Slide has been fixed. Please refresh. (Removing comments about bug in eqn to avoid confusion).
@WALL-E. u + v need not equal 1 here, but u + v <= 1. Why is that the case?
WALL-E
The way I understand it, we are trying to form a affine subspace of 3 points p0,p1 and p2 which is $\lambda_0$p0 + $\lambda_1$p1 + $\lambda_2$p2 where $\sum \lambda_i = 1$ and $\lambda_i >=0$ $\forall i$.
Another explanation without definitions I can think of is I am adding the vectors p0p1 and p0p2 linearly and it should result in a vector p0p3 such that p3 is inside the triangle. Therefore u,v can't be negative as it may result in subtracting the vectors making p3 go out of the triangle and also I can't scale the vectors p0p1 and p0p2 more than 1 as it'll again result in going outside the triangle. So f(u,v)-p0 = u(p1-p0) + v(p2-p0) resulting in the expression above.
kapalani
I think another way to understand why it must be the case that (u+v<=1) is because u+v==1 represents the boundaries, and since we just want to know if the point in inside the triangle is (u+v<=1)
Also is it necessary that u+v = 1 here?
Slide has been fixed. Please refresh. (Removing comments about bug in eqn to avoid confusion).
@WALL-E. u + v need not equal 1 here, but u + v <= 1. Why is that the case?
The way I understand it, we are trying to form a affine subspace of 3 points p0,p1 and p2 which is $\lambda_0$p0 + $\lambda_1$p1 + $\lambda_2$p2 where $\sum \lambda_i = 1$ and $\lambda_i >=0$ $\forall i$. Another explanation without definitions I can think of is I am adding the vectors p0p1 and p0p2 linearly and it should result in a vector p0p3 such that p3 is inside the triangle. Therefore u,v can't be negative as it may result in subtracting the vectors making p3 go out of the triangle and also I can't scale the vectors p0p1 and p0p2 more than 1 as it'll again result in going outside the triangle. So f(u,v)-p0 = u(p1-p0) + v(p2-p0) resulting in the expression above.
I think another way to understand why it must be the case that (u+v<=1) is because u+v==1 represents the boundaries, and since we just want to know if the point in inside the triangle is (u+v<=1)