Computational Geometry Convex Hull Line Segment Intersection ...

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• For each pair of points p, q, form the line that passes through p and q and determine if all the other points are on one side of the line. – If so the line from p to q is on the convex hull – Otherwise not • Time Complexity is O(n 3 ) – Constant time to test if point is on one side of the line 0 = (q − p )x + (p − q )y + p q − p 2 2 1 CSE 589 - Lecture 10 - Autumn 2001 1 2 1 1 q 2 8
• Sort the points from left to right (sort on the first coordinate in increasing order) CSE 589 - Lecture 10 - Autumn 2001 9
Page 1 and 2: Autumn 2001 Computational Geometry
Page 3 and 4: • Given n points on the plane fin
Page 5 and 6: • Input: Set of points p 1, p 2,
Page 7: • For each pair of points p, q de
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
Page 55 and 56: • We maintain ordered list of seg
Page 57 and 58: • 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
Page 67 and 68:
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
Page 83 and 84:
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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