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Diffstat (limited to 'src/2geom/elliptical-arc-from-sbasis.cpp')
| -rw-r--r-- | src/2geom/elliptical-arc-from-sbasis.cpp | 341 |
1 files changed, 341 insertions, 0 deletions
diff --git a/src/2geom/elliptical-arc-from-sbasis.cpp b/src/2geom/elliptical-arc-from-sbasis.cpp new file mode 100644 index 0000000..c536d89 --- /dev/null +++ b/src/2geom/elliptical-arc-from-sbasis.cpp @@ -0,0 +1,341 @@ +/** @file + * @brief Fitting elliptical arc to SBasis + * + * This file contains the implementation of the function arc_from_sbasis. + *//* + * 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 <2geom/curve.h> +#include <2geom/angle.h> +#include <2geom/utils.h> +#include <2geom/bezier-curve.h> +#include <2geom/elliptical-arc.h> +#include <2geom/sbasis-curve.h> // for non-native methods +#include <2geom/numeric/vector.h> +#include <2geom/numeric/fitting-tool.h> +#include <2geom/numeric/fitting-model.h> +#include <algorithm> + +namespace Geom { + +// forward declaration +namespace detail +{ + struct ellipse_equation; +} + +/* + * make_elliptical_arc + * + * convert a parametric polynomial curve given in symmetric power basis form + * into an EllipticalArc type; in order to be successful the input curve + * has to look like an actual elliptical arc even if a certain tolerance + * is allowed through an ad-hoc parameter. + * The conversion is performed through an interpolation on a certain amount of + * sample points computed on the input curve; + * the interpolation computes the coefficients of the general implicit equation + * of an ellipse (A*X^2 + B*XY + C*Y^2 + D*X + E*Y + F = 0), then from the + * implicit equation we compute the parametric form. + * + */ +class make_elliptical_arc +{ + public: + typedef D2<SBasis> curve_type; + + /* + * constructor + * + * it doesn't execute the conversion but set the input and output parameters + * + * _ea: the output EllipticalArc that will be generated; + * _curve: the input curve to be converted; + * _total_samples: the amount of sample points to be taken + * on the input curve for performing the conversion + * _tolerance: how much likelihood is required between the input curve + * and the generated elliptical arc; the smaller it is the + * the tolerance the higher it is the likelihood. + */ + make_elliptical_arc( EllipticalArc& _ea, + curve_type const& _curve, + unsigned int _total_samples, + double _tolerance ); + + private: + bool bound_exceeded( unsigned int k, detail::ellipse_equation const & ee, + double e1x, double e1y, double e2 ); + + bool check_bound(double A, double B, double C, double D, double E, double F); + + void fit(); + + bool make_elliptiarc(); + + void print_bound_error(unsigned int k) + { + std::cerr + << "tolerance error" << std::endl + << "at point: " << k << std::endl + << "error value: "<< dist_err << std::endl + << "bound: " << dist_bound << std::endl + << "angle error: " << angle_err + << " (" << angle_tol << ")" << std::endl; + } + + public: + /* + * perform the actual conversion + * return true if the conversion is successful, false on the contrary + */ + bool operator()() + { + // initialize the reference + const NL::Vector & coeff = fitter.result(); + fit(); + if ( !check_bound(1, coeff[0], coeff[1], coeff[2], coeff[3], coeff[4]) ) + return false; + if ( !(make_elliptiarc()) ) return false; + return true; + } + + private: + EllipticalArc& ea; // output elliptical arc + const curve_type & curve; // input curve + Piecewise<D2<SBasis> > dcurve; // derivative of the input curve + NL::LFMEllipse model; // model used for fitting + // perform the actual fitting task + NL::least_squeares_fitter<NL::LFMEllipse> fitter; + // tolerance: the user-defined tolerance parameter; + // tol_at_extr: the tolerance at end-points automatically computed + // on the value of "tolerance", and usually more strict; + // tol_at_center: tolerance at the center of the ellipse + // angle_tol: tolerance for the angle btw the input curve tangent + // versor and the ellipse normal versor at the sample points + double tolerance, tol_at_extr, tol_at_center, angle_tol; + Point initial_point, final_point; // initial and final end-points + unsigned int N; // total samples + unsigned int last; // N-1 + double partitions; // N-1 + std::vector<Point> p; // sample points + double dist_err, dist_bound, angle_err; +}; + +namespace detail +{ +/* + * ellipse_equation + * + * this is an helper struct, it provides two routines: + * the first