| /* QuadCurve2D.java -- represents a parameterized quadratic curve in 2-D space |
| Copyright (C) 2002, 2003, 2004 Free Software Foundation |
| |
| This file is part of GNU Classpath. |
| |
| GNU Classpath is free software; you can redistribute it and/or modify |
| it under the terms of the GNU General Public License as published by |
| the Free Software Foundation; either version 2, or (at your option) |
| any later version. |
| |
| GNU Classpath is distributed in the hope that it will be useful, but |
| WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| General Public License for more details. |
| |
| You should have received a copy of the GNU General Public License |
| along with GNU Classpath; see the file COPYING. If not, write to the |
| Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA |
| 02111-1307 USA. |
| |
| Linking this library statically or dynamically with other modules is |
| making a combined work based on this library. Thus, the terms and |
| conditions of the GNU General Public License cover the whole |
| combination. |
| |
| As a special exception, the copyright holders of this library give you |
| permission to link this library with independent modules to produce an |
| executable, regardless of the license terms of these independent |
| modules, and to copy and distribute the resulting executable under |
| terms of your choice, provided that you also meet, for each linked |
| independent module, the terms and conditions of the license of that |
| module. An independent module is a module which is not derived from |
| or based on this library. If you modify this library, you may extend |
| this exception to your version of the library, but you are not |
| obligated to do so. If you do not wish to do so, delete this |
| exception statement from your version. */ |
| |
| package java.awt.geom; |
| |
| import java.awt.Rectangle; |
| import java.awt.Shape; |
| import java.util.NoSuchElementException; |
| |
| /** |
| * A two-dimensional curve that is parameterized with a quadratic |
| * function. |
| * |
| * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180" |
| * alt="A drawing of a QuadCurve2D" /> |
| * |
| * @author Eric Blake (ebb9@email.byu.edu) |
| * @author Graydon Hoare (graydon@redhat.com) |
| * @author Sascha Brawer (brawer@dandelis.ch) |
| * @author Sven de Marothy (sven@physto.se) |
| * |
| * @since 1.2 |
| */ |
| public abstract class QuadCurve2D implements Shape, Cloneable |
| { |
| private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0; |
| private static final double EPSILON = 1E-10; |
| |
| /** |
| * Constructs a new QuadCurve2D. Typical users will want to |
| * construct instances of a subclass, such as {@link |
| * QuadCurve2D.Float} or {@link QuadCurve2D.Double}. |
| */ |
| protected QuadCurve2D() |
| { |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s start |
| * point. |
| */ |
| public abstract double getX1(); |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s start |
| * point. |
| */ |
| public abstract double getY1(); |
| |
| /** |
| * Returns the curve’s start point. |
| */ |
| public abstract Point2D getP1(); |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s control |
| * point. |
| */ |
| public abstract double getCtrlX(); |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s control |
| * point. |
| */ |
| public abstract double getCtrlY(); |
| |
| /** |
| * Returns the curve’s control point. |
| */ |
| public abstract Point2D getCtrlPt(); |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s end |
| * point. |
| */ |
| public abstract double getX2(); |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s end |
| * point. |
| */ |
| public abstract double getY2(); |
| |
| /** |
| * Returns the curve’s end point. |
| */ |
| public abstract Point2D getP2(); |
| |
| /** |
| * Changes the curve geometry, separately specifying each coordinate |
| * value. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s new start |
| * point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s new start |
| * point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s new end |
| * point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s new end |
| * point. |
| */ |
| public abstract void setCurve(double x1, double y1, double cx, double cy, |
| double x2, double y2); |
| |
| /** |
| * Changes the curve geometry, passing coordinate values in an |
| * array. |
| * |
| * @param coords an array containing the new coordinate values. The |
| * <i>x</i> coordinate of the new start point is located at |
| * <code>coords[offset]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the |
| * new control point is located at <code>coords[offset + 2]</code>, |
| * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The |
| * <i>x</i> coordinate of the new end point is located at |
| * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 5]</code>. |
| * |
| * @param offset the offset of the first coordinate value in |
| * <code>coords</code>. |
| */ |
