module8 - Computational Geometry TOPICS Preliminaries Point...

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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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CSE5311 3 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 4 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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module8 - Computational Geometry TOPICS Preliminaries Point...

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