add missing files

diff --git a/src/2geom/line.cpp b/src/2geom/line.cpp
new file mode 100644 (file)
index 0000000..a91ff03
--- /dev/null
+++ b/src/2geom/line.cpp
@@ -0,0 +1,376 @@
+/*
+ * Infinite Straight Line
+ *
+ * Copyright 2008  Marco Cecchetti <mrcekets at gmail.com>
+ * Nathan Hurst
+ *
+ * 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.
+ */
+
+
+#include <2geom/line.h>
+
+#include <algorithm>
+
+
+namespace Geom
+{
+
+namespace detail
+{
+
+inline
+OptCrossing intersection_impl(Point const& V1, Point const O1,
+                        Point const& V2, Point const O2 )
+{
+    double detV1V2 = V1[X] * V2[Y] - V2[X] * V1[Y];
+    if (are_near(detV1V2, 0)) return OptCrossing();
+
+    Point B = O2 - O1;
+    double detBV2 = B[X] * V2[Y] - V2[X] * B[Y];
+    double detV1B =    B[X] * V1[Y] - V1[X] * B[Y];
+    double inv_detV1V2 = 1 / detV1V2;
+
+    Crossing c;
+    c.ta = detBV2 * inv_detV1V2;
+    c.tb = detV1B * inv_detV1V2;
+//     std::cerr << "ta = " << solution.ta << std::endl;
+//     std::cerr << "tb = " << solution.tb << std::endl;
+    return OptCrossing(c);
+}
+
+
+OptCrossing intersection_impl(Ray const& r1, Line const& l2, unsigned int i)
+{
+    OptCrossing crossing = 
+        intersection_impl(r1.versor(), r1.origin(),
+                          l2.versor(), l2.origin() );
+    
+    if (crossing)
+    {
+        if (crossing->ta < 0)
+        {
+            return OptCrossing();
+        }
+        else
+        {
+            if (i != 0)
+            {
+                std::swap(crossing->ta, crossing->tb);
+            }
+            return crossing;
+        }
+    }
+    if (are_near(r1.origin(), l2))
+    {
+        THROW_INFINITESOLUTIONS();
+    }
+    else
+    {
+        return OptCrossing();
+    }
+}
+
+
+OptCrossing intersection_impl( LineSegment const& ls1,
+                               Line const& l2,
+                               unsigned int i )
+{
+    OptCrossing crossing = 
+        intersection_impl(ls1.finalPoint() - ls1.initialPoint(),
+                          ls1.initialPoint(),
+                          l2.versor(),
+                          l2.origin() );
+
+    if (crossing)
+    {
+        if ( crossing->getTime(0) < 0
+             || crossing->getTime(0) > 1 )
+        {
+            return OptCrossing();
+        }
+        else
+        {
+            if (i != 0)
+            {
+                std::swap((*crossing).ta, (*crossing).tb);
+            }
+            return crossing;
+        }
+    }
+    if (are_near(ls1.initialPoint(), l2))
+    {
+        THROW_INFINITESOLUTIONS();
+    }
+    else
+    {
+        return OptCrossing();
+    }
+}
+
+
+OptCrossing intersection_impl( LineSegment const& ls1,
+                               Ray const& r2,
+                               unsigned int i )
+{
+    Point direction = ls1.finalPoint() - ls1.initialPoint();
+    OptCrossing crossing = 
+        intersection_impl( direction,
+                           ls1.initialPoint(),
+                           r2.versor(),
+                           r2.origin() );
+
+    if (crossing)
+    {
+        if ( crossing->getTime(0) < 0
+             || crossing->getTime(0) > 1
+             || crossing->getTime(1) < 0 )
+        {
+            return OptCrossing();
+        }
+        else
+        {
+            if (i != 0)
+            {
+                std::swap(crossing->ta, crossing->tb);
+            }
+            return crossing;
+        }
+    }
+
+    if ( are_near(r2.origin(), ls1) )
+    {
+        bool eqvs = (dot(direction, r2.versor()) > 0);
+        if ( are_near(ls1.initialPoint(), r2.origin()) && !eqvs  )
+        {
+            crossing->ta = crossing->tb = 0;
+            return crossing;
+        }
