273 lines
7.0 KiB
C
273 lines
7.0 KiB
C
|
// Copyright (c) 1999
|
||
|
|
// Utrecht University (The Netherlands),
|
||
|
|
// ETH Zurich (Switzerland),
|
||
|
|
// INRIA Sophia-Antipolis (France),
|
||
|
|
// Max-Planck-Institute Saarbruecken (Germany),
|
||
|
|
// and Tel-Aviv University (Israel). All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
|
||
|
|
// modify it under the terms of the GNU Lesser General Public License as
|
||
|
|
// published by the Free Software Foundation; either version 3 of the License,
|
||
|
|
// or (at your option) any later version.
|
||
|
|
//
|
||
|
|
// Licensees holding a valid commercial license may use this file in
|
||
|
|
// accordance with the commercial license agreement provided with the software.
|
||
|
|
//
|
||
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||
|
|
//
|
||
|
|
// $URL$
|
||
|
|
// $Id$
|
||
|
|
// SPDX-License-Identifier: LGPL-3.0+
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Author(s) : Stefan Schirra
|
||
|
|
|
||
|
|
|
||
|
|
#ifndef CGAL_RATIONAL_ROTATION_H
|
||
|
|
#define CGAL_RATIONAL_ROTATION_H
|
||
|
|
|
||
|
|
#include <algorithm>
|
||
|
|
#include <CGAL/number_type_basic.h>
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
template < class NT >
|
||
|
|
void
|
||
|
|
rational_rotation_approximation( const NT & dirx, // dir.x()
|
||
|
|
const NT & diry, // dir.y()
|
||
|
|
NT & sin_num, // return
|
||
|
|
NT & cos_num, // return
|
||
|
|
NT & denom, // return
|
||
|
|
const NT & eps_num, // quality_bound
|
||
|
|
const NT & eps_den )
|
||
|
|
{
|
||
|
|
|
||
|
|
const NT& n = eps_num;
|
||
|
|
const NT& d = eps_den;
|
||
|
|
const NT NT0 = NT(0) ;
|
||
|
|
const NT NT1 = NT(1) ;
|
||
|
|
CGAL_kernel_precondition( (dirx != NT0) || (diry != NT0));
|
||
|
|
CGAL_kernel_precondition( n > NT0 );
|
||
|
|
CGAL_kernel_precondition( d > NT0 );
|
||
|
|
NT & sin = sin_num;
|
||
|
|
NT & cos = cos_num;
|
||
|
|
NT & den = denom;
|
||
|
|
NT dx = CGAL_NTS abs(dirx);
|
||
|
|
NT dy = CGAL_NTS abs(diry);
|
||
|
|
NT sq_hypotenuse = dx*dx + dy*dy;
|
||
|
|
NT common_part;
|
||
|
|
NT diff_part;
|
||
|
|
NT rhs;
|
||
|
|
bool lower_ok;
|
||
|
|
bool upper_ok;
|
||
|
|
|
||
|
|
if (dy > dx)
|
||
|
|
{
|
||
|
|
std::swap (dx,dy);
|
||
|
|
}
|
||
|
|
// approximate sin = dy / sqrt(sq_hypotenuse)
|
||
|
|
// if ( dy / sqrt(sq_hypotenuse) < n/d )
|
||
|
|
if (dy * dy * d * d < sq_hypotenuse * n * n)
|
||
|
|
{
|
||
|
|
cos = NT1;
|
||
|
|
sin = NT0;
|
||
|
|
den = NT1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
NT p;
|
||
|
|
NT q;
|
||
|
|
NT p0 = NT0;
|
||
|
|
NT q0 = NT1;
|
||
|
|
NT p1 = NT1;
|
||
|
|
NT q1 = NT1;
|
||
|
|
|
||
|
|
for(;;)
|
||
|
|
{
|
||
|
|
p = p0 + p1;
|
||
|
|
q = q0 + q1;
|
||
|
|
sin = NT(2)*p*q;
|
||
|
|
den = p*p + q*q;
|
||
|
|
|
||
|
|
// sanity check for approximation
|
||
|
|
// sin/den < dy/sqrt(hypotenuse) + n/d
|
||
|
|
// && sin/den > dy/sqrt(hypotenuse) - n/d
|
||
|
|
// === sin/den - n/d < dy/sqrt(sq_hypotenuse)
|
||
|
|
// && sin/den + n/d > dy/sqrt(sq_hypotenuse)
|
||
|
|
// === (sin^2 d^2 + n^2 den^2)sq_hypotenuse - 2... < dy^2 d^2 den^2
|
||
|
|
// && (sin^2 d^2 + n^2 den^2)sq_hypotenuse + 2... > dy^2 d^2 den^2
|
||
|
|
|
||
|
|
common_part = (sin*sin*d*d + n*n*den*den)*sq_hypotenuse;
|
||
|
|
diff_part = NT(2)*n*sin*d*den*sq_hypotenuse;
|
||
|
|
rhs = dy*dy*d*d*den*den;
|
||
|
|
|
||
|
|
upper_ok = (common_part - diff_part < rhs);
|
||
|
|
lower_ok = (common_part + diff_part > rhs);
|
||
|
|
|
||
|
|
if ( lower_ok && upper_ok )
|
||
|
|
{
|
||
|
|
// if ( (p*p)%2 + (q*q)%2 > NT1)
|
||
|
|
// {
|
||
|
|
// sin = p*q;
|
||
|
|
// cos = (q*q - p*p)/2; // exact division
|
||
|
|
// den = (p*p + q*q)/2; // exact division
|
||
|
|
// }
|
||
|
|
// else
|
||
|
|
// {
|
||
|
|
cos = q*q - p*p;
|
||
|
|
