式都是渲染(即绘制)在二维的显示设备上的图像。下面是一个简单（可能并不完全）的分类…
之前实验室组会讨论时，我找过类似的资料，可以跟题主分享一下。像&a href=&/people/miloyip& class=&internal&&Milo Yip&/a&说的，非真实感在学术上感觉不太活跃，我个人觉得一方面是因为非真实感渲染非主流趋势，更多的是一些小众的需求；另一方面，其实偶尔SIGGRAPH也有非真实感渲染的session，只是不再局限于传统上的感觉的那种“纯正”的非真实渲染，我下面会提到一些这样的文章。其实非真实感渲染的涵盖范围很广。&br&&br&==========论文===========&br&&br&先说论文吧。如果你有看SIGGRAPH 2014的话，应该会发现非真实感渲染有一个专门的session（&a href=&///?target=http%3A//s2014.siggraph.org/attendees/technical-papers/sessions/non-photorealistic-rendering& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Non-Photorealistic Rendering&i class=&icon-external&&&/i&&/a&）。我主要看过其中的两篇：&br&&ul&&li&Ink-and-Ray: Bas-Relief Meshes for Adding Global Illumination Effects to Hand-Drawn Characters&br&这篇我尝试实现过。它主要是根据一张输入的手绘图片，自动+手动输入生成一张浅浮雕的模型，从而让图片具有三维立体感。&br&&img src=&/4d748ceea47e8a651825_b.png& data-rawwidth=&576& data-rawheight=&145& class=&origin_image zh-lightbox-thumb& width=&576& data-original=&/4d748ceea47e8a651825_r.png&&&br&&/li&&li&Computing Smooth Surface Contours
with Accurate Topology&br&这篇是Pixar写的，主要目的是精确识别出每一帧中三维模型的封闭轮廓，并对它们进行修正。最后就可以对轮廓进行风格化渲染。&br&&img src=&/def6510fef399aeaaa2786fbc605a093_b.png& data-rawwidth=&2095& data-rawheight=&964& class=&origin_image zh-lightbox-thumb& width=&2095& data-original=&/def6510fef399aeaaa2786fbc605a093_r.png&&&br&&/li&&/ul&SIGGRAPH 2013（&a href=&///?target=http%3A///sig2013.html& class=& external& target=&_blank& rel=&nofollow noreferrer&&&span class=&invisible&&http://&/span&&span class=&visible&&&/span&&span class=&invisible&&/sig2013.html&/span&&span class=&ellipsis&&&/span&&i class=&icon-external&&&/i&&/a&）中虽然没有叫NPR的session，但也有一个很类似的部分，叫Artistic Rendering & Stylization。泛读过几篇。&br&&ul&&li&Stylizing Animation By Example&br&这篇同样也是Pixar出的。这篇文章的动机主要是为了当前的动画产业。因为艺术家们通过手绘创建的风格化图像，在动画中缺少时间上的连贯性，主要是由于物体复杂的纹理造成的。
他们受到静态的“图片类比”方法的启发，这种方法使用一对图片（左边的两张图片）来定义风格的转换，然后再给定一张输入图片（第三张图片），就可以输出具有新风格的图片（最右）。 &br&&img src=&/fc0bdf70e7d4a728fa5e75e9b779b7d4_b.png& data-rawwidth=&1744& data-rawheight=&601& class=&origin_image zh-lightbox-thumb& width=&1744& data-original=&/fc0bdf70e7d4a728fa5e75e9b779b7d4_r.png&&&br&&/li&&li& RealBrush: Painting with Examples of Physical Media&br&这篇是Adobe & Google出的。他们的动机是，在现实世界中绘图的美术人员有非常大的发挥空间，而使用数字板绘图的艺术家们却很受画图工具材料的限制。
现有的系统往往依靠一些算法来模拟一些真实世界中的颜料，例如油画和水彩。但是这些系统很难混合生成新的颜料，比如在真实世界里画家可以随意混合各种颜色的油彩来产生不同的艺术效果。因此，艺术家们就会被这些内置的工具所限制。 作者提出了一种新的绘图系统，RealBrush，它是一种靠数据驱动的绘图方法。 他们通过分析真实的绘图颜料，把这些颜料的行为分为四个种类：形状，拖尾，涂抹和合成，最后负责合成重叠组合不同颜色的画笔。
他们的算法首先收集这三种样本，处理后生成一个颜料库。然后如果在绘图过程中一个画笔覆盖了画布上之前绘制的颜料，就会匹配一个拖尾效果。如果需要进行涂抹，就会从涂抹库中合成一个涂抹效果。
&br&&img src=&/72a5cabfafeebb1a82eeedfa88f1f4ee_b.png& data-rawwidth=&1950& data-rawheight=&435& class=&origin_image zh-lightbox-thumb& width=&1950& data-original=&/72a5cabfafeebb1a82eeedfa88f1f4ee_r.png&&&br&&/li&&/ul&近两年SIGGRAPH上的非真实感渲染大概就是这些。当然，我相信其他会议期刊上肯定也陆陆续续都有，只是我们总是只关注SIGGRAPH上的。。。&br&&br&==========NPAR===========&br&&br&&b&日更新：&/b&&br&&br&SIGGRAPH发起了一个专门针对NPR的symposium——NPAR（&a href=&///?target=http%3A//dl.acm.org/event.cfm%3Fid%3DRE267& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Event: NPAR&i class=&icon-external&&&/i&&/a&），很多之前很有名的论文都是在上面发表的。例如：&br&&ul&&li&2000年的Stylized Rendering Techniques For Scalable Real-Time 3D Animation&br&&img src=&/43da51b8f91d2e1a4c13daba_b.png& data-rawwidth=&323& data-rawheight=&275& class=&content_image& width=&323&&如果看过《Real-time Rendering》中的NPR一章的话应该还记得这张图片吧。&/li&&li&2000年的Artistic Silhouettes: A Hybrid Approach&br&&img src=&/75adcde715acdfe8a03bf9bd82b1d7cd_b.png& data-rawwidth=&296& data-rawheight=&231& class=&content_image& width=&296&&眼熟吧。。。&/li&&li&2004年的Cartoon Rendering of Smoke Animations&br&&img src=&/be230cb1dd1e0c137b645_b.png& data-rawwidth=&332& data-rawheight=&235& class=&content_image& width=&332&&&/li&&li&2014年的Stylized Keyframe Animation of Fluid Simulations&br&&img src=&/7daf74bb518accf065e6e_b.png& data-rawwidth=&681& data-rawheight=&140& class=&origin_image zh-lightbox-thumb& width=&681& data-original=&/7daf74bb518accf065e6e_r.png&&&br&&/li&&/ul&太多啦，常去翻翻会发现不少有意思的论文。&br&&br&==========实验室===========&br&&br&题主可以关注几个实验室，Pixar的动画工作室（&a href=&///?target=http%3A///& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Pixar&i class=&icon-external&&&/i&&/a&），Disney的工作室（&a href=&///?target=http%3A///research-labs/disney-research-zurich/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&Disney Research&i class=&icon-external&&&/i&&/a&，这个是捷克分部的），苏黎世联邦理工学院（ETH Zurich）的igl实验室（&a href=&///?target=http%3A//igl.ethz.ch/publications/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&igl | Interactive Geometry Lab&i class=&icon-external&&&/i&&/a&），捷克的DCGI学院（&a href=&///?target=http%3A//dcgi.felk.cvut.cz/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&DCGI Home&i class=&icon-external&&&/i&&/a&），这是我所知道的在非真实感渲染方向比较活跃的机构。&br&&br&==========书籍===========&br&&br&说完了论文，这里再推荐一本书吧，也是我无意中找到的——The Algorithms and Principles of Non-photorealistic Graphics。&br&&img src=&/94efb79ac314d932888cec_b.png& data-rawwidth=&480& data-rawheight=&729& class=&origin_image zh-lightbox-thumb& width=&480& data-original=&/94efb79ac314d932888cec_r.png&&是浙江大学的Weidong Geng教授写的。这本书的结构有点类似于《Real-time Rendering》这种的，它会给一个方面，然后给出这个方面有哪些研究工作给出论文的名字，实现部分没有写的很具体，但可以知道去哪里查论文。&br&&br&=========&br&大概想到的就这些了。
