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Convex Hull
 most ubiquitous structure in
computational geometry
useful to construct other structures
many applications: robot motion
planning, shape analysis etc.
 a beautiful object, one of the early
success stories in computational
geometry that sparked interest
among Computer Scientists
by
the invention of O(nlogn) algorithm
rather than a O(n**3) algorithm.
 intimately related to sorting
algorithm
for both lower and upper bound.
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View Full Document Convex hulls
Preliminaries and definitions
Intuitive definition 1
Given a set
S
= {
p
1
,
p
2
, …,
p
N
} of points in the plane,
the convex hull
H
(
S
) is the smallest convex polygon in the plane
that contains all of the points of
S
.
Imagine nails pounded halfway into the plane at the points of
S
.
The convex hull corresponds to a rubber band stretch around them.
Convex hulls
Preliminaries and definitions
Convex polygon
A polygon is
convex
iff for any two points in the polygon
(interior
∪
boundary) the segment connecting the points is
entirely within the polygon.
convex
not convex
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View Full Document
Preliminaries and definitions
Vertices
A polygon vertex is
convex
if its interior angle
≤ π (180°
29.
It is
reflex
if its interior angle >
π (180°
29.
convex
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This note was uploaded on 07/14/2011 for the course COT 5520 taught by Professor Mukherjee during the Summer '11 term at University of Central Florida.
 Summer '11
 Mukherjee

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