elliptical-arc.cpp revision 69340304f32eac4d438c67b5e1f6bc2f0a05ea22
/*
* SVG Elliptical Arc Class
*
* Copyright 2008 Marco Cecchetti <mrcekets at gmail.com>
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#include "elliptical-arc.h"
#include "bezier-curve.h"
#include "poly.h"
#include <cfloat>
#include <limits>
namespace Geom
{
Rect EllipticalArc::boundsExact() const
{
std::vector<double> extremes(4);
double cosrot = std::cos(rotation_angle());
double sinrot = std::sin(rotation_angle());
extremes[0] = std::atan2( -ray(Y) * sinrot, ray(X) * cosrot );
extremes[1] = extremes[0] + M_PI;
if ( extremes[0] < 0 ) extremes[0] += 2*M_PI;
extremes[2] = std::atan2( ray(Y) * cosrot, ray(X) * sinrot );
extremes[3] = extremes[2] + M_PI;
if ( extremes[2] < 0 ) extremes[2] += 2*M_PI;
std::vector<double>arc_extremes(4);
arc_extremes[0] = initialPoint()[X];
arc_extremes[1] = finalPoint()[X];
if ( arc_extremes[0] < arc_extremes[1] )
std::swap(arc_extremes[0], arc_extremes[1]);
arc_extremes[2] = initialPoint()[Y];
arc_extremes[3] = finalPoint()[Y];
if ( arc_extremes[2] < arc_extremes[3] )
std::swap(arc_extremes[2], arc_extremes[3]);
if ( start_angle() < end_angle() )
{
if ( sweep_flag() )
{
for ( unsigned int i = 0; i < extremes.size(); ++i )
{
if ( start_angle() < extremes[i] && extremes[i] < end_angle() )
{
arc_extremes[i] = pointAtAngle(extremes[i])[i >> 1];
}
}
}
else
{
for ( unsigned int i = 0; i < extremes.size(); ++i )
{
if ( start_angle() > extremes[i] || extremes[i] > end_angle() )
{
arc_extremes[i] = pointAtAngle(extremes[i])[i >> 1];
}
}
}
}
else
{
if ( sweep_flag() )
{
for ( unsigned int i = 0; i < extremes.size(); ++i )
{
if ( start_angle() < extremes[i] || extremes[i] < end_angle() )
{
arc_extremes[i] = pointAtAngle(extremes[i])[i >> 1];
}
}
}
else
{
for ( unsigned int i = 0; i < extremes.size(); ++i )
{
if ( start_angle() > extremes[i] && extremes[i] > end_angle() )
{
arc_extremes[i] = pointAtAngle(extremes[i])[i >> 1];
}
}
}
}
return Rect( Point(arc_extremes[1], arc_extremes[3]) ,
Point(arc_extremes[0], arc_extremes[2]) );
}
std::vector<double>
EllipticalArc::roots(double v, Dim2 d) const
{
if ( d > Y )
{
THROW_RANGEERROR("dimention out of range");
}
std::vector<double> sol;
if ( are_near(ray(X), 0) && are_near(ray(Y), 0) )
{
if ( center(d) == v )
sol.push_back(0);
return sol;
}
const char* msg[2][2] =
{
{ "d == X; ray(X) == 0; "
"s = (v - center(X)) / ( -ray(Y) * std::sin(rotation_angle()) ); "
"s should be contained in [-1,1]",
"d == X; ray(Y) == 0; "
"s = (v - center(X)) / ( ray(X) * std::cos(rotation_angle()) ); "
"s should be contained in [-1,1]"
},
{ "d == Y; ray(X) == 0; "
"s = (v - center(X)) / ( ray(Y) * std::cos(rotation_angle()) ); "
"s should be contained in [-1,1]",
"d == Y; ray(Y) == 0; "
"s = (v - center(X)) / ( ray(X) * std::sin(rotation_angle()) ); "
"s should be contained in [-1,1]"
},
};
for ( unsigned int dim = 0; dim < 2; ++dim )
{
if ( are_near(ray(dim), 0) )
{
if ( initialPoint()[d] == v && finalPoint()[d] == v )
{
THROW_INFINITESOLUTIONS(0);
}
if ( (initialPoint()[d] < finalPoint()[d])
&& (initialPoint()[d] > v || finalPoint()[d] < v) )
{
return sol;
}
if ( (initialPoint()[d] > finalPoint()[d])
&& (finalPoint()[d] > v || initialPoint()[d] < v) )
{
return sol;
}
double ray_prj;
switch(d)
{
case X:
switch(dim)
{
case X: ray_prj = -ray(Y) * std::sin(rotation_angle());
break;
case Y: ray_prj = ray(X) * std::cos(rotation_angle());
break;
}
break;
case Y:
switch(dim)
{
case X: ray_prj = ray(Y) * std::cos(rotation_angle());
break;
case Y: ray_prj = ray(X) * std::sin(rotation_angle());
break;
}
break;
}
double s = (v - center(d)) / ray_prj;
if ( s < -1 || s > 1 )
{
THROW_LOGICALERROR(msg[d][dim]);
