d2.h

Go to the documentation of this file.

/*
 * Authors:
 *   Michael Sloan <mgsloan@gmail.com>
 *   Krzysztof Kosiński <tweenk.pl@gmail.com>
 *
 * Copyright 2007-2015 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, output 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_D2_H
#define LIB2GEOM_SEEN_D2_H
 
#include <iterator>
#include <boost/concept/assert.hpp>
#include <boost/iterator/transform_iterator.hpp>
#include <2geom/point.h>
#include <2geom/interval.h>
#include <2geom/affine.h>
#include <2geom/rect.h>
#include <2geom/concepts.h>
 
namespace Geom {
template <typename T>
class D2
{
private:
    T f[2];
 
public:
    typedef T D1Value;
    typedef T &D1Reference;
    typedef T const &D1ConstReference;
 
    D2() {f[X] = f[Y] = T();}
    explicit D2(Point const &a) {
        f[X] = T(a[X]); f[Y] = T(a[Y]);
    }
 
    D2(T const &a, T const &b) {
        f[X] = a;
        f[Y] = b;
    }
 
    template <typename Iter>
    D2(Iter first, Iter last) {
        typedef typename std::iterator_traits<Iter>::value_type V;
        typedef typename boost::transform_iterator<GetAxis<X,V>, Iter> XIter;
        typedef typename boost::transform_iterator<GetAxis<Y,V>, Iter> YIter;
 
        XIter xfirst(first, GetAxis<X,V>()), xlast(last, GetAxis<X,V>());
        f[X] = T(xfirst, xlast);
        YIter yfirst(first, GetAxis<Y,V>()), ylast(last, GetAxis<Y,V>());
        f[Y] = T(yfirst, ylast);
    }
 
    D2(std::vector<Point> const &vec) {
        typedef Point V;
        typedef std::vector<Point>::const_iterator Iter;
        typedef boost::transform_iterator<GetAxis<X,V>, Iter> XIter;
        typedef boost::transform_iterator<GetAxis<Y,V>, Iter> YIter;
 
        XIter xfirst(vec.begin(), GetAxis<X,V>()), xlast(vec.end(), GetAxis<X,V>());
        f[X] = T(xfirst, xlast);
        YIter yfirst(vec.begin(), GetAxis<Y,V>()), ylast(vec.end(), GetAxis<Y,V>());
        f[Y] = T(yfirst, ylast);
    }
 
    //TODO: ask MenTaLguY about operator= as seen in Point
 
    T& operator[](unsigned i)              { return f[i]; }
    T const & operator[](unsigned i) const { return f[i]; }
    Point point(unsigned i) const {
        Point ret(f[X][i], f[Y][i]);
        return ret;
    }
 
    //IMPL: FragmentConcept
    typedef Point output_type;
    bool isZero(double eps=EPSILON) const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return f[X].isZero(eps) && f[Y].isZero(eps);
    }
    bool isConstant(double eps=EPSILON) const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return f[X].isConstant(eps) && f[Y].isConstant(eps);
    }
    bool isFinite() const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return f[X].isFinite() && f[Y].isFinite();
    }
    Point at0() const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return Point(f[X].at0(), f[Y].at0());
    }
    Point at1() const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return Point(f[X].at1(), f[Y].at1());
    }
    Point pointAt(double t) const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return (*this)(t);
    }
    Point valueAt(double t) const {
        // TODO: remove this alias
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return (*this)(t);
    }
    std::vector<Point > valueAndDerivatives(double t, unsigned n) const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        std::vector<Coord> x = f[X].valueAndDerivatives(t, n),
                           y = f[Y].valueAndDerivatives(t, n); // always returns a vector of size n+1
        std::vector<Point> res(n+1);
        for(unsigned i = 0; i <= n; i++) {
            res[i] = Point(x[i], y[i]);
        }
        return res;
    }
    D2<SBasis> toSBasis() const {
        BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
        return D2<SBasis>(f[X].toSBasis(), f[Y].toSBasis());
    }
 
