d2.h revision c8589a6c7367d09fa756755cef0dd448c7328a71
/**
* \file
* \brief Lifts one dimensional objects into 2d
*//*
* Copyright 2007 Michael Sloan <mgsloan@gmail.com>
*
* 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 SEEN_LIB2GEOM_D2_H
#define SEEN_LIB2GEOM_D2_H
#include <2geom/point.h>
#include <2geom/interval.h>
#include <2geom/affine.h>
#include <2geom/rect.h>
#include <boost/concept_check.hpp>
#include <2geom/concepts.h>
namespace Geom{
/**
* The D2 class takes two instances of a scalar data type and treats them
* like a point. All operations which make sense on a point are deļ¬ned for D2.
* A D2<double> is a Point. A D2<Interval> is a standard axis aligned rectangle.
* D2<SBasis> provides a 2d parametric function which maps t to a point
* x(t), y(t)
*/
template <class T>
class D2{
//BOOST_CLASS_REQUIRE(T, boost, AssignableConcept);
private:
T f[2];
public:
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;
}
//TODO: ask mental about operator= as seen in Point
T& operator[](unsigned i) { return f[i]; }
T const & operator[](unsigned i) const { return f[i]; }
//IMPL: FragmentConcept
typedef Point output_type;
bool isZero(double eps=EPSILON) const {
boost::function_requires<FragmentConcept<T> >();
return f[X].isZero(eps) && f[Y].isZero(eps);
}
bool isConstant(double eps=EPSILON) const {
boost::function_requires<FragmentConcept<T> >();
return f[X].isConstant(eps) && f[Y].isConstant(eps);
}
bool isFinite() const {
boost::function_requires<FragmentConcept<T> >();
return f[X].isFinite() && f[Y].isFinite();
}
Point at0() const {
boost::function_requires<FragmentConcept<T> >();
return Point(f[X].at0(), f[Y].at0());
}
Point at1() const {
boost::function_requires<FragmentConcept<T> >();
return Point(f[X].at1(), f[Y].at1());
}
Point valueAt(double t) const {
boost::function_requires<FragmentConcept<T> >();
return (*this)(t);
}
std::vector<Point > valueAndDerivatives(double t, unsigned n) const {
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::function_requires<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::function_requires<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::function_requires<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::function_requires<FragmentConcept<T> >();
return D2<T>(portion(a[X], i), portion(a[Y], i));
}
//IMPL: boost::EqualityComparableConcept
template <typename T>
inline bool
operator==(D2<T> const &a, D2<T> const &b) {
boost::function_requires<boost::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::function_requires<boost::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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<AddableConcept<T> >();
boost::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<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::function_requires<AddableConcept<T> >();
boost::function_requires<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::function_requires<AddableConcept<T> >();
boost::function_requires<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::function_requires<ScalableConcept<T> >();
boost::function_requires<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::function_requires<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;
}
} //end namespace Geom
#include <2geom/d2-sbasis.h>
namespace Geom{
//Some D2 Fragment implementation which requires rect:
template <typename T>
OptRect bounds_fast(const D2<T> &a) {
boost::function_requires<FragmentConcept<T> >();
return OptRect(bounds_fast(a[X]), bounds_fast(a[Y]));
}
template <typename T>
OptRect bounds_exact(const D2<T> &a) {
boost::function_requires<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::function_requires<FragmentConcept<T> >();
return OptRect(bounds_local(a[X], t), bounds_local(a[Y], t));
}
};
/*
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 :
#endif