| public void setCurve(double[] coords, int offset) |
| { |
| setCurve(coords[offset++], coords[offset++], coords[offset++], |
| coords[offset++], coords[offset++], coords[offset++]); |
| } |
| |
| /** |
| * Changes the curve geometry, specifying coordinate values in |
| * separate Point objects. |
| * |
| * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180" |
| * alt="A drawing of a QuadCurve2D" /> |
| * |
| * <p>The curve does not keep any reference to the passed point |
| * objects. Therefore, a later change to <code>p1</code>, |
| * <code>c</code> <code>p2</code> will not affect the curve |
| * geometry. |
| * |
| * @param p1 the new start point. |
| * @param c the new control point. |
| * @param p2 the new end point. |
| */ |
| public void setCurve(Point2D p1, Point2D c, Point2D p2) |
| { |
| setCurve(p1.getX(), p1.getY(), c.getX(), c.getY(), p2.getX(), p2.getY()); |
| } |
| |
| /** |
| * Changes the curve geometry, specifying coordinate values in an |
| * array of Point objects. |
| * |
| * <p><img src="doc-files/QuadCurve2D-1.png" width="350" height="180" |
| * alt="A drawing of a QuadCurve2D" /> |
| * |
| * <p>The curve does not keep references to the passed point |
| * objects. Therefore, a later change to the <code>pts</code> array |
| * or any of its elements will not affect the curve geometry. |
| * |
| * @param pts an array containing the points. The new start point |
| * is located at <code>pts[offset]</code>, the new control |
| * point at <code>pts[offset + 1]</code>, and the new end point |
| * at <code>pts[offset + 2]</code>. |
| * |
| * @param offset the offset of the start point in <code>pts</code>. |
| */ |
| public void setCurve(Point2D[] pts, int offset) |
| { |
| setCurve(pts[offset].getX(), pts[offset].getY(), pts[offset + 1].getX(), |
| pts[offset + 1].getY(), pts[offset + 2].getX(), |
| pts[offset + 2].getY()); |
| } |
| |
| /** |
| * Changes the geometry of the curve to that of another curve. |
| * |
| * @param c the curve whose coordinates will be copied. |
| */ |
| public void setCurve(QuadCurve2D c) |
| { |
| setCurve(c.getX1(), c.getY1(), c.getCtrlX(), c.getCtrlY(), c.getX2(), |
| c.getY2()); |
| } |
| |
| /** |
| * Calculates the squared flatness of a quadratic curve, directly |
| * specifying each coordinate value. The flatness is the distance of |
| * the control point to the line between start and end point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the square of the distance between C and the gray line, i.e. |
| * the squared length of the red line. |
| * |
| * @param x1 the <i>x</i> coordinate of the start point P1. |
| * @param y1 the <i>y</i> coordinate of the start point P1. |
| * @param cx the <i>x</i> coordinate of the control point C. |
| * @param cy the <i>y</i> coordinate of the control point C. |
| * @param x2 the <i>x</i> coordinate of the end point P2. |
| * @param y2 the <i>y</i> coordinate of the end point P2. |
| */ |
| public static double getFlatnessSq(double x1, double y1, double cx, |
| double cy, double x2, double y2) |
| { |
| return Line2D.ptSegDistSq(x1, y1, x2, y2, cx, cy); |
| } |
| |
| /** |
| * Calculates the flatness of a quadratic curve, directly specifying |
| * each coordinate value. The flatness is the distance of the |
| * control point to the line between start and end point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the distance between C and the gray line, i.e. the length of |
| * the red line. |
| * |
| * @param x1 the <i>x</i> coordinate of the start point P1. |
| * @param y1 the <i>y</i> coordinate of the start point P1. |
| * @param cx the <i>x</i> coordinate of the control point C. |
| * @param cy the <i>y</i> coordinate of the control point C. |
| * @param x2 the <i>x</i> coordinate of the end point P2. |
| * @param y2 the <i>y</i> coordinate of the end point P2. |
| */ |
| public static double getFlatness(double x1, double y1, double cx, double cy, |
| double x2, double y2) |
| { |
| return Line2D.ptSegDist(x1, y1, x2, y2, cx, cy); |
| } |
| |
| /** |
| * Calculates the squared flatness of a quadratic curve, specifying |
| * the coordinate values in an array. The flatness is the distance |
| * of the control point to the line between start and end point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the square of the distance between C and the gray line, i.e. |
| * the squared length of the red line. |
| * |
| * @param coords an array containing the coordinate values. The |
| * <i>x</i> coordinate of the start point P1 is located at |
| * <code>coords[offset]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the |
| * control point C is located at <code>coords[offset + 2]</code>, |
| * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The |
| * <i>x</i> coordinate of the end point P2 is located at |
| * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 5]</code>. |
| * |
| * @param offset the offset of the first coordinate value in |
| * <code>coords</code>. |
| */ |
| public static double getFlatnessSq(double[] coords, int offset) |
| { |