    Point operator()(double t) const;
    Point operator()(double x, double y) const;
};
template <typename T>
inline D2<T> reverse(const D2<T> &a) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return D2<T>(reverse(a[X]), reverse(a[Y]));
}
 
template <typename T>
inline D2<T> portion(const D2<T> &a, Coord f, Coord t) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return D2<T>(portion(a[X], f, t), portion(a[Y], f, t));
}
 
template <typename T>
inline D2<T> portion(const D2<T> &a, Interval i) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return D2<T>(portion(a[X], i), portion(a[Y], i));
}
 
//IMPL: EqualityComparableConcept
template <typename T>
inline bool
operator==(D2<T> const &a, D2<T> const &b) {
    BOOST_CONCEPT_ASSERT((EqualityComparableConcept<T>));
    return a[0]==b[0] && a[1]==b[1];
}
template <typename T>
inline bool
operator!=(D2<T> const &a, D2<T> const &b) {
    BOOST_CONCEPT_ASSERT((EqualityComparableConcept<T>));
    return a[0]!=b[0] || a[1]!=b[1];
}
 
//IMPL: NearConcept
template <typename T>
inline bool
are_near(D2<T> const &a, D2<T> const &b, double tol) {
    BOOST_CONCEPT_ASSERT((NearConcept<T>));
    return are_near(a[0], b[0], tol) && are_near(a[1], b[1], tol);
}
 
//IMPL: AddableConcept
template <typename T>
inline D2<T>
operator+(D2<T> const &a, D2<T> const &b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
 
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] + b[i];
    return r;
}
template <typename T>
inline D2<T>
operator-(D2<T> const &a, D2<T> const &b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
 
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] - b[i];
    return r;
}
template <typename T>
inline D2<T>
operator+=(D2<T> &a, D2<T> const &b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
 
    for(unsigned i = 0; i < 2; i++)
        a[i] += b[i];
    return a;
}
template <typename T>
inline D2<T>
operator-=(D2<T> &a, D2<T> const & b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
 
    for(unsigned i = 0; i < 2; i++)
        a[i] -= b[i];
    return a;
}
 
//IMPL: ScalableConcept
template <typename T>
inline D2<T>
operator-(D2<T> const & a) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = -a[i];
    return r;
}
template <typename T>
inline D2<T>
operator*(D2<T> const & a, Point const & b) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
 
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] * b[i];
    return r;
}
template <typename T>
inline D2<T>
operator/(D2<T> const & a, Point const & b) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    //TODO: b==0?
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] / b[i];
    return r;
}
template <typename T>
inline D2<T>
operator*=(D2<T> &a, Point const & b) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
 
    for(unsigned i = 0; i < 2; i++)
        a[i] *= b[i];
    return a;
}
template <typename T>
inline D2<T>
operator/=(D2<T> &a, Point const & b) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    //TODO: b==0?
    for(unsigned i = 0; i < 2; i++)
        a[i] /= b[i];
    return a;
}
 
template <typename T>
inline D2<T> operator*(D2<T> const & a, double b) { return D2<T>(a[0]*b, a[1]*b); }
template <typename T>
inline D2<T> operator*=(D2<T> & a, double b) { a[0] *= b; a[1] *= b; return a; }
template <typename T>
inline D2<T> operator/(D2<T> const & a, double b) { return D2<T>(a[0]/b, a[1]/b); }
template <typename T>
inline D2<T> operator/=(D2<T> & a, double b) { a[0] /= b; a[1] /= b; return a; }
 
template<typename T>
D2<T> operator*(D2<T> const &v, Affine const &m) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    D2<T> ret;
    for(unsigned i = 0; i < 2; i++)
        ret[i] = v[X] * m[i] + v[Y] * m[i + 2] + m[i + 4];
    return ret;
}
 
//IMPL: MultiplicableConcept
template <typename T>
inline D2<T>
operator*(D2<T> const & a, T const & b) {
    BOOST_CONCEPT_ASSERT((MultiplicableConcept<T>));
    D2<T> ret;
    for(unsigned i = 0; i < 2; i++)
        ret[i] = a[i] * b;
    return ret;
}
 