之前实验室组会讨论时，我找过类似的资料，可以跟题主分享一下。像说的，非真实感在学术上感觉不太活跃，我个人觉得一方面是因为非真实感渲染非主流趋势，更多的是一些小众的需求；另一方面，其实偶尔SIGGRAPH也有非真实感渲染的session，只是不再…
99行的全局光照程序 &a href=&///?target=http%3A///smallpt/& class=& wrap external& target=&_blank& rel=&nofollow noreferrer&&smallpt&i class=&icon-external&&&/i&&/a&，它使用蒙地卡罗路径追踪。&br&&div class=&highlight&&&pre&&code class=&language-cpp&&&span class=&cp&&#include &math.h&
&/span&&span class=&c1&&// smallpt, a Path Tracer by Kevin Beason, 2008&/span&
&span class=&cp&&#include &stdlib.h& &/span&&span class=&c1&&// Make : g++ -O3 -fopenmp smallpt.cpp -o smallpt&/span&
&span class=&cp&&#include &stdio.h&
&/span&&span class=&c1&&//
Remove &-fopenmp& for g++ version & 4.2&/span&
&span class=&k&&struct&/span& &span class=&n&&Vec&/span& &span class=&p&&{&/span&
&span class=&c1&&// Usage: time ./smallpt 5000 && xv image.ppm&/span&
&span class=&kt&&double&/span& &span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&y&/span&&span class=&p&&,&/span& &span class=&n&&z&/span&&span class=&p&&;&/span&
&span class=&c1&&// position, also color (r,g,b)&/span&
&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&kt&&double&/span& &span class=&n&&x_&/span&&span class=&o&&=&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span& &span class=&kt&&double&/span& &span class=&n&&y_&/span&&span class=&o&&=&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span& &span class=&kt&&double&/span& &span class=&n&&z_&/span&&span class=&o&&=&/span&&span class=&mi&&0&/span&&span class=&p&&){&/span& &span class=&n&&x&/span&&span class=&o&&=&/span&&span class=&n&&x_&/span&&span class=&p&&;&/span& &span class=&n&&y&/span&&span class=&o&&=&/span&&span class=&n&&y_&/span&&span class=&p&&;&/span& &span class=&n&&z&/span&&span class=&o&&=&/span&&span class=&n&&z_&/span&&span class=&p&&;&/span& &span class=&p&&}&/span&
&span class=&n&&Vec&/span& &span class=&k&&operator&/span&&span class=&o&&+&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Vec&/span& &span class=&o&&&&/span&&span class=&n&&b&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&+&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&o&&+&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span&&span class=&n&&z&/span&&span class=&o&&+&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&);&/span& &span class=&p&&}&/span&
&span class=&n&&Vec&/span& &span class=&k&&operator&/span&&span class=&o&&-&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Vec&/span& &span class=&o&&&&/span&&span class=&n&&b&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span&&span class=&n&&z&/span&&span class=&o&&-&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&);&/span& &span class=&p&&}&/span&
&span class=&n&&Vec&/span& &span class=&k&&operator&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&kt&&double&/span& &span class=&n&&b&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&,&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&);&/span& &span class=&p&&}&/span&
&span class=&n&&Vec&/span& &span class=&n&&mult&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Vec&/span& &span class=&o&&&&/span&&span class=&n&&b&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&);&/span& &span class=&p&&}&/span&
&span class=&n&&Vec&/span&&span class=&o&&&&/span& &span class=&n&&norm&/span&&span class=&p&&(){&/span& &span class=&k&&return&/span& &span class=&o&&*&/span&&span class=&k&&this&/span& &span class=&o&&=&/span& &span class=&o&&*&/span&&span class=&k&&this&/span& &span class=&o&&*&/span& &span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&/&/span&&span class=&n&&sqrt&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&x&/span&&span class=&o&&+&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&y&/span&&span class=&o&&+&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&z&/span&&span class=&p&&));&/span& &span class=&p&&}&/span&
