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Visibility Problem

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The space is a 2D one. The environment is created with directed segments. A clockwise wounded polygon (list of segments, no strips) specifies an unaccessible region. And it is also nonseethrough. What I need to determine is the set of all segments that can be seen (through a noninterupted straight ray) from a certain position. The segments are static. A naive implementation would be to check for each line the respective culled lines. I was considering using a BSP tree for the job. But since this is my first confrontation with it, am a bit fuzzy on the use of it. Resources are always talking about the view frustum in relation to the planes. The bottom line: Is the BSP fit for the job? How? If not, what shall I do?

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