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9.3 Convex Hull

  • Construct the shortest polygon enclosing a given set of points on a plan.
  • Intuitively, the polygon can be determined by placing a rubber around the set.
 •|- ||---- | ---- |• --- | • ---- • --------------- - •

Graham’s Scan

  • Determine an extreme point with the largest x coordinate.
  • Sort the points in order of increasing angles, relatively to the extreme point.
• - b --- ---- c•---- ---- -•------ •----d---------- e -a•
  • Traverse the points in the sorted order
  • Adding a point less than 180 degrees
  • Backtrack when making a larger turn.
b •|-- ||---- •c --- d---- e • ---- • -•a        b •|-- ||||-- •c-- ---- --- d --- e • --- • -•a       
b •|-- | ---- •c- ||||- --| d|--- e---|-• |- ---- • ||||| -•a        b •|--- | --- •c- ---- --- d ---- e • --- • •a       
b •|-- | --- •c ---- d --- e • --- • -•a        b •|-- ||||-- •c - ---- ||||- d --- e • ---- • -•a       
b •|-- | ---- •c --- d --- e • ---- • -•a        b •--- --- •c ---- d ---- e • --- • -•a       
b •--| |||---- |•c ---- | d --- e • ---- • -•a        b •---- | --- |•c ---- ||| d ---- e-----• --- • ----------•a

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