What is the best algorithm for clipping a bezier path

I know two common Greiner-Horman and Watti algorithms. They work with polygons. I want to implement logical operations on bezier paths. I want to extend these algorithms to work with bezier paths. But this is a numerical problem. What is the best way to trim the bezier path? (and what is the best modification of the Greiner-Horman algorithm for arbitrary polygons (with self-intersections))

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Here is the proposed algorithm.

  • Use the four control points to define the polygon spanning the Bezier curve.

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