What if some of the directions chosen hit the light source but some do not?
Sybil
Since we are integrating over the area of the light source, they should all hit
jacheng
Is the reason that it's less noisy because more points are actually being hit by the light source, whereas in the previous example, you were probably throwing away a lot of points since they weren't being hit by any light, so then there were more gaps in the areas that should be hit by light?
atarng
@jacheng In the previous example, some of the points on the ground that should have been lit up were sampling in directions away from the light source, thus not adding to the integral. Here, since we point all the samples at the light source, we are always adding to the integral if there is no occlusion.
keenan
@atarng has it exactly right: you're trying to figure out what fraction of directions are illuminated by the light source. So, it's a waste of time to shoot rays in any direction other than at the light. From there, you just need to determine whether you hit something else before hitting the light. For the same number of samples, this will give you a better estimate of the fraction than shooting in completely random directions.
What if some of the directions chosen hit the light source but some do not?
Since we are integrating over the area of the light source, they should all hit
Is the reason that it's less noisy because more points are actually being hit by the light source, whereas in the previous example, you were probably throwing away a lot of points since they weren't being hit by any light, so then there were more gaps in the areas that should be hit by light?
@jacheng In the previous example, some of the points on the ground that should have been lit up were sampling in directions away from the light source, thus not adding to the integral. Here, since we point all the samples at the light source, we are always adding to the integral if there is no occlusion.
@atarng has it exactly right: you're trying to figure out what fraction of directions are illuminated by the light source. So, it's a waste of time to shoot rays in any direction other than at the light. From there, you just need to determine whether you hit something else before hitting the light. For the same number of samples, this will give you a better estimate of the fraction than shooting in completely random directions.