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+/**
+ *  \file
+ *  \brief Various trigoniometric helper functions
+ *//*
+ *  Authors:
+ *   Johan Engelen <goejendaagh@zonnet.nl>
+ *   Marco Cecchetti <mrcekets at gmail.com>
+ *   Krzysztof Kosiński <tweenk.pl@gmail.com>
+ *
+ * Copyright (C) 2007-2010 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 LIB2GEOM_SEEN_ANGLE_H
+#define LIB2GEOM_SEEN_ANGLE_H
+
+#include <cmath>
+#include <boost/operators.hpp>
+#include <2geom/exception.h>
+#include <2geom/coord.h>
+#include <2geom/point.h>
+
+namespace Geom {
+
+#ifndef M_PI
+# define M_PI 3.14159265358979323846
+#endif
+#ifndef M_1_2PI
+# define M_1_2PI 0.159154943091895335768883763373
+#endif
+
+/** @brief Wrapper for angular values.
+ *
+ * This class is a convenience wrapper that implements the behavior generally expected of angles,
+ * like addition modulo \f$2\pi\f$. The value returned from the default conversion
+ * to <tt>double</tt> is in the range \f$[-\pi, \pi)\f$ - the convention used by C's
+ * math library.
+ *
+ * This class holds only a single floating point value, so passing it by value will generally
+ * be faster than passing it by const reference.
+ *
+ * @ingroup Primitives
+ */
+class Angle
+    : boost::additive< Angle
+    , boost::additive< Angle, Coord
+    , boost::equality_comparable< Angle
+    , boost::equality_comparable< Angle, Coord
+      > > > >
+{
+public:
+    Angle() : _angle(0) {}
+    Angle(Coord v) : _angle(v) { _normalize(); } // this can be called implicitly
+    explicit Angle(Point const &p) : _angle(atan2(p)) { _normalize(); }
+    Angle(Point const &a, Point const &b) : _angle(angle_between(a, b)) { _normalize(); }
+    operator Coord() const { return radians(); }
+    Angle &operator+=(Angle o) {
+        _angle += o._angle;
+        _normalize();
+        return *this;
+    }
+    Angle &operator-=(Angle o) {
+        _angle -= o._angle;
+        _normalize();
+        return *this;
+    }
+    Angle &operator+=(Coord a) {
+        *this += Angle(a);
+        return *this;
+    }
+    Angle &operator-=(Coord a) {
+        *this -= Angle(a);
+        return *this;
+    }
+    bool operator==(Angle o) const {
+        return _angle == o._angle;
+    }
+    bool operator==(Coord c) const {
+        return _angle == Angle(c)._angle;
+    }
+
+    /** @brief Get the angle as radians.
+     * @return Number in range \f$[-\pi, \pi)\f$. */
+    Coord radians() const {
+        return _angle >= M_PI ? _angle - 2*M_PI : _angle;
+    }
+    /** @brief Get the angle as positive radians.
+     * @return Number in range \f$[0, 2\pi)\f$. */
+    Coord radians0() const {
+        return _angle;
+    }
+    /** @brief Get the angle as degrees in math convention.
+     * @return Number in range [-180, 180) obtained by scaling the result of radians()
+     *         by \f$180/\pi\f$. */
+    Coord degrees() const { return radians() * (180.0 / M_PI); }
+    /** @brief Get the angle as degrees in clock convention.
+     * This method converts the angle to the "clock convention": angles start from the +Y axis
+     * and grow clockwise. This means that 0 corresponds to \f$\pi/2\f$ radians,
+     * 90 to 0 radians, 180 to \f$-\pi/2\f$ radians, and 270 to \f$\pi\f$ radians.
+     * @return A number in the range [0, 360).
+     */
+    Coord degreesClock() const {
+        Coord ret = 90.0 - _angle * (180.0 / M_PI);
+        if (ret < 0) ret += 360;
+        return ret;
+    }
+    /** @brief Create an angle from its measure in radians. */
+    static Angle from_radians(Coord d) {
+        Angle a(d);
+        return a;
+    }
+    /** @brief Create an angle from its measure in degrees. */
+    static Angle from_degrees(Coord d) {
+        Angle a(d * (M_PI / 180.0));
+        return a;
+    }
+    /** @brief Create an angle from its measure in degrees in clock convention.