&span class=&kt&&double&/span& &span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Vec&/span& &span class=&o&&&&/span&&span class=&n&&b&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&k&&return&/span& &span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&o&&+&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&o&&+&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&;&/span& &span class=&p&&}&/span& &span class=&c1&&// cross:&/span&
&span class=&n&&Vec&/span& &span class=&k&&operator&/span&&span class=&o&&%&/span&&span class=&p&&(&/span&&span class=&n&&Vec&/span&&span class=&o&&&&/span&&span class=&n&&b&/span&&span class=&p&&){&/span&&span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&o&&-&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&p&&,&/span&&span class=&n&&z&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&o&&-&/span&&span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&,&/span&&span class=&n&&x&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&o&&-&/span&&span class=&n&&y&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&);}&/span&
&span class=&p&&};&/span&
&span class=&k&&struct&/span& &span class=&n&&Ray&/span& &span class=&p&&{&/span& &span class=&n&&Vec&/span& &span class=&n&&o&/span&&span class=&p&&,&/span& &span class=&n&&d&/span&&span class=&p&&;&/span& &span class=&n&&Ray&/span&&span class=&p&&(&/span&&span class=&n&&Vec&/span& &span class=&n&&o_&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span& &span class=&n&&d_&/span&&span class=&p&&)&/span& &span class=&o&&:&/span& &span class=&n&&o&/span&&span class=&p&&(&/span&&span class=&n&&o_&/span&&span class=&p&&),&/span& &span class=&n&&d&/span&&span class=&p&&(&/span&&span class=&n&&d_&/span&&span class=&p&&)&/span& &span class=&p&&{}&/span& &span class=&p&&};&/span&
&span class=&k&&enum&/span& &span class=&n&&Refl_t&/span& &span class=&p&&{&/span& &span class=&n&&DIFF&/span&&span class=&p&&,&/span& &span class=&n&&SPEC&/span&&span class=&p&&,&/span& &span class=&n&&REFR&/span& &span class=&p&&};&/span&
&span class=&c1&&// material types, used in radiance()&/span&
&span class=&k&&struct&/span& &span class=&n&&Sphere&/span& &span class=&p&&{&/span&
&span class=&kt&&double&/span& &span class=&n&&rad&/span&&span class=&p&&;&/span&
&span class=&c1&&// radius&/span&
&span class=&n&&Vec&/span& &span class=&n&&p&/span&&span class=&p&&,&/span& &span class=&n&&e&/span&&span class=&p&&,&/span& &span class=&n&&c&/span&&span class=&p&&;&/span&
&span class=&c1&&// position, emission, color&/span&
&span class=&n&&Refl_t&/span& &span class=&n&&refl&/span&&span class=&p&&;&/span&
&span class=&c1&&// reflection type (DIFFuse, SPECular, REFRactive)&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&kt&&double&/span& &span class=&n&&rad_&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span& &span class=&n&&p_&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span& &span class=&n&&e_&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span& &span class=&n&&c_&/span&&span class=&p&&,&/span& &span class=&n&&Refl_t&/span& &span class=&n&&refl_&/span&&span class=&p&&)&/span&&span class=&o&&:&/span&
&span class=&n&&rad&/span&&span class=&p&&(&/span&&span class=&n&&rad_&/span&&span class=&p&&),&/span& &span class=&n&&p&/span&&span class=&p&&(&/span&&span class=&n&&p_&/span&&span class=&p&&),&/span& &span class=&n&&e&/span&&span class=&p&&(&/span&&span class=&n&&e_&/span&&span class=&p&&),&/span& &span class=&n&&c&/span&&span class=&p&&(&/span&&span class=&n&&c_&/span&&span class=&p&&),&/span& &span class=&n&&refl&/span&&span class=&p&&(&/span&&span class=&n&&refl_&/span&&span class=&p&&)&/span& &span class=&p&&{}&/span&
&span class=&kt&&double&/span& &span class=&n&&intersect&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Ray&/span& &span class=&o&&&&/span&&span class=&n&&r&/span&&span class=&p&&)&/span& &span class=&k&&const&/span& &span class=&p&&{&/span& &span class=&c1&&// returns distance, 0 if nohit&/span&
&span class=&n&&Vec&/span& &span class=&n&&op&/span& &span class=&o&&=&/span& &span class=&n&&p&/span&&span class=&o&&-&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&o&/span&&span class=&p&&;&/span& &span class=&c1&&// Solve t^2*d.d + 2*t*(o-p).d + (o-p).(o-p)-R^2 = 0&/span&
