This slide is demonstrating that the irradiance on a surface is proportional to the cosine of the angle between the light source and the surface normal. Is there a generalized approach that works even if the surface isn't flat? It seems like this law holds due if we are looking over some tiny surface dA that we assume is flat, but I wonder if that assumption is or is not reasonable in graphics settings.
patrickrz
Adding on the Austin's comment from above, I wonder if we would need to take on a random sampling sort of approach for surfaces that aren't flat. Additionally, I was wondering if we how Lambert's Cosine Law would apply to surfaces that are round.
CardiacMangoes
I'm a bit confused by the geometric picture in this slide. I've never seen Lambert's law explained like this and it's more intuitive than just doing the algebra. I understand by the algebra that we get cos(π/3)=21, but I don't understand where the axis of rotation is for the surface. Is it where the vertical arrow points to in the third picture?
jacklishufan
@CardiacMangoes it should be noted that Irradiance is an "differential" value hence where the axis of rotation is does not matter, its the direction of the axis. In particular, the baseline is a plane which is orthogonal to the light ray. Then the angle θ is defined by the angle of normal vectors between the actual surface and base surface. In this particular case, the axis rotation is a vector othogonal to the screen (popping out of the screen and pointing at viewer)
This slide is demonstrating that the irradiance on a surface is proportional to the cosine of the angle between the light source and the surface normal. Is there a generalized approach that works even if the surface isn't flat? It seems like this law holds due if we are looking over some tiny surface dA that we assume is flat, but I wonder if that assumption is or is not reasonable in graphics settings.
Adding on the Austin's comment from above, I wonder if we would need to take on a random sampling sort of approach for surfaces that aren't flat. Additionally, I was wondering if we how Lambert's Cosine Law would apply to surfaces that are round.
I'm a bit confused by the geometric picture in this slide. I've never seen Lambert's law explained like this and it's more intuitive than just doing the algebra. I understand by the algebra that we get cos(π/3)=21, but I don't understand where the axis of rotation is for the surface. Is it where the vertical arrow points to in the third picture?
@CardiacMangoes it should be noted that Irradiance is an "differential" value hence where the axis of rotation is does not matter, its the direction of the axis. In particular, the baseline is a plane which is orthogonal to the light ray. Then the angle θ is defined by the angle of normal vectors between the actual surface and base surface. In this particular case, the axis rotation is a vector othogonal to the screen (popping out of the screen and pointing at viewer)