Can we also do this in non-homogeneous coordinates and say nn^T is the 3x3 matrix that encodes the distance or does this property only hold in homogeneous coordinates?

daria

How do we use this to determine the cost of edge collapse

gloose

I'm not really clear on the relationship between points in homogeneous coordinates and planes in 3d. Is it just that a plane can be represented by 4 parameters a, b, c, and d, and a homogeneous point also happens to have 4 components? Or is there some deeper geometric meaning to it?

ScreenTime

What does adding d to the fourth component make sense?

I think the signed distance should be ax+by+cz-d

Why is the offset <n, p> instead of -<n, p>?

Can we also do this in non-homogeneous coordinates and say nn^T is the 3x3 matrix that encodes the distance or does this property only hold in homogeneous coordinates?

How do we use this to determine the cost of edge collapse

I'm not really clear on the relationship between points in homogeneous coordinates and planes in 3d. Is it just that a plane can be represented by 4 parameters a, b, c, and d, and a homogeneous point also happens to have 4 components? Or is there some deeper geometric meaning to it?

What does adding d to the fourth component make sense?

Should it be -d here?