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- 1. Convex Hull Algorithms Kasun Ranga Wijeweera (krw19870829@gmail.com)
- 2. Formal Definitions (Convex Set)• A set S is convex if x in S and y in S implies that the segment xy is a subset of S• Example in 2D:
- 3. Formal Definitions (Convex Hull of a Set of Points)• The convex hull of a set S of points is the smallest convex set containing all the points in S• Example in 2D:
- 4. Intuitive Appreciations (Convex Hull of a Set of Points in 2D)• The convex hull of a set of points in two dimensions is the shape taken by a rubber band stretched around nails pounded into the plane at each point• Example:
- 5. Intuitive Appreciations (Convex Hull of a Set of Points in 3D)• The boundary of the convex hull of points in three dimensions is the shape taken by plastic wrap stretched tightly around the points• Example:
- 6. Applications• Collision Avoidance
- 7. Applications• Minimum Bounding Box
- 8. Applications• Shape Analysis
- 9. Existing Convex Hull Algorithms• Gift Wrapping (1970)• Graham Scan (1972)• Quick Hull (1977)• Divide and Conquer (1977)• Monotone Chain (1979)• Incremental (1984)• Marriage before Conquest (1986)• Chan (1996)
- 10. Interior Points AlgorithmBased on the following Lemma A point is non-extreme if and only if it is inside some (closed) triangle whose vertices are points of the set and is not itself a corner of that triangle
- 11. Interior Points AlgorithmAlgorithm: INTERIOR POINTSfor each i do for each j != i do for each k != i != j do for each l != k != i != j do if p(l) in Triangle{ p(i), p(j), p(k) } then p(l) is non-extreme
- 12. Any Questions?
- 13. Thank You!

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