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Getting shadows in a 2D room offline?

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Hello, I'm writing a program that will generate me a CPU shadow for a 2D room with a light source and any number of polygons.The light is also blocked by the walls.This is the algorithm I've got so far:

1.Sort all polygon vertices by their angle from the light.
2.Generate an array of all lines between 2 vertices.
3.Iterate sorted list and for each polygon check the entire "lines" array to see if the light intersects that and check if the intersection point is closer than the current vertex
4.Each 3 generated vertices make a triangle and add it to the buffer that will be used for the shadow mesh.

Is this the correct way to proceed?

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