Just a quick thought: if you want a programatic way of determining which half plane to use for each line (above or below), I think it's possible to just select the half plane in which the centroid of the triangle lies in
Staffyirenng
@doinksta -- good idea, and I am sure you can get this approach to work. However, the usual implementation makes the correct choice about which side of the line to test for, without using the centroid. I described how in lecture (perhaps not entirely clearly!), and it is related to being consistent about the ordering of pairs of P0, P1 and P2 when creating the three line equations.
Perhaps some other commenters may like to spell this out, or explain the intuition or proof of this in more detail.
(This comment uses Markdown to embed math in this comment.)
Staffyirenng
I just saw that ML2000-LT has a relevant comment involving the right hand rule in slide 48.
Just a quick thought: if you want a programatic way of determining which half plane to use for each line (above or below), I think it's possible to just select the half plane in which the centroid of the triangle lies in
@doinksta -- good idea, and I am sure you can get this approach to work. However, the usual implementation makes the correct choice about which side of the line to test for, without using the centroid. I described how in lecture (perhaps not entirely clearly!), and it is related to being consistent about the ordering of pairs of P0, P1 and P2 when creating the three line equations.
Perhaps some other commenters may like to spell this out, or explain the intuition or proof of this in more detail.
(This comment uses Markdown to embed math in this comment.)
I just saw that ML2000-LT has a relevant comment involving the right hand rule in slide 48.