| return Line2D.ptSegDistSq(coords[offset], coords[offset + 1], |
| coords[offset + 4], coords[offset + 5], |
| coords[offset + 2], coords[offset + 3]); |
| } |
| |
| /** |
| * Calculates the flatness of a quadratic curve, specifying the |
| * coordinate values in an array. The flatness is the distance of |
| * the control point to the line between start and end point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the the distance between C and the gray line, i.e. the length of |
| * the red line. |
| * |
| * @param coords an array containing the coordinate values. The |
| * <i>x</i> coordinate of the start point P1 is located at |
| * <code>coords[offset]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the |
| * control point C is located at <code>coords[offset + 2]</code>, |
| * its <i>y</i> coordinate at <code>coords[offset + 3]</code>. The |
| * <i>x</i> coordinate of the end point P2 is located at |
| * <code>coords[offset + 4]</code>, its <i>y</i> coordinate at |
| * <code>coords[offset + 5]</code>. |
| * |
| * @param offset the offset of the first coordinate value in |
| * <code>coords</code>. |
| */ |
| public static double getFlatness(double[] coords, int offset) |
| { |
| return Line2D.ptSegDist(coords[offset], coords[offset + 1], |
| coords[offset + 4], coords[offset + 5], |
| coords[offset + 2], coords[offset + 3]); |
| } |
| |
| /** |
| * Calculates the squared flatness of this curve. The flatness is |
| * the distance of the control point to the line between start and |
| * end point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the square of the distance between C and the gray line, i.e. the |
| * squared length of the red line. |
| */ |
| public double getFlatnessSq() |
| { |
| return Line2D.ptSegDistSq(getX1(), getY1(), getX2(), getY2(), getCtrlX(), |
| getCtrlY()); |
| } |
| |
| /** |
| * Calculates the flatness of this curve. The flatness is the |
| * distance of the control point to the line between start and end |
| * point. |
| * |
| * <p><img src="doc-files/QuadCurve2D-4.png" width="350" height="180" |
| * alt="A drawing that illustrates the flatness" /> |
| * |
| * <p>In the above drawing, the straight line connecting start point |
| * P1 and end point P2 is depicted in gray. The result will be the |
| * the distance between C and the gray line, i.e. the length of the |
| * red line. |
| */ |
| public double getFlatness() |
| { |
| return Line2D.ptSegDist(getX1(), getY1(), getX2(), getY2(), getCtrlX(), |
| getCtrlY()); |
| } |
| |
| /** |
| * Subdivides this curve into two halves. |
| * |
| * <p><img src="doc-files/QuadCurve2D-3.png" width="700" |
| * height="180" alt="A drawing that illustrates the effects of |
| * subdividing a QuadCurve2D" /> |
| * |
| * @param left a curve whose geometry will be set to the left half |
| * of this curve, or <code>null</code> if the caller is not |
| * interested in the left half. |
| * |
| * @param right a curve whose geometry will be set to the right half |
| * of this curve, or <code>null</code> if the caller is not |
| * interested in the right half. |
| */ |
| public void subdivide(QuadCurve2D left, QuadCurve2D right) |
| { |
| // Use empty slots at end to share single array. |
| double[] d = new double[] |
| { |
| getX1(), getY1(), getCtrlX(), getCtrlY(), getX2(), getY2(), |
| 0, 0, 0, 0 |
| }; |
| subdivide(d, 0, d, 0, d, 4); |
| if (left != null) |
| left.setCurve(d, 0); |
| if (right != null) |
| right.setCurve(d, 4); |
| } |
| |
| /** |
| * Subdivides a quadratic curve into two halves. |
| * |
| * <p><img src="doc-files/QuadCurve2D-3.png" width="700" |
| * height="180" alt="A drawing that illustrates the effects of |
| * subdividing a QuadCurve2D" /> |
| * |
| * @param src the curve to be subdivided. |
| * |
| * @param left a curve whose geometry will be set to the left half |
| * of <code>src</code>, or <code>null</code> if the caller is not |
| * interested in the left half. |
| * |
| * @param right a curve whose geometry will be set to the right half |
| * of <code>src</code>, or <code>null</code> if the caller is not |
| * interested in the right half. |
| */ |
| public static void subdivide(QuadCurve2D src, QuadCurve2D left, |
| QuadCurve2D right) |
| { |
| src.subdivide(left, right); |
| } |
| |
| /** |
| * Subdivides a quadratic curve into two halves, passing all |
| * coordinates in an array. |
| * |
| * <p><img src="doc-files/QuadCurve2D-3.png" width="700" |
| * height="180" alt="A drawing that illustrates the effects of |
| * subdividing a QuadCurve2D" /> |
| * |
| * <p>The left end point and the right start point will always be |
| * identical. Memory-concious programmers thus may want to pass the |
| * same array for both <code>left</code> and <code>right</code>, and |
| * set <code>rightOff</code> to <code>leftOff + 4</code>. |
| * |
| * @param src an array containing the coordinates of the curve to be |
| * subdivided. The <i>x</i> coordinate of the start point is |
| * located at <code>src[srcOff]</code>, its <i>y</i> at |
