在閱讀有關圓錐跟踪的論文時,作者是否犯了錯誤?


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我正在閱讀this document,它討論有符號距離場渲染。

在該文檔的第6.3節中,關於圓錐跟踪,它說:

Cone tracing is an extension of the sphere tracing algorithm. In addition to the ray, a cone is created and expanded in the marching direction. At each sampling step, the current cone radius is compared with the minimum distance from the distance field. If the SDF value is smaller than the current radius, the cone has intersected an object [14]. This incurs very little additional cost to the normal sphere trace, while providing useful intersection information.

尤其是:If the SDF value is smaller than the current radius, the cone has intersected an object

我讀錯了嗎?沒有辦法是真的。考慮下圖:

enter image description here

從該圖可以明顯看出,對於任何圓錐半徑 $ R $ ,都存在一個SDF值 $ \ epsilon$ ,這樣 $ R> \ epsilon $ 且圓錐不與球體相交。

我把文件解釋錯了嗎?

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It’s kind of inaccurately stated—by comparing the SDF with a linearly increasing radius, the shape that’s being traced out is a cone with a hemisphere on the end, something like this:

diagram

At any point along the horizontal center line, if the distance to the nearest surface is less than the current test radius, the cone-plus-hemisphere has intersected that surface.