&span class=&kt&&double&/span& &span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&n&&eps&/span&&span class=&o&&=&/span&&span class=&mf&&1e-4&/span&&span class=&p&&,&/span& &span class=&n&&b&/span&&span class=&o&&=&/span&&span class=&n&&op&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&p&&),&/span& &span class=&n&&det&/span&&span class=&o&&=&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&o&&-&/span&&span class=&n&&op&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&op&/span&&span class=&p&&)&/span&&span class=&o&&+&/span&&span class=&n&&rad&/span&&span class=&o&&*&/span&&span class=&n&&rad&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&det&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span& &span class=&k&&return&/span& &span class=&mi&&0&/span&&span class=&p&&;&/span& &span class=&k&&else&/span& &span class=&n&&det&/span&&span class=&o&&=&/span&&span class=&n&&sqrt&/span&&span class=&p&&(&/span&&span class=&n&&det&/span&&span class=&p&&);&/span&
&span class=&k&&return&/span& &span class=&p&&(&/span&&span class=&n&&t&/span&&span class=&o&&=&/span&&span class=&n&&b&/span&&span class=&o&&-&/span&&span class=&n&&det&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&n&&eps&/span& &span class=&o&&?&/span& &span class=&nl&&t&/span& &span class=&p&&:&/span& &span class=&p&&((&/span&&span class=&n&&t&/span&&span class=&o&&=&/span&&span class=&n&&b&/span&&span class=&o&&+&/span&&span class=&n&&det&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&n&&eps&/span& &span class=&o&&?&/span& &span class=&nl&&t&/span& &span class=&p&&:&/span& &span class=&mi&&0&/span&&span class=&p&&);&/span&
&span class=&p&&}&/span&
&span class=&p&&};&/span&
&span class=&n&&Sphere&/span& &span class=&n&&spheres&/span&&span class=&p&&[]&/span& &span class=&o&&=&/span& &span class=&p&&{&/span&&span class=&c1&&//Scene: radius, position, emission, color, material&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span& &span class=&mf&&1e5&/span&&span class=&o&&+&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mf&&40.8&/span&&span class=&p&&,&/span&&span class=&mf&&81.6&/span&&span class=&p&&),&/span& &span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.25&/span&&span class=&p&&,&/span&&span class=&mf&&.25&/span&&span class=&p&&),&/span&&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Left&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&o&&-&/span&&span class=&mf&&1e5&/span&&span class=&o&&+&/span&&span class=&mi&&99&/span&&span class=&p&&,&/span&&span class=&mf&&40.8&/span&&span class=&p&&,&/span&&span class=&mf&&81.6&/span&&span class=&p&&),&/span&&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mf&&.25&/span&&span class=&p&&,&/span&&span class=&mf&&.25&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&),&/span&&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Rght&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&p&&,&/span&&span class=&mf&&40.8&/span&&span class=&p&&,&/span& &span class=&mf&&1e5&/span&&span class=&p&&),&/span&
&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&),&/span&&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Back&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&p&&,&/span&&span class=&mf&&40.8&/span&&span class=&p&&,&/span&&span class=&o&&-&/span&&span class=&mf&&1e5&/span&&span class=&o&&+&/span&&span class=&mi&&170&/span&&span class=&p&&),&/span& &span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(),&/span&
&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Frnt&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&p&&,&/span& &span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&mf&&81.6&/span&&span class=&p&&),&/span&
&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&),&/span&&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Botm&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&1e5&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&p&&,&/span&&span class=&o&&-&/span&&span class=&mf&&1e5&/span&&span class=&o&&+&/span&&span class=&mf&&81.6&/span&&span class=&p&&,&/span&&span class=&mf&&81.6&/span&&span class=&p&&),&/span&&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&,&/span&&span class=&mf&&.75&/span&&span class=&p&&),&/span&&span class=&n&&DIFF&/span&&span class=&p&&),&/span&&span class=&c1&&//Top&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&16.5&/span&&span class=&p&&,&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&27&/span&&span class=&p&&,&/span&&span class=&mf&&16.5&/span&&span class=&p&&,&/span&&span class=&mi&&47&/span&&span class=&p&&),&/span&
&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&mf&&.999&/span&&span class=&p&&,&/span& &span class=&n&&SPEC&/span&&span class=&p&&),&/span&&span class=&c1&&//Mirr&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mf&&16.5&/span&&span class=&p&&,&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&73&/span&&span class=&p&&,&/span&&span class=&mf&&16.5&/span&&span class=&p&&,&/span&&span class=&mi&&78&/span&&span class=&p&&),&/span&
