Handouts:
9/23/08: Chapter 2 material:
Planar subdivisions and intersection problems
See the powerpoint slides.
Begin discussion of Chapter 2 material:
Planar subdivisions and intersection problems
Basic problems of line segment intersection: Detect, Report, Count
1D results: use sorting! (O(n log n) for detect, O(k+n log n) for report)
Mention briefly: Lower bound (1D) from Element Uniqueness: Omega(n log n)
Planar straight-line graphs; data structures
(winged-edge, quad-edge, DCEL (main one we use)). Details of
the DCEL.
Planar straight-line graphs; review Euler formula (f-e-v=c+1); linearity of size
Plane sweep paradigm: Apply to arbitrary segments in the
plane: O(n log n) to detect.
Bentley-Ottmann sweep to Report all intersections: O((k + n) log
n) to report all k intersections.
Bentley-Ottmann plane sweep paradigm: Sweep a vertical line
from left to right (or a horizontal
line from top to bottom, etc). Maintain two data structures: Event Queue
(EQ) and the Sweep Line Status (SLS).
I give details of how to process each of 3 types of
events: (a). left endpoint, (b) right endpoint, (c) crossing point.