diff options
Diffstat (limited to 'src/2geom/ellipse.h')
| -rw-r--r-- | src/2geom/ellipse.h | 118 |
1 files changed, 105 insertions, 13 deletions
diff --git a/src/2geom/ellipse.h b/src/2geom/ellipse.h index a67969933..6fb5ed254 100644 --- a/src/2geom/ellipse.h +++ b/src/2geom/ellipse.h @@ -37,8 +37,10 @@ #include <vector> #include <2geom/angle.h> +#include <2geom/bezier-curve.h> #include <2geom/exception.h> -#include <2geom/point.h> +#include <2geom/forward.h> +#include <2geom/line.h> #include <2geom/transforms.h> namespace Geom { @@ -46,7 +48,14 @@ namespace Geom { class EllipticalArc; class Circle; -/** @brief Set of points with a constant sum of distances from two foci +/** @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 @@ -54,7 +63,8 @@ class Ellipse , boost::multipliable< Ellipse, Rotate , boost::multipliable< Ellipse, Zoom , boost::multipliable< Ellipse, Affine - > > > > > + , boost::equality_comparable< Ellipse + > > > > > > { Point _center; Point _rays; @@ -74,13 +84,16 @@ public: 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; @@ -88,31 +101,97 @@ public: _rays[Y] = ry; _angle = a; } - - // build an ellipse by its implicit equation: - // Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0 + /// Set an ellipse by solving its implicit equation. void setCoefficients(double A, double B, double C, double D, double E, double F); - - // biuld up the best fitting ellipse wrt the passed points - // prerequisite: at least 5 points must be passed - void fit(std::vector<Point> const& points); - - EllipticalArc *arc(Point const &ip, Point const &inner, Point const &fp, - bool svg_compliant = true); + /// 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; } + /** @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 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; + + /// 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; @@ -130,8 +209,21 @@ public: } 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 |