| * <code>src[srcOff + 1]</code>. The <i>x</i> coordinate of the |
| * control point is located at <code>src[srcOff + 2]</code>, its |
| * <i>y</i> at <code>src[srcOff + 3]</code>. The <i>x</i> |
| * coordinate of the end point is located at <code>src[srcOff + |
| * 4]</code>, its <i>y</i> at <code>src[srcOff + 5]</code>. |
| * |
| * @param srcOff an offset into <code>src</code>, specifying |
| * the index of the start point’s <i>x</i> coordinate. |
| * |
| * @param left an array that will receive the coordinates of the |
| * left half of <code>src</code>. It is acceptable to pass |
| * <code>src</code>. A caller who is not interested in the left half |
| * can pass <code>null</code>. |
| * |
| * @param leftOff an offset into <code>left</code>, specifying the |
| * index where the start point’s <i>x</i> coordinate will be |
| * stored. |
| * |
| * @param right an array that will receive the coordinates of the |
| * right half of <code>src</code>. It is acceptable to pass |
| * <code>src</code> or <code>left</code>. A caller who is not |
| * interested in the right half can pass <code>null</code>. |
| * |
| * @param rightOff an offset into <code>right</code>, specifying the |
| * index where the start point’s <i>x</i> coordinate will be |
| * stored. |
| */ |
| public static void subdivide(double[] src, int srcOff, double[] left, |
| int leftOff, double[] right, int rightOff) |
| { |
| double x1; |
| double y1; |
| double xc; |
| double yc; |
| double x2; |
| double y2; |
| |
| x1 = src[srcOff]; |
| y1 = src[srcOff + 1]; |
| xc = src[srcOff + 2]; |
| yc = src[srcOff + 3]; |
| x2 = src[srcOff + 4]; |
| y2 = src[srcOff + 5]; |
| |
| if (left != null) |
| { |
| left[leftOff] = x1; |
| left[leftOff + 1] = y1; |
| } |
| |
| if (right != null) |
| { |
| right[rightOff + 4] = x2; |
| right[rightOff + 5] = y2; |
| } |
| |
| x1 = (x1 + xc) / 2; |
| x2 = (xc + x2) / 2; |
| xc = (x1 + x2) / 2; |
| y1 = (y1 + yc) / 2; |
| y2 = (y2 + yc) / 2; |
| yc = (y1 + y2) / 2; |
| |
| if (left != null) |
| { |
| left[leftOff + 2] = x1; |
| left[leftOff + 3] = y1; |
| left[leftOff + 4] = xc; |
| left[leftOff + 5] = yc; |
| } |
| |
| if (right != null) |
| { |
| right[rightOff] = xc; |
| right[rightOff + 1] = yc; |
| right[rightOff + 2] = x2; |
| right[rightOff + 3] = y2; |
| } |
| } |
| |
| /** |
| * Finds the non-complex roots of a quadratic equation, placing the |
| * results into the same array as the equation coefficients. The |
| * following equation is being solved: |
| * |
| * <blockquote><code>eqn[2]</code> · <i>x</i><sup>2</sup> |
| * + <code>eqn[1]</code> · <i>x</i> |
| * + <code>eqn[0]</code> |
| * = 0 |
| * </blockquote> |
| * |
| * <p>For some background about solving quadratic equations, see the |
| * article <a href= |
| * "http://planetmath.org/encyclopedia/QuadraticFormula.html" |
| * >“Quadratic Formula”</a> in <a href= |
| * "http://planetmath.org/">PlanetMath</a>. For an extensive library |
| * of numerical algorithms written in the C programming language, |
| * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific |
| * Library</a>. |
| * |
| * @see #solveQuadratic(double[], double[]) |
| * @see CubicCurve2D#solveCubic(double[], double[]) |
| * |
| * @param eqn an array with the coefficients of the equation. When |
| * this procedure has returned, <code>eqn</code> will contain the |
| * non-complex solutions of the equation, in no particular order. |
| * |
| * @return the number of non-complex solutions. A result of 0 |
| * indicates that the equation has no non-complex solutions. A |
| * result of -1 indicates that the equation is constant (i.e., |
| * always or never zero). |
| * |
| * @author Brain Gouph (bjg@network-theory.com) |
| * (original C implementation in the <a href= |
| * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>) |
| * |
| * @author Sascha Brawer (brawer@dandelis.ch) |
| * (adaptation to Java) |
| */ |
| public static int solveQuadratic(double[] eqn) |
| { |
| return solveQuadratic(eqn, eqn); |
| } |
| |
| /** |
| * Finds the non-complex roots of a quadratic equation. The |
| * following equation is being solved: |
| * |
| * <blockquote><code>eqn[2]</code> · <i>x</i><sup>2</sup> |
| * + <code>eqn[1]</code> · <i>x</i> |
| * + <code>eqn[0]</code> |
| * = 0 |
| * </blockquote> |
| * |
| * <p>For some background about solving quadratic equations, see the |
| * article <a href= |
| * "http://planetmath.org/encyclopedia/QuadraticFormula.html" |
| * >“Quadratic Formula”</a> in <a href= |
| * "http://planetmath.org/">PlanetMath</a>. For an extensive library |
| * of numerical algorithms written in the C programming language, |
| * see the <a href="http://www.gnu.org/software/gsl/">GNU Scientific |
| * Library</a>. |
| * |
| * @see CubicCurve2D#solveCubic(double[],double[]) |
| * |
| * @param eqn an array with the coefficients of the equation. |
| * |
| * @param res an array into which the non-complex roots will be |
| * stored. The results may be in an arbitrary order. It is safe to |
| * pass the same array object reference for both <code>eqn</code> |
