| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /** @file | ||
| 2 | * @brief Ellipse shape | ||
| 3 | *//* | ||
| 4 | * Authors: | ||
| 5 | * Marco Cecchetti <mrcekets at gmail.com> | ||
| 6 | * Krzysztof Kosiński <tweenk.pl@gmail.com> | ||
| 7 | * | ||
| 8 | * Copyright 2008 authors | ||
| 9 | * | ||
| 10 | * This library is free software; you can redistribute it and/or | ||
| 11 | * modify it either under the terms of the GNU Lesser General Public | ||
| 12 | * License version 2.1 as published by the Free Software Foundation | ||
| 13 | * (the "LGPL") or, at your option, under the terms of the Mozilla | ||
| 14 | * Public License Version 1.1 (the "MPL"). If you do not alter this | ||
| 15 | * notice, a recipient may use your version of this file under either | ||
| 16 | * the MPL or the LGPL. | ||
| 17 | * | ||
| 18 | * You should have received a copy of the LGPL along with this library | ||
| 19 | * in the file COPYING-LGPL-2.1; if not, write to the Free Software | ||
| 20 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | ||
| 21 | * You should have received a copy of the MPL along with this library | ||
| 22 | * in the file COPYING-MPL-1.1 | ||
| 23 | * | ||
| 24 | * The contents of this file are subject to the Mozilla Public License | ||
| 25 | * Version 1.1 (the "License"); you may not use this file except in | ||
| 26 | * compliance with the License. You may obtain a copy of the License at | ||
| 27 | * http://www.mozilla.org/MPL/ | ||
| 28 | * | ||
| 29 | * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY | ||
| 30 | * OF ANY KIND, either express or implied. See the LGPL or the MPL for | ||
| 31 | * the specific language governing rights and limitations. | ||
| 32 | */ | ||
| 33 | |||
| 34 | |||
| 35 | #ifndef LIB2GEOM_SEEN_ELLIPSE_H | ||
| 36 | #define LIB2GEOM_SEEN_ELLIPSE_H | ||
| 37 | |||
| 38 | #include <vector> | ||
| 39 | #include <2geom/angle.h> | ||
| 40 | #include <2geom/bezier-curve.h> | ||
| 41 | #include <2geom/exception.h> | ||
| 42 | #include <2geom/forward.h> | ||
| 43 | #include <2geom/line.h> | ||
| 44 | #include <2geom/transforms.h> | ||
| 45 | |||
| 46 | namespace Geom { | ||
| 47 | |||
| 48 | class EllipticalArc; | ||
| 49 | class Circle; | ||
| 50 | |||
| 51 | /** @brief Set of points with a constant sum of distances from two foci. | ||
| 52 | * | ||
| 53 | * An ellipse can be specified in several ways. Internally, 2Geom uses | ||
| 54 | * the SVG style representation: center, rays and angle between the +X ray | ||
| 55 | * and the +X axis. Another popular way is to use an implicit equation, | ||
| 56 | * which is as follows: | ||
| 57 | * \f$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0\f$ | ||
| 58 | * | ||
| 59 | * @ingroup Shapes */ | ||
| 60 | class Ellipse | ||
| 61 | : boost::multipliable< Ellipse, Translate | ||
| 62 | , boost::multipliable< Ellipse, Scale | ||
| 63 | , boost::multipliable< Ellipse, Rotate | ||
| 64 | , boost::multipliable< Ellipse, Zoom | ||
| 65 | , boost::multipliable< Ellipse, Affine | ||
| 66 | , boost::equality_comparable< Ellipse | ||
| 67 | > > > > > > | ||
| 68 | { | ||
| 69 | Point _center; | ||
| 70 | Point _rays; | ||
| 71 | Angle _angle; | ||
| 72 | public: | ||
| 73 | 2 | Ellipse() {} | |
| 74 | Ellipse(Point const &c, Point const &r, Coord angle) | ||
| 75 | : _center(c) | ||
| 76 | , _rays(r) | ||
| 77 | , _angle(angle) | ||
| 78 | {} | ||
| 79 | 7 | Ellipse(Coord cx, Coord cy, Coord rx, Coord ry, Coord angle) | |
| 80 | 7 | : _center(cx, cy) | |
| 81 | 7 | , _rays(rx, ry) | |
| 82 | 7 | , _angle(angle) | |
| 83 | 7 | {} | |
| 84 | ✗ | Ellipse(double A, double B, double C, double D, double E, double F) { | |
| 85 | ✗ | setCoefficients(A, B, C, D, E, F); | |
| 86 | ✗ | } | |
| 87 | /// Construct ellipse from a circle. | ||
| 88 | Ellipse(Geom::Circle const &c); | ||
| 89 | |||
| 90 | /// Set center, rays and angle. | ||
| 91 | ✗ | void set(Point const &c, Point const &r, Coord angle) { | |
| 92 | ✗ | _center = c; | |
| 93 | ✗ | _rays = r; | |