+        else if ( are_near(ls1.finalPoint(), r2.origin()) && eqvs )
+        {
+            if (i == 0)
+            {
+                crossing->ta = 1;
+                crossing->tb = 0;
+            }
+            else
+            {
+                crossing->ta = 0;
+                crossing->tb = 1;
+            }
+            return crossing;
+        }
+        else
+        {
+            THROW_INFINITESOLUTIONS();
+        }
+    }
+    else if ( are_near(ls1.initialPoint(), r2) )
+    {
+        THROW_INFINITESOLUTIONS();
+    }
+    else
+    {
+        OptCrossing no_crossing;
+        return no_crossing;
+    }
+}
+
+}  // end namespace detail
+
+
+
+OptCrossing intersection(Line const& l1, Line const& l2)
+{
+    OptCrossing crossing = 
+        detail::intersection_impl( l1.versor(), l1.origin(),
+                                   l2.versor(), l2.origin() );
+    if (crossing)
+    {
+        return crossing;
+    }
+    if (are_near(l1.origin(), l2))
+    {
+        THROW_INFINITESOLUTIONS();
+    }
+    else
+    {
+        return crossing;
+    }
+}
+
+
+OptCrossing intersection(Ray const& r1, Ray const& r2)
+{
+    OptCrossing crossing = 
+    detail::intersection_impl( r1.versor(), r1.origin(),
+                               r2.versor(), r2.origin() );
+
+    if (crossing)
+    {
+        if ( crossing->ta < 0
+             || crossing->tb < 0 )
+        {
+            OptCrossing no_crossing;
+            return no_crossing;
+        }
+        else
+        {
+            return crossing;
+        }
+    }
+
+    if ( are_near(r1.origin(), r2) || are_near(r2.origin(), r1) )
+    {
+        if ( are_near(r1.origin(), r2.origin())
+             && !are_near(r1.versor(), r2.versor()) )
+        {
+            crossing->ta = crossing->tb = 0;
+            return crossing;
+        }
+        else
+        {
+            THROW_INFINITESOLUTIONS();
+        }
+    }
+    else
+    {
+        OptCrossing no_crossing;
+        return no_crossing;
+    }
+}
+
+
+OptCrossing intersection( LineSegment const& ls1, LineSegment const& ls2 )
+{
+    Point direction1 = ls1.finalPoint() - ls1.initialPoint();
+    Point direction2 = ls2.finalPoint() - ls2.initialPoint();
+    OptCrossing crossing =
+        detail::intersection_impl( direction1,
+                                   ls1.initialPoint(),
+                                   direction2,
+                                   ls2.initialPoint() );
+
+    if (crossing)
+    {
+        if ( crossing->getTime(0) < 0
+             || crossing->getTime(0) > 1
+             || crossing->getTime(1) < 0
+             || crossing->getTime(1) > 1 )
+        {
+            OptCrossing no_crossing;
+            return no_crossing;
+        }
+        else
+        {
+            return crossing;
+        }
+    }
+
+    bool eqvs = (dot(direction1, direction2) > 0);
+    if ( are_near(ls2.initialPoint(), ls1) )
+    {
+        if ( are_near(ls1.initialPoint(), ls2.initialPoint()) && !eqvs )
+        {
+            crossing->ta = crossing->tb = 0;
+            return crossing;
+        }
+        else if ( are_near(ls1.finalPoint(), ls2.initialPoint()) && eqvs )
+        {
+            crossing->ta = 1;
+            crossing->tb = 0;
+            return crossing;
+        }
+        else
+        {
+            THROW_INFINITESOLUTIONS();
+        }
+    }
+    else if ( are_near(ls2.finalPoint(), ls1) )
+    {
+        if ( are_near(ls1.finalPoint(), ls2.finalPoint()) && !eqvs )
+        {
+            crossing->ta = crossing->tb = 1;
+            return crossing;
+        }
+        else if ( are_near(ls1.initialPoint(), ls2.finalPoint()) && eqvs )
+        {
+            crossing->ta = 0;
+            crossing->tb = 1;