one evaluates the implicit form of an ellipse on a given point + * the second one computes the normal versor at a given point of an ellipse + * in implicit form + */ +struct ellipse_equation +{ + ellipse_equation(double a, double b, double c, double d, double e, double f) + : A(a), B(b), C(c), D(d), E(e), F(f) + { + } + + double operator()(double x, double y) const + { + // A * x * x + B * x * y + C * y * y + D * x + E * y + F; + return (A * x + B * y + D) * x + (C * y + E) * y + F; + } + + double operator()(Point const& p) const + { + return (*this)(p[X], p[Y]); + } + + Point normal(double x, double y) const + { + Point n( 2 * A * x + B * y + D, 2 * C * y + B * x + E ); + return unit_vector(n); + } + + Point normal(Point const& p) const + { + return normal(p[X], p[Y]); + } + + double A, B, C, D, E, F; +}; + +} // end namespace detail + +make_elliptical_arc:: +make_elliptical_arc( EllipticalArc& _ea, + curve_type const& _curve, + unsigned int _total_samples, + double _tolerance ) + : ea(_ea), curve(_curve), + dcurve( unitVector(derivative(curve)) ), + model(), fitter(model, _total_samples), + tolerance(_tolerance), tol_at_extr(tolerance/2), + tol_at_center(0.1), angle_tol(0.1), + initial_point(curve.at0()), final_point(curve.at1()), + N(_total_samples), last(N-1), partitions(N-1), p(N) +{ +} + +/* + * check that the coefficients computed by the fit method satisfy + * the tolerance parameters at the k-th sample point + */ +bool +make_elliptical_arc:: +bound_exceeded( unsigned int k, detail::ellipse_equation const & ee, + double e1x, double e1y, double e2 ) +{ + dist_err = std::fabs( ee(p[k]) ); + dist_bound = std::fabs( e1x * p[k][X] + e1y * p[k][Y] + e2 ); + // check that the angle btw the tangent versor to the input curve + // and the normal versor of the elliptical arc, both evaluate + // at the k-th sample point, are really othogonal + angle_err = std::fabs( dot( dcurve(k/partitions), ee.normal(p[k]) ) ); + //angle_err *= angle_err; + return ( dist_err > dist_bound || angle_err > angle_tol ); +} + +/* + * check that the coefficients computed by the fit method satisfy + * the tolerance parameters at each sample point + */ +bool +make_elliptical_arc:: +check_bound(double A, double B, double C, double D, double E, double F) +{ + detail::ellipse_equation ee(A, B, C, D, E, F); + + // check error magnitude at the end-points + double e1x = (2*A + B) * tol_at_extr; + double e1y = (B + 2*C) * tol_at_extr; + double e2 = ((D + E) + (A + B + C) * tol_at_extr) * tol_at_extr; + if (bound_exceeded(0, ee, e1x, e1y, e2)) + { + print_bound_error(0); + return false; + } + if (bound_exceeded(0, ee, e1x, e1y, e2)) + { + print_bound_error(last); + return false; + } + + // e1x = derivative((ee(x,y), x) | x->tolerance, y->tolerance + e1x = (2*A + B) * tolerance; + // e1y = derivative((ee(x,y), y) | x->tolerance, y->tolerance + e1y = (B + 2*C) * tolerance; + // e2 = ee(tolerance, tolerance) - F; + e2 = ((D + E) + (A + B + C) * tolerance) * tolerance; +// std::cerr << "e1x = " << e1x << std::endl; +// std::cerr << "e1y = " << e1y << std::endl; +// std::cerr << "e2 = " << e2 << std::endl; + + // check error magnitude at sample points + for ( unsigned int k = 1; k < last; ++k ) + { + if ( bound_exceeded(k, ee, e1x, e1y, e2) ) + { + print_bound_error(k); + return false; + } + } + + return true; +} + +/* + * fit + * + * supply the samples to the fitter and compute + * the ellipse implicit equation coefficients + */ +void make_elliptical_arc::fit() +{ + for (unsigned int k = 0; k < N; ++k) + { + p[k] = curve( k / partitions ); + fitter.append(p[k]); + } + fitter.update(); + + NL::Vector z(N, 0.0); + fitter.result(z); +} + +bool make_elliptical_arc::make_elliptiarc() +{ + const NL::Vector & coeff = fitter.result(); + Ellipse e; + try + { + e.setCoefficients(1, coeff[0], coeff[1], coeff[2], coeff[3], coeff[4]); + } + catch(LogicalError const &exc) + { + return false; + } + + Point inner_point = curve(0.5); + + std::unique_ptr<EllipticalArc> arc( e.arc(initial_point, inner_point, final_point) ); + ea = *arc; + + if ( !are_near( e.center(), + ea.center(), + tol_at_center * std::min(e.ray(X),e.ray(Y)) + ) + ) + { + return false; + } + return true; +} + + + +bool arc_from_sbasis(EllipticalArc &ea, D2<SBasis> const &in, + double tolerance, unsigned num_samples) +{ + make_elliptical_arc convert(ea, in, num_samples, tolerance); + return convert(); +} + +} // 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:fileencoding=utf-8:textwidth=99 : |