I think one way to decide which side of the line a point q is on is taking the cross product of the vector P_i->q and P_i->P_j (by a->b, I mean the vector that starts from a and ends at b). Depending on whether the cross product is positive or negative, we can tell what side it is on.
peanut
Agree with above comment! Following this thread.
keenan
@nghandi Yep, that's a great way to do it!
by a->b, I mean the vector that starts from a and ends at b
By the way, some people would write this as $b-a$ ;-)
pw123
Having trouble understanding why the cross product allows us to determine what side it's on, is it because our "starting point" for both vectors is P_i and thus taking the cross product gives us some indication of the angle between the two vectors?
I think one way to decide which side of the line a point q is on is taking the cross product of the vector P_i->q and P_i->P_j (by a->b, I mean the vector that starts from a and ends at b). Depending on whether the cross product is positive or negative, we can tell what side it is on.
Agree with above comment! Following this thread.
@nghandi Yep, that's a great way to do it!
By the way, some people would write this as $b-a$ ;-)
Having trouble understanding why the cross product allows us to determine what side it's on, is it because our "starting point" for both vectors is P_i and thus taking the cross product gives us some indication of the angle between the two vectors?