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The solution outline: Step 1. Verify, that all the initial (at the moment $t=0$) wave circles don't contain your starting point $(0,0)$. If yes, then continue - otherwise exit, no escape. Step 2. For each wave circle $W_i$ you need to find an escape sector - the range of directions, where the escape is guaranteed. Imagine a circle of your possible ...


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I only noticed after posting that my first answer does not directly address your specific question. So now my answer is in two parts. (1) As suggested by @HEKTO, to find the closest segment, you could first compute the Voronoi diagram: CGAL 2D Segment Voronoi Diagrams. Then next you need to perform point location within the (non-rectilinear) cells of the ...


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