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/*
* Ellipse Curve
*
* Authors:
* Marco Cecchetti <mrcekets at gmail.com>
*
* Copyright 2008 authors
*
* 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 <2geom/ellipse.h>
#include <2geom/svg-elliptical-arc.h>
#include <2geom/numeric/fitting-tool.h>
#include <2geom/numeric/fitting-model.h>
namespace Geom
{
void Ellipse::set(double A, double B, double C, double D, double E, double F)
{
double den = 4*A*C - B*B;
if ( den == 0 )
{
THROW_LOGICALERROR("den == 0, while computing ellipse centre");
}
m_centre[X] = (B*E - 2*C*D) / den;
m_centre[Y] = (B*D - 2*A*E) / den;
// evaluate the a coefficient of the ellipse equation in normal form
// E(x,y) = a*(x-cx)^2 + b*(x-cx)*(y-cy) + c*(y-cy)^2 = 1
// where b = a*B , c = a*C, (cx,cy) == centre
double num = A * sqr(m_centre[X])
+ B * m_centre[X] * m_centre[Y]
+ C * sqr(m_centre[Y])
- F;
//evaluate ellipse rotation angle
double rot = std::atan2( -B, -(A - C) )/2;
// std::cerr << "rot = " << rot << std::endl;
bool swap_axes = false;
if ( are_near(rot, 0) ) rot = 0;
if ( are_near(rot, M_PI/2) || rot < 0 )
{
swap_axes = true;
}
// evaluate the length of the ellipse rays
double cosrot = std::cos(rot);
double sinrot = std::sin(rot);
double cos2 = cosrot * cosrot;
double sin2 = sinrot * sinrot;
double cossin = cosrot * sinrot;
den = A * cos2 + B * cossin + C * sin2;
if ( den == 0 )
{
THROW_LOGICALERROR("den == 0, while computing 'rx' coefficient");
}
double rx2 = num/den;
if ( rx2 < 0 )
{
THROW_LOGICALERROR("rx2 < 0, while computing 'rx' coefficient");
}
double rx = std::sqrt(rx2);
den = C * cos2 - B * cossin + A * sin2;
if ( den == 0 )
{
THROW_LOGICALERROR("den == 0, while computing 'ry' coefficient");
}
double ry2 = num/den;
if ( ry2 < 0 )
{
THROW_LOGICALERROR("ry2 < 0, while computing 'rx' coefficient");
}
double ry = std::sqrt(ry2);
// the solution is not unique so we choose always the ellipse
// with a rotation angle between 0 and PI/2
if ( swap_axes ) std::swap(rx, ry);
if ( are_near(rot, M_PI/2)
|| are_near(rot, -M_PI/2)
|| are_near(rx, ry) )
{
rot = 0;
}
else if ( rot < 0 )
{
rot += M_PI/2;
}
m_ray[X] = rx;
m_ray[Y] = ry;
m_angle = rot;
}
std::vector<double> Ellipse::implicit_form_coefficients() const
{
if (ray(X) == 0 || ray(Y) == 0)
{
THROW_LOGICALERROR("a degenerate ellipse doesn't own an implicit form");
}
std::vector<double> coeff(6);
double cosrot = std::cos(rot_angle());
double sinrot = std::sin(rot_angle());
double cos2 = cosrot * cosrot;
double sin2 = sinrot * sinrot;
double cossin = cosrot * sinrot;
double invrx2 = 1 / (ray(X) * ray(X));
double invry2 = 1 / (ray(Y) * ray(Y));
coeff[0] = invrx2 * cos2 + invry2 * sin2;
coeff[1] = 2 * (invrx2 - invry2) * cossin;
coeff[2] = invrx2 * sin2 + invry2 * cos2;
coeff[3] = -(2 * coeff[0] * center(X) + coeff[1] * center(Y));
coeff[4] = -(2 * coeff[2] * center(Y) + coeff[1] * center(X));
coeff[5] = coeff[0] * center(X) * center(X)
+ coeff[1] * center(X) * center(Y)
+ coeff[2] * center(Y) * center(Y)
- 1;
return coeff;
}
void Ellipse::set(std::vector<Point> const& points)
{
size_t sz = points.size();
if (sz < 5)
{
THROW_RANGEERROR("fitting error: too few points passed");
}
NL::LFMEllipse model;
NL::least_squeares_fitter<NL::LFMEllipse> fitter(model, sz);
for (size_t i = 0; i < sz; ++i)
{
fitter.append(points[i]);
}
fitter.update();
NL::Vector z(sz, 0.0);
model.instance(*this, fitter.result(z));
}
SVGEllipticalArc
Ellipse::arc(Point const& initial, Point const& inner, Point const& final,
bool _svg_compliant)
{
Point sp_cp = initial - center();
Point ep_cp = final - center();
Point ip_cp = inner - center();
double angle1 = angle_between(sp_cp, ep_cp);
double angle2 = angle_between(sp_cp, ip_cp);
double angle3 = angle_between(ip_cp, ep_cp);
bool large_arc_flag = true;
bool sweep_flag = true;
if ( angle1 > 0 )
{
if ( angle2 > 0 && angle3 > 0 )
{
large_arc_flag = false;
sweep_flag = true;
}
else
{
large_arc_flag = true;
sweep_flag = false;
}
}
else
{
if ( angle2 < 0 && angle3 < 0 )
{
large_arc_flag = false;
sweep_flag = false;
}
else
{
large_arc_flag = true;
sweep_flag = true;
}
}
SVGEllipticalArc ea( initial, ray(X), ray(Y), rot_angle(),
large_arc_flag, sweep_flag, final, _svg_compliant);
return ea;
}
Ellipse Ellipse::transformed(Matrix const& m) const
{
double cosrot = std::cos(rot_angle());
double sinrot = std::sin(rot_angle());
Matrix A( ray(X) * cosrot, ray(X) * sinrot,
-ray(Y) * sinrot, ray(Y) * cosrot,
0, 0 );
Point new_center = center() * m;
Matrix M = m.without_translation();
Matrix AM = A * M;
if ( are_near(AM.det(), 0) )
{
double angle;
if (AM[0] != 0)
{
angle = std::atan2(AM[2], AM[0]);
}
else if (AM[1] != 0)
{
angle = std::atan2(AM[3], AM[1]);
}
else
{
angle = M_PI/2;
}
Point V(std::cos(angle), std::sin(angle));
V *= AM;
double rx = L2(V);
angle = atan2(V);
return Ellipse(new_center[X], new_center[Y], rx, 0, angle);
}
std::vector<double> coeff = implicit_form_coefficients();
Matrix Q( coeff[0], coeff[1]/2,
coeff[1]/2, coeff[2],
0, 0 );
Matrix invm = M.inverse();
Q = invm * Q ;
std::swap( invm[1], invm[2] );
Q *= invm;
Ellipse e(Q[0], 2*Q[1], Q[3], 0, 0, -1);
e.m_centre = new_center;
return e;
}
Ellipse::Ellipse(Geom::Circle const &c)
{
m_centre = c.center();
m_ray[X] = m_ray[Y] = c.ray();
}
} // 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 :
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