}
switch(dim)
{
case X:
s = std::asin(s); // return a value in [-PI/2,PI/2]
if ( logical_xor( sweep_flag(), are_near(start_angle(), M_PI/2) ) )
{
if ( s < 0 ) s += 2*M_PI;
}
else
{
s = M_PI - s;
if (!(s < 2*M_PI) ) s -= 2*M_PI;
}
break;
case Y:
s = std::acos(s); // return a value in [0,PI]
if ( logical_xor( sweep_flag(), are_near(start_angle(), 0) ) )
{
s = 2*M_PI - s;
if ( !(s < 2*M_PI) ) s -= 2*M_PI;
}
break;
}
//std::cerr << "s = " << rad_to_deg(s);
s = map_to_01(s);
//std::cerr << " -> t: " << s << std::endl;
if ( !(s < 0 || s > 1) )
sol.push_back(s);
return sol;
}
}
double rotx, roty;
switch(d)
{
case X:
rotx = std::cos(rotation_angle());
roty = -std::sin(rotation_angle());
break;
case Y:
rotx = std::sin(rotation_angle());
roty = std::cos(rotation_angle());
break;
}
double rxrotx = ray(X) * rotx;
double c_v = center(d) - v;
double a = -rxrotx + c_v;
double b = ray(Y) * roty;
double c = rxrotx + c_v;
//std::cerr << "a = " << a << std::endl;
//std::cerr << "b = " << b << std::endl;
//std::cerr << "c = " << c << std::endl;
if ( are_near(a,0) )
{
sol.push_back(M_PI);
if ( !are_near(b,0) )
{
double s = 2 * std::atan(-c/(2*b));
if ( s < 0 ) s += 2*M_PI;
sol.push_back(s);
}
}
else
{
double delta = b * b - a * c;
//std::cerr << "delta = " << delta << std::endl;
if ( are_near(delta, 0) )
{
double s = 2 * std::atan(-b/a);
if ( s < 0 ) s += 2*M_PI;
sol.push_back(s);
}
else if ( delta > 0 )
{
double sq = std::sqrt(delta);
double s = 2 * std::atan( (-b - sq) / a );
if ( s < 0 ) s += 2*M_PI;
sol.push_back(s);
s = 2 * std::atan( (-b + sq) / a );
if ( s < 0 ) s += 2*M_PI;
sol.push_back(s);
}
}
std::vector<double> arc_sol;
for (unsigned int i = 0; i < sol.size(); ++i )
{
//std::cerr << "s = " << rad_to_deg(sol[i]);
sol[i] = map_to_01(sol[i]);
//std::cerr << " -> t: " << sol[i] << std::endl;
if ( !(sol[i] < 0 || sol[i] > 1) )
arc_sol.push_back(sol[i]);
}
return arc_sol;
// return SBasisCurve(toSBasis()).roots(v, d);
}
// D(E(t,C),t) = E(t+PI/2,O)
Curve* EllipticalArc::derivative() const
{
EllipticalArc* result = new EllipticalArc(*this);
result->m_center[X] = result->m_center[Y] = 0;
result->m_start_angle += M_PI/2;
if( !( result->m_start_angle < 2*M_PI ) )
{
result->m_start_angle -= 2*M_PI;
}
result->m_end_angle += M_PI/2;
if( !( result->m_end_angle < 2*M_PI ) )
{
result->m_end_angle -= 2*M_PI;
}
result->m_initial_point = result->pointAtAngle( result->start_angle() );
result->m_final_point = result->pointAtAngle( result->end_angle() );
return result;
}
std::vector<Point>
EllipticalArc::pointAndDerivatives(Coord t, unsigned int n) const
{
std::vector<Point> result;
result.reserve(n);
double angle = map_unit_interval_on_circular_arc(t, start_angle(),
end_angle(), sweep_flag());
EllipticalArc ea(*this);
ea.m_center = Point(0,0);
unsigned int m = std::min(n, 4u);
for ( unsigned int i = 0; i < m; ++i )
{
result.push_back( ea.pointAtAngle(angle) );
angle += M_PI/2;
if ( !(angle < 2*M_PI) ) angle -= 2*M_PI;
}
m = n / 4;
for ( unsigned int i = 1; i < m; ++i )
{
for ( unsigned int j = 0; j < 4; ++j )
result.push_back( result[j] );
}
m = n - 4 * m;
for ( unsigned int i = 0; i < m; ++i )
{
result.push_back( result[i] );
}
if ( !result.empty() ) // n != 0
result[0] = pointAtAngle(angle);
return result;
}
D2<SBasis> EllipticalArc::toSBasis() const
{
// the interval of parametrization has to be [0,1]
Coord et = start_angle() + ( sweep_flag() ? sweep_angle() : -sweep_angle() );
Linear param(start_angle(), et);
Coord cos_rot_angle = std::cos(rotation_angle());
Coord sin_rot_angle = std::sin(rotation_angle());
// order = 4 seems to be enough to get a perfect looking elliptical arc
// should it be choosen in function of the arc length anyway ?
