/** * \file * \brief Elliptical arc curve * *//* * Authors: * MenTaLguY * Marco Cecchetti * Krzysztof Kosiński * * Copyright 2007-2009 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_ELLIPTICAL_ARC_H #define LIB2GEOM_SEEN_ELLIPTICAL_ARC_H #include #include <2geom/affine.h> #include <2geom/angle.h> #include <2geom/bezier-curve.h> #include <2geom/curve.h> #include <2geom/ellipse.h> #include <2geom/sbasis-curve.h> // for non-native methods #include <2geom/utils.h> namespace Geom { class EllipticalArc : public Curve { public: /** @brief Creates an arc with all variables set to zero. */ EllipticalArc() : _initial_point(0,0) , _final_point(0,0) , _large_arc(false) {} /** @brief Create a new elliptical arc. * @param ip Initial point of the arc * @param r Rays of the ellipse as a point * @param rot Angle of rotation of the X axis of the ellipse in radians * @param large If true, the large arc is chosen (always >= 180 degrees), otherwise * the smaller arc is chosen * @param sweep If true, the clockwise arc is chosen, otherwise the counter-clockwise * arc is chosen * @param fp Final point of the arc */ EllipticalArc( Point const &ip, Point const &r, Coord rot_angle, bool large_arc, bool sweep, Point const &fp ) : _initial_point(ip) , _final_point(fp) , _ellipse(0, 0, r[X], r[Y], rot_angle) , _angles(0, 0, sweep) , _large_arc(large_arc) { _updateCenterAndAngles(); } /// Create a new elliptical arc, giving the ellipse's rays as separate coordinates. EllipticalArc( Point const &ip, Coord rx, Coord ry, Coord rot_angle, bool large_arc, bool sweep, Point const &fp ) : _initial_point(ip) , _final_point(fp) , _ellipse(0, 0, rx, ry, rot_angle) , _angles(0, 0, sweep) , _large_arc(large_arc) { _updateCenterAndAngles(); } /// @name Retrieve basic information /// @{ /** @brief Get a coordinate of the elliptical arc's center. * @param d The dimension to retrieve * @return The selected coordinate of the center */ Coord center(Dim2 d) const { return _ellipse.center(d); } /** @brief Get the arc's center * @return The arc's center, situated on the intersection of the ellipse's rays */ Point center() const { return _ellipse.center(); } /** @brief Get one of the ellipse's rays * @param d Dimension to retrieve * @return The selected ray of the ellipse */ Coord ray(Dim2 d) const { return _ellipse.ray(d); } /** @brief Get both rays as a point * @return Point with X equal to the X ray and Y to Y ray */ Point rays() const { return _ellipse.rays(); } /** @brief Get the defining ellipse's rotation * @return Angle between the +X ray of the ellipse and the +X axis */ Angle rotationAngle() const { return _ellipse.rotationAngle(); } /** @brief Whether the arc is larger than half an ellipse. * @return True if the arc is larger than \f$\pi\f$, false otherwise */ bool largeArc() const { return _large_arc; } /** @brief Whether the arc turns clockwise * @return True if the arc makes a clockwise turn when going from initial to final * point, false otherwise */ bool sweep() const { return _angles.sweep(); } Angle initialAngle() const { return _angles.initialAngle(); } Angle finalAngle() const { return _angles.finalAngle(); } /// @} /// @name Modify parameters /// @{ /// Change all of the arc's parameters. void set( Point const &ip, double rx, double ry, double rot_angle, bool large_arc, bool sweep, Point const &fp ) { _initial_point = ip; _final_point = fp; _ellipse.setRays(rx, ry); _ellipse.setRotationAngle(rot_angle); _angles.setSweep(sweep); _large_arc = large_arc; _updateCenterAndAngles(); } /// Change all of the arc's parameters. void set( Point const &ip, Point const &r, Angle rot_angle, bool large_arc, bool sweep, Point const &fp ) { _initial_point = ip; _final_point = fp; _ellipse.setRays(r); _ellipse.setRotationAngle(rot_angle); _angles.setSweep(sweep); _large_arc = large_arc; _updateCenterAndAngles(); } /** @brief Change the initial and final point in one operation. * This method exists because modifying any of the endpoints causes rather costly * recalculations of the center and extreme angles. * @param ip New initial point * @param fp New final point */ void setEndpoints(Point const &ip, Point const &fp) { _initial_point = ip; _final_point = fp; _updateCenterAndAngles(); } /// @} /// @name Evaluate the arc as a function /// @{ /** Check whether the arc contains the given angle * @param t The angle to check * @return True if the arc contains the angle, false otherwise */ bool containsAngle(Angle angle) const { return _angles.contains(angle); } /** @brief Evaluate the arc at the specified angular coordinate * @param t Angle * @return Point corresponding to the given angle */ Point pointAtAngle(Coord t) const; /** @brief Evaluate one of the arc's coordinates at the specified angle * @param t Angle * @param d The dimension to retrieve * @return Selected coordinate of the arc at the specified angle */ Coord valueAtAngle(Coord t, Dim2 d) const; /// Compute the curve time value corresponding to the given angular value. Coord timeAtAngle(Angle a) const { return _angles.timeAtAngle(a); } /// Compute the angular domain value corresponding to the given time value. Angle angleAt(Coord t) const { return _angles.angleAt(t); } /** @brief Compute the amount by which the angle parameter changes going from start to end. * This has range \f$(-2\pi, 2\pi)\f$ and thus cannot be represented as instance * of the class Angle. Add this to the initial angle to obtain the final angle. */ Coord sweepAngle() const { return _angles.sweepAngle(); } /** @brief Get the elliptical angle spanned by the arc. * This is basically the absolute value of sweepAngle(). */ Coord angularExtent() const { return _angles.extent(); } /// Get the angular interval of the arc. AngleInterval angularInterval() const { return _angles; } /// Evaluate the arc in the curve domain, i.e. \f$[0, 1]\f$. Point pointAt(Coord t) const override; /// Evaluate a single coordinate on the arc in the curve domain. Coord valueAt(Coord t, Dim2 d) const override; /** @brief Compute a transform that maps the unit circle to the arc's ellipse. * Each ellipse can be interpreted as a translated, scaled and rotate unit circle. * This function returns the transform that maps the unit circle to the arc's ellipse. * @return Transform from unit circle to the arc's ellipse */ Affine unitCircleTransform() const { Affine result = _ellipse.unitCircleTransform(); return result; } /** @brief Compute a transform that maps the arc's ellipse to the unit circle. */ Affine inverseUnitCircleTransform() const { Affine result = _ellipse.inverseUnitCircleTransform(); return result; } /// @} /// @name Deal with degenerate ellipses. /// @{ /** @brief Check whether both rays are nonzero. * If they are not, the arc is represented as a line segment instead. */ bool isChord() const { return ray(X) == 0 || ray(Y) == 0; } /** @brief Get the line segment connecting the arc's endpoints. * @return A linear segment with initial and final point corresponding to those of the arc. */ LineSegment chord() const { return LineSegment(_initial_point, _final_point); } /// @} // implementation of overloads goes here Point initialPoint() const override { return _initial_point; } Point finalPoint() const override { return _final_point; } Curve* duplicate() const override { return new EllipticalArc(*this); } void setInitial(Point const &p) override { _initial_point = p; _updateCenterAndAngles(); } void setFinal(Point const &p) override { _final_point = p; _updateCenterAndAngles(); } bool isDegenerate() const override { return _initial_point == _final_point; } bool isLineSegment() const override { return isChord(); } Rect boundsFast() const override { return boundsExact(); } Rect boundsExact() const override; void expandToTransformed(Rect &bbox, Affine const &transform) const override; // TODO: native implementation of the following methods OptRect boundsLocal(OptInterval const &i, unsigned int deg) const override { return SBasisCurve(toSBasis()).boundsLocal(i, deg); } std::vector roots(double v, Dim2 d) const override; #ifdef HAVE_GSL std::vector allNearestTimes( Point const& p, double from = 0, double to = 1 ) const override; double nearestTime( Point const& p, double from = 0, double to = 1 ) const override { if ( are_near(ray(X), ray(Y)) && are_near(center(), p) ) { return from; } return allNearestTimes(p, from, to).front(); } #endif std::vector intersect(Curve const &other, Coord eps=EPSILON) const override; int degreesOfFreedom() const override { return 7; } Curve *derivative() const override; using Curve::operator*=; void operator*=(Translate const &tr) override; void operator*=(Scale const &s) override; void operator*=(Rotate const &r) override; void operator*=(Zoom const &z) override; void operator*=(Affine const &m) override; std::vector pointAndDerivatives(Coord t, unsigned int n) const override; D2 toSBasis() const override; Curve *portion(double f, double t) const override; Curve *reverse() const override; bool operator==(Curve const &c) const override; bool isNear(Curve const &other, Coord precision) const override; void feed(PathSink &sink, bool moveto_initial) const override; int winding(Point const &p) const override; private: void _updateCenterAndAngles(); std::vector _filterIntersections(std::vector &&xs, bool is_first) const; bool _validateIntersection(ShapeIntersection &xing, bool is_first) const; std::vector _intersectSameEllipse(EllipticalArc const *other) const; Point _initial_point, _final_point; Ellipse _ellipse; AngleInterval _angles; bool _large_arc; }; // end class EllipticalArc // implemented in elliptical-arc-from-sbasis.cpp /** @brief Fit an elliptical arc to an SBasis fragment. * @relates EllipticalArc */ bool arc_from_sbasis(EllipticalArc &ea, D2 const &in, double tolerance = EPSILON, unsigned num_samples = 20); /** @brief Debug output for elliptical arcs. * @relates EllipticalArc */ std::ostream &operator<<(std::ostream &out, EllipticalArc const &ea); } // end namespace Geom #endif // LIB2GEOM_SEEN_ELLIPTICAL_ARC_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 :