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Given a trapezoidal map of a simple polygon $P$, is it possible to compute the triangulation of $P$ in $\mathcal{O}(n)$ time?

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    $\begingroup$ Yes it is possible. $\endgroup$ – Evil Nov 28 '17 at 11:29
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Yes, "it's easy to derive from such a decomposition of $P$ in linear time a triangulation of $P$."

Take a look at lemma 1. here.

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