Parallel Triangulation of a Polygon in Two Calls to the Trapezoidal Map

Chee Keng Yap

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It remains to triangulate Q' .
Lemma 5 Polygon Q' is monotone along the direction of uo^'n. I-^- the ordered sequence of low vertices uo, ... , Uk of Q when projected to I'ot'n in the direction normal to voVn preserves the original order in uq, . . . , U/t- Proof. We use a homotopic proof again: imagine the (simultaneous) projec- tion of the points uq, ••-, «* onto uo^n continuously parameterized by some

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