+     * @see Angle::degreesClock() */
+    static Angle from_degrees_clock(Coord d) {
+        // first make sure d is in [0, 360)
+        d = std::fmod(d, 360.0);
+        if (d < 0) d += 360.0;
+        Coord rad = M_PI/2 - d * (M_PI / 180.0);
+        if (rad < 0) rad += 2*M_PI;
+        Angle a;
+        a._angle = rad;
+        return a;
+    }
+private:
+
+    void _normalize() {
+        _angle = std::fmod(_angle, 2*M_PI);
+        if (_angle < 0) _angle += 2*M_PI;
+        //_angle -= floor(_angle * (1.0/(2*M_PI))) * 2*M_PI;
+    }
+    Coord _angle; // this is always in [0, 2pi)
+    friend class AngleInterval;
+};
+
+inline Angle distance(Angle const &a, Angle const &b) {
+    // the distance cannot be larger than M_PI.
+    Coord ac = a.radians0();
+    Coord bc = b.radians0();
+    Coord d = fabs(ac - bc);
+    return Angle(d > M_PI ? 2*M_PI - d : d);
+}
+
+/** @brief Directed angular interval.
+ *
+ * Wrapper for directed angles with defined start and end values. Useful e.g. for representing
+ * the portion of an ellipse in an elliptical arc. Both extreme angles are contained
+ * in the interval (it is a closed interval). Angular intervals can also be interptered
+ * as functions \f$f: [0, 1] \to [-\pi, \pi)\f$, which return the start angle for 0,
+ * the end angle for 1, and interpolate linearly for other values. Note that such functions
+ * are not continuous if the interval crosses the angle \f$\pi\f$.
+ *
+ * This class can represent all directed angular intervals, including empty ones.
+ * However, not all possible intervals can be created with the constructors.
+ * For full control, use the setInitial(), setFinal() and setAngles() methods.
+ *
+ * @ingroup Primitives
+ */
+class AngleInterval
+    : boost::equality_comparable< AngleInterval >
+{
+public:
+    AngleInterval() {}
+    /** @brief Create an angular interval from two angles and direction.
+     * If the initial and final angle are the same, a degenerate interval
+     * (containing only one angle) will be created.
+     * @param s Starting angle
+     * @param e Ending angle
+     * @param cw Which direction the interval goes. True means that it goes
+     *   in the direction of increasing angles, while false means in the direction
+     *   of decreasing angles. */
+    AngleInterval(Angle s, Angle e, bool cw = false)
+        : _start_angle(s), _end_angle(e), _sweep(cw), _full(false)
+    {}
+    AngleInterval(double s, double e, bool cw = false)
+        : _start_angle(s), _end_angle(e), _sweep(cw), _full(false)
+    {}
+    /** @brief Create an angular interval from three angles.
+     * If the inner angle is exactly equal to initial or final angle,
+     * the sweep flag will be set to true, i.e. the interval will go
+     * in the direction of increasing angles.
+     *
+     * If the initial and final angle are the same, but the inner angle
+     * is different, a full angle in the direction of increasing angles
+     * will be created.
+     *
+     * @param s Initial angle
+     * @param inner Angle contained in the interval
+     * @param e Final angle */
+    AngleInterval(Angle s, Angle inner, Angle e)
+        : _start_angle(s)
+        , _end_angle(e)
+        , _sweep((inner-s).radians0() <= (e-s).radians0())
+        , _full(s == e && s != inner)
+    {
+        if (_full) {
+            _sweep = true;
+        }
+    }
+
+    /// Get the start angle.
+    Angle initialAngle() const { return _start_angle; }
+    /// Get the end angle.
+    Angle finalAngle() const { return _end_angle; }
+    /// Check whether the interval goes in the direction of increasing angles.
+    bool sweep() const { return _sweep; }
+    /// Check whether the interval contains only a single angle.
+    bool isDegenerate() const {
+        return _start_angle == _end_angle && !_full;
+    }
+    /// Check whether the interval contains all angles.
+    bool isFull() const {
+        return _start_angle == _end_angle && _full;
+    }
+
+    /** @brief Set the initial angle.
+     * @param a Angle to set
+     * @param prefer_full Whether to set a full angular interval when
+     * the initial angle is set to the final angle */
+    void setInitial(Angle a, bool prefer_full = false) {
+        _start_angle = a;
+        _full = prefer_full && a == _end_angle;
+    }
+
+    /** @brief Set the final angle.
+     * @param a Angle to set
+     * @param prefer_full Whether to set a full angular interval when
+     * the initial angle is set to the final angle */
+    void setFinal(Angle a, bool prefer_full = false) {
+        _end_angle = a;
+        _full = prefer_full && a == _start_angle;
+    }
+    /** @brief Set both angles at once.
+     * The direction (sweep flag) is left unchanged.
+     * @param s Initial angle
+     * @param e Final angle
+     * @param prefer_full Whether to set a full interval when the passed
+     * initial and final angle are the same */
+    void setAngles(Angle s, Angle e, bool prefer_full = false) {
+        _start_angle = s;
+        _end_angle = e;
+        _full = prefer_full && s == e;
+    }
+    /// Set whether the interval goes in the direction of increasing angles.
