On the Degree of Standard Geometric Predicates for Line Transversals in 3D

转自：www.loria.fr/~lazard/paper/predicates1.pdf 

 A predicate is a function that returns a value from a discrete set. Typically, geometric predicates answer questions of the type “Is a point inside, outside or on the boundary of a set?”.  We consider predicates that are evaluated by boolean functions of more elementary predicates, the latter being functions that return the sign (−, 0 or +) of a multi- variate polynomial whose arguments are a subset of the input parameters of the problem instance (see, for instance [1]). Bydegree of a procedure for evaluating a predicate, we mean the maximum degree in the input parameters among all polynomials used in the evaluation of the predicate by the procedure. In what follows we casually refer to this measure

as the degree of the predicate. We are interested in the degree because it provides a measure of the number of bits required for an exact evaluation of our predicates when the input parameters are integers or floating-point numbers; the number of bits required is then roughly the product of the degree with the number of bits used in representing each input value.