+            return crossing;
+        }
+        else
+        {
+            THROW_INFINITESOLUTIONS();
+        }
+    }
+    else
+    {
+        OptCrossing no_crossing;
+        return no_crossing;
+    }
+}
+
+
+
+Line make_angle_bisector_line(Line const& l1, Line const& l2)
+{
+    OptCrossing crossing;
+    try
+    {
+        crossing = intersection(l1, l2);
+    }
+    catch(InfiniteSolutions e)
+    {
+        return l1;
+    }
+    if (!crossing)
+    {
+        THROW_RANGEERROR("passed lines are parallel");
+    }
+    Point O = l1.pointAt(crossing->ta);
+    Point A = l1.pointAt(crossing->ta + 1);
+    double angle = angle_between(l1.versor(), l2.versor());
+    Point B = (angle > 0) ? l2.pointAt(crossing->tb + 1)
+        : l2.pointAt(crossing->tb - 1);
+
+    return make_angle_bisector_line(A, O, B);
+}
+
+
+}  // end namespace Geom
+
+
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(substatement-open . 0))
+  indent-tabs-mode:nil
+  c-brace-offset:0
+  fill-column:99
+  End:
+  vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4 :
+*/

diff --git a/src/2geom/line.h b/src/2geom/line.h
new file mode 100644 (file)
index 0000000..e04c35c
--- /dev/null
+++ b/src/2geom/line.h
@@ -0,0 +1,445 @@
+/**
+ * \file
+ * \brief  Infinite Straight Line
+ *
+ * Copyright 2008  Marco Cecchetti <mrcekets at 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, 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_LINE_H_
+#define _2GEOM_LINE_H_
+
+
+#include <cmath>
+
+#include <2geom/bezier-curve.h> // for LineSegment
+#include <2geom/crossing.h>
+#include <2geom/exception.h>
+
+#include <2geom/ray.h>
+
+
+namespace Geom
+{
+
+class Line
+{
+  public:
+       Line()
+               : m_origin(0,0), m_versor(1,0)
+       {
+       }
+
+       Line(Point const& _origin, Coord angle )
+               : m_origin(_origin), m_versor(std::cos(angle), std::sin(angle))
+       {
+       }
+
+       Line(Point const& A, Point const& B)
+       {
+               setBy2Points(A, B);
+       }
+
+       explicit
+       Line(LineSegment const& _segment)
+       {
+               setBy2Points(_segment.initialPoint(), _segment.finalPoint());
+       }
+
+       explicit
+       Line(Ray const& _ray)
+               : m_origin(_ray.origin()), m_versor(_ray.versor())
+       {
+       }
+    
+    static Line fromNormalDistance(Point n, double c) {
+        Point P = n*c/(dot(n,n));
+    
+        return Line(P, P+rot90(n));
+    }
+
+       Line* duplicate() const
+       {
+               return new Line(*this);
+       }
+
+       Point origin() const
+       {
+               return m_origin;
+       }
+
+       Point versor() const
+       {
+               return m_versor;
+       }
+
+       void origin(Point const& _point)
+       {
+               m_origin = _point;
+       }
+
+       void versor(Point const& _versor)
+       {
+               m_versor = _versor;
+       }
+
+       // return the angle described by rotating the X-axis in cw direction
+       // until it overlaps the line
+       // the returned value is in the interval [0, PI[
+       Coord angle() const
+       {
+               double a = std::atan2(m_versor[Y], m_versor[X]);
+               if (a < 0) a += M_PI;
+               if (a == M_PI) a = 0;
+               return a;
+       }
+
+       void angle(Coord _angle)
+       {
+               m_versor[X] = std::cos(_angle);
+               m_versor[Y] = std::sin(_angle);
+       }
+
+       void setBy2Points(Point const& A, Point const& B)
+       {
+               m_origin = A;
+               m_versor = B - A;
+               if ( are_near(m_versor, Point(0,0)) )
+                       m_versor = Point(0,0);
+               else
+                       m_versor.normalize();
