Visibility determination

Hi everyone,

I am working on visibility determination. Basically, I have a, let’s say Player 1 which has a visibility triangle attached to it. And the object (in pink, below) to be tested.

So the ideas is that, if the pink object falls into the area of the triangle, test should come out to be true.

Well I’m trying to figure out the test necessary for it.

I know that, in 3D, the dot product of the center vector of the pink object and a plane gives positive result if the object is to the positive side of the plane. However, I am dealing with 2D here. And I did try dotting the vectors of the sides with the object to see if it is + or negative but no luck.

Anyone have any idea?