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5.2.3 Classification by number system

In our discussion of intersection problems, we will refer to various classes of numbers:

  1. Rational numbers, $ m/n$ , $ n \neq 0$ , where $ m, n$ are integers.
  2. Floating point (FP) numbers in a computer (which are a subset of rational numbers, see Sect. 4.8.1 and [4]).
  3. Algebraic numbers (roots of polynomials with integer coefficients).
  4. Real numbers, e.g. transcendental numbers such as $ e$ , $ \pi$ , trigonometric, etc.
  5. Interval numbers, $ [a,b]$ , where $ a, b$ are real numbers.
  6. Rounded interval numbers, $ [c,d]$ , where $ c, d$ are FP numbers.

Issues relating to floating point and interval numbers affecting the robustness of intersection algorithms were addressed in Chap. 4 in the context of nonlinear solvers as well as in [4,105,179,178,392].


December 2009