模拟球形广告牌的变形

问题描述

我需要制作球形广告牌（即设定深度），但要考虑透视投影 - 理想情况下包括偏离中心的截屏。

我没有能够找到任何成功的人参考 - 尽管有很多解释为什么标准广告牌没有视角扭曲。不幸的是，对于我的申请来说，缺乏并不是一个表面缺陷;这对算法来说非常重要。

我自己做了一些调查：

事实上，I没有找到一个好的解决方案，我找不到任何人。任何人都有想法？

解决方案

在浏览这个问题时甚至没有进行远程处理，我偶然发现了，这非常接近。链接教程展示了如何计算光栅化球体的边界椭圆;获得深度（最糟糕的是，使用raycast）应该很容易推导出来。

I need to make spherical billboards (i.e., setting depth), but taking into account perspective projection--ideally including off-center frusta.

I wasn't able to find any references to anyone succeeding at this--although there are plenty of explanations as to why standard billboards don't have perspective distortions. Unfortunately, for my application, the lack isn't a cosmetic defect; it's actually important to the algorithm.

I did a bit of investigation on my own:

Point of fact, I didn't find a good solution, and I couldn't find anyone who has. Anyone have an idea?

解决方案

While browsing around not even remotely working on this problem, I stumbled on http://iquilezles.org/www/articles/sphereproj/sphereproj.htm, which is pretty close. The linked tutorial shows how to compute a bounding ellipse for a rasterized sphere; getting the depth (at worst, using a raycast) should be fairly easy to derive.

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