//IMPL:
 
//IMPL: OffsetableConcept
template <typename T>
inline D2<T>
operator+(D2<T> const & a, Point b) {
    BOOST_CONCEPT_ASSERT((OffsetableConcept<T>));
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] + b[i];
    return r;
}
template <typename T>
inline D2<T>
operator-(D2<T> const & a, Point b) {
    BOOST_CONCEPT_ASSERT((OffsetableConcept<T>));
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = a[i] - b[i];
    return r;
}
template <typename T>
inline D2<T>
operator+=(D2<T> & a, Point b) {
    BOOST_CONCEPT_ASSERT((OffsetableConcept<T>));
    for(unsigned i = 0; i < 2; i++)
        a[i] += b[i];
    return a;
}
template <typename T>
inline D2<T>
operator-=(D2<T> & a, Point b) {
    BOOST_CONCEPT_ASSERT((OffsetableConcept<T>));
    for(unsigned i = 0; i < 2; i++)
        a[i] -= b[i];
    return a;
}
 
template <typename T>
inline T
dot(D2<T> const & a, D2<T> const & b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
    BOOST_CONCEPT_ASSERT((MultiplicableConcept<T>));
 
    T r;
    for(unsigned i = 0; i < 2; i++)
        r += a[i] * b[i];
    return r;
}
 
template <typename T>
inline T
dot(D2<T> const & a, Point const & b) {
    BOOST_CONCEPT_ASSERT((AddableConcept<T>));
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
 
    T r;
    for(unsigned i = 0; i < 2; i++) {
        r += a[i] * b[i];
    }
    return r;
}
 
template <typename T>
inline T
cross(D2<T> const & a, D2<T> const & b) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    BOOST_CONCEPT_ASSERT((MultiplicableConcept<T>));
 
    return a[1] * b[0] - a[0] * b[1];
}
 
 
//equivalent to cw/ccw, for use in situations where rotation direction doesn't matter.
template <typename T>
inline D2<T>
rot90(D2<T> const & a) {
    BOOST_CONCEPT_ASSERT((ScalableConcept<T>));
    return D2<T>(-a[Y], a[X]);
}
 
//TODO: concepterize the following functions
template <typename T>
inline D2<T>
compose(D2<T> const & a, T const & b) {
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = compose(a[i],b);
    return r;
}
 
template <typename T>
inline D2<T>
compose_each(D2<T> const & a, D2<T> const & b) {
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = compose(a[i],b[i]);
    return r;
}
 
template <typename T>
inline D2<T>
compose_each(T const & a, D2<T> const & b) {
    D2<T> r;
    for(unsigned i = 0; i < 2; i++)
        r[i] = compose(a,b[i]);
    return r;
}
 
 
template<typename T>
inline Point
D2<T>::operator()(double t) const {
    Point p;
    for(unsigned i = 0; i < 2; i++)
       p[i] = (*this)[i](t);
    return p;
}
 
//TODO: we might want to have this take a Point as the parameter.
template<typename T>
inline Point
D2<T>::operator()(double x, double y) const {
    Point p;
    for(unsigned i = 0; i < 2; i++)
       p[i] = (*this)[i](x, y);
    return p;
}
 
 
template<typename T>
D2<T> derivative(D2<T> const & a) {
    return D2<T>(derivative(a[X]), derivative(a[Y]));
}
template<typename T>
D2<T> integral(D2<T> const & a) {
    return D2<T>(integral(a[X]), integral(a[Y]));
}
 
template <typename T>
inline std::ostream &operator<< (std::ostream &out_file, const Geom::D2<T> &in_d2) {
    out_file << "X: " << in_d2[X] << "  Y: " << in_d2[Y];
    return out_file;
}
 
