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Unformatted text preview: vex hull is a p oint in P . CONVEX HULLS ne the convex hull as the largest convex p olygon whose vertices are
o✦ ex nvex on thaCH(Ptainf P set ofhpoe verticis the almallinst in
nv Co p olyg Hull, t con ), os a and w os ints P es are s l p o e ts
ntercor vexnps thatnare nt tcoertices of the convex hull.
io n p oi t olygo tha o vntains P A set of p oints and its convex hull.
Convex hull vertices are black; interior p oints are white. ✦ largest convex polygon whose vertices are all po ints in P e✦hungque ncrnve,xweolyigloreprestncothe p ointsain dPwby se eir Cartesia
t i ni s co co ete p w l n thae t ntains P n
ho th
[1 .verticesY [re..al]l. pWe ts ill rPpresent the convex hull as a circula
. n] and a 1 n o in w in e
terclockwise order. if the ith p oint is a vertex of the convex hull, ne CONVEXIT Y Convexity A set C ⊂ IRd is convex iff ∀(p, q ) ∈ C 2 the line segment pq is
contained in C . p q Convex p q
Non convex Compu HULL PROex hu
CONVEXting a convBLEM ll
Input: the set P = {p1 , p2 , . . . pn } ⊂ IR2
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 Fall '08
 UNGOR
 Algorithms, Data Mining, Databases

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