Algorithm -- Monotone Decomposition -- Plane Sweep Method

• use plane sweep method
• move an imaginary sweep line downward over the plane
• halt the line on every vertex
• handle the event depending on the vertex type
• events:
• edge starts (just be aware of it)
• edge ends (add a diagonal if the helper is a merge vertex)
• edge changes a helper (add a diagonal if old helper was a merge vertex)
• new vertex is a split vertex (must add a diagonal)

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