科学与数学rantonels.github.io
光线追踪黑洞
Raytracing a Black Hole
2015 — 2018，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这个页面讲如何用光线追踪渲染黑洞：在广义相对论框架下追踪光线在弯曲时空中的路径，并解释相关的物理计算与可视化。作者配有直观的图解和渲染结果，展示黑洞附近光线弯曲带来的视觉效果。
为什么经久不衰：它把严谨的物理推导、渲染实现思路和漂亮的图像结合在一起，既有教学价值又有视觉冲击，所以多年后仍值得读。
HN 评论精选
半开玩笑地把渲染黑洞概括为解测地线方程，并感慨这种物理语言真的成了日常。
简单。取史瓦西度规，求克里斯托费尔符号，再求导，写下测地线方程，换到某种笛卡尔坐标以避免无尽折磨，得到一个巨大的多行常微分方程，积分。大概就是这样。小时候看的电视和书让我觉得未来的人会经常这样说话；现在生活在未来，我很高兴这竟然成真了。
pavlov查看英文原文
Easy. Take the Schwarzschild metric, find the Christoffel symbols, find their derivative, write down the geodesic equation, change to some cartesian coordinates to avoid endless suffering, get an immense multiline ODE, integrate. That's pretty much it. The TV and books I consumed as a kid made it seem plausible that people in the future will regularly talk like that. Now, living in the future, I'm happy that it turned out to be true.
建议分块渲染以改善 CPU 缓存局部性，可能显著提速。
性能想法：我喜欢你一次性光线追踪整张图，很聪明，但也许能更快。现在你一次处理整张图，可 1080p×4 字节的图像约 777,600 字节，我相信你有好几份这样的数组，它们大到足以冲掉 CPU 缓存。把图像切成 8、16 或 32 个方形、矩形或条状小块依次处理可能快得多，这样能更频繁地命中工作数组的相同部分并留在缓存中。也就是 for patch 里套 for iter（目前你的外层渲染循环），可能是个快速性能收益，值得试试。很棒的文章，谢谢！
gridspy查看英文原文
Performance thought: I like the way you raytrace the entire image at once. Clever, but you might be able to make it faster... Right now you process the entire image in one hit. However a 1080p * 4 byte image is 777,600 bytes - from a quick read I believe you have several of these. They're large enough to blow the caches in your CPU. It might be much faster to break the image into 8,16 or 32 square or rectangular or line shaped "patches" and process each in sequence. That would help you hit the same parts of your working arrays more often and keep them in cache between iterations. I'm thinking for patch in patches for iter in iterations <-- currently your outer rendering loop Might be a quick performance win worth playing with. Hit me up at tom at gridspy (.co.nz) if you want to discuss further. Amazing article, thankyou!
指正作者关于共形映射的数学表述：去点球面与单位圆盘并不共形等价。
这真的很酷！解释得很好（包括一些非常有效的图），可视化也很棒。[旁注：讨论事件视界畸变时，作者说“我怀疑去点球面到圆盘的映射是共形/双全纯的”。去点球面和平面之间确实有共形映射，但开单位圆盘和整个平面之间没有共形双射。因此，去点球面和单位圆盘不可能共形等价。]
Steuard查看英文原文
This is really cool! It's a nice explanation of the topic (including some very effective diagrams), and the resulting visualizations are great. [Side note: In discussing the distortion of the event horizon, the author says "I suspect the punctured sphere → disk map is conformal/biholomorphic". There is a conformal map between the punctured sphere and the plane[0], but there is no conformal bijective map between the open unit disk and the full plane.[1] Thus, the punctured sphere and the unit disk cannot be conformally equivalent.] [0] http://en.wikipedia.org/wiki/Stereographic_projection [1] http://en.wikipedia.org/wiki/Unit_disk#The_open_unit_disk.2C_the_plane.2C_and_the_upper_half-plane
回忆渲染该黑洞镜头时，粒子模拟给存储和 RAID 带来极端压力。
我在 dneg 工作时，正是这个镜头在渲染。据我记得渲染分几步，第一部分是巨大的粒子模拟。我是系统工程师，职责是让系统保持运行。那个粒子模拟吃掉至少 7 块，甚至更多硬盘；不管它做了什么，它毁掉了 8TB 硬盘。最糟的是我们不能把那台文件服务器下线，因为渲染需要完成。但不仅渲染在猛击和吞噬磁盘，RAID 阵列还同时拼命重建。一组刚重建完，另一块盘就坏了。真是欢乐。一有余量，我们就从那台服务器迁走，给它安排了压力小些的活。
KaiserPro查看英文原文
I worked at dneg when this very shot was being rendered. From what I remeber there were a few steps to this being rendered, the first part was a massive particle sim. I was a systems engineer, so my job was to keep the system running. That particle sim ate at least 7, if not more hard disks. What ever it did, it destroyed 8tb HDDs. The worst part was we couldn't take that file server offline, as the render needed to finish. But, not only was the render hammering and eating disks, the raid array was desperatly trying to rebuild the groups at the same time. As soon as the group was rebuilt, another disk would fail. so much joy. As soon as we had some slack, we migrated away from that server and gave something less stressful to do.
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