Complexity Draw a new contour E Compute E's relationshi p with d Is d + E wellformed ? Add E to d Compute Split zones Generate new Zones Update Marked
{"Image DocumentName": "Compute E s relationship with d", "Image ImageDescription": "Complexity. d is a wellformed diagram. O(|Z|) O(|C|) d +E is a wellformed diagram. Each arc splits exactly 1 zone. # arcs = O(|C|) Consecutive arcs split zones which differ by one exactly contour, so we order the points of inter(E). E. E. Draw a new contour E. Compute E s relationship with d. Is d +E wellformed ? Add E to d. Compute Split zones. Generate new Zones. Update Marked Points. Update covered Zones. O(|C|) O(|C|) Cont(E) Over(E) Inter(E) E. yes. no. Reject A. O(C log C) steps to order the points of intersection of E, there being O(C) such points since E intersects each contour at most 4 times (actually at most twice for WF case), O(C) to compute the first point, then O(1) for the rest giving total of O(C log C). Note that the more naive approach here would be to compute each zone separately, giving O(C) zones to compute, each taking O(C) time, yielding O(C^2). E. E. O(|C|) O(|C| log |C|)", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}