CGAL::Fixed_precision_nt

Definition

The class Fixed_precision_nt provides 24-bit numbers in fixed point representation. Basically these numbers are integers in the range $$[-2²⁴,2²⁴] with a multiplying factor $$2^b. The multiplying factor $$2^b has to be initialized by the user before the construction of the first Fixed_precision_nt and is common to all variables.

The interest of such a number type is that geometric predicates can be overloaded to get exact and very efficient predicates. The drawback is that any Fixed_precision_nt is rounded to the nearest multiple of $$2^b, which yields to a very poor arithmetic. The idea is to not use the arithmetic on Fixed_precision_nt but only the specialized predicates.

Note: you must call CGAL::force_ieee_double_precision() in order for the Fixed_precision_nt to work properly on Intel platforms. This initializes the FPU to an IEEE compliant rounding mode which is not the default.

#include <CGAL/Fixed_precision_nt.h>

Is Model for the Concepts

Creation

Operations

Fixed_precision_nt &
	fvar = fval	Assignment.
bool	is_valid ( fval)	In case of overflow or division by 0, numbers becomes invalid. If the precision is changed by usage of Fixed_precision_nt::init(), already existing numbers may become invalid if they are no longer multiple of $$2b.
bool	is_finite ( fval)	Fixed_precision_nt do not implement infinite numbers. is_finite is identical to is_valid.

The comparison operations $$==, $$!=, $$<, $$>, $$<=, and $$>= are all available.

The arithmetic operators $$+, $$-, $$*, $$/, $$+=, $$-=, $$*= and $$/= are all available. The result of the computation is rounded to the nearest legal Fixed_precision_nt. Overflow is possible, and even probable in case of multiplication or division. Fixed_precision_nt are designed to use specialized predicates, not to use arithmetic.

double

to_double ( fval)

casts to double.

Precision initialization

static bool	init ( float B)	$$B is an upper bound on the data, $$b is the smallest integer such that $$|B| 2b. The result of the function is false if initialization was already done, in that case already existing Fixed_precision_nt may become invalid.
static float	unit_value ()	returns $$2b.
static float	upper_bound ()	returns $$224+b.

Perturbation scheme

Fixed_precision_nt implements perturbation scheme as described by Alliez, Devillers and Snoeyink [ADS98]. The perturbation mode can be activated or deactivated for different kinds of perturbations. The default mode is no perturbation.

static void	perturb_incircle ()
		Activate. side_of_oriented_circle predicate of 4 cocircular points answers degenerate only if the 4 points are collinear.
static void	unperturb_incircle ()
		Deactivate
static bool	is_perturbed_incircle ()
		returns current mode
static void	perturb_insphere ()
		Activate. side_of_oriented_sphere predicate of 5 cospherical points answers degenerate only if the 5 points are coplanar.
static void	unperturb_insphere ()
		Deactivate
static bool	is_perturbed_insphere ()
		returns current mode

Geometric predicates

Through overloading mechanisms, functions such that orientation for Point_2<Cartesian< Fixed_precision_nt> > will correctly call the function below.

Orientation	orientationC2 ( x0, y0, x1, y1, x2, y2)
Oriented_side	side_of_oriented_circleC2 ( x0, y0, x1, y1, x2, y2, x3, y3)
		Perturbation mode can be activated.
Orientation	orientationC3 ( x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3)
Oriented_side	side_of_oriented_sphereC3 ( x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3, x4, y4, z4)
		Perturbation mode can be activated.