// }
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// if ( dy/sqrt(sq_hypotenuse) < sin/den )
|
||
|
|
if ( dy*dy*den*den < sin*sin*sq_hypotenuse )
|
||
|
|
{
|
||
|
|
p1 = p;
|
||
|
|
q1 = q;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
p0 = p;
|
||
|
|
q0 = q;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} // for(;;)
|
||
|
|
}
|
||
|
|
dx = dirx;
|
||
|
|
dy = diry;
|
||
|
|
|
||
|
|
if (CGAL_NTS abs(dy) > CGAL_NTS abs(dx) ) { std::swap (sin,cos); }
|
||
|
|
|
||
|
|
if (dx < NT0) { cos = - cos; }
|
||
|
|
|
||
|
|
if (dy < NT0) { sin = - sin; }
|
||
|
|
|
||
|
|
sin_num = sin;
|
||
|
|
cos_num = cos;
|
||
|
|
denom = den;
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template < class NT >
|
||
|
|
void
|
||
|
|
rational_rotation_approximation( const double& angle,
|
||
|
|
NT & sin_num, // return
|
||
|
|
NT & cos_num, // return
|
||
|
|
NT & denom, // return
|
||
|
|
const NT & eps_num, // quality_bound
|
||
|
|
const NT & eps_den )
|
||
|
|
{
|
||
|
|
|
||
|
|
const NT& n = eps_num;
|
||
|
|
const NT& d = eps_den;
|
||
|
|
const NT NT0 = NT(0) ;
|
||
|
|
const NT NT1 = NT(1) ;
|
||
|
|
CGAL_kernel_precondition( n > NT0 );
|
||
|
|
CGAL_kernel_precondition( d > NT0 );
|
||
|
|
NT& isin = sin_num;
|
||
|
|
NT& icos = cos_num;
|
||
|
|
NT& iden = denom;
|
||
|
|
double dsin = std::sin(angle);
|
||
|
|
double dcos = std::cos(angle);
|
||
|
|
double dn = CGAL::to_double(n);
|
||
|
|
double dd = CGAL::to_double(d);
|
||
|
|
double eps = dn / dd;
|
||
|
|
dsin = CGAL_NTS abs( dsin);
|
||
|
|
dcos = CGAL_NTS abs( dcos);
|
||
|
|
NT common_part;
|
||
|
|
NT diff_part;
|
||
|
|
NT os;
|
||
|
|
bool lower_ok;
|
||
|
|
bool upper_ok;
|
||
|
|
bool swapped = false;
|
||
|
|
|
||
|
|
if (dsin > dcos)
|
||
|
|
{
|
||
|
|
swapped = true;
|
||
|
|
std::swap (dsin,dcos);
|
||
|
|
}
|
||
|
|
if ( dsin < eps )
|
||
|
|
{
|
||
|
|
icos = NT1;
|
||
|
|
isin = NT0;
|
||
|
|
iden = NT1;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
NT p;
|
||
|
|
NT q;
|
||
|
|
NT p0 = NT0;
|
||
|
|
NT q0 = NT1;
|
||
|
|
NT p1 = NT1;
|
||
|
|
NT q1 = NT1;
|
||
|
|
|
||
|
|
for(;;)
|
||
|
|
{
|
||
|
|
p = p0 + p1;
|
||
|
|
q = q0 + q1;
|
||
|
|
isin = NT(2)*p*q;
|
||
|
|
iden = p*p + q*q;
|
||
|
|
|
||
|
|
// XXX sanity check for approximation
|
||
|
|
// sin/den < dsin + n/d
|
||
|
|
// && sin/den > dsin - n/d
|
||
|
|
// sin < dsin * den + n/d * den
|
||
|
|
// && sin > dsin * den - n/d * den
|
||
|
|
os = CGAL::to_double(isin);
|
||
|
|
diff_part = eps * CGAL::to_double(iden);
|
||
|
|
common_part = dsin * CGAL::to_double(iden);
|
||
|
|
|
||
|
|
upper_ok = (common_part - diff_part < os);
|
||
|
|
lower_ok = (os < common_part + diff_part);
|
||
|
|
|
||
|
|
if ( lower_ok && upper_ok )
|
||
|
|
{
|
||
|
|
// if ( (p*p)%2 + (q*q)%2 > NT1)
|
||
|
|
// {
|
||
|
|
// isin = p*q;
|
||
|
|
// icos = (q*q - p*p)/2; // exact division
|
||
|
|
// iden = (p*p + q*q)/2; // exact division
|
||
|
|
// }
|
||
|
|
// else
|
||
|
|
// {
|
||
|
|
icos = q*q - p*p;
|
||
|
|
// }
|
||
|
|
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
// XXX if ( dsin < sin/den )
|
||
|
|
if ( dsin * CGAL::to_double(iden) < CGAL::to_double(isin) )
|
||
|
|
{
|
||
|
|
p1 = p;
|
||
|
|
q1 = q;
|
||
|
|
}
|
||
|
|
else
|
||
|
|
{
|
||
|
|
p0 = p;
|
||
|
|
q0 = q;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
} // for(;;)
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( swapped ) { std::swap (isin,icos); }
|
||
|
|
|
||
|
|
dsin = std::sin( angle);
|
||
|
|
dcos = std::cos( angle);
|
||
|
|
if (dcos < 0.0) { icos = - icos; }
|
||
|
|
if (dsin < 0.0) { isin = - isin; }
|
||
|
|
|
||
|
|
sin_num = isin;
|
||
|
|
cos_num = icos;
|
||
|
|
denom = iden;
|
||
|
|
}
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif // CGAL_RATIONAL_ROTATION_H
|