A bit confused about where the triangle is here - it seems like we have a triangle with a non-zero height?

Is half space test literally the same thing as the half plane test except in 3D?

I'm confused about what the planes here are for. Are we combining the plane test with the space test?

What are different considerations we have to make for half space vs. half plane tests?

If you're trying to see if the projection of the point is in the triangle, why can't you do 3 half plane tests?

A bit confused about where the triangle is here - it seems like we have a triangle with a non-zero height?

Is half space test literally the same thing as the half plane test except in 3D?

I'm confused about what the planes here are for. Are we combining the plane test with the space test?

What are different considerations we have to make for half space vs. half plane tests?

If you're trying to see if the projection of the point is in the triangle, why can't you do 3 half plane tests?