// or maybe a user settable parameter: toSBasis(unsigned int order) ?
SBasis arc_x = ray(X) * cos(param,4);
SBasis arc_y = ray(Y) * sin(param,4);
D2<SBasis> arc;
arc[0] = arc_x * cos_rot_angle - arc_y * sin_rot_angle + Linear(center(X),center(X));
arc[1] = arc_x * sin_rot_angle + arc_y * cos_rot_angle + Linear(center(Y),center(Y));
return arc;
}
bool EllipticalArc::containsAngle(Coord angle) const
{
if ( sweep_flag() )
if ( start_angle() < end_angle() )
return ( !( angle < start_angle() || angle > end_angle() ) );
else
return ( !( angle < start_angle() && angle > end_angle() ) );
else
if ( start_angle() > end_angle() )
return ( !( angle > start_angle() || angle < end_angle() ) );
else
return ( !( angle > start_angle() && angle < end_angle() ) );
}
double EllipticalArc::valueAtAngle(Coord t, Dim2 d) const
{
double sin_rot_angle = std::sin(rotation_angle());
double cos_rot_angle = std::cos(rotation_angle());
if ( d == X )
{
return ray(X) * cos_rot_angle * std::cos(t)
- ray(Y) * sin_rot_angle * std::sin(t)
+ center(X);
}
else if ( d == Y )
{
return ray(X) * sin_rot_angle * std::cos(t)
+ ray(Y) * cos_rot_angle * std::sin(t)
+ center(Y);
}
THROW_RANGEERROR("dimension parameter out of range");
}
Curve* EllipticalArc::portion(double f, double t) const
{
if (f < 0) f = 0;
if (f > 1) f = 1;
if (t < 0) t = 0;
if (t > 1) t = 1;
if ( are_near(f, t) )
{
EllipticalArc* arc = new EllipticalArc();
arc->m_center = arc->m_initial_point = arc->m_final_point = pointAt(f);
arc->m_start_angle = arc->m_end_angle = m_start_angle;
arc->m_rot_angle = m_rot_angle;
arc->m_sweep = m_sweep;
arc->m_large_arc = m_large_arc;
}
EllipticalArc* arc = new EllipticalArc( *this );
arc->m_initial_point = pointAt(f);
arc->m_final_point = pointAt(t);
double sa = sweep_flag() ? sweep_angle() : -sweep_angle();
arc->m_start_angle = m_start_angle + sa * f;
if ( !(arc->m_start_angle < 2*M_PI) )
arc->m_start_angle -= 2*M_PI;
if ( arc->m_start_angle < 0 )
arc->m_start_angle += 2*M_PI;
arc->m_end_angle = m_start_angle + sa * t;
if ( !(arc->m_end_angle < 2*M_PI) )
arc->m_end_angle -= 2*M_PI;
if ( arc->m_end_angle < 0 )
arc->m_end_angle += 2*M_PI;
if ( f > t ) arc->m_sweep = !sweep_flag();
if ( large_arc_flag() && (arc->sweep_angle() < M_PI) )
arc->m_large_arc = false;
return arc;
}
// NOTE: doesn't work with 360 deg arcs
void EllipticalArc::calculate_center_and_extreme_angles()
{
if ( are_near(initialPoint(), finalPoint()) )
{
if ( are_near(ray(X), 0) && are_near(ray(Y), 0) )
{
m_start_angle = m_end_angle = 0;
m_center = initialPoint();
return;
}
else
{
THROW_RANGEERROR("initial and final point are the same");
}
}
if ( are_near(ray(X), 0) && are_near(ray(Y), 0) )
{ // but initialPoint != finalPoint
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints: "
"ray(X) == 0 && ray(Y) == 0 but initialPoint != finalPoint"
);
}
if ( are_near(ray(Y), 0) )
{
Point v = initialPoint() - finalPoint();
if ( are_near(L2sq(v), 4*ray(X)*ray(X)) )
{
double angle = std::atan2(v[Y], v[X]);
if (angle < 0) angle += 2*M_PI;
if ( are_near( angle, rotation_angle() ) )
{
m_start_angle = 0;
m_end_angle = M_PI;
m_center = v/2 + finalPoint();
