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Diffstat (limited to 'include/2geom/sbasis-geometric.h')
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diff --git a/include/2geom/sbasis-geometric.h b/include/2geom/sbasis-geometric.h new file mode 100644 index 0000000..7f1e8aa --- /dev/null +++ b/include/2geom/sbasis-geometric.h @@ -0,0 +1,146 @@ +/** + * \file + * \brief two-dimensional geometric operators. + * + * These operators are built on a more 'polynomially robust' + * transformation to map a function that takes a [0,1] parameter to a + * 2d vector into a function that takes the same [0,1] parameter to a + * unit vector with the same direction. + * + * Rather that using (X/sqrt(X))(t) which involves two unstable + * operations, sqrt and divide, this approach forms a curve directly + * from the various tangent directions at each end (angular jet). As + * a result, the final path has a convergence behaviour derived from + * that of the sin and cos series. -- njh + *//* + * Copyright 2007, JFBarraud + * Copyright 2007, njh + * + * 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. + */ + +#ifndef LIB2GEOM_SEEN_SBASIS_GEOMETRIC_H +#define LIB2GEOM_SEEN_SBASIS_GEOMETRIC_H + +#include <2geom/d2.h> +#include <2geom/piecewise.h> +#include <vector> + +namespace Geom { + +Piecewise<D2<SBasis> > +cutAtRoots(Piecewise<D2<SBasis> > const &M, double tol=1e-4); + +Piecewise<SBasis> +atan2(D2<SBasis> const &vect, + double tol=.01, unsigned order=3); + +Piecewise<SBasis> +atan2(Piecewise<D2<SBasis> >const &vect, + double tol=.01, unsigned order=3); + +D2<Piecewise<SBasis> > +tan2(SBasis const &angle, + double tol=.01, unsigned order=3); + +D2<Piecewise<SBasis> > +tan2(Piecewise<SBasis> const &angle, + double tol=.01, unsigned order=3); + +Piecewise<D2<SBasis> > +unitVector(D2<SBasis> const &vect, + double tol=.01, unsigned order=3); +Piecewise<D2<SBasis> > +unitVector(Piecewise<D2<SBasis> > const &vect, + double tol=.01, unsigned order=3); + +// Piecewise<D2<SBasis> > +// uniform_speed(D2<SBasis> const M, +// double tol=.1); + +Piecewise<SBasis> curvature( D2<SBasis> const &M, double tol=.01); +Piecewise<SBasis> curvature(Piecewise<D2<SBasis> > const &M, double tol=.01); + +Piecewise<SBasis> arcLengthSb( D2<SBasis> const &M, double tol=.01); +Piecewise<SBasis> arcLengthSb(Piecewise<D2<SBasis> > const &M, double tol=.01); + +double length( D2<SBasis> const &M, double tol=.01); +double length(Piecewise<D2<SBasis> > const &M, double tol=.01); + +void length_integrating(D2<SBasis> const &B, double &result, double &abs_error, double tol); + +Piecewise<D2<SBasis> > +arc_length_parametrization(D2<SBasis> const &M, + unsigned order=3, + double tol=.01); +Piecewise<D2<SBasis> > +arc_length_parametrization(Piecewise<D2<SBasis> > const &M, + unsigned order=3, + double tol=.01); + + +unsigned centroid(Piecewise<D2<SBasis> > const &p, Point& centroid, double &area); + +std::vector<D2<SBasis> > +cubics_fitting_curvature(Point const &M0, Point const &M1, + Point const &dM0, Point const &dM1, + double d2M0xdM0, double d2M1xdM1, + int insist_on_speed_signs = 1, + double epsilon = 1e-5); + +std::vector<D2<SBasis> > +cubics_fitting_curvature(Point const &M0, Point const &M1, + Point const &dM0, Point const &dM1, + Point const &d2M0, Point const &d2M1, + int insist_on_speed_signs = 1, + double epsilon = 1e-5); + +std::vector<D2<SBasis> > +cubics_with_prescribed_curvature(Point const &M0, Point const &M1, + Point const &dM0, Point const &dM1, + double k0, double k1, + int insist_on_speed_signs = 1, + double error = 1e-5); + + +std::vector<double> find_tangents(Point P, D2<SBasis> const &A); +std::vector<double> find_tangents_by_vector(Point V, D2<SBasis> const &A); +std::vector<double> find_normals(Point P, D2<SBasis> const &A); +std::vector<double> find_normals_by_vector(Point V, D2<SBasis> const &A); + +}; + +#endif + +/* + 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 : + |