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

Robust Geometric Primitives
Incircle will return 0 if all four points are cocircular, a positive value if d is inside the circle, and
negative if d is outside.
Check out the implementations described below before you attempt to build your own.
Implementations: LEDA (see Section ) provides a very complete set of geometric primitives for
planar geometry, written in C++. If you are writing a significant geometric application, you should
consider basing it on LEDA. At least check them out before you try to write your own.
O'Rourke [O'R94] provides implementations in C of most of the primitives discussed in this section. See
Section . These primitives were implemented primarily for exposition rather than production use, but
they should be quite reliable and might be more appropriate than LEDA for small applications.
A robust implementation of the basic geometric primitives in C++ using exact arithmetic, by Jonathan
Shewchuk, is available at http://www.cs.cmu.edu/ quake/robust.html. Don't expect them to be very
fast.
Pascal implementations of basic geometric primitives appear in [MS91]. Sedgewick [Sed92] provides
fragments of the basic primitives in C++. See Section for both of them.
An alternative C++ library of geometric algorithms and data structures (although you are almost certainly
better off sticking to LEDA) is Geolab, written by Pedro J. de Rezende, Welson R. Jacometti, Cesar N.
Gon, and Laerte F. Morgado, Universidade Estadual de Campinas, Brazil. Geolab requires the SUN C++
compiler, but a Sparc binary and visualization environment is included along with all source code.
Geolab appears to be primarily for the brave, since its robustness is uncertain and it contains little
documentation, but it does provide 40 algorithms, including such advanced topics as farthest point
Voronoi diagrams, nearest neighbor search, and ray shooting.
Notes: O'Rourke [O'R94] provides an implementation-oriented introduction to computational geometry,
which stresses robust geometric primitives and is recommended reading.
Shewchuk [She96] and Fortune and van Wyk [FvW93] present careful studies on the costs of using
arbitrary-precision arithmetic for geometric computation. By being careful about when to use it,
reasonable efficiency can be maintained while achieving complete robustness. Other approaches to
achieving robustness include [DS88, Hof89, Mil89].
file:///E|/BOOK/BOOK4/NODE184.HTM (4 of 5) [19/1/2003 1:31:35]