I'd like to do a simple 2D shadow calculation algorithm by rendering my environment into a texture, and then use raytracing to determine what pixels of the texture are not visible to the point light (simply handed to the shader as a vec2 position) .

A simple brute force algorithm per pixel would looks like this:

line_segment = line segment between current pixel of texture and light source

For each pixel in the texture:
{
  if pixel is not just empty space && pixel is on line_segment
       output = black
  else
       output = normal color of the pixel

}

This is, of course, probably not the fastest way to do it. Question is: What are faster ways to do it or what are some optimizations that can be applied to this technique?