| * and <code>res</code>. |
| * |
| * @return the number of non-complex solutions. A result of 0 |
| * indicates that the equation has no non-complex solutions. A |
| * result of -1 indicates that the equation is constant (i.e., |
| * always or never zero). |
| * |
| * @author Brian Gouph (bjg@network-theory.com) |
| * (original C implementation in the <a href= |
| * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>) |
| * |
| * @author Sascha Brawer (brawer@dandelis.ch) |
| * (adaptation to Java) |
| */ |
| public static int solveQuadratic(double[] eqn, double[] res) |
| { |
| // Taken from poly/solve_quadratic.c in the GNU Scientific Library |
| // (GSL), cvs revision 1.7 of 2003-07-26. For the original source, |
| // see http://www.gnu.org/software/gsl/ |
| // |
| // Brian Gough, the author of that code, has granted the |
| // permission to use it in GNU Classpath under the GNU Classpath |
| // license, and has assigned the copyright to the Free Software |
| // Foundation. |
| // |
| // The Java implementation is very similar to the GSL code, but |
| // not a strict one-to-one copy. For example, GSL would sort the |
| // result. |
| double a; |
| double b; |
| double c; |
| double disc; |
| |
| c = eqn[0]; |
| b = eqn[1]; |
| a = eqn[2]; |
| |
| // Check for linear or constant functions. This is not done by the |
| // GNU Scientific Library. Without this special check, we |
| // wouldn't return -1 for constant functions, and 2 instead of 1 |
| // for linear functions. |
| if (a == 0) |
| { |
| if (b == 0) |
| return -1; |
| |
| res[0] = -c / b; |
| return 1; |
| } |
| |
| disc = b * b - 4 * a * c; |
| |
| if (disc < 0) |
| return 0; |
| |
| if (disc == 0) |
| { |
| // The GNU Scientific Library returns two identical results here. |
| // We just return one. |
| res[0] = -0.5 * b / a; |
| return 1; |
| } |
| |
| // disc > 0 |
| if (b == 0) |
| { |
| double r; |
| |
| r = Math.abs(0.5 * Math.sqrt(disc) / a); |
| res[0] = -r; |
| res[1] = r; |
| } |
| else |
| { |
| double sgnb; |
| double temp; |
| |
| sgnb = (b > 0 ? 1 : -1); |
| temp = -0.5 * (b + sgnb * Math.sqrt(disc)); |
| |
| // The GNU Scientific Library sorts the result here. We don't. |
| res[0] = temp / a; |
| res[1] = c / temp; |
| } |
| return 2; |
| } |
| |
| /** |
| * Determines whether a point is inside the area bounded |
| * by the curve and the straight line connecting its end points. |
| * |
| * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180" |
| * alt="A drawing of the area spanned by the curve" /> |
| * |
| * <p>The above drawing illustrates in which area points are |
| * considered “inside” a QuadCurve2D. |
| */ |
| public boolean contains(double x, double y) |
| { |
| if (! getBounds2D().contains(x, y)) |
| return false; |
| |
| return ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0); |
| } |
| |
| /** |
| * Determines whether a point is inside the area bounded |
| * by the curve and the straight line connecting its end points. |
| * |
| * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180" |
| * alt="A drawing of the area spanned by the curve" /> |
| * |
| * <p>The above drawing illustrates in which area points are |
| * considered “inside” a QuadCurve2D. |
| */ |
| public boolean contains(Point2D p) |
| { |
| return contains(p.getX(), p.getY()); |
| } |
| |
| /** |
| * Determines whether any part of a rectangle is inside the area bounded |
| * by the curve and the straight line connecting its end points. |
| * |
| * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180" |
| * alt="A drawing of the area spanned by the curve" /> |
| * |
| * <p>The above drawing illustrates in which area points are |
| * considered “inside” in a CubicCurve2D. |
| */ |
| public boolean intersects(double x, double y, double w, double h) |
| { |
| if (! getBounds2D().contains(x, y, w, h)) |
| return false; |
| |
| /* Does any edge intersect? */ |
| if (getAxisIntersections(x, y, true, w) != 0 /* top */ |
| || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */ |
| || getAxisIntersections(x + w, y, false, h) != 0 /* right */ |
| || getAxisIntersections(x, y, false, h) != 0) /* left */ |
| return true; |
| |
| /* No intersections, is any point inside? */ |
| if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0) |
| return true; |
| |
| return false; |
| } |
| |
| /** |
| * Determines whether any part of a Rectangle2D is inside the area bounded |
| * by the curve and the straight line connecting its end points. |
| * @see #intersects(double, double, double, double) |
| */ |
| public boolean intersects(Rectangle2D r) |
| { |
| return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight()); |
| } |
| |
| /** |
| * Determines whether a rectangle is entirely inside the area bounded |
| * by the curve and the straight line connecting its end points. |
| * |
| * <p><img src="doc-files/QuadCurve2D-5.png" width="350" height="180" |
| * alt="A drawing of the area spanned by the curve" /> |
| * |
| * <p>The above drawing illustrates in which area points are |
