We give a worst-case bound of Θ(m2/3n2/3+ n) on the complexity of m convex polygons whose sides come from n lines. The same bound applies to the complexity of the horizon of a segment that intersects m faces in an incrementally-constructed erased arrangement of n lines. We also show that Chazelle's notch-cutting procedure, when applied to a polyhedron with n faces and rreflex dihedral angles, gives a convex decomposition with Θ(nr+r7/3) worst-case complexity.
CITATION STYLE
Hershberger, J., & Snoeyink, J. (1992). Convex polygons made from few lines and convex decompositions of polyhedra. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 621 LNCS, pp. 376–387). Springer Verlag. https://doi.org/10.1007/3-540-55706-7_34
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