+       }
+
+       bool isDegenerate() const
+       {
+               return ( m_versor[X] == 0 && m_versor[Y] == 0 );
+       }
+
+       Point pointAt(Coord t) const
+       {
+               return m_origin + m_versor * t;
+       }
+
+       Coord valueAt(Coord t, Dim2 d) const
+       {
+               if (d < 0 || d > 1)
+                       THROW_RANGEERROR("Ray::valueAt, dimension argument out of range");
+               return m_origin[d] + m_versor[d] * t;
+       }
+
+       std::vector<Coord> roots(Coord v, Dim2 d) const
+       {
+               if (d < 0 || d > 1)
+                       THROW_RANGEERROR("Ray::roots, dimension argument out of range");
+               std::vector<Coord> result;
+               if ( m_versor[d] != 0 )
+               {
+                       result.push_back( (v - m_origin[d]) / m_versor[d] );
+               }
+               // TODO: else ?
+               return result;
+       }
+
+       // require are_near(_point, *this)
+       // on the contrary the result value is meaningless
+       Coord timeAt(Point const& _point) const
+       {
+               Coord t;
+               if ( m_versor[X] != 0 )
+               {
+                       t = (_point[X] - m_origin[X]) / m_versor[X];
+               }
+               else if ( m_versor[Y] != 0 )
+               {
+                       t = (_point[Y] - m_origin[Y]) / m_versor[Y];
+               }
+               else // degenerate case
+               {
+                       t = 0;
+               }
+               return t;
+       }
+
+       Coord timeAtProjection(Point const& _point) const
+       {
+               if ( isDegenerate() ) return 0;
+               return dot( _point - m_origin, m_versor );
+       }
+
+       Coord nearestPoint(Point const& _point) const
+       {
+               return timeAtProjection(_point);
+       }
+
+       Line reverse() const
+       {
+               Line result;
+               result.origin(m_origin);
+               result.versor(-m_versor);
+               return result;
+       }
+
+       Curve* portion(Coord  f, Coord t) const
+       {
+               LineSegment* seg = new LineSegment(pointAt(f), pointAt(t));
+               return seg;
+       }
+
+       LineSegment segment(Coord  f, Coord t) const
+       {
+               return LineSegment(pointAt(f), pointAt(t));
+       }
+
+       Ray ray(Coord t)
+       {
+               Ray result;
+               result.origin(pointAt(t));
+               result.versor(m_versor);
+               return result;
+       }
+
+       Line derivative() const
+       {
+               Line result;
+               result.origin(m_versor);
+               result.versor(Point(0,0));
+               return result;
+       }
+
+       Line transformed(Matrix const& m) const
+       {
+               return Line(m_origin * m, (m_origin + m_versor) * m);
+       }
+    
+    static Line from_normal_and_dist(Point const &n, double d) {
+        return Line(n*d, n*d + rot90(n));
+    }
+
+  private:
+       Point m_origin;
+       Point m_versor;
+
+}; // end class Line
+
+
+inline
+double distance(Point const& _point, Line const& _line)
+{
+       if ( _line.isDegenerate() )
+       {
+               return distance( _point, _line.origin() );
+       }
+       else
+       {
+               return fabs( dot(_point - _line.origin(), _line.versor().ccw()) );
+       }
+}
+
+inline
+bool are_near(Point const& _point, Line const& _line, double eps = EPSILON)
+{
+       return are_near(distance(_point, _line), 0, eps);
+}
+
+inline
+bool are_parallel(Line const& l1, Line const& l2, double eps = EPSILON)
+{
+       return ( are_near(l1.versor(), l2.versor(), eps)