&span class=&n&&Vec&/span&&span class=&p&&(),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&mf&&.999&/span&&span class=&p&&,&/span& &span class=&n&&REFR&/span&&span class=&p&&),&/span&&span class=&c1&&//Glas&/span&
&span class=&n&&Sphere&/span&&span class=&p&&(&/span&&span class=&mi&&600&/span&&span class=&p&&,&/span& &span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&50&/span&&span class=&p&&,&/span&&span class=&mf&&681.6&/span&&span class=&o&&-&/span&&span class=&mf&&.27&/span&&span class=&p&&,&/span&&span class=&mf&&81.6&/span&&span class=&p&&),&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&12&/span&&span class=&p&&,&/span&&span class=&mi&&12&/span&&span class=&p&&,&/span&&span class=&mi&&12&/span&&span class=&p&&),&/span&
&span class=&n&&Vec&/span&&span class=&p&&(),&/span& &span class=&n&&DIFF&/span&&span class=&p&&)&/span& &span class=&c1&&//Lite&/span&
&span class=&p&&};&/span&
&span class=&kr&&inline&/span& &span class=&kt&&double&/span& &span class=&nf&&clamp&/span&&span class=&p&&(&/span&&span class=&kt&&double&/span& &span class=&n&&x&/span&&span class=&p&&){&/span& &span class=&k&&return&/span& &span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span& &span class=&o&&?&/span& &span class=&mi&&0&/span& &span class=&o&&:&/span& &span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&mi&&1&/span& &span class=&o&&?&/span& &span class=&mi&&1&/span& &span class=&o&&:&/span& &span class=&n&&x&/span&&span class=&p&&;&/span& &span class=&p&&}&/span&
&span class=&kr&&inline&/span& &span class=&kt&&int&/span& &span class=&nf&&toInt&/span&&span class=&p&&(&/span&&span class=&kt&&double&/span& &span class=&n&&x&/span&&span class=&p&&){&/span& &span class=&k&&return&/span& &span class=&kt&&int&/span&&span class=&p&&(&/span&&span class=&n&&pow&/span&&span class=&p&&(&/span&&span class=&n&&clamp&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&),&/span&&span class=&mi&&1&/span&&span class=&o&&/&/span&&span class=&mf&&2.2&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&mi&&255&/span&&span class=&o&&+&/span&&span class=&mf&&.5&/span&&span class=&p&&);&/span& &span class=&p&&}&/span&
&span class=&kr&&inline&/span& &span class=&kt&&bool&/span& &span class=&nf&&intersect&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Ray&/span& &span class=&o&&&&/span&&span class=&n&&r&/span&&span class=&p&&,&/span& &span class=&kt&&double&/span& &span class=&o&&&&/span&&span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&kt&&int&/span& &span class=&o&&&&/span&&span class=&n&&id&/span&&span class=&p&&){&/span&
&span class=&kt&&double&/span& &span class=&n&&n&/span&&span class=&o&&=&/span&&span class=&k&&sizeof&/span&&span class=&p&&(&/span&&span class=&n&&spheres&/span&&span class=&p&&)&/span&&span class=&o&&/&/span&&span class=&k&&sizeof&/span&&span class=&p&&(&/span&&span class=&n&&Sphere&/span&&span class=&p&&),&/span& &span class=&n&&d&/span&&span class=&p&&,&/span& &span class=&n&&inf&/span&&span class=&o&&=&/span&&span class=&n&&t&/span&&span class=&o&&=&/span&&span class=&mf&&1e20&/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=&o&&=&/span&&span class=&kt&&int&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&p&&);&/span&&span class=&n&&i&/span&&span class=&o&&--&/span&&span class=&p&&;)&/span& &span class=&k&&if&/span&&span class=&p&&((&/span&&span class=&n&&d&/span&&span class=&o&&=&/span&&span class=&n&&spheres&/span&&span class=&p&&[&/span&&span class=&n&&i&/span&&span class=&p&&].&/span&&span class=&n&&intersect&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&))&/span&&span class=&o&&&&&/span&&span class=&n&&d&/span&&span class=&o&&&&/span&&span class=&n&&t&/span&&span class=&p&&){&/span&&span class=&n&&t&/span&&span class=&o&&=&/span&&span class=&n&&d&/span&&span class=&p&&;&/span&&span class=&n&&id&/span&&span class=&o&&=&/span&&span class=&n&&i&/span&&span class=&p&&;}&/span&
&span class=&k&&return&/span& &span class=&n&&t&/span&&span class=&o&&&&/span&&span class=&n&&inf&/span&&span class=&p&&;&/span&
&span class=&p&&}&/span&
&span class=&n&&Vec&/span& &span class=&nf&&radiance&/span&&span class=&p&&(&/span&&span class=&k&&const&/span& &span class=&n&&Ray&/span& &span class=&o&&&&/span&&span class=&n&&r&/span&&span class=&p&&,&/span& &span class=&kt&&int&/span& &span class=&n&&depth&/span&&span class=&p&&,&/span& &span class=&kt&&unsigned&/span& &span class=&kt&&short&/span& &span class=&o&&*&/span&&span class=&n&&Xi&/span&&span class=&p&&){&/span&
