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robotichuman

Typo? Then toss out any samples not in "circle" (easy).

niyiqiul

This is like the bounding box construction in BVH.

kkzhang

Isn't the efficiency of the technique always constant since we can only define one square (of side lengths d) for a disk of diameter d?

Alan7996

What are the benefits of using previous complicated idea versus this simple idea?

L1TTLEM4N

Since you would always oversample, is rejection sampling always not as efficient as the previous technique for circles?

willowpet

I'm thinking of a test for whether or not to use rejection sampling being whether or not the shape is convex/does a ray pass through it twice. Would that lead to shapes with better efficiency when rejection sampling?

twizzler

We can also use this to estimate the area of the shape inside of the square, right?

air54321

Do we choose a circle because it maximizes the ratio?

jefftan

Is there a better way to generalize rejection sampling to higher dimensional spheres? In 2D, pi * r^2 / (2r)^2 = pi/4 which is about 78.5% but in 3D, 4pi/3 * r^3 / (2r)^3 = pi/6 which is about 52.4% and I imagine it drops quite rapidly when you go up to 10D spheres

gfkang

Why does this still result in uniform sampling over the circle if the original samples are over the square?

minhsual

Does this uniform sampling technique generalize to other inner shapes given we put a square around it? Are there any other shapes that can produce similar results that can be placed on the outside other than a square?

jefftan

Is there a better way to generalize rejection sampling to higher dimensional spheres? In 2D, pi * r^2 / (2r)^2 = pi/4 which is about 78.5% but in 3D, 4pi/3 * r^3 / (2r)^3 = pi/6 which is about 52.4% and I imagine it drops quite rapidly when you go up to 10D spheres