+                        || are_near(l1.versor(), -l2.versor(), eps) );
+}
+
+inline
+bool are_same(Line const& l1, Line const& l2, double eps = EPSILON)
+{
+       return are_parallel(l1, l2, eps) && are_near(l1.origin(), l2, eps);
+}
+
+inline
+bool are_orthogonal(Line const& l1, Line const& l2, double eps = EPSILON)
+{
+       return ( are_near(l1.versor(), l2.versor().cw(), eps)
+                        || are_near(l1.versor(), l2.versor().ccw(), eps) );
+}
+
+inline
+bool are_collinear(Point const& p1, Point const& p2, Point const& p3,
+                          double eps = EPSILON)
+{
+       return are_near( cross(p3, p2) - cross(p3, p1) + cross(p2, p1), 0, eps);
+}
+
+// evaluate the angle between l1 and l2 rotating l1 in cw direction
+// until it overlaps l2
+// the returned value is an angle in the interval [0, PI[
+inline
+double angle_between(Line const& l1, Line const& l2)
+{
+       double angle = angle_between(l1.versor(), l2.versor());
+       if (angle < 0) angle += M_PI;
+       if (angle == M_PI) angle = 0;
+       return angle;
+}
+
+inline
+double distance(Point const& _point, LineSegment const& _segment)
+{
+    double t = _segment.nearestPoint(_point);
+    return L2(_point - _segment.pointAt(t));
+}
+
+inline
+bool are_near(Point const& _point, LineSegment const& _segment,
+                     double eps = EPSILON)
+{
+       return are_near(distance(_point, _segment), 0, eps);
+}
+
+// build a line passing by _point and orthogonal to _line
+inline
+Line make_orthogonal_line(Point const& _point, Line const& _line)
+{
+       Line l;
+       l.origin(_point);
+       l.versor(_line.versor().cw());
+       return l;
+}
+
+// build a line passing by _point and parallel to _line
+inline
+Line make_parallel_line(Point const& _point, Line const& _line)
+{
+       Line l(_line);
+       l.origin(_point);
+       return l;
+}
+
+// build a line passing by the middle point of _segment and orthogonal to it.
+inline
+Line make_bisector_line(LineSegment const& _segment)
+{
+       return make_orthogonal_line( middle_point(_segment), Line(_segment) );
+}
+
+// build the bisector line of the angle between ray(O,A) and ray(O,B)
+inline
+Line make_angle_bisector_line(Point const& A, Point const& O, Point const& B)
+{
+       Point M = middle_point(A,B);
+       return Line(O,M);
+}
+
+// prj(P) = rot(v, Point( rot(-v, P-O)[X], 0 )) + O
+inline
+Point projection(Point const& _point, Line const& _line)
+{
+       return _line.pointAt( _line.nearestPoint(_point) );
+}
+
+inline
+LineSegment projection(LineSegment const& _segment, Line const& _line)
+{
+       return _line.segment( _line.nearestPoint(_segment.initialPoint()),
+                                             _line.nearestPoint(_segment.finalPoint()) );
+}
+
+
+
+
+namespace detail
+{
+
+OptCrossing intersection_impl(Ray const& r1, Line const& l2, unsigned int i);
+OptCrossing intersection_impl( LineSegment const& ls1,
+                             Line const& l2,
+                             unsigned int i );
+OptCrossing intersection_impl( LineSegment const& ls1,
+                             Ray const& r2,
+                             unsigned int i );
+}
+
+
+inline
+OptCrossing intersection(Ray const& r1, Line const& l2)
+{
+    return detail::intersection_impl(r1,  l2, 0);
+
+}
+
+inline
+OptCrossing intersection(Line const& l1, Ray const& r2)
+{
+    return detail::intersection_impl(r2,  l1, 1);
+}
+
+inline
+OptCrossing intersection(LineSegment const& ls1, Line const& l2)
+{
+    return detail::intersection_impl(ls1,  l2, 0);
+}
+
+inline
+OptCrossing intersection(Line const& l1, LineSegment const& ls2)
+{
+    return detail::intersection_impl(ls2,  l1, 1);
+}
+
+inline
+OptCrossing intersection(LineSegment const& ls1, Ray const& r2)
