This preview shows page 1. Sign up to view the full content.
Unformatted text preview: utput: a sequence L = (c1 , c2 , . . . ch ) of ver tices of
C H(P ) in counterclockwise order
Example: L = (p3 , p4 , p8 , p6 , p1 , p5 ) p6 p1 p8
p2 p7
p4 p5
p3
C H(P ) Introduction, Convex Hulls – p.13/40 CONVEX Characterizationization
HULL  Character
The directed edge (p, q ) is an edge of C H(P ) iff q
p C H(P ) CONVEX CharacChaization tion
HULL  ter racteriza
The directed edge (p, q ) is an edge of C H(P ) iff q
p
r −
all r ∈ P \ {p, q } lies to the left of line pq (oriented by →).
pq CONVEX HULLrization
Characte PROBLEM
The directed edge (p, q ) is an edge of C H(P ) iff q
p
r ∀r ∈ P \ {p, q } the triangle (p, q , r) is oriented counterclock wise. Introduction, Convex Hulls – p.16/40 OCONVEX HULL t
rientation tes
We denote
C C W (p, q , r) = xp xq xr
yp yq yr
111 = (xq − xp )(yr − yp ) − (xr − xp )(yq − yp ) Triangle (p, q , r) is counterclockwise iff C C W (p, q , r) > 0.
How fast can we perform this test?
2 multiplications and 5 subtractions
takes O(1) time CONVEX HULL  tNaive Aithrithm
Firs algor lgo m
Algorithm SlowConvexHull (P)...
View
Full
Document
This note was uploaded on 01/15/2012 for the course COT 5405 taught by Professor Ungor during the Fall '08 term at University of Florida.
 Fall '08
 UNGOR
 Algorithms, Data Mining, Databases

Click to edit the document details