return;
}
angle -= M_PI;
if ( angle < 0 ) angle += 2*M_PI;
if ( are_near( angle, rotation_angle() ) )
{
m_start_angle = M_PI;
m_end_angle = 0;
m_center = v/2 + finalPoint();
return;
}
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints: "
"ray(Y) == 0 "
"and slope(initialPoint - finalPoint) != rotation_angle "
"and != rotation_angle + PI"
);
}
if ( L2sq(v) > 4*ray(X)*ray(X) )
{
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints: "
"ray(Y) == 0 and distance(initialPoint, finalPoint) > 2*ray(X)"
);
}
else
{
THROW_RANGEERROR(
"there is infinite ellipses that satisfy the given constraints: "
"ray(Y) == 0 and distance(initialPoint, finalPoint) < 2*ray(X)"
);
}
}
if ( are_near(ray(X), 0) )
{
Point v = initialPoint() - finalPoint();
if ( are_near(L2sq(v), 4*ray(Y)*ray(Y)) )
{
double angle = std::atan2(v[Y], v[X]);
if (angle < 0) angle += 2*M_PI;
double rot_angle = rotation_angle() + M_PI/2;
if ( !(rot_angle < 2*M_PI) ) rot_angle -= 2*M_PI;
if ( are_near( angle, rot_angle ) )
{
m_start_angle = M_PI/2;
m_end_angle = 3*M_PI/2;
m_center = v/2 + finalPoint();
return;
}
angle -= M_PI;
if ( angle < 0 ) angle += 2*M_PI;
if ( are_near( angle, rot_angle ) )
{
m_start_angle = 3*M_PI/2;
m_end_angle = M_PI/2;
m_center = v/2 + finalPoint();
return;
}
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints: "
"ray(X) == 0 "
"and slope(initialPoint - finalPoint) != rotation_angle + PI/2 "
"and != rotation_angle + (3/2)*PI"
);
}
if ( L2sq(v) > 4*ray(Y)*ray(Y) )
{
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints: "
"ray(X) == 0 and distance(initialPoint, finalPoint) > 2*ray(Y)"
);
}
else
{
THROW_RANGEERROR(
"there is infinite ellipses that satisfy the given constraints: "
"ray(X) == 0 and distance(initialPoint, finalPoint) < 2*ray(Y)"
);
}
}
double sin_rot_angle = std::sin(rotation_angle());
double cos_rot_angle = std::cos(rotation_angle());
Point sp = sweep_flag() ? initialPoint() : finalPoint();
Point ep = sweep_flag() ? finalPoint() : initialPoint();
Matrix m( ray(X) * cos_rot_angle, ray(X) * sin_rot_angle,
-ray(Y) * sin_rot_angle, ray(Y) * cos_rot_angle,
0, 0 );
Matrix im = m.inverse();
Point sol = (ep - sp) * im;
double half_sum_angle = std::atan2(-sol[X], sol[Y]);
double half_diff_angle;
if ( are_near(std::fabs(half_sum_angle), M_PI/2) )
{
double anti_sgn_hsa = (half_sum_angle > 0) ? -1 : 1;
double arg = anti_sgn_hsa * sol[X] / 2;
// if |arg| is a little bit > 1 acos returns nan
if ( are_near(arg, 1) )
half_diff_angle = 0;
else if ( are_near(arg, -1) )
half_diff_angle = M_PI;
else
{
if ( !(-1 < arg && arg < 1) )
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints"
);
// assert( -1 < arg && arg < 1 );
// if it fails
// => there is no ellipse that satisfies the given constraints
half_diff_angle = std::acos( arg );
}
half_diff_angle = M_PI/2 - half_diff_angle;
}
else
{
double arg = sol[Y] / ( 2 * std::cos(half_sum_angle) );
// if |arg| is a little bit > 1 asin returns nan
if ( are_near(arg, 1) )
half_diff_angle = M_PI/2;
else if ( are_near(arg, -1) )
half_diff_angle = -M_PI/2;
else
{
if ( !(-1 < arg && arg < 1) )
THROW_RANGEERROR(
