When we calculate the distance, what if x is on the other side of the line?
Is it better to define d(x) = |N(n-p)|?
zhengbol
I think it is better to define d(x) as "signed distance".
keenan
@fronteva Right, we really do want the signed distance here. In this case, the reason is not so much that we care about + vs. -, but because using the signed distance will ultimately allow us to use a very convenient representation of the distance to each collection of planes: a quadratic form, encoded by a 4x4 matrix. If we instead use the signed distance, it's no longer so easy to "combine" distances by just taking linear combinations of those 4x4 matrices.
When we calculate the distance, what if x is on the other side of the line? Is it better to define d(x) = |N(n-p)|?
I think it is better to define d(x) as "signed distance".
@fronteva Right, we really do want the signed distance here. In this case, the reason is not so much that we care about + vs. -, but because using the signed distance will ultimately allow us to use a very convenient representation of the distance to each collection of planes: a quadratic form, encoded by a 4x4 matrix. If we instead use the signed distance, it's no longer so easy to "combine" distances by just taking linear combinations of those 4x4 matrices.