&span class=&kt&&double&/span& &span class=&n&&t&/span&&span class=&p&&;&/span&
&span class=&c1&&// distance to intersection&/span&
&span class=&kt&&int&/span& &span class=&n&&id&/span&&span class=&o&&=&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&c1&&// id of intersected object&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&o&&!&/span&&span class=&n&&intersect&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&,&/span& &span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&n&&id&/span&&span class=&p&&))&/span& &span class=&k&&return&/span& &span class=&n&&Vec&/span&&span class=&p&&();&/span& &span class=&c1&&// if miss, return black&/span&
&span class=&k&&const&/span& &span class=&n&&Sphere&/span& &span class=&o&&&&/span&&span class=&n&&obj&/span& &span class=&o&&=&/span& &span class=&n&&spheres&/span&&span class=&p&&[&/span&&span class=&n&&id&/span&&span class=&p&&];&/span&
&span class=&c1&&// the hit object&/span&
&span class=&n&&Vec&/span& &span class=&n&&x&/span&&span class=&o&&=&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&o&/span&&span class=&o&&+&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&o&&*&/span&&span class=&n&&t&/span&&span class=&p&&,&/span& &span class=&n&&n&/span&&span class=&o&&=&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&o&&-&/span&&span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&p&/span&&span class=&p&&).&/span&&span class=&n&&norm&/span&&span class=&p&&(),&/span& &span class=&n&&nl&/span&&span class=&o&&=&/span&&span class=&n&&n&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span&&span class=&o&&?&/span&&span class=&nl&&n&/span&&span class=&p&&:&/span&&span class=&n&&n&/span&&span class=&o&&*-&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span& &span class=&n&&f&/span&&span class=&o&&=&/span&&span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&c&/span&&span class=&p&&;&/span&
&span class=&kt&&double&/span& &span class=&n&&p&/span& &span class=&o&&=&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&y&/span& &span class=&o&&&&&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&o&&&&/span&&span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&z&/span& &span class=&o&&?&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&nl&&x&/span& &span class=&p&&:&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&y&/span&&span class=&o&&&&/span&&span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&z&/span& &span class=&o&&?&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&nl&&y&/span& &span class=&p&&:&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&z&/span&&span class=&p&&;&/span& &span class=&c1&&// max refl&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&o&&++&/span&&span class=&n&&depth&/span&&span class=&o&&&&/span&&span class=&mi&&5&/span&&span class=&p&&)&/span& &span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&erand48&/span&&span class=&p&&(&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&n&&p&/span&&span class=&p&&)&/span& &span class=&n&&f&/span&&span class=&o&&=&/span&&span class=&n&&f&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&/&/span&&span class=&n&&p&/span&&span class=&p&&);&/span& &span class=&k&&else&/span& &span class=&k&&return&/span& &span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&e&/span&&span class=&p&&;&/span& &span class=&c1&&//R.R.&/span&
&span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&refl&/span& &span class=&o&&==&/span& &span class=&n&&DIFF&/span&&span class=&p&&){&/span&
&span class=&c1&&// Ideal DIFFUSE reflection&/span&
&span class=&kt&&double&/span& &span class=&n&&r1&/span&&span class=&o&&=&/span&&span class=&mi&&2&/span&&span class=&o&&*&/span&&span class=&n&&M_PI&/span&&span class=&o&&*&/span&&span class=&n&&erand48&/span&&span class=&p&&(&/span&&span class=&n&&Xi&/span&&span class=&p&&),&/span& &span class=&n&&r2&/span&&span class=&o&&=&/span&&span class=&n&&erand48&/span&&span class=&p&&(&/span&&span class=&n&&Xi&/span&&span class=&p&&),&/span& &span class=&n&&r2s&/span&&span class=&o&&=&/span&&span class=&n&&sqrt&/span&&span class=&p&&(&/span&&span class=&n&&r2&/span&&span class=&p&&);&/span&