"there is no ellipse that satisfies the given constraints"
);
// assert( -1 < arg && arg < 1 );
// if it fails
// => there is no ellipse that satisfies the given constraints
half_diff_angle = std::asin( arg );
}
}
if ( ( m_large_arc && half_diff_angle > 0 )
|| (!m_large_arc && half_diff_angle < 0 ) )
{
half_diff_angle = -half_diff_angle;
}
if ( half_sum_angle < 0 ) half_sum_angle += 2*M_PI;
if ( half_diff_angle < 0 ) half_diff_angle += M_PI;
m_start_angle = half_sum_angle - half_diff_angle;
m_end_angle = half_sum_angle + half_diff_angle;
// 0 <= m_start_angle, m_end_angle < 2PI
if ( m_start_angle < 0 ) m_start_angle += 2*M_PI;
if( !(m_end_angle < 2*M_PI) ) m_end_angle -= 2*M_PI;
sol[0] = std::cos(m_start_angle);
sol[1] = std::sin(m_start_angle);
m_center = sp - sol * m;
if ( !sweep_flag() )
{
double angle = m_start_angle;
m_start_angle = m_end_angle;
m_end_angle = angle;
}
}
Coord EllipticalArc::map_to_02PI(Coord t) const
{
if ( sweep_flag() )
{
Coord angle = start_angle() + sweep_angle() * t;
if ( !(angle < 2*M_PI) )
angle -= 2*M_PI;
return angle;
}
else
{
Coord angle = start_angle() - sweep_angle() * t;
if ( angle < 0 ) angle += 2*M_PI;
return angle;
}
}
Coord EllipticalArc::map_to_01(Coord angle) const
{
return map_circular_arc_on_unit_interval(angle, start_angle(),
end_angle(), sweep_flag());
}
std::vector<double> EllipticalArc::
allNearestPoints( Point const& p, double from, double to ) const
{
if ( from > to ) std::swap(from, to);
if ( from < 0 || to > 1 )
{
THROW_RANGEERROR("[from,to] interval out of range");
}
std::vector<double> result;
if ( ( are_near(ray(X), 0) && are_near(ray(Y), 0) ) || are_near(from, to) )
{
result.push_back(from);
return result;
}
else if ( are_near(ray(X), 0) || are_near(ray(Y), 0) )
{
LineSegment seg(pointAt(from), pointAt(to));
Point np = seg.pointAt( seg.nearestPoint(p) );
if ( are_near(ray(Y), 0) )
{
if ( are_near(rotation_angle(), M_PI/2)
|| are_near(rotation_angle(), 3*M_PI/2) )
{
result = roots(np[Y], Y);
}
else
{
result = roots(np[X], X);
}
}
else
{
if ( are_near(rotation_angle(), M_PI/2)
|| are_near(rotation_angle(), 3*M_PI/2) )
{
result = roots(np[X], X);
}
else
{
result = roots(np[Y], Y);
}
}
return result;
}
else if ( are_near(ray(X), ray(Y)) )
{
Point r = p - center();
if ( are_near(r, Point(0,0)) )
{
THROW_INFINITESOLUTIONS(0);
}
// TODO: implement case r != 0
// Point np = ray(X) * unit_vector(r);
// std::vector<double> solX = roots(np[X],X);
// std::vector<double> solY = roots(np[Y],Y);
// double t;
// if ( are_near(solX[0], solY[0]) || are_near(solX[0], solY[1]))
// {
// t = solX[0];
// }
// else
// {
// t = solX[1];
// }
// if ( !(t < from || t > to) )
// {
// result.push_back(t);
// }
// else
// {
//
// }
}
// solve the equation <D(E(t),t)|E(t)-p> == 0
// that provides min and max distance points
// on the ellipse E wrt the point p
// after the substitutions:
// cos(t) = (1 - s^2) / (1 + s^2)
// sin(t) = 2t / (1 + s^2)
// where s = tan(t/2)
// we get a 4th degree equation in s
/*
* ry s^4 ((-cy + py) Cos[Phi] + (cx - px) Sin[Phi]) +
* ry ((cy - py) Cos[Phi] + (-cx + px) Sin[Phi]) +