| * considered “inside” a QuadCurve2D. |
| * @see #contains(double, double) |
| */ |
| public boolean contains(double x, double y, double w, double h) |
| { |
| if (! getBounds2D().intersects(x, y, w, h)) |
| return false; |
| |
| /* Does any edge intersect? */ |
| if (getAxisIntersections(x, y, true, w) != 0 /* top */ |
| || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */ |
| || getAxisIntersections(x + w, y, false, h) != 0 /* right */ |
| || getAxisIntersections(x, y, false, h) != 0) /* left */ |
| return false; |
| |
| /* No intersections, is any point inside? */ |
| if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0) |
| return true; |
| |
| return false; |
| } |
| |
| /** |
| * Determines whether a Rectangle2D is entirely inside the area that is |
| * bounded by the curve and the straight line connecting its end points. |
| * @see #contains(double, double, double, double) |
| */ |
| public boolean contains(Rectangle2D r) |
| { |
| return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); |
| } |
| |
| /** |
| * Determines the smallest rectangle that encloses the |
| * curve’s start, end and control point. As the illustration |
| * below shows, the invisible control point may cause the bounds to |
| * be much larger than the area that is actually covered by the |
| * curve. |
| * |
| * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180" |
| * alt="An illustration of the bounds of a QuadCurve2D" /> |
| */ |
| public Rectangle getBounds() |
| { |
| return getBounds2D().getBounds(); |
| } |
| |
| public PathIterator getPathIterator(final AffineTransform at) |
| { |
| return new PathIterator() |
| { |
| /** Current coordinate. */ |
| private int current = 0; |
| |
| public int getWindingRule() |
| { |
| return WIND_NON_ZERO; |
| } |
| |
| public boolean isDone() |
| { |
| return current >= 2; |
| } |
| |
| public void next() |
| { |
| current++; |
| } |
| |
| public int currentSegment(float[] coords) |
| { |
| int result; |
| switch (current) |
| { |
| case 0: |
| coords[0] = (float) getX1(); |
| coords[1] = (float) getY1(); |
| result = SEG_MOVETO; |
| break; |
| case 1: |
| coords[0] = (float) getCtrlX(); |
| coords[1] = (float) getCtrlY(); |
| coords[2] = (float) getX2(); |
| coords[3] = (float) getY2(); |
| result = SEG_QUADTO; |
| break; |
| default: |
| throw new NoSuchElementException("quad iterator out of bounds"); |
| } |
| if (at != null) |
| at.transform(coords, 0, coords, 0, 2); |
| return result; |
| } |
| |
| public int currentSegment(double[] coords) |
| { |
| int result; |
| switch (current) |
| { |
| case 0: |
| coords[0] = getX1(); |
| coords[1] = getY1(); |
| result = SEG_MOVETO; |
| break; |
| case 1: |
| coords[0] = getCtrlX(); |
| coords[1] = getCtrlY(); |
| coords[2] = getX2(); |
| coords[3] = getY2(); |
| result = SEG_QUADTO; |
| break; |
| default: |
| throw new NoSuchElementException("quad iterator out of bounds"); |
| } |
| if (at != null) |
| at.transform(coords, 0, coords, 0, 2); |
| return result; |
| } |
| }; |
| } |
| |
| public PathIterator getPathIterator(AffineTransform at, double flatness) |
| { |
| return new FlatteningPathIterator(getPathIterator(at), flatness); |
| } |
| |
| /** |
| * Creates a new curve with the same contents as this one. |
| * |
| * @return the clone. |
| */ |
| public Object clone() |
| { |
| try |
| { |
| return super.clone(); |
| } |
| catch (CloneNotSupportedException e) |
| { |
| throw (Error) new InternalError().initCause(e); // Impossible |
| } |
| } |
| |
| /** |
| * Helper method used by contains() and intersects() methods |
| * Return the number of curve/line intersections on a given axis |
| * extending from a certain point. useYaxis is true for using the Y axis, |
| * @param x x coordinate of the origin point |
| * @param y y coordinate of the origin point |
| * @param useYaxis axis to follow, if true the positive Y axis is used, |
| * false uses the positive X axis. |
| * |
| * This is an implementation of the line-crossings algorithm, |
| * Detailed in an article on Eric Haines' page: |
| * http://www.acm.org/tog/editors/erich/ptinpoly/ |
| */ |
| private int getAxisIntersections(double x, double y, boolean useYaxis, |
| double distance) |
| { |
| int nCrossings = 0; |
| double a0; |
| double a1; |
| double a2; |
| double b0; |
| double b1; |
| double b2; |
| double[] r = new double[3]; |
| int nRoots; |
| |
| a0 = a2 = 0.0; |
| |
| if (useYaxis) |
| { |
| a0 = getY1() - y; |
| a1 = getCtrlY() - y; |
| a2 = getY2() - y; |
| b0 = getX1() - x; |
| b1 = getCtrlX() - x; |
| b2 = getX2() - x; |
| } |
| else |
| { |
| a0 = getX1() - x; |
| a1 = getCtrlX() - x; |
| a2 = getX2() - x; |
| b0 = getY1() - y; |
| b1 = getCtrlY() - y; |
| b2 = getY2() - y; |
| } |
| |
| /* If the axis intersects a start/endpoint, shift it up by some small |
| amount to guarantee the line is 'inside' |
| If this is not done,bad behaviour may result for points on that axis. */ |
| if (a0 == 0.0 || a2 == 0.0) |
| { |
| double small = getFlatness() * EPSILON; |