+{
+    return detail::intersection_impl(ls1,  r2, 0);
+
+}
+
+inline
+OptCrossing intersection(Ray const& r1, LineSegment const& ls2)
+{
+    return detail::intersection_impl(ls2,  r1, 1);
+}
+
+
+OptCrossing intersection(Line const& l1, Line const& l2);
+
+OptCrossing intersection(Ray const& r1, Ray const& r2);
+
+OptCrossing intersection(LineSegment const& ls1, LineSegment const& ls2);
+
+
+} // end namespace Geom
+
+
+#endif // _2GEOM_LINE_H_
+
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(substatement-open . 0))
+  indent-tabs-mode:nil
+  c-brace-offset:0
+  fill-column:99
+  End:
+  vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4 :
+*/

diff --git a/src/2geom/ray.h b/src/2geom/ray.h
new file mode 100644 (file)
index 0000000..3156a94
--- /dev/null
+++ b/src/2geom/ray.h
@@ -0,0 +1,260 @@
+/**
+ * \file
+ * \brief  Infinite Straight Ray
+ *
+ * Copyright 2008  Marco Cecchetti <mrcekets at 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, 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_RAY_H_
+#define _2GEOM_RAY_H_
+
+#include <2geom/point.h>
+#include <2geom/bezier-curve.h> // for LineSegment
+#include <2geom/exception.h>
+
+#include <vector>
+
+
+namespace Geom
+{
+
+class Ray
+{
+public:
+       Ray()
+               : m_origin(0,0), m_versor(1,0)
+       {
+       }
+
+       Ray(Point const& _origin, Coord angle )
+               : m_origin(_origin), m_versor(std::cos(angle), std::sin(angle))
+       {
+       }
+
+       Ray(Point const& A, Point const& B)
+       {
+               setBy2Points(A, B);
+       }
+
+       Point origin() const
+       {
+               return m_origin;
+       }
+
+       Point versor() const
+       {
+               return m_versor;
+       }
+
+       void origin(Point const& _point)
+       {
+               m_origin = _point;
+       }
+
+       void versor(Point const& _versor)
+       {
+               m_versor = _versor;
+       }
+
+       Coord angle() const
+       {
+               double a = std::atan2(m_versor[Y], m_versor[X]);
+               if (a < 0) a += 2*M_PI;
+               return a;
+       }
+
+       void angle(Coord _angle)
+       {
+               m_versor[X] = std::cos(_angle);
+               m_versor[Y] = std::sin(_angle);
+       }
+
+       void setBy2Points(Point const& A, Point const& B)
+       {
+               m_origin = A;
+               m_versor = B - A;
+               if ( are_near(m_versor, Point(0,0)) )
+                       m_versor = Point(0,0);
+               else
+                       m_versor.normalize();
+       }
+
+       bool isDegenerate() const
+       {
+               return ( m_versor[X] == 0 && m_versor[Y] == 0 );
+       }
+
+       Point pointAt(Coord t) const
+       {
+               if (t < 0)      THROW_RANGEERROR("Ray::pointAt, negative t value passed");
+               return m_origin + m_versor * t;
+       }
+
+       Coord valueAt(Coord t, Dim2 d) const
+       {
+               if (t < 0)
+                       THROW_RANGEERROR("Ray::valueAt, negative t value passed");
+               if (d < 0 || d > 1)
+                       THROW_RANGEERROR("Ray::valueAt, dimension argument out of range");
+               return m_origin[d] + m_versor[d] * t;
+       }
+
+       std::vector<Coord> roots(Coord v, Dim2 d) const
+       {
+               if (d < 0 || d > 1)
+                       THROW_RANGEERROR("Ray::roots, dimension argument out of range");
+               std::vector<Coord> result;
+               if ( m_versor[d] != 0 )
+               {
+                       double t = (v - m_origin[d]) / m_versor[d];
+                       if (t >= 0)     result.push_back(t);
+               }
+               // TODO: else ?