| 94 | ✗ | _angle = angle; | |
| 95 | ✗ | } | |
| 96 | /// Set center, rays and angle as constituent values. | ||
| 97 | ✗ | void set(Coord cx, Coord cy, Coord rx, Coord ry, Coord a) { | |
| 98 | ✗ | _center[X] = cx; | |
| 99 | ✗ | _center[Y] = cy; | |
| 100 | ✗ | _rays[X] = rx; | |
| 101 | ✗ | _rays[Y] = ry; | |
| 102 | ✗ | _angle = a; | |
| 103 | ✗ | } | |
| 104 | /// Set an ellipse by solving its implicit equation. | ||
| 105 | void setCoefficients(double A, double B, double C, double D, double E, double F); | ||
| 106 | /// Set the center. | ||
| 107 | 11589 | void setCenter(Point const &p) { _center = p; } | |
| 108 | /// Set the center by coordinates. | ||
| 109 | 42 | void setCenter(Coord cx, Coord cy) { _center[X] = cx; _center[Y] = cy; } | |
| 110 | /// Set both rays of the ellipse. | ||
| 111 | 52 | void setRays(Point const &p) { _rays = p; } | |
| 112 | /// Set both rays of the ellipse as coordinates. | ||
| 113 | 11601 | void setRays(Coord x, Coord y) { _rays[X] = x; _rays[Y] = y; } | |
| 114 | /// Set one of the rays of the ellipse. | ||
| 115 | void setRay(Coord r, Dim2 d) { _rays[d] = r; } | ||
| 116 | /// Set the angle the X ray makes with the +X axis. | ||
| 117 | 1226 | void setRotationAngle(Angle a) { _angle = a; } | |
| 118 | |||
| 119 | 135468 | Point center() const { return _center; } | |
| 120 | 212968 | Coord center(Dim2 d) const { return _center[d]; } | |
| 121 | /// Get both rays as a point. | ||
| 122 | 10413 | Point rays() const { return _rays; } | |
| 123 | /// Get one ray of the ellipse. | ||
| 124 | 1810477 | Coord ray(Dim2 d) const { return _rays[d]; } | |
| 125 | /// Get the angle the X ray makes with the +X axis. | ||
| 126 | 20702 | Angle rotationAngle() const { return _angle; } | |
| 127 | /// Get the point corresponding to the +X ray of the ellipse. | ||
| 128 | Point initialPoint() const; | ||
| 129 | /// Get the point corresponding to the +X ray of the ellipse. | ||
| 130 | Point finalPoint() const { return initialPoint(); } | ||
| 131 | |||
| 132 | /** @brief Create an ellipse passing through the specified points | ||
| 133 | * At least five points have to be specified. */ | ||
| 134 | void fit(std::vector<Point> const& points); | ||
| 135 | |||
| 136 | /** @brief Create an elliptical arc from a section of the ellipse. | ||
| 137 | * This is mainly useful to determine the flags of the new arc. | ||
| 138 | * The passed points should lie on the ellipse, otherwise the results | ||
| 139 | * will be undefined. | ||
| 140 | * @param ip Initial point of the arc | ||
| 141 | * @param inner Point in the middle of the arc, used to pick one of two possibilities | ||
| 142 | * @param fp Final point of the arc | ||
| 143 | * @return Newly allocated arc, delete when no longer used */ | ||
| 144 | EllipticalArc *arc(Point const &ip, Point const &inner, Point const &fp); | ||
| 145 | |||
| 146 | /** @brief Return an ellipse with less degrees of freedom. | ||
| 147 | * The canonical form always has the angle less than \f$\frac{\pi}{2}\f$, | ||
| 148 | * and zero if the rays are equal (i.e. the ellipse is a circle). */ | ||
| 149 | Ellipse canonicalForm() const; | ||
| 150 | void makeCanonical(); | ||
| 151 | |||
| 152 | /** @brief Compute the transform that maps the unit circle to this ellipse. | ||
| 153 | * Each ellipse can be interpreted as a translated, scaled and rotate unit circle. | ||
| 154 | * This function returns the transform that maps the unit circle to this ellipse. | ||
| 155 | * @return Transform from unit circle to the ellipse */ | ||
| 156 | Affine unitCircleTransform() const; | ||
| 157 | /** @brief Compute the transform that maps this ellipse to the unit circle. | ||
| 158 | * This may be a little more precise and/or faster than simply using | ||
| 159 | * unitCircleTransform().inverse(). An exception will be thrown for | ||
| 160 | * degenerate ellipses. */ | ||
| 161 | Affine inverseUnitCircleTransform() const; | ||
| 162 | |||
| 163 |
2/2✓ Branch 2 taken 30000 times.
