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CSE5311
1
Computational Geometry
TOPICS
±
Preliminaries
±
Point in a Polygon
±
Polygon Construction
±
Convex Hulls
Further Reading
Chapter 35 from
Text book
CSE5311
2
Geometric Algorithms
Geometric Algorithms find applications in such areas
as
•
Computer Graphics
•
Computer Aided Design
•
VLSI Design
•
GIS
•
Robotics
During this week we will study
algorithms dealing
with
points, lines, line segments, and polygons
In particular, the algorithms will
•
Determine whether a point is inside a Polygon
•
Construct a Polygon
•
Determine Convex Hulls

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Preliminaries:
A point p is represented as a pair of
coordinates (x,y)
A line is represented by a pair of points
A path is a sequence of points p
1
,p
2
, . . . p
n
and the line segments
connecting them,
p
1
-p
2
, p
2
-p
3
, . . . , p
k-1
-p
k
.
A closed path whose last point is the same as the first is a polygon.
A simple polygon is one whose corresponding path does not
intersect itself. It encloses a region in the plane.
A Convex Polygon is a polygon such that any line segment
connecting two points inside the polygon
is itself entirely in the
polygon.
The convex hull of a set of points is defined as the smallest convex
polygon enclosing all the given points.
CSE5311
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A line segment
connecting two
points:
The points are
inside the polygon
The line segment is
not entirely in the
polygon
This is not a convex
polygon
p(x
1
,y
1
)
q(x
2
,y
2
)
r(x
3
,y
3
)
s(x
4
,y
4
)

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