+               return result;
+       }
+
+       // require are_near(_point, *this)
+       // on the contrary the result value is meaningless
+       Coord timeAt(Point const& _point) const
+       {
+               Coord t;
+               if ( m_versor[X] != 0 )
+               {
+                       t = (_point[X] - m_origin[X]) / m_versor[X];
+               }
+               else if ( m_versor[Y] != 0 )
+               {
+                       t = (_point[Y] - m_origin[Y]) / m_versor[Y];
+               }
+               else // degenerate case
+               {
+                       t = 0;
+               }
+               return t;
+       }
+
+       Coord nearestPoint(Point const& _point) const
+       {
+               if ( isDegenerate() ) return 0;
+               double t = dot( _point - m_origin, m_versor );
+               if (t < 0) t = 0;
+               return t;
+       }
+
+       Ray reverse() const
+       {
+               Ray result;
+               result.origin(m_origin);
+               result.versor(-m_versor);
+               return result;
+       }
+
+       Curve* portion(Coord  f, Coord t) const
+       {
+               LineSegment* seg = new LineSegment(pointAt(f), pointAt(t));
+               return seg;
+       }
+
+       LineSegment segment(Coord  f, Coord t) const
+       {
+               return LineSegment(pointAt(f), pointAt(t));
+       }
+
+       Ray transformed(Matrix const& m) const
+       {
+               return Ray(m_origin * m, (m_origin + m_versor) * m);
+       }
+
+private:
+       Point m_origin;
+       Point m_versor;
+
+};  // end class ray
+
+inline
+double distance(Point const& _point, Ray const& _ray)
+{
+       double t = _ray.nearestPoint(_point);
+       return distance(_point, _ray.pointAt(t));
+}
+
+inline
+bool are_near(Point const& _point, Ray const& _ray, double eps = EPSILON)
+{
+       return are_near(distance(_point, _ray), 0, eps);
+}
+
+inline
+bool are_same(Ray const& r1, Ray const& r2, double eps = EPSILON)
+{
+       return are_near(r1.versor(), r2.versor(), eps)
+                       && are_near(r1.origin(), r2.origin(), eps);
+}
+
+// evaluate the angle between r1 and r2 rotating r1 in cw or ccw direction on r2
+// the returned value is an angle in the interval [0, 2PI[
+inline
+double angle_between(Ray const& r1, Ray const& r2, bool cw = true)
+{
+       double angle = angle_between(r1.versor(), r2.versor());
+       if (angle < 0) angle += 2*M_PI;
+       if (!cw) angle = 2*M_PI - angle;
+       return angle;
+}
+
+
+inline
+Ray make_angle_bisector_ray(Ray const& r1, Ray const& r2)
+{
+    if ( !are_near(r1.origin(), r2.origin()) )
+    {
+        THROW_RANGEERROR("passed rays have not the same origin");
+    }
+
+    Point M = middle_point(r1.pointAt(1), r2.pointAt(1) );
+    if (angle_between(r1, r2) > M_PI)  M = 2 * r1.origin() - M;
+    return Ray(r1.origin(), M);
+}
+
+
+}  // end namespace Geom
+
+
+
+#endif /*_2GEOM_RAY_H_*/
+
+
+/*
+  Local Variables:
+  mode:c++
+  c-file-style:"stroustrup"
+  c-file-offsets:((innamespace . 0)(substatement-open . 0))
+  indent-tabs-mode:nil
+  c-brace-offset:0
+  fill-column:99
+  End:
+  vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4 :
+*/