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CompGeomIntro

# Q convex hull gift wrapping start w ith theole lectst

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Unformatted text preview: Mepo y the two co lve p p q p p q p q q p q Merging the left and right subhulls. q CONVEX HULL - Gift Wrapping ✦ Start w ith theole-Lectst e o int onvex Hullaroun d N n ftmour pE: C an d wrap s l p=l l p p p p l F l l p The execution of Jarvis’s March. In other words, if q is the vertex following p, and r is any other input , r is in counter-clockwise HULL e caGift eachrsuppingvertex in lin order. W - n ﬁnd W a ccessive CONVEX series of O(n) counter-clockwise tests. JarvisMarch(X [1 .. n], Y [1 .. n]): ←1 for i ← 2 to n if X [i] < X [ ] ←i p← rep eat q ←p+1 Make sure p = q for i ← 2 to n if CCW(p, i, q ) q←i next[p] ← q ; pr ev [q ] ← p p←q until p = algorithm sp ends O(n) time for each convex hull vertex, the worst-case ru CONVEXithm is optimal (within aBounant factor), he HULL - Lower const d Our algor proof by reduction from sor ting. let N = (x1 , x2 , . . . xn ) ⊂ IR for all i let pi = (xi , x2 ) i compute C H(P ) P : y = x2 C H(P ) p3 p2 p1 p4 Intro Line-segment intersection Given n line segments, does an...
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