O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science

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Intersection of Nonconvex Polygons • Variation on Bentley- Ottmann sweep • Maintain status for each piece of sweep line: • 0: exterior to P, Q • P: inside P, outside Q • Q: inside Q, outside P • PQ: inside P , inside Q • Useful for CAD/CAM P source: O’Rourke Q For n-vertex P, , m-vertex Q, , O((n+m n+m)log( )log(n+m)+k) time to compute: P ∩ Q P ∪ Q P \ Q
Extreme Point of Convex Polygon Algorithm: HIGHEST POINT of CONVEX POLYGON Initialize a and b /* highest h point is in [a,b] */ repeat forever c index midway from a to b if P[c] is locally highest then return c if A points up and C points down then [a,b] [a,c] /* highest point is in [a,c] */ else if A points down and C points up then [a,b] [c,b] /* highest point is in [c,b] */ else if A points up and C points up if P[a] is above P[c] then [a,b] [a,c] else [a,b] [c,b] /* highest point is in [c,b] */ else if A points down and C points down if P[a] is below P[c] then [a,b] [a,c] /* highest point is in [a,c] */ else [a,b] [c,b] /* highest point is in [c,b] */ source: O’Rourke I iti li d b A Geometric Binary Search C c b A Unimodality allows B Binary Search O(lg n) a
Page 1 and 2: UMass Lowell Computer Science 91.50
Page 3 and 4: Segment-Segment Intersection • Fi
Page 5 and 6: Point in Polygon An application: GU
Page 7 and 8: Point in Polyhedron source: O’Rou
Page 9 and 10: Intersection of Convex Polygons sou
Page 11 and 12: Intersection of >2 Line Segments Sw
Page 13 and 14: Intersection of >2 Line Segments Ti
Page 15: Intersection of Segments • Goal:
Page 19 and 20: Extremal Polytope Queries: Main Ide
Page 21 and 22: Extremal Polytope Queries: Main Ide
Page 23 and 24: Extremal Polytope Queries Details (
Page 25 and 26: Extremal Polytope Queries Dtil Deta
Page 27 and 28: Extremal Polytope Queries Summary A
Page 29 and 30: Planar Point Location (continued)
Page 31 and 32: Planar Point Location (continued) s
Page 33 and 34: Planar Point Location (continued) s

O'Rourke Chapter 7: Search & Intersection in PDF - Computer Science

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