Algorithm -- Monotone Decomposition -- Overview

• how do we go about decomposing a polygon into y-monotone pieces?
• imagine walking from the topmost vertex to the bottommost vertex following one side of the polygon
• vertices where the direction changes from downward to upward or upward to downward are called turn vertices
• to have y-monotone pieces, we need to get rid of turn vertices
• when we encounter a turn vertex, it might be necessary to introduce a diagonal and split the polygon into pieces where this vertex is no longer a turn vertex

• we will not add diagonals at all turn vertices

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