From: johanengelen Date: Sun, 13 Apr 2008 21:00:01 +0000 (+0000) Subject: sync with current 2geom, SVGEllipticalArc X-Git-Url: https://git.tokkee.org/?a=commitdiff_plain;h=18caee0b72be3d63dfd6d134ac56bafe0993905f;p=inkscape.git sync with current 2geom, SVGEllipticalArc --- diff --git a/src/2geom/svg-elliptical-arc.cpp b/src/2geom/svg-elliptical-arc.cpp new file mode 100644 index 000000000..3bd8fc501 --- /dev/null +++ b/src/2geom/svg-elliptical-arc.cpp @@ -0,0 +1,209 @@ +/* + * SVG Elliptical Arc Class + * + * Copyright 2008 Marco Cecchetti + * + * 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 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 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 : + +