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+/**
+ * \file
+ * \brief Lifts one dimensional objects into 2D
+ *//*
+ * 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 {
+/**
+ * @brief Adaptor that creates 2D functions from 1D ones.
+ * @ingroup Fragments
+ */
+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;
+}
+
+/** @brief Calculates the 'dot product' or 'inner product' of \c a and \c b
+ * @return \f$a \bullet b = a_X b_X + a_Y b_Y\f$.
+ * @relates D2 */
+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;
+}
+
+/** @brief Calculates the 'cross product' or 'outer product' of \c a and \c b
+ * @return \f$a \times b = a_Y b_X - a_X b_Y\f$.
+ * @relates D2 */
+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]));
+}
+
+/** A function to print out the Point. It just prints out the coords
+ on the given output stream */
+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 :
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