✓ Branch 3 taken 10000 times.
|
40000 | LineSegment majorAxis() const { return ray(X) >= ray(Y) ? axis(X) : axis(Y); } |
| 164 | LineSegment minorAxis() const { return ray(X) < ray(Y) ? axis(X) : axis(Y); } | ||
| 165 | LineSegment semimajorAxis(int sign = 1) const { | ||
| 166 | return ray(X) >= ray(Y) ? semiaxis(X, sign) : semiaxis(Y, sign); | ||
| 167 | } | ||
| 168 | LineSegment semiminorAxis(int sign = 1) const { | ||
| 169 | return ray(X) < ray(Y) ? semiaxis(X, sign) : semiaxis(Y, sign); | ||
| 170 | } | ||
| 171 | LineSegment axis(Dim2 d) const; | ||
| 172 | LineSegment semiaxis(Dim2 d, int sign = 1) const; | ||
| 173 | |||
| 174 | /// Get the tight-fitting bounding box of the ellipse. | ||
| 175 | Rect boundsExact() const; | ||
| 176 | |||
| 177 | /** @brief Get a fast to compute bounding box which contains the ellipse. | ||
| 178 | * | ||
| 179 | * The returned rectangle engulfs the ellipse but it may not be the smallest | ||
| 180 | * axis-aligned rectangle with this property. | ||
| 181 | */ | ||
| 182 | Rect boundsFast() const; | ||
| 183 | |||
| 184 | /// Get the coefficients of the ellipse's implicit equation. | ||
| 185 | std::vector<double> coefficients() const; | ||
| 186 | void coefficients(Coord &A, Coord &B, Coord &C, Coord &D, Coord &E, Coord &F) const; | ||
| 187 | |||
| 188 | /** @brief Evaluate a point on the ellipse. | ||
| 189 | * The parameter range is \f$[0, 2\pi)\f$; larger and smaller values | ||
| 190 | * wrap around. */ | ||
| 191 | Point pointAt(Coord t) const; | ||
| 192 | /// Evaluate a single coordinate of a point on the ellipse. | ||
| 193 | Coord valueAt(Coord t, Dim2 d) const; | ||
| 194 | |||
| 195 | /** @brief Find the time value of a point on an ellipse. | ||
| 196 | * If the point is not on the ellipse, the returned time value will correspond | ||
| 197 | * to an intersection with a ray from the origin passing through the point | ||
| 198 | * with the ellipse. Note that this is NOT the nearest point on the ellipse. */ | ||
| 199 | Coord timeAt(Point const &p) const; | ||
| 200 | |||
| 201 | /// Get the value of the derivative at time t normalized to unit length. | ||
| 202 | Point unitTangentAt(Coord t) const; | ||
| 203 | |||
| 204 | /// Check whether the ellipse contains the given point. | ||
| 205 | bool contains(Point const &p) const; | ||
| 206 | |||
| 207 | /// Compute intersections with an infinite line. | ||
| 208 | std::vector<ShapeIntersection> intersect(Line const &line) const; | ||
| 209 | /// Compute intersections with a line segment. | ||
| 210 | std::vector<ShapeIntersection> intersect(LineSegment const &seg) const; | ||
| 211 | /// Compute intersections with another ellipse. | ||
| 212 | std::vector<ShapeIntersection> intersect(Ellipse const &other) const; | ||
| 213 | /// Compute intersections with a 2D Bezier polynomial. | ||
| 214 | std::vector<ShapeIntersection> intersect(D2<Bezier> const &other) const; | ||
| 215 | |||
| 216 | ✗ | Ellipse &operator*=(Translate const &t) { | |
| 217 | ✗ | _center *= t; | |
| 218 | ✗ | return *this; | |
| 219 | } | ||
| 220 | 4 | Ellipse &operator*=(Scale const &s) { | |
| 221 | 4 | _center *= s; | |
| 222 | 4 | _rays *= s; | |
| 223 | 4 | return *this; | |
| 224 | } | ||
| 225 | ✗ | Ellipse &operator*=(Zoom const &z) { | |
| 226 | ✗ | _center *= z; | |
| 227 | ✗ | _rays *= z.scale(); | |
| 228 | ✗ | return *this; | |
| 229 | } | ||
| 230 | Ellipse &operator*=(Rotate const &r); | ||
| 231 | Ellipse &operator*=(Affine const &m); | ||
| 232 | |||
| 233 | /// Compare ellipses for exact equality. | ||
| 234 | bool operator==(Ellipse const &other) const; | ||
| 235 | }; | ||
| 236 | |||
| 237 | /** @brief Test whether two ellipses are approximately the same. | ||
| 238 | * This will check whether no point on ellipse a is further away from | ||
| 239 | * the corresponding point on ellipse b than precision. | ||
| 240 | * @relates Ellipse */ | ||
| 241 | bool are_near(Ellipse const &a, Ellipse const &b, Coord precision = EPSILON); | ||
| 242 | |||
| 243 | /** @brief Outputs ellipse data, useful for debugging. | ||
| 244 | * @relates Ellipse */ | ||
| 245 | std::ostream &operator<<(std::ostream &out, Ellipse const &e); | ||
| 246 | |||
| 247 | } // end namespace Geom | ||
| 248 | |||
| 249 | #endif // LIB2GEOM_SEEN_ELLIPSE_H | ||
| 250 | |||
| 251 | /* | ||
| 252 | Local Variables: | ||
| 253 | mode:c++ | ||
| 254 | c-file-style:"stroustrup" | ||
| 255 | c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +)) | ||
| 256 | indent-tabs-mode:nil | ||
| 257 | fill-column:99 | ||
| 258 | End: | ||
| 259 | */ | ||
| 260 | // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 : | ||
| 261 |