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/**
* \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 :
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