Just curious, why the fact that object A, B are convex is highlighted here?
Arthas007
I have bad memories of probability analysis from 15210
keenan
@Bananya Because in the convex case, the area ratio really gives you the exact probability that a random ray that hits B also hits A. Not true in the nonconvex case.
0x484884
For 2d, it seems like we could use the perimeter of the convex hull for non-convex shapes but an analogous approach doesn't seem to work in 3d.
I'm only considering the case where the rays start outside of B and pass through it.
0x484884
Does anyone know of a proof for this? It seems like you could do some sort of surface integral to integrate over the different rays that intersect B vs both A and B but I can't think of a nice way to do this.
Just curious, why the fact that object A, B are convex is highlighted here?
I have bad memories of probability analysis from 15210
@Bananya Because in the convex case, the area ratio really gives you the exact probability that a random ray that hits B also hits A. Not true in the nonconvex case.
For 2d, it seems like we could use the perimeter of the convex hull for non-convex shapes but an analogous approach doesn't seem to work in 3d.
I'm only considering the case where the rays start outside of B and pass through it.
Does anyone know of a proof for this? It seems like you could do some sort of surface integral to integrate over the different rays that intersect B vs both A and B but I can't think of a nice way to do this.