Computational Geometry Convex Hull Line Segment Intersection ...

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1. A vertex is the center of a circle through at least three sites CSE 589 - Lecture 10 - Autumn 2001 82
2. A point on a perpendicular bisector of sites p and q is on an edge if the circle centered at the point through p and q contains no other sites. CSE 589 - Lecture 10 - Autumn 2001 83
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Autumn 2001 Computational Geometry
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• Given n points on the plane fin
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• Input: Set of points p 1, p 2,
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• For each pair of points p, q de
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• Sort the points from left to ri
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• Right Turn CSE 589 - Lecture 10
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• Left Turn - back up CSE 589 - L
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CSE 589 - Lecture 10 - Autumn 2001
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CSE 589 - Lecture 10 - Autumn 2001
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• Upper convex hull is complete C
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Page 31 and 32: • Right Turn CSE 589 - Lecture 10
Page 33 and 34: • Left Turn - back up CSE 589 - L
Page 35 and 36: • Right Turn CSE 589 - Lecture 10
Page 37 and 38: CSE 589 - Lecture 10 - Autumn 2001
Page 39 and 40: • Left Turn - back up CSE 589 - L
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 49 and 50: CSE 589 - Lecture 10 - Autumn 2001
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: • F = E - V + 2 (Euler’s equati
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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