Is there any algorithm or library can generate alternative path ?

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Example case:

I want to generate an alternative path to avoid colliding with the polygons (red area) by C or PHP or Nodejs in Linux.


The alternative path must meet the following criteria:
1. Turning angle less than 15 degrees for each segment ( 1 minutes per segment)
2. Keep certain distance between red polygons and plane, eg at least 15KM

What data I have:
1. The data of original path (Yellow path)
2. The data of red area (black polygon) in lat long



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