/usr/include/CGAL/Conic_misc.h is in libcgal-dev 4.7-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 | // Copyright (c) 2000,2001
// 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.
//
// $URL$
// $Id$
//
//
// Author(s) : Bernd Gaertner, Sven Schoenherr <sven@inf.ethz.ch>
#ifndef CGAL_CONIC_MISC_H
#define CGAL_CONIC_MISC_H
#include <cmath>
#include <CGAL/number_utils.h>
#include <CGAL/kernel_assertions.h>
namespace CGAL {
template < class R>
class Conic_2;
enum Conic_type
{
HYPERBOLA = -1,
PARABOLA,
ELLIPSE
};
typedef CGAL::Bounded_side Convex_side;
const Convex_side ON_CONVEX_SIDE = CGAL::ON_BOUNDED_SIDE;
const Convex_side ON_NONCONVEX_SIDE = CGAL::ON_UNBOUNDED_SIDE;
template < class NT >
NT best_value (NT *values, int nr_values,
NT a2, NT a1, NT a0,
NT b3, NT b2, NT b1, NT b0)
{
bool det_positive = false;
NT d, q, max_det = 0, det, best = -1;
for (int i=0; i<nr_values; ++i) {
NT x = values[i];
d = (a2*x+a1)*x+a0;
q = ((b3*x+b2)*x+b1)*x+b0;
det = d*d*d/(q*q);
// if q==0, this root value doesn't qualify for the
// best value. Under roundoff errors, q might be very
// small but nonzero, so that the value is erroneously
// being considered; however, d should be very small
// in this case as well, so that det won't compete
// for max_det below.
if (CGAL_NTS is_positive(det) && !CGAL_NTS is_zero(q))
if (!det_positive || (det > max_det)) {
max_det = det;
best = x;
det_positive = true;
}
}
CGAL_kernel_precondition (det_positive);
return best;
}
template < class NT >
int solve_cubic (NT c3, NT c2, NT c1, NT c0,
NT& r1, NT& r2, NT& r3)
{
if (c3 == 0.0) {
// quadratic equation
if (c2 == 0) {
// linear equation
CGAL_kernel_precondition (c1 != 0);
r1 = -c0/c1;
return 1;
}
NT D = c1*c1-4*c2*c0;
if (D < 0.0)
// only complex roots
return 0;
if (D == 0.0) {
// one real root
r1 = -c1/(2.0*c2);
return 1;
}
// two real roots
r1 = (-c1 + CGAL_NTS sqrt(D))/(2.0*c2);
r2 = (-c1 - CGAL_NTS sqrt(D))/(2.0*c2);
return 2;
}
// cubic equation
// define the gamma_i
NT g2 = c2/c3,
g1 = c1/c3,
g0 = c0/c3;
// define a, b
NT a = g1 - g2*g2/3.0,
b = 2.0*g2*g2*g2/27.0 - g1*g2/3.0 + g0;
if (a == 0) {
// one real root
/***** r1 = cbrt(-b) - g2/3.0; *****/
r1 = exp(log(-b)/3.0) - g2/3.0;
return 1;
}
// define D
NT D = a*a*a/27.0 + b*b/4.0;
if (D >= 0.0) {
// real case
/***** NT u = cbrt(-b/2.0 + CGAL_NTS sqrt(D)), *****/
NT u = exp(log(-b/2.0 + CGAL_NTS sqrt(D))),
alpha = 1.0 - a/(3.0*u*u);
if (D == 0) {
// two distinct real roots
r1 = u*alpha - g2/3.0;
r2 = -0.5*alpha*u - g2/3.0;
return 2;
}
// one real root
r1 = u*alpha - g2/3.0;
return 1;
}
// complex case
NT r_prime = CGAL_NTS sqrt(-a/3),
phi_prime = acos (-b/(2.0*r_prime*r_prime*r_prime))/3.0,
u_R = r_prime * cos (phi_prime),
u_I = r_prime * sin (phi_prime);
// three distinct real roots
r1 = 2.0*u_R - g2/3.0;
r2 = -u_R + u_I*std::sqrt(3.0) - g2/3.0;
r3 = -u_R - u_I*std::sqrt(3.0) - g2/3.0;
return 3;
}
} //namespace CGAL
#endif // CGAL_CONIC_MISC_H
// ===== EOF ==================================================================
|