I am currently reading the Ray Tracing in One Weekend tutorial (link), and I am dubious about their fix for shadow acne, which is to ignore ray-geometry intersections that occur at very small times.
For background, my understanding of the basic algorithm of raytracing and shadow acne is as follows:
- For each pixel in the image, shoot a light ray from the eye point / camera through the pixel's designated region in the image plane.
- To find the color of each pixel, calculate the closest intersection of the ray with the objects in the scene. Also, use multiple random rays for each pixel (anti-aliasing).
- Shadow acne: Now, say that we have some ray $R$ and say its closest intersection time is some floating-point number $t$. Then, $t$ may be inaccurate; if it is a little larger than the actual closest intersection time, then the calculated intersection point will be little inside the first object $R$ intersects, rather than being flush with its surface. As a result, the reflected ray will originate from inside the object, and so it will bounce off the inside surface next and continue to bounce inside the object, losing color each time and resulting in the pixel being darker than it should be (essentially, the object will shadow itself).
Now, the book suggests the following solution. Observe that if the next ray originates from inside the sphere due to $t$ being a little larger than it should have been, then the intersection time for the next ray will be very small, like $0.000001$. The book thus claims that ignoring small intersection times (such as all those below $0.001$) suffices to stop such occurrences of shadow acne.
However, I am dubious. Consider the following scenario:
- Say we have a sphere $S$ and a ray $R$ that intersects $S$ at two times $t_1 < t_2$.
- Now, say that $t_1 < 0.001$. Then $t_1$ will be ignored by the book's method, and so $t_2$ will be chosen as the correct intersection time.
- However, if a ray intersects a sphere twice, then the second intersection will actually be when the ray intersects the sphere from the inside! As a result, the ray will be reflected inside the sphere as well, and so then it will bounce and bounce off the interior surface theoretically forever, which has resulted in stack overflows in my code and the given code.
The main issue here is that ignoring small intersection times may cause larger intersection times, where the ray actually goes through objects, to be counted as the correct one.
How do we resolve this fundamental issue with the approach of ignoring smaller intersection times where dealing with shadow acne? Is this a known problem?