&span class=&n&&Vec&/span& &span class=&n&&w&/span&&span class=&o&&=&/span&&span class=&n&&nl&/span&&span class=&p&&,&/span& &span class=&n&&u&/span&&span class=&o&&=&/span&&span class=&p&&((&/span&&span class=&n&&fabs&/span&&span class=&p&&(&/span&&span class=&n&&w&/span&&span class=&p&&.&/span&&span class=&n&&x&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mf&&.1&/span&&span class=&o&&?&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&0&/span&&span class=&p&&,&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&:&/span&&span class=&n&&Vec&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&p&&))&/span&&span class=&o&&%&/span&&span class=&n&&w&/span&&span class=&p&&).&/span&&span class=&n&&norm&/span&&span class=&p&&(),&/span& &span class=&n&&v&/span&&span class=&o&&=&/span&&span class=&n&&w&/span&&span class=&o&&%&/span&&span class=&n&&u&/span&&span class=&p&&;&/span&
&span class=&n&&Vec&/span& &span class=&n&&d&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&n&&u&/span&&span class=&o&&*&/span&&span class=&n&&cos&/span&&span class=&p&&(&/span&&span class=&n&&r1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&r2s&/span& &span class=&o&&+&/span& &span class=&n&&v&/span&&span class=&o&&*&/span&&span class=&n&&sin&/span&&span class=&p&&(&/span&&span class=&n&&r1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&r2s&/span& &span class=&o&&+&/span& &span class=&n&&w&/span&&span class=&o&&*&/span&&span class=&n&&sqrt&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&r2&/span&&span class=&p&&)).&/span&&span class=&n&&norm&/span&&span class=&p&&();&/span&
&span class=&k&&return&/span& &span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&e&/span& &span class=&o&&+&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&mult&/span&&span class=&p&&(&/span&&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&Ray&/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&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&));&/span&
&span class=&p&&}&/span& &span class=&k&&else&/span& &span class=&k&&if&/span& &span class=&p&&(&/span&&span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&refl&/span& &span class=&o&&==&/span& &span class=&n&&SPEC&/span&&span class=&p&&)&/span&
&span class=&c1&&// Ideal SPECULAR reflection&/span&
&span class=&k&&return&/span& &span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&e&/span& &span class=&o&&+&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&mult&/span&&span class=&p&&(&/span&&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&Ray&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&o&&-&/span&&span class=&n&&n&/span&&span class=&o&&*&/span&&span class=&mi&&2&/span&&span class=&o&&*&/span&&span class=&n&&n&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&p&&)),&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&));&/span&
&span class=&n&&Ray&/span& &span class=&n&&reflRay&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span& &span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&o&&-&/span&&span class=&n&&n&/span&&span class=&o&&*&/span&&span class=&mi&&2&/span&&span class=&o&&*&/span&&span class=&n&&n&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&p&&));&/span&
&span class=&c1&&// Ideal dielectric REFRACTION&/span&
&span class=&kt&&bool&/span& &span class=&n&&into&/span& &span class=&o&&=&/span& &span class=&n&&n&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&nl&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span&&span class=&p&&;&/span&
&span class=&c1&&// Ray from outside going in?&/span&
&span class=&kt&&double&/span& &span class=&n&&nc&/span&&span class=&o&&=&/span&&span class=&mi&&1&/span&&span class=&p&&,&/span& &span class=&n&&nt&/span&&span class=&o&&=&/span&&span class=&mf&&1.5&/span&&span class=&p&&,&/span& &span class=&n&&nnt&/span&&span class=&o&&=&/span&&span class=&n&&into&/span&&span class=&o&&?&/span&&span class=&n&&nc&/span&&span class=&o&&/&/span&&span class=&nl&&nt&/span&&span class=&p&&:&/span&&span class=&n&&nt&/span&&span class=&o&&/&/span&&span class=&n&&nc&/span&&span class=&p&&,&/span& &span class=&n&&ddn&/span&&span class=&o&&=&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&nl&/span&&span class=&p&&),&/span& &span class=&n&&cos2t&/span&&span class=&p&&;&/span&
&span class=&k&&if&/span& &span class=&p&&((&/span&&span class=&n&&cos2t&/span&&span class=&o&&=&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&nnt&/span&&span class=&o&&*&/span&&span class=&n&&nnt&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&ddn&/span&&span class=&o&&*&/span&&span class=&n&&ddn&/span&&span class=&p&&))&/span&&span class=&o&&&&/span&&span class=&mi&&0&/span&&span class=&p&&)&/span&
&span class=&c1&&// Total internal reflection&/span&
&span class=&k&&return&/span& &span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&e&/span& &span class=&o&&+&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&mult&/span&&span class=&p&&(&/span&&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&reflRay&/span&&span class=&p&&,&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&));&/span&