| if (a0 == 0.0) |
| a0 -= small; |
| |
| if (a2 == 0.0) |
| a2 -= small; |
| } |
| |
| r[0] = a0; |
| r[1] = 2 * (a1 - a0); |
| r[2] = (a2 - 2 * a1 + a0); |
| |
| nRoots = solveQuadratic(r); |
| for (int i = 0; i < nRoots; i++) |
| { |
| double t = r[i]; |
| if (t >= 0.0 && t <= 1.0) |
| { |
| double crossing = t * t * (b2 - 2 * b1 + b0) + 2 * t * (b1 - b0) |
| + b0; |
| /* single root is always doubly degenerate in quads */ |
| if (crossing > 0 && crossing < distance) |
| nCrossings += (nRoots == 1) ? 2 : 1; |
| } |
| } |
| |
| if (useYaxis) |
| { |
| if (Line2D.linesIntersect(b0, a0, b2, a2, EPSILON, 0.0, distance, 0.0)) |
| nCrossings++; |
| } |
| else |
| { |
| if (Line2D.linesIntersect(a0, b0, a2, b2, 0.0, EPSILON, 0.0, distance)) |
| nCrossings++; |
| } |
| |
| return (nCrossings); |
| } |
| |
| /** |
| * A two-dimensional curve that is parameterized with a quadratic |
| * function and stores coordinate values in double-precision |
| * floating-point format. |
| * |
| * @see QuadCurve2D.Float |
| * |
| * @author Eric Blake (ebb9@email.byu.edu) |
| * @author Sascha Brawer (brawer@dandelis.ch) |
| */ |
| public static class Double extends QuadCurve2D |
| { |
| /** |
| * The <i>x</i> coordinate of the curve’s start point. |
| */ |
| public double x1; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s start point. |
| */ |
| public double y1; |
| |
| /** |
| * The <i>x</i> coordinate of the curve’s control point. |
| */ |
| public double ctrlx; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s control point. |
| */ |
| public double ctrly; |
| |
| /** |
| * The <i>x</i> coordinate of the curve’s end point. |
| */ |
| public double x2; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s end point. |
| */ |
| public double y2; |
| |
| /** |
| * Constructs a new QuadCurve2D that stores its coordinate values |
| * in double-precision floating-point format. All points are |
| * initially at position (0, 0). |
| */ |
| public Double() |
| { |
| } |
| |
| /** |
| * Constructs a new QuadCurve2D that stores its coordinate values |
| * in double-precision floating-point format, specifying the |
| * initial position of each point. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s start |
| * point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s start |
| * point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s control |
| * point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s control |
| * point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s end |
| * point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s end |
| * point. |
| */ |
| public Double(double x1, double y1, double cx, double cy, double x2, |
| double y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| ctrlx = cx; |
| ctrly = cy; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s start |
| * point. |
| */ |
| public double getX1() |
| { |
| return x1; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s start |
| * point. |
| */ |
| public double getY1() |
| { |
| return y1; |
| } |
| |
| /** |
| * Returns the curve’s start point. |
| */ |
| public Point2D getP1() |
| { |
| return new Point2D.Double(x1, y1); |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s control |
| * point. |
| */ |
| public double getCtrlX() |
| { |
| return ctrlx; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s control |
| * point. |
| */ |
| public double getCtrlY() |
| { |
| return ctrly; |
| } |
| |
| /** |
| * Returns the curve’s control point. |
| */ |
| public Point2D getCtrlPt() |
| { |
| return new Point2D.Double(ctrlx, ctrly); |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s end |
| * point. |
| */ |
| public double getX2() |
| { |
| return x2; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s end |
| * point. |
| */ |
| public double getY2() |
| { |
| return y2; |
| } |
| |
| /** |
| * Returns the curve’s end point. |
| */ |
| public Point2D getP2() |
| { |
| return new Point2D.Double(x2, y2); |
| } |
| |
| /** |
| * Changes the geometry of the curve. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s new |
| * end point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s new |
| * end point. |
| */ |
| public void setCurve(double x1, double y1, double cx, double cy, |
| double x2, double y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| ctrlx = cx; |
| ctrly = cy; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * Determines the smallest rectangle that encloses the |
| * curve’s start, end and control point. As the |
| * illustration below shows, the invisible control point may cause |
| * the bounds to be much larger than the area that is actually |
| * covered by the curve. |
| * |
| * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180" |
| * alt="An illustration of the bounds of a QuadCurve2D" /> |
| */ |
| public Rectangle2D getBounds2D() |
| { |
| double nx1 = Math.min(Math.min(x1, ctrlx), x2); |
| double ny1 = Math.min(Math.min(y1, ctrly), y2); |
| double nx2 = Math.max(Math.max(x1, ctrlx), x2); |