+    void setSweep(bool s) { _sweep = s; }
+
+    /// Reverse the direction of the interval while keeping contained values the same.
+    void reverse() {
+        using std::swap;
+        swap(_start_angle, _end_angle);
+        _sweep = !_sweep;
+    }
+    /// Get a new interval with reversed direction.
+    AngleInterval reversed() const {
+        AngleInterval result(*this);
+        result.reverse();
+        return result;
+    }
+
+    /// Get an angle corresponding to the specified time value.
+    Angle angleAt(Coord t) const {
+        Coord span = extent();
+        Angle ret = _start_angle.radians0() + span * (_sweep ? t : -t);
+        return ret;
+    }
+    Angle operator()(Coord t) const { return angleAt(t); }
+
+    /** @brief Compute a time value that would evaluate to the given angle.
+     * If the start and end angle are exactly the same, NaN will be returned.
+     * Negative values will be returned for angles between the initial angle
+     * and the angle exactly opposite the midpoint of the interval. */
+    Coord timeAtAngle(Angle a) const {
+        if (_full) {
+            Angle ta = _sweep ? a - _start_angle : _start_angle - a;
+            return ta.radians0() / (2*M_PI);
+        }
+        Coord ex = extent();
+        Coord outex = 2*M_PI - ex;
+        if (_sweep) {
+            Angle midout = _start_angle - outex / 2;
+            Angle acmp = a - midout, scmp = _start_angle - midout;
+            if (acmp.radians0() >= scmp.radians0()) {
+                return (a - _start_angle).radians0() / ex;
+            } else {
+                return -(_start_angle - a).radians0() / ex;
+            }
+        } else {
+            Angle midout = _start_angle + outex / 2;
+            Angle acmp = a - midout, scmp = _start_angle - midout;
+            if (acmp.radians0() <= scmp.radians0()) {
+                return (_start_angle - a).radians0() / ex;
+            } else {
+                return -(a - _start_angle).radians0() / ex;
+            }
+        }
+    }
+
+    /// Check whether the interval includes the given angle.
+    bool contains(Angle a) const {
+        if (_full) return true;
+        Coord s = _start_angle.radians0();
+        Coord e = _end_angle.radians0();
+        Coord x = a.radians0();
+        if (_sweep) {
+            if (s < e) return x >= s && x <= e;
+            return x >= s || x <= e;
+        } else {
+            if (s > e) return x <= s && x >= e;
+            return x <= s || x >= e;
+        }
+    }
+    /** @brief Extent of the angle interval.
+     * Equivalent to the absolute value of the sweep angle.
+     * @return Extent in range \f$[0, 2\pi)\f$. */
+    Coord extent() const {
+        if (_full) return 2*M_PI;
+        return _sweep
+            ? (_end_angle - _start_angle).radians0()
+            : (_start_angle - _end_angle).radians0();
+    }
+    /** @brief Get the sweep angle of the interval.
+     * This is the value you need to add to the initial angle to get the final angle.
+     * It is positive when sweep is true. Denoted as \f$\Delta\theta\f$ in the SVG
+     * elliptical arc implementation notes. */
+    Coord sweepAngle() const {
+        if (_full) return _sweep ? 2*M_PI : -2*M_PI;
+        Coord sa = _end_angle.radians0() - _start_angle.radians0();
+        if (_sweep && sa < 0) sa += 2*M_PI;
+        if (!_sweep && sa > 0) sa -= 2*M_PI;
+        return sa;
+    }
+
+    /// Check another interval for equality.
+    bool operator==(AngleInterval const &other) const {
+        if (_start_angle != other._start_angle) return false;
+        if (_end_angle != other._end_angle) return false;
+        if (_sweep != other._sweep) return false;
+        if (_full != other._full) return false;
+        return true;
+    }
+
+    static AngleInterval create_full(Angle start, bool sweep = true) {
+        AngleInterval result;
+        result._start_angle = result._end_angle = start;
+        result._sweep = sweep;
+        result._full = true;
+        return result;
+    }
+
+private:
+    Angle _start_angle;
+    Angle _end_angle;
+    bool _sweep;
+    bool _full;
+};
+
+/** @brief Given an angle in degrees, return radians
+ * @relates Angle */
+inline Coord rad_from_deg(Coord deg) { return deg*M_PI/180.0;}
+/** @brief Given an angle in radians, return degrees
+ * @relates Angle */
+inline Coord deg_from_rad(Coord rad) { return rad*180.0/M_PI;}
+
+} // end namespace Geom
+
+namespace std {
+template <> class iterator_traits<Geom::Angle> {};
+}
+
+#endif // LIB2GEOM_SEEN_ANGLE_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:fileencoding=utf-8:textwidth=99 :