Best way to render specific area darker?

Greetings.

I'm currently working on a project where I need to render specific area darker.

The area A is determined by the following rules:

1. Point data T, and a list of Point data S[] are provided.

2. For each pixel P on the screen, draw a closed line that starts from P and ends at T. If resulting line passes any one of points in S[], point P is determined to be in the area A.

3. The final result should render area A with gradient around it.

I've succeeded to render S[] as white dots on black texture, and pass the texture to shader.

I also can pass T to shader as vector, so that my shader is provided with required data.

Now, how will I be able to achive step 2 and 3 as written above?

Any help would be appreciated !