//Some D2 Fragment implementation which requires rect:
template <typename T>
OptRect bounds_fast(const D2<T> &a) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return OptRect(bounds_fast(a[X]), bounds_fast(a[Y]));
}
template <typename T>
OptRect bounds_exact(const D2<T> &a) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return OptRect(bounds_exact(a[X]), bounds_exact(a[Y]));
}
template <typename T>
OptRect bounds_local(const D2<T> &a, const OptInterval &t) {
    BOOST_CONCEPT_ASSERT((FragmentConcept<T>));
    return OptRect(bounds_local(a[X], t), bounds_local(a[Y], t));
}
 
 
 
// SBasis-specific declarations
 
inline D2<SBasis> compose(D2<SBasis> const & a, SBasis const & b) {
    return D2<SBasis>(compose(a[X], b), compose(a[Y], b));
}
 
SBasis L2(D2<SBasis> const & a, unsigned k);
double L2(D2<double> const & a);
 
D2<SBasis> multiply(Linear const & a, D2<SBasis> const & b);
inline D2<SBasis> operator*(Linear const & a, D2<SBasis> const & b) { return multiply(a, b); }
D2<SBasis> multiply(SBasis const & a, D2<SBasis> const & b);
inline D2<SBasis> operator*(SBasis const & a, D2<SBasis> const & b) { return multiply(a, b); }
D2<SBasis> truncate(D2<SBasis> const & a, unsigned terms);
 
unsigned sbasis_size(D2<SBasis> const & a);
double tail_error(D2<SBasis> const & a, unsigned tail);
 
//Piecewise<D2<SBasis> > specific declarations
 
Piecewise<D2<SBasis> > sectionize(D2<Piecewise<SBasis> > const &a);
D2<Piecewise<SBasis> > make_cuts_independent(Piecewise<D2<SBasis> > const &a);
Piecewise<D2<SBasis> > rot90(Piecewise<D2<SBasis> > const &a);
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);
Piecewise<SBasis> dot(Piecewise<D2<SBasis> > const &a, Point const &b);
Piecewise<SBasis> cross(Piecewise<D2<SBasis> > const &a, Piecewise<D2<SBasis> > const &b);
 
Piecewise<D2<SBasis> > operator*(Piecewise<D2<SBasis> > const &a, Affine const &m);
 
Piecewise<D2<SBasis> > force_continuity(Piecewise<D2<SBasis> > const &f, double tol=0, bool closed=false);
 
std::vector<Piecewise<D2<SBasis> > > fuse_nearby_ends(std::vector<Piecewise<D2<SBasis> > > const &f, double tol=0);
 
std::vector<Geom::Piecewise<Geom::D2<Geom::SBasis> > > split_at_discontinuities (Geom::Piecewise<Geom::D2<Geom::SBasis> > const & pwsbin, double tol = .0001);
 
Point unitTangentAt(D2<SBasis> const & a, Coord t, unsigned n = 3);
 
//bounds specializations with order
inline OptRect bounds_fast(D2<SBasis> const & s, unsigned order=0) {
    OptRect retval;
    OptInterval xint = bounds_fast(s[X], order);
    if (xint) {
        OptInterval yint = bounds_fast(s[Y], order);
        if (yint) {
            retval = Rect(*xint, *yint);
        }
    }
    return retval;
}
inline OptRect bounds_local(D2<SBasis> const & s, OptInterval i, unsigned order=0) {
    OptRect retval;
    OptInterval xint = bounds_local(s[X], i, order);
    OptInterval yint = bounds_local(s[Y], i, order);
    if (xint && yint) {
        retval = Rect(*xint, *yint);
    }
    return retval;
}
 
std::vector<Interval> level_set( D2<SBasis> const &f, Rect region);
std::vector<Interval> level_set( D2<SBasis> const &f, Point p, double tol);
std::vector<std::vector<Interval> > level_sets( D2<SBasis> const &f, std::vector<Rect> regions);
std::vector<std::vector<Interval> > level_sets( D2<SBasis> const &f, std::vector<Point> pts, double tol);
 
 
} // end namespace Geom
 
#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 :