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Diffstat (limited to 'include/2geom/ellipse.h')
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diff --git a/include/2geom/ellipse.h b/include/2geom/ellipse.h new file mode 100644 index 0000000..0d1567a --- /dev/null +++ b/include/2geom/ellipse.h @@ -0,0 +1,260 @@ +/** @file + * @brief Ellipse shape + *//* + * Authors: + * Marco Cecchetti <mrcekets at gmail.com> + * Krzysztof Kosiński <tweenk.pl@gmail.com> + * + * Copyright 2008 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_ELLIPSE_H +#define LIB2GEOM_SEEN_ELLIPSE_H + +#include <vector> +#include <2geom/angle.h> +#include <2geom/bezier-curve.h> +#include <2geom/exception.h> +#include <2geom/forward.h> +#include <2geom/line.h> +#include <2geom/transforms.h> + +namespace Geom { + +class EllipticalArc; +class Circle; + +/** @brief Set of points with a constant sum of distances from two foci. + * + * An ellipse can be specified in several ways. Internally, 2Geom uses + * the SVG style representation: center, rays and angle between the +X ray + * and the +X axis. Another popular way is to use an implicit equation, + * which is as follows: + * \f$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\f$ + * + * @ingroup Shapes */ +class Ellipse + : boost::multipliable< Ellipse, Translate + , boost::multipliable< Ellipse, Scale + , boost::multipliable< Ellipse, Rotate + , boost::multipliable< Ellipse, Zoom + , boost::multipliable< Ellipse, Affine + , boost::equality_comparable< Ellipse + > > > > > > +{ + Point _center; + Point _rays; + Angle _angle; +public: + Ellipse() {} + Ellipse(Point const &c, Point const &r, Coord angle) + : _center(c) + , _rays(r) + , _angle(angle) + {} + Ellipse(Coord cx, Coord cy, Coord rx, Coord ry, Coord angle) + : _center(cx, cy) + , _rays(rx, ry) + , _angle(angle) + {} + Ellipse(double A, double B, double C, double D, double E, double F) { + setCoefficients(A, B, C, D, E, F); + } + /// Construct ellipse from a circle. + Ellipse(Geom::Circle const &c); + + /// Set center, rays and angle. + void set(Point const &c, Point const &r, Coord angle) { + _center = c; + _rays = r; + _angle = angle; + } + /// Set center, rays and angle as constituent values. + void set(Coord cx, Coord cy, Coord rx, Coord ry, Coord a) { + _center[X] = cx; + _center[Y] = cy; + _rays[X] = rx; + _rays[Y] = ry; + _angle = a; + } + /// Set an ellipse by solving its implicit equation. + void setCoefficients(double A, double B, double C, double D, double E, double F); + /// Set the center. + void setCenter(Point const &p) { _center = p; } + /// Set the center by coordinates. + void setCenter(Coord cx, Coord cy) { _center[X] = cx; _center[Y] = cy; } + /// Set both rays of the ellipse. + void setRays(Point const &p) { _rays = p; } + /// Set both rays of the ellipse as coordinates. + void setRays(Coord x, Coord y) { _rays[X] = x; _rays[Y] = y; } + /// Set one of the rays of the ellipse. + void setRay(Coord r, Dim2 d) { _rays[d] = r; } + /// Set the angle the X ray makes with the +X axis. + void setRotationAngle(Angle a) { _angle = a; } + + Point center() const { return _center; } + Coord center(Dim2 d) const { return _center[d]; } + /// Get both rays as a point. + Point rays() const { return _rays; } + /// Get one ray of the ellipse. + Coord ray(Dim2 d) const { return _rays[d]; } + /// Get the angle the X ray makes with the +X axis. + Angle rotationAngle() const { return _angle; } + /// Get the point corresponding to the +X ray of the ellipse. + Point initialPoint() const; + /// Get the point corresponding to the +X ray of the ellipse. + Point finalPoint() const { return initialPoint(); } + + /** @brief Create an ellipse passing through the specified points + * At least five points have to be specified. */ + void fit(std::vector<Point> const& points); + + /** @brief Create an elliptical arc from a section of the ellipse. + * This is mainly useful to determine the flags of the new arc. + * The passed points should lie on the ellipse, otherwise the results + * will be undefined. + * @param ip Initial point of the arc + * @param inner Point in the middle of the arc, used to pick one of two possibilities + * @param fp Final point of the arc + * @return Newly allocated