CGAL 4.7 - 2D and 3D Linear Geometry Kernel: CGAL::rational_rotation_approximation()

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CGAL 4.7 - 2D and 3D Linear Geometry Kernel

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Functions
CGAL::rational_rotation_approximation()
Global Kernel Functions

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## 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` \( )\). More...

## Function Documentation

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` \( )\).

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

Precondition
  `eps_num` \( \neq0\).

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>`

`#include <CGAL/rational_rotation.h>`