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/**
* \file
* \brief Abstract Curve Type
*
* Authors:
* MenTaLguY <mental@rydia.net>
* Marco Cecchetti <mrcekets at gmail.com>
*
* Copyright 2007-2008 authors
*
* 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 _2GEOM_CURVE_H_
#define _2GEOM_CURVE_H_
#include <2geom/coord.h>
#include <2geom/point.h>
#include <2geom/interval.h>
#include <2geom/nearest-point.h>
#include <2geom/sbasis.h>
#include <2geom/d2.h>
#include <2geom/matrix.h>
#include <2geom/exception.h>
#include <vector>
namespace Geom
{
class Curve;
struct CurveHelpers {
protected:
static int root_winding(Curve const &c, Point p);
};
class Curve : private CurveHelpers {
public:
virtual ~Curve() {}
virtual Point initialPoint() const = 0;
virtual Point finalPoint() const = 0;
/* isDegenerate returns true if the curve has "zero length".
* For a bezier curve this means for example that all handles are at the same point */
virtual bool isDegenerate() const = 0;
virtual Curve *duplicate() const = 0;
virtual OptRect boundsFast() const = 0;
virtual OptRect boundsExact() const = 0;
virtual OptRect boundsLocal(OptInterval i, unsigned deg) const = 0;
OptRect boundsLocal(OptInterval i) const { return boundsLocal(i, 0); }
virtual std::vector<double> roots(double v, Dim2 d) const = 0;
virtual int winding(Point p) const { return root_winding(*this, p); }
virtual int degreesOfFreedom() const { return 0;}
//mental: review these
virtual Curve *portion(double f, double t) const = 0;
virtual Curve *reverse() const { return portion(1, 0); }
virtual Curve *derivative() const = 0;
virtual void setInitial(Point v) = 0;
virtual void setFinal(Point v) = 0;
virtual
double nearestPoint( Point const& p, double from = 0, double to = 1 ) const
{
return nearest_point(p, toSBasis(), from, to);
}
virtual
std::vector<double>
allNearestPoints( Point const& p, double from = 0, double to = 1 ) const
{
return all_nearest_points(p, toSBasis(), from, to);
}
/*
Path operator*=(Matrix)
This is not possible, because:
A Curve can be many things, for example a HLineSegment.
Such a segment cannot be transformed and stay a HLineSegment in general (take for example rotations).
This means that these curves become a different type of curve, hence one should use "transformed(Matrix).
*/
virtual Curve *transformed(Matrix const &m) const = 0;
virtual Point pointAt(Coord t) const { return pointAndDerivatives(t, 0).front(); }
virtual Coord valueAt(Coord t, Dim2 d) const { return pointAt(t)[d]; }
virtual Point operator() (double t) const { return pointAt(t); }
/* pointAndDerivatives returns a vector that looks like the following:
* [ point at t, 1st derivative at t, 2nd derivative at t, ... , n'th derivative at t] */
virtual std::vector<Point> pointAndDerivatives(Coord t, unsigned n) const = 0;
/* unitTangentAt returns the unit vector tangent to the curve at position t
* (in the direction of increasing t). The method uses l'Hopital's rule when the derivative
* is (0,0), parameter n determines the maximum nr of iterations (for when higher derivatives are also (0,0) ).
* Point(0,0) is returned if no non-zero derivative could be found.
* Note that unitTangentAt(1) will probably not give the desired result. Probably one should do:
* Curve * c_reverse = c.reverse();
* Point tangent = - c_reverse->unitTangentAt(0);
* delete c_reverse;
*/
virtual Point unitTangentAt(Coord t, unsigned n = 3) const
{
std::vector<Point> derivs = pointAndDerivatives(t, n);
for (unsigned deriv_n = 1; deriv_n < derivs.size(); deriv_n++) {
Coord length = derivs[deriv_n].length();
if ( ! are_near(length, 0) ) {
// length of derivative is non-zero, so return unit vector
return derivs[deriv_n] / length;
}
}
return Point (0,0);
};
virtual D2<SBasis> toSBasis() const = 0;
virtual bool operator==(Curve const &c) const { return this == &c;}
};
inline
Coord nearest_point(Point const& p, Curve const& c)
{
return c.nearestPoint(p);
}
} // end namespace Geom
#endif // _2GEOM_CURVE_H_
/*
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 :
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