The.Algorithm.Design.Manual.Springer-Verlag.1998

Intersection Detection
Implementations: LEDA (see Section ) provides a C++ implementation of the Bentley-Ottmann
sweepline algorithm [BO79], finding all k intersection points between n line segments in the plane in
time.
O'Rourke [O'R94] provides a robust program in C to compute the intersection of two convex polygons.
See Section .
RAPID is a ``Rapid and Accurate Polygon Interference Detection library'' for large environments
composed of polygonal models. It is free for noncommercial use and available from
http://www.cs.unc.edu/ geom/OBB/OBBT.html.
Model Pascal subroutines for convexity testing and for finding an intersection in a set of line segments
appear in [MS91]. See Section for details. XTango (see Section ) includes an animation of
polygon clipping against a polygonal window.
Finding the mutual intersection of a collection of half-spaces is a special case of higher-dimensional
convex hulls, and Qhull [BDH97] is convex hull code of choice for general dimensions. Qhull has been
widely used in scientific applications and has a well-maintained home page at
http://www.geom.umn.edu/software/qhull/.
Notes: Good expositions on line segment intersection detection [BO79, SH75] include [CLR90, Man89,
NH93, PS85]. Good expositions on polygon and polyhedra intersection [HMMN84, MP78, SH76]
include [PS85]. Preparata and Shamos [PS85] provide a good exposition on the special case of finding
intersections and unions of axis-oriented rectangles, a problem that arises often in VLSI design.
An optimal algorithm for computing line segment intersections is due to Chazelle and
Edelsbrunner [CE92]. Simpler, randomized algorithms achieving the same time bound are thoroughly
presented by Mulmuley [Mul94].
Surveys on hidden-surface removal include [Dor94, SSS74].
Related Problems: Maintaining arrangements (see page ), motion planning (see page ).
Next: Bin Packing Up: Computational Geometry Previous: Point Location
file:///E|/BOOK/BOOK4/NODE191.HTM (4 of 5) [19/1/2003 1:31:48]