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cs.CG2026
A greedy maximal sweepline algorithm for a Jordan curve
Apurva Mudgal
We give a greedy sweepline algorithm for a Jordan curve and prove that it is maximal in the sense of [1]. Our proof uses Kőnig's lemma.
cs.CG2026
A proof of Jordan curve theorem based on the sweepline algorithm for trapezoidal decomposition of a polygon
Apurva Mudgal
We prove the Jordan curve theorem by generalizing the sweepline algorithm for trapezoidal decomposition of a polygon. Our proof uses Zorn's lemma (or, equivalently the axiom of cho…