As we know, irradiance refers to the flux of radiant energy per unit area. In particular, I think irradiance from the environment sort of comes from "everywhere" and think that it's really cool that there is a methodological way to compute such a quantity. Furthermore, after some googling I found this really cool paper discussing a process to compute and create irradiance environment maps: https://graphics.stanford.edu/papers/ravir_thesis/chapter4.pdf
Michael-hsiu
I wonder how we consider a surface that isn't a half-sphere, such as in this example. For a mesh, which may have valleys which are concave, perhaps we would have to consider a flipped over hemisphere. For a saddle-like shape, perhaps we would have to integrate over the concave and convex parts separately, and somehow account for any sharp divides connecting them.
yzyz
I think that the exact shape of the surface doesn't really matter. The hemisphere is not the surface, but really just a visualization of all possible directions of incoming light. We can approximate the surface near the point as a flat surface (this is dA), and since light can't hit the point from under the surface, the set of all unit vectors representing directions that light can come from is a hemisphere. We can also think of this as integrating over all possible directions, which would be integrating over a sphere, but we already know that no light can come from the bottom hemisphere as it would intersect our surface from the bottom, so the only hemisphere we care about is the top one.
raghav-cs184
I know it's easy to calculate flux in electromagnetism using gauss's law (and general flux calculations can be simplified that way as well). What would be an equivalent of the charge setup from gauss's law to calculate the flux/ irradiance through the sphere easily here?
rahulmalayappan
We can't really apply Gauss's law here; that comes from special properties of the electric field. Also, I don't think we should think of the hemisphere as a surface in its own right; as mentioned above, it just visualizes the total range of solid angles over which we integrate.
As we know, irradiance refers to the flux of radiant energy per unit area. In particular, I think irradiance from the environment sort of comes from "everywhere" and think that it's really cool that there is a methodological way to compute such a quantity. Furthermore, after some googling I found this really cool paper discussing a process to compute and create irradiance environment maps: https://graphics.stanford.edu/papers/ravir_thesis/chapter4.pdf
I wonder how we consider a surface that isn't a half-sphere, such as in this example. For a mesh, which may have valleys which are concave, perhaps we would have to consider a flipped over hemisphere. For a saddle-like shape, perhaps we would have to integrate over the concave and convex parts separately, and somehow account for any sharp divides connecting them.
I think that the exact shape of the surface doesn't really matter. The hemisphere is not the surface, but really just a visualization of all possible directions of incoming light. We can approximate the surface near the point as a flat surface (this is dA), and since light can't hit the point from under the surface, the set of all unit vectors representing directions that light can come from is a hemisphere. We can also think of this as integrating over all possible directions, which would be integrating over a sphere, but we already know that no light can come from the bottom hemisphere as it would intersect our surface from the bottom, so the only hemisphere we care about is the top one.
I know it's easy to calculate flux in electromagnetism using gauss's law (and general flux calculations can be simplified that way as well). What would be an equivalent of the charge setup from gauss's law to calculate the flux/ irradiance through the sphere easily here?
We can't really apply Gauss's law here; that comes from special properties of the electric field. Also, I don't think we should think of the hemisphere as a surface in its own right; as mentioned above, it just visualizes the total range of solid angles over which we integrate.