module9 - TOPICS Preliminaries Point in a Polygon Polygon...

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Click to edit Master subtitle style  CSE5311  11 Computational Geometry TOPICS Preliminaries Point in a Polygon Polygon Construction Convex Hulls Further Reading
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 CSE5311  22 Geometric Algorithms   Geometric Algorithms find applications in such areas as n Computer Graphics n Computer Aided Design n VLSI Design n GIS n Robotics We will study algorithms dealing with points, lines, line segments, and polygons In particular, the algorithms will n Determine whether a point is inside a Polygon n Construct a Polygon n Determine Convex Hulls
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 CSE5311  33 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 p1,p2, . . . pn and the line segments connecting them, p1-p2, p2-p3, . . . , p k-1-pk. 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.
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 CSE5311  44 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(x1,y1 ) q(x2,y2 ) r(x3,y3 ) s(x4,y4 )
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 CSE5311  55 Determining whether a point is inside a polygon Given a simple polygon polygon P, and a point q, determine whether the point is inside or outside the polygon. (a non-convex polygon)
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 CSE5311  66 Procedure Point_in_a_Polygon(P,q) Input : P ( a simple polygon with vertices p1,p2, … pn, and edges e1,e2,e3, … en and q (x0,y0) a point.
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module9 - TOPICS Preliminaries Point in a Polygon Polygon...

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