m3-convex-hull - Convex Hull COMP 215 Lecture 5...

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Unformatted text preview: Convex Hull COMP 215 Lecture 5 Computational Geometry ● The area of CS concerned with solving geometric  problems. ● Examples: – Finding intersections between line segments. – Finding closest pairs of points. – Finding the convex hull. (More on this in a second.) ● Uses in: – Graphics. – Robotics. – VLSI design. – etc. Convex Hull ● The convex hull of a set  Q  of points is the smallest  convex polygon  P  for which each point  Q  is either on the  boundary of  P  or in its interior.  (Introduction to Algorithms, Cormen et. al. 2001) ● The problem: For an arbitrary set of points  Q , find the  corresponding  P . Line Segments Properties ● First question: – Given two directed line segments:           and           , is                 clockwise from          ?    p p 1  p p 2  p p 1  p p 2 p p 1 p 2 Cross Product ● 2d cross product: ● When this is positive  p 1  is clockwise from  p 2 .   ● When this is negative  p 2  is clockwise from  p 1 .  p 1 p 2 p 1 × p 2 = x 1 y 2 − x 2 y 1 Solution to Clockwise Problem...
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This note was uploaded on 04/23/2011 for the course COMPUTER CSI4526 taught by Professor Kim during the Spring '09 term at Yonsei University.

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m3-convex-hull - Convex Hull COMP 215 Lecture 5...

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