@article{kar-kie-nac-91-ratvor,
  author = {Michael Karasick and Deter Kieber and Lee R. Nackman},
  title = {Efficient Delaunay Triangulation using Rational Arithmetic},
  journal = {ACM Transactions on Graphics},
  volume = {10},
  number = {1},
  pages = {71--91},
  year = 1991,
  month = jan,
  issn = {0730-0301},
  comment = {Many fundamental tests performed by geometric algorithms can be formulated in terms of finding the sign of a determinant. When these tests are implemented using fixed precision arithmetic such as floating point, they can produce incorrect answers; when they are implemented using arbitrary-precision arithmetic, they are expensive to compute. We present adaptive-precision algorithms for finding the signs of determinants of matrices with integer and rational elements. These algorithms were developed and tested by integrating them into the Guibas-Stolfi Delaunay triangulation algorithm. Through a combination of algorithm design and careful engineering of the implementation, the resulting program can triangulate a set of random rational points in the unit circle only four to five times slower than can a floating-point implementation of the algorithm. The algorithms, engineering process, and software tools developed are described.},
  altkeys = {Karasick:1991:EDT}
}