arc, delete when no longer used */ + EllipticalArc *arc(Point const &ip, Point const &inner, Point const &fp); + + /** @brief Return an ellipse with less degrees of freedom. + * The canonical form always has the angle less than \f$\frac{\pi}{2}\f$, + * and zero if the rays are equal (i.e. the ellipse is a circle). */ + Ellipse canonicalForm() const; + void makeCanonical(); + + /** @brief Compute the transform that maps the unit circle to this 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 this ellipse. + * @return Transform from unit circle to the ellipse */ + Affine unitCircleTransform() const; + /** @brief Compute the transform that maps this ellipse to the unit circle. + * This may be a little more precise and/or faster than simply using + * unitCircleTransform().inverse(). An exception will be thrown for + * degenerate ellipses. */ + Affine inverseUnitCircleTransform() const; + + LineSegment majorAxis() const { return ray(X) >= ray(Y) ? axis(X) : axis(Y); } + LineSegment minorAxis() const { return ray(X) < ray(Y) ? axis(X) : axis(Y); } + LineSegment semimajorAxis(int sign = 1) const { + return ray(X) >= ray(Y) ? semiaxis(X, sign) : semiaxis(Y, sign); + } + LineSegment semiminorAxis(int sign = 1) const { + return ray(X) < ray(Y) ? semiaxis(X, sign) : semiaxis(Y, sign); + } + LineSegment axis(Dim2 d) const; + LineSegment semiaxis(Dim2 d, int sign = 1) const; + + /// Get the tight-fitting bounding box of the ellipse. + Rect boundsExact() const; + + /** @brief Get a fast to compute bounding box which contains the ellipse. + * + * The returned rectangle engulfs the ellipse but it may not be the smallest + * axis-aligned rectangle with this property. + */ + Rect boundsFast() const; + + /// Get the coefficients of the ellipse's implicit equation. + std::vector<double> coefficients() const; + void coefficients(Coord &A, Coord &B, Coord &C, Coord &D, Coord &E, Coord &F) const; + + /** @brief Evaluate a point on the ellipse. + * The parameter range is \f$[0, 2\pi)\f$; larger and smaller values + * wrap around. */ + Point pointAt(Coord t) const; + /// Evaluate a single coordinate of a point on the ellipse. + Coord valueAt(Coord t, Dim2 d) const; + + /** @brief Find the time value of a point on an ellipse. + * If the point is not on the ellipse, the returned time value will correspond + * to an intersection with a ray from the origin passing through the point + * with the ellipse. Note that this is NOT the nearest point on the ellipse. */ + Coord timeAt(Point const &p) const; + + /// Get the value of the derivative at time t normalized to unit length. + Point unitTangentAt(Coord t) const; + + /// Check whether the ellipse contains the given point. + bool contains(Point const &p) const; + + /// Compute intersections with an infinite line. + std::vector<ShapeIntersection> intersect(Line const &line) const; + /// Compute intersections with a line segment. + std::vector<ShapeIntersection> intersect(LineSegment const &seg) const; + /// Compute intersections with another ellipse. + std::vector<ShapeIntersection> intersect(Ellipse const &other) const; + /// Compute intersections with a 2D Bezier polynomial. + std::vector<ShapeIntersection> intersect(D2<Bezier> const &other) const; + + Ellipse &operator*=(Translate const &t) { + _center *= t; + return *this; + } + Ellipse &operator*=(Scale const &s) { + _center *= s; + _rays *= s; + return *this; + } + Ellipse &operator*=(Zoom const &z) { + _center *= z; + _rays *= z.scale(); + return *this; + } + Ellipse &operator*=(Rotate const &r); + Ellipse &operator*=(Affine const &m); + + /// Compare ellipses for exact equality. + bool operator==(Ellipse const &other) const; +}; + +/** @brief Test whether two ellipses are approximately the same. + * This will check whether no point on ellipse a is further away from + * the corresponding point on ellipse b than precision. + * @relates Ellipse */ +bool are_near(Ellipse const &a, Ellipse const &b, Coord precision = EPSILON); + +/** @brief Outputs ellipse data, useful for debugging. + * @relates Ellipse */ +std::ostream &operator<<(std::ostream &out, Ellipse const &e); + +} // end namespace Geom + +#endif // LIB2GEOM_SEEN_ELLIPSE_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 : |