Quadrilateral meshes for PSLGs

07/20/2020

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by   Christopher J. Bishop, et al.

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We prove that every planar straight line graph with n vertices has a conforming quadrilateral mesh with O(n^2) elements, all angles ≤ 120^∘ and all new angles ≥ 60^∘. Both the complexity and the angle bounds are sharp. Moreover, all but O(n) of the angles may be taken in a smaller interval, say [89^∘, 91^∘].