Computational Geometry Convex Hull Line Segment Intersection ...

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• The convex hull is a polygon whose vertices are some of the points. CSE 589 - Lecture 10 - Autumn 2001 4
• Input: Set of points p 1, p 2, ... , p n in 2 space. (Each point is an ordered pair p = (x,y) of reals.) • Output: A sequence of points p i1, p i2, ... , p ik such that traversing these points in order gives the convex hull. CSE 589 - Lecture 10 - Autumn 2001 5
Page 1 and 2: Autumn 2001 Computational Geometry
Page 3: • Given n points on the plane fin
Page 7 and 8: • For each pair of points p, q de
Page 9 and 10: • Sort the points from left to ri
Page 11 and 12: • Right Turn CSE 589 - Lecture 10
Page 13 and 14: • Left Turn - back up CSE 589 - L
Page 15 and 16: CSE 589 - Lecture 10 - Autumn 2001
Page 27 and 28: • Upper convex hull is complete C
Page 41 and 42: • Done! CSE 589 - Lecture 10 - Au
Page 43 and 44: • Sort - First increasing in x -
Page 45 and 46: • Sorting - O(n log n) • During
Page 47 and 48: • Given two convex hulls compute
Page 51 and 52: • What if no line segment interse
Page 53 and 54: • With n line segments there may
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• We maintain ordered list of seg
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• Event Queue - contains all the
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intersection event event a b c 1. R
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c Segment List Event Queue b a , b
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c Segment List b, a Event Queue b c
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c Segment List c, d, b, a Event Que
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c Segment List b, c, d, a Event Que
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c Segment List b, e, c, a Event Que
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c Segment List c, e, a Event Queue
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c Segment List c, a Event Queue e a
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c Segment List Event Queue b d e a
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• Total time for plane sweep algo
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• Each Voronoi area is the inters
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• F = E - V + 2 (Euler’s equati
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2. A point on a perpendicular bisec
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each line event queue a, b, c b a C
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points equidistant from point and l
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eakpoint segment beach line a, b, a
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each line a, b, a, c, a event queue
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each line a, b, c, a event queue b
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• Contains site events and circle
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• For each site output the vertic
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• Voronoi diagram - Dirichlet (18
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Computational Geometry Convex Hull Line Segment Intersection ...

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