&span class=&n&&Vec&/span& &span class=&n&&tdir&/span& &span class=&o&&=&/span& &span class=&p&&(&/span&&span class=&n&&r&/span&&span class=&p&&.&/span&&span class=&n&&d&/span&&span class=&o&&*&/span&&span class=&n&&nnt&/span& &span class=&o&&-&/span& &span class=&n&&n&/span&&span class=&o&&*&/span&&span class=&p&&((&/span&&span class=&n&&into&/span&&span class=&o&&?&/span&&span class=&mi&&1&/span&&span class=&o&&:-&/span&&span class=&mi&&1&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&p&&(&/span&&span class=&n&&ddn&/span&&span class=&o&&*&/span&&span class=&n&&nnt&/span&&span class=&o&&+&/span&&span class=&n&&sqrt&/span&&span class=&p&&(&/span&&span class=&n&&cos2t&/span&&span class=&p&&)))).&/span&&span class=&n&&norm&/span&&span class=&p&&();&/span&
&span class=&kt&&double&/span& &span class=&n&&a&/span&&span class=&o&&=&/span&&span class=&n&&nt&/span&&span class=&o&&-&/span&&span class=&n&&nc&/span&&span class=&p&&,&/span& &span class=&n&&b&/span&&span class=&o&&=&/span&&span class=&n&&nt&/span&&span class=&o&&+&/span&&span class=&n&&nc&/span&&span class=&p&&,&/span& &span class=&n&&R0&/span&&span class=&o&&=&/span&&span class=&n&&a&/span&&span class=&o&&*&/span&&span class=&n&&a&/span&&span class=&o&&/&/span&&span class=&p&&(&/span&&span class=&n&&b&/span&&span class=&o&&*&/span&&span class=&n&&b&/span&&span class=&p&&),&/span& &span class=&n&&c&/span& &span class=&o&&=&/span& &span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&p&&(&/span&&span class=&n&&into&/span&&span class=&o&&?-&/span&&span class=&nl&&ddn&/span&&span class=&p&&:&/span&&span class=&n&&tdir&/span&&span class=&p&&.&/span&&span class=&n&&dot&/span&&span class=&p&&(&/span&&span class=&n&&n&/span&&span class=&p&&));&/span&
&span class=&kt&&double&/span& &span class=&n&&Re&/span&&span class=&o&&=&/span&&span class=&n&&R0&/span&&span class=&o&&+&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&R0&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&c&/span&&span class=&o&&*&/span&&span class=&n&&c&/span&&span class=&o&&*&/span&&span class=&n&&c&/span&&span class=&o&&*&/span&&span class=&n&&c&/span&&span class=&o&&*&/span&&span class=&n&&c&/span&&span class=&p&&,&/span&&span class=&n&&Tr&/span&&span class=&o&&=&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&Re&/span&&span class=&p&&,&/span&&span class=&n&&P&/span&&span class=&o&&=&/span&&span class=&mf&&.25&/span&&span class=&o&&+&/span&&span class=&mf&&.5&/span&&span class=&o&&*&/span&&span class=&n&&Re&/span&&span class=&p&&,&/span&&span class=&n&&RP&/span&&span class=&o&&=&/span&&span class=&n&&Re&/span&&span class=&o&&/&/span&&span class=&n&&P&/span&&span class=&p&&,&/span&&span class=&n&&TP&/span&&span class=&o&&=&/span&&span class=&n&&Tr&/span&&span class=&o&&/&/span&&span class=&p&&(&/span&&span class=&mi&&1&/span&&span class=&o&&-&/span&&span class=&n&&P&/span&&span class=&p&&);&/span&
&span class=&k&&return&/span& &span class=&n&&obj&/span&&span class=&p&&.&/span&&span class=&n&&e&/span& &span class=&o&&+&/span& &span class=&n&&f&/span&&span class=&p&&.&/span&&span class=&n&&mult&/span&&span class=&p&&(&/span&&span class=&n&&depth&/span&&span class=&o&&&&/span&&span class=&mi&&2&/span& &span class=&o&&?&/span& &span class=&p&&(&/span&&span class=&n&&erand48&/span&&span class=&p&&(&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&&&/span&&span class=&n&&P&/span& &span class=&o&&?&/span&
&span class=&c1&&// Russian roulette&/span&
&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&reflRay&/span&&span class=&p&&,&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&nl&&RP&/span&&span class=&p&&:&/span&&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&Ray&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&tdir&/span&&span class=&p&&),&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&TP&/span&&span class=&p&&)&/span& &span class=&o&&:&/span&
&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&reflRay&/span&&span class=&p&&,&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span class=&n&&Re&/span&&span class=&o&&+&/span&&span class=&n&&radiance&/span&&span class=&p&&(&/span&&span class=&n&&Ray&/span&&span class=&p&&(&/span&&span class=&n&&x&/span&&span class=&p&&,&/span&&span class=&n&&tdir&/span&&span class=&p&&),&/span&&span class=&n&&depth&/span&&span class=&p&&,&/span&&span class=&n&&Xi&/span&&span class=&p&&)&/span&&span class=&o&&*&/span&&span cl}