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/*
* 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 "path.h"
namespace Geom
{
D2<SBasis> SVGEllipticalArc::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;
}
double SVGEllipticalArc::valueAt(Coord t, Dim2 d) const
{
Coord tt = from_01_to_02PI(t);
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(tt)
- ray(Y) * sin_rot_angle * std::sin(tt)
+ center(X);
}
else
{
return ray(X) * sin_rot_angle * std::cos(tt)
+ ray(Y) * cos_rot_angle * std::sin(tt)
+ center(Y);
}
}
Curve* SVGEllipticalArc::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;
SVGEllipticalArc* arc = new SVGEllipticalArc( *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 SVGEllipticalArc::calculate_center_and_extreme_angles()
{
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
{
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
{
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 SVGEllipticalArc::from_01_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;
}
}
} // 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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