svg-elliptical-arc.cpp revision c8589a6c7367d09fa756755cef0dd448c7328a71
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * SVG Elliptical Arc Class
43a9ecef56abdf431763b9fb95469e70da237abbLiam P. White * Copyright 2008 Marco Cecchetti <mrcekets at gmail.com>
43a9ecef56abdf431763b9fb95469e70da237abbLiam P. White * This library is free software; you can redistribute it and/or
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * modify it either under the terms of the GNU Lesser General Public
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * License version 2.1 as published by the Free Software Foundation
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * (the "LGPL") or, at your option, under the terms of the Mozilla
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * Public License Version 1.1 (the "MPL"). If you do not alter this
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * notice, a recipient may use your version of this file under either
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the MPL or the LGPL.
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * You should have received a copy of the LGPL along with this library
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * in the file COPYING-LGPL-2.1; if not, write to the Free Software
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * You should have received a copy of the MPL along with this library
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * in the file COPYING-MPL-1.1
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * The contents of this file are subject to the Mozilla Public License
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * Version 1.1 (the "License"); you may not use this file except in
a6b5d41707fe985d397907d52766cbcdcca9735fJabiertxof * compliance with the License. You may obtain a copy of the License at
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * OF ANY KIND, either express or implied. See the LGPL or the MPL for
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the specific language governing rights and limitations.
26b55a439f4a219fec9c2b46a6b9d02640da6d76Jabiertxof * @class SVGEllipticalArc
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof * @brief SVG 1.1-compliant elliptical arc.
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof * This class is almost identical to the normal elliptical arc, but it differs slightly
26b55a439f4a219fec9c2b46a6b9d02640da6d76Jabiertxof * in the handling of degenerate arcs to be compliant with SVG 1.1 implementation guidelines.
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof * @ingroup Curves
26b55a439f4a219fec9c2b46a6b9d02640da6d76Jabiertxof * ellipse_equation
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * this is an helper struct, it provides two routines:
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the first one evaluates the implicit form of an ellipse on a given point
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the second one computes the normal versor at a given point of an ellipse
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * in implicit form
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof ellipse_equation(double a, double b, double c, double d, double e, double f)
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof : A(a), B(b), C(c), D(d), E(e), F(f)
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof double operator()(double x, double y) const
2ce2003d5713154f99c32af18fb904a1af109031Jabiertxof // A * x * x + B * x * y + C * y * y + D * x + E * y + F;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof return (A * x + B * y + D) * x + (C * y + E) * y + F;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof double operator()(Point const& p) const
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof return (*this)(p[X], p[Y]);
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof Point n( 2 * A * x + B * y + D, 2 * C * y + B * x + E );
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof return normal(p[X], p[Y]);
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof double A, B, C, D, E, F;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof initial_point(curve.at0()), final_point(curve.at1()),
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof N(_total_samples), last(N-1), partitions(N-1), p(N),
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * check that the coefficients computed by the fit method satisfy
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the tolerance parameters at the k-th sample point
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxofbound_exceeded( unsigned int k, detail::ellipse_equation const & ee,
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof dist_bound = std::fabs( e1x * p[k][X] + e1y * p[k][Y] + e2 );
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof // check that the angle btw the tangent versor to the input curve
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof // and the normal versor of the elliptical arc, both evaluate
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof // at the k-th sample point, are really othogonal
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof angle_err = std::fabs( dot( dcurve(k/partitions), ee.normal(p[k]) ) );
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof //angle_err *= angle_err;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof return ( dist_err > dist_bound || angle_err > angle_tol );
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * check that the coefficients computed by the fit method satisfy
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the tolerance parameters at each sample point
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxofcheck_bound(double A, double B, double C, double D, double E, double F)
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof // check error magnitude at the end-points
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof double e2 = ((D + E) + (A + B + C) * tol_at_extr) * tol_at_extr;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof return false;
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof return false;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof // e1x = derivative((ee(x,y), x) | x->tolerance, y->tolerance
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof // e1y = derivative((ee(x,y), y) | x->tolerance, y->tolerance
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof // e2 = ee(tolerance, tolerance) - F;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof e2 = ((D + E) + (A + B + C) * tolerance) * tolerance;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof// std::cerr << "e1x = " << e1x << std::endl;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof// std::cerr << "e1y = " << e1y << std::endl;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof// std::cerr << "e2 = " << e2 << std::endl;
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof // check error magnitude at sample points
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof return false;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof return true;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof * supply the samples to the fitter and compute
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof * the ellipse implicit equation coefficients
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof for (unsigned int k = 0; k < N; ++k)
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof e.set(1, coeff[0], coeff[1], coeff[2], coeff[3], coeff[4]);
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof return false;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof std::unique_ptr<EllipticalArc> arc( e.arc(initial_point, inner_point, final_point, true) );
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof std::auto_ptr<EllipticalArc> arc( e.arc(initial_point, inner_point, final_point, true) );
23e68a9a2e8c92bff1885ab56a74c13f6b4691a3Jabiertxof eap( e.arc(initial_point, inner_point, final_point, false) );
23e68a9a2e8c92bff1885ab56a74c13f6b4691a3Jabiertxof return false;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof return false;
6103fefae34cb76c1ab70a8077454534aba342c5Jabiertxof return true;
2ea303d5a80b7efba4d23ab33e7d5ea0c9b546b2Jabiertxof} // end namespace Geom
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof Local Variables:
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof c-file-style:"stroustrup"
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof indent-tabs-mode:nil
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof fill-column:99
b14e0c4cb620016f312432acc32db04b70f3fabcJabiertxof// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :