CGAL::rational_rotation_approximation()

Functions
template<RingNumberType>
void	CGAL::rational_rotation_approximation (const RingNumberType &dirx, const RingNumberType &diry, RingNumberType &sin_num, RingNumberType &cos_num, RingNumberType &denom, const RingNumberType &eps_num, const RingNumberType &eps_den)
	computes integers sin_num, cos_num and denom, such that sin_num/denom approximates the sine of direction \( (\)dirx,diry \( )\).

Function Documentation

rational_rotation_approximation()

template<RingNumberType>

void CGAL::rational_rotation_approximation	(	const RingNumberType &	dirx,
		const RingNumberType &	diry,
		RingNumberType &	sin_num,
		RingNumberType &	cos_num,
		RingNumberType &	denom,
		const RingNumberType &	eps_num,
		const RingNumberType &	eps_den )

#include <CGAL/rational_rotation.h>

computes integers sin_num, cos_num and denom, such that sin_num/denom approximates the sine of direction \( (\)dirx,diry \( )\).

The difference between the sine and the approximating rational is bounded by eps_num/eps_den.

Precondition

eps_num != 0.

Implementation

The approximation is based on Farey sequences as described in the rational rotation method presented by Canny and Ressler at the 8th SoCG 1992. We use a slower version which needs no division operation in the approximation.

See also

CGAL::Aff_transformation_2<Kernel>