Computational Geometry Convex Hull Line Segment Intersection ...

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• Slope increases from one segment to next (p 1 ,p 2 ) left turn (q 1 ,q 2 ) q q 2 1 − p − p (r 1 ,r 2 ) CSE 589 - Lecture 10 - Autumn 2001 2 1 r2 < r 1 − q − q (q − p r − q ) < ( r − q )( q − p ) to avoid dividing by zero 2 2)( 1 1 2 2 1 1 2 1 44
• Sorting – O(n log n) • During the scan each point is “visited” at most twice – Initial visit – back up visit (happens at most once) • Scan - O(n) • Total time O(n log n) • This is best possible because sorting is reducible to finding convex hull. CSE 589 - Lecture 10 - Autumn 2001 45
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 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: • Sort - First increasing in x -
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
Page 59 and 60: intersection event event a b c 1. R
Page 61 and 62: c Segment List Event Queue b a , b
Page 63 and 64: c Segment List b, a Event Queue b c
Page 65 and 66: c Segment List c, d, b, a Event Que
Page 67 and 68: c Segment List b, c, d, a Event Que
Page 69 and 70: c Segment List b, e, c, a Event Que
Page 71 and 72: c Segment List c, e, a Event Queue
Page 73 and 74: c Segment List c, a Event Queue e a
Page 75 and 76: c Segment List Event Queue b d e a
Page 77 and 78: • Total time for plane sweep algo
Page 79 and 80: • Each Voronoi area is the inters
Page 81 and 82: • F = E - V + 2 (Euler’s equati
Page 83 and 84: 2. A point on a perpendicular bisec
Page 85 and 86: each line event queue a, b, c b a C
Page 87 and 88: points equidistant from point and l
Page 89 and 90: eakpoint segment beach line a, b, a
Page 91 and 92: each line a, b, a, c, a event queue
Page 93 and 94: each line a, b, c, a event queue b
Page 95 and 96:
• Contains site events and circle
Page 97 and 98:
• For each site output the vertic
Page 99 and 100:
• Voronoi diagram - Dirichlet (18
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Computational Geometry Convex Hull Line Segment Intersection ...

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