+1, I'm a bit confused about the meaning of the w vector and why we're performing the normalize operation to generate w
sushain
$w$ is the ray that actually hits $p$ the point that we're interested in, i.e. $w$ is the ray from the light source $p_L$ to the surface point $p$. This is in contrast to $d$ which is the direction that the spotlight is "pointing" or centered at.
imm
What does the normalize operation do? And is the theta in the diagram supposed to be the angle between w and d?
Jessica
If w and d are normalized, w \dot d will be the angle between them.
cs248acct
wouldn't it be cos of the angle between them? So we should be comparing to cos theta, not theta?
alexz
Here theta should have been cos(theta)? is this a typo?
dawwctor
Why exactly do we make the approximation of L(w) ~= w * d when the spotlight intensity falls off from direction d? Do we also assume d to be normalized, which is why we can model it as the dot product between d and w?
sarukkai
I believe both w and d are assumed to be normalized, as the cosine computation where cos(theta) = dot(w, d) does not work unless both w and d are normalized.
What exactly is the w vector representing here?
+1, I'm a bit confused about the meaning of the
wvector and why we're performing the normalize operation to generatew$w$ is the ray that actually hits $p$ the point that we're interested in, i.e. $w$ is the ray from the light source $p_L$ to the surface point $p$. This is in contrast to $d$ which is the direction that the spotlight is "pointing" or centered at.
What does the normalize operation do? And is the theta in the diagram supposed to be the angle between w and d?
If w and d are normalized, w \dot d will be the angle between them.
wouldn't it be cos of the angle between them? So we should be comparing to cos theta, not theta?
Here theta should have been cos(theta)? is this a typo?
Why exactly do we make the approximation of L(w) ~= w * d when the spotlight intensity falls off from direction d? Do we also assume d to be normalized, which is why we can model it as the dot product between d and w?
I believe both w and d are assumed to be normalized, as the cosine computation where cos(theta) = dot(w, d) does not work unless both w and d are normalized.