* 2 s^3 (rx^2 - ry^2 + (-cx + px) rx Cos[Phi] + (-cy + py) rx Sin[Phi]) +
* 2 s (-rx^2 + ry^2 + (-cx + px) rx Cos[Phi] + (-cy + py) rx Sin[Phi])
*/
Point p_c = p - center();
double rx2_ry2 = (ray(X) - ray(Y)) * (ray(X) + ray(Y));
double cosrot = std::cos( rotation_angle() );
double sinrot = std::sin( rotation_angle() );
double expr1 = ray(X) * (p_c[X] * cosrot + p_c[Y] * sinrot);
Poly coeff;
coeff.resize(5);
coeff[4] = ray(Y) * ( p_c[Y] * cosrot - p_c[X] * sinrot );
coeff[3] = 2 * ( rx2_ry2 + expr1 );
coeff[2] = 0;
coeff[1] = 2 * ( -rx2_ry2 + expr1 );
coeff[0] = -coeff[4];
// for ( unsigned int i = 0; i < 5; ++i )
// std::cerr << "c[" << i << "] = " << coeff[i] << std::endl;
std::vector<double> real_sol;
// gsl_poly_complex_solve raises an error
// if the leading coefficient is zero
if ( are_near(coeff[4], 0) )
{
real_sol.push_back(0);
if ( !are_near(coeff[3], 0) )
{
double sq = -coeff[1] / coeff[3];
if ( sq > 0 )
{
double s = std::sqrt(sq);
real_sol.push_back(s);
real_sol.push_back(-s);
}
}
}
else
{
real_sol = solve_reals(coeff);
}
// else
// {
// double sol[8];
// gsl_poly_complex_workspace * w = gsl_poly_complex_workspace_alloc(5);
// gsl_poly_complex_solve(coeff, 5, w, sol );
// gsl_poly_complex_workspace_free(w);
//
// for ( unsigned int i = 0; i < 4; ++i )
// {
// if ( sol[2*i+1] == 0 ) real_sol.push_back(sol[2*i]);
// }
// }
for ( unsigned int i = 0; i < real_sol.size(); ++i )
{
real_sol[i] = 2 * std::atan(real_sol[i]);
if ( real_sol[i] < 0 ) real_sol[i] += 2*M_PI;
}
// when s -> Infinity then <D(E)|E-p> -> 0 iff coeff[4] == 0
// so we add M_PI to the solutions being lim arctan(s) = PI when s->Infinity
if ( (real_sol.size() % 2) != 0 )
{
real_sol.push_back(M_PI);
}
double mindistsq1 = std::numeric_limits<double>::max();
double mindistsq2 = std::numeric_limits<double>::max();
double dsq;
unsigned int mi1, mi2;
for ( unsigned int i = 0; i < real_sol.size(); ++i )
{
dsq = distanceSq(p, pointAtAngle(real_sol[i]));
if ( mindistsq1 > dsq )
{
mindistsq2 = mindistsq1;
mi2 = mi1;
mindistsq1 = dsq;
mi1 = i;
}
else if ( mindistsq2 > dsq )
{
mindistsq2 = dsq;
mi2 = i;
}
}
double t = map_to_01( real_sol[mi1] );
if ( !(t < from || t > to) )
{
result.push_back(t);
}
bool second_sol = false;
t = map_to_01( real_sol[mi2] );
if ( real_sol.size() == 4 && !(t < from || t > to) )
{
if ( result.empty() || are_near(mindistsq1, mindistsq2) )
{
result.push_back(t);
second_sol = true;
}
}
// we need to test extreme points too
double dsq1 = distanceSq(p, pointAt(from));
double dsq2 = distanceSq(p, pointAt(to));
if ( second_sol )
{
if ( mindistsq2 > dsq1 )
{
result.clear();
result.push_back(from);
mindistsq2 = dsq1;
}
else if ( are_near(mindistsq2, dsq) )
{
result.push_back(from);
}
if ( mindistsq2 > dsq2 )
{
result.clear();
result.push_back(to);
}
else if ( are_near(mindistsq2, dsq2) )
{
result.push_back(to);
}
}
else
{
if ( result.empty() )
{
if ( are_near(dsq1, dsq2) )
{
result.push_back(from);
result.push_back(to);
}
else if ( dsq2 > dsq1 )
{
result.push_back(from);
}
else
{
result.push_back(to);
}
}
}
return result;
}
} // end namespace Geom
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :