In our discussion of intersection problems, we will refer to various
classes of numbers:
Rational numbers,
,
, where
are integers.
Floating point (FP) numbers in a computer (which are a subset of
rational numbers, see Sect. 4.8.1 and [4]).
Algebraic numbers (roots of polynomials with integer coefficients).
Real numbers, e.g. transcendental numbers such as
,
,
trigonometric, etc.
Interval numbers,
, where
are real numbers.
Rounded interval numbers,
, where
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].