| double ny2 = Math.max(Math.max(y1, ctrly), y2); |
| return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1); |
| } |
| } |
| |
| /** |
| * A two-dimensional curve that is parameterized with a quadratic |
| * function and stores coordinate values in single-precision |
| * floating-point format. |
| * |
| * @see QuadCurve2D.Double |
| * |
| * @author Eric Blake (ebb9@email.byu.edu) |
| * @author Sascha Brawer (brawer@dandelis.ch) |
| */ |
| public static class Float extends QuadCurve2D |
| { |
| /** |
| * The <i>x</i> coordinate of the curve’s start point. |
| */ |
| public float x1; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s start point. |
| */ |
| public float y1; |
| |
| /** |
| * The <i>x</i> coordinate of the curve’s control point. |
| */ |
| public float ctrlx; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s control point. |
| */ |
| public float ctrly; |
| |
| /** |
| * The <i>x</i> coordinate of the curve’s end point. |
| */ |
| public float x2; |
| |
| /** |
| * The <i>y</i> coordinate of the curve’s end point. |
| */ |
| public float y2; |
| |
| /** |
| * Constructs a new QuadCurve2D that stores its coordinate values |
| * in single-precision floating-point format. All points are |
| * initially at position (0, 0). |
| */ |
| public Float() |
| { |
| } |
| |
| /** |
| * Constructs a new QuadCurve2D that stores its coordinate values |
| * in single-precision floating-point format, specifying the |
| * initial position of each point. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s start |
| * point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s start |
| * point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s control |
| * point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s control |
| * point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s end |
| * point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s end |
| * point. |
| */ |
| public Float(float x1, float y1, float cx, float cy, float x2, float y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| ctrlx = cx; |
| ctrly = cy; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s start |
| * point. |
| */ |
| public double getX1() |
| { |
| return x1; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s start |
| * point. |
| */ |
| public double getY1() |
| { |
| return y1; |
| } |
| |
| /** |
| * Returns the curve’s start point. |
| */ |
| public Point2D getP1() |
| { |
| return new Point2D.Float(x1, y1); |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s control |
| * point. |
| */ |
| public double getCtrlX() |
| { |
| return ctrlx; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s control |
| * point. |
| */ |
| public double getCtrlY() |
| { |
| return ctrly; |
| } |
| |
| /** |
| * Returns the curve’s control point. |
| */ |
| public Point2D getCtrlPt() |
| { |
| return new Point2D.Float(ctrlx, ctrly); |
| } |
| |
| /** |
| * Returns the <i>x</i> coordinate of the curve’s end |
| * point. |
| */ |
| public double getX2() |
| { |
| return x2; |
| } |
| |
| /** |
| * Returns the <i>y</i> coordinate of the curve’s end |
| * point. |
| */ |
| public double getY2() |
| { |
| return y2; |
| } |
| |
| /** |
| * Returns the curve’s end point. |
| */ |
| public Point2D getP2() |
| { |
| return new Point2D.Float(x2, y2); |
| } |
| |
| /** |
| * Changes the geometry of the curve, specifying coordinate values |
| * as double-precision floating-point numbers. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s new |
| * end point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s new |
| * end point. |
| */ |
| public void setCurve(double x1, double y1, double cx, double cy, |
| double x2, double y2) |
| { |
| this.x1 = (float) x1; |
| this.y1 = (float) y1; |
| ctrlx = (float) cx; |
| ctrly = (float) cy; |
| this.x2 = (float) x2; |
| this.y2 = (float) y2; |
| } |
| |
| /** |
| * Changes the geometry of the curve, specifying coordinate values |
| * as single-precision floating-point numbers. |
| * |
| * @param x1 the <i>x</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param y1 the <i>y</i> coordinate of the curve’s new |
| * start point. |
| * |
| * @param cx the <i>x</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param cy the <i>y</i> coordinate of the curve’s new |
| * control point. |
| * |
| * @param x2 the <i>x</i> coordinate of the curve’s new |
| * end point. |
| * |
| * @param y2 the <i>y</i> coordinate of the curve’s new |
| * end point. |
| */ |
| public void setCurve(float x1, float y1, float cx, float cy, float x2, |
| float y2) |
| { |
| this.x1 = x1; |
| this.y1 = y1; |
| ctrlx = cx; |
| ctrly = cy; |
| this.x2 = x2; |
| this.y2 = y2; |
| } |
| |
| /** |
| * Determines the smallest rectangle that encloses the |
| * curve’s start, end and control point. As the |
| * illustration below shows, the invisible control point may cause |
| * the bounds to be much larger than the area that is actually |
| * covered by the curve. |
| * |
| * <p><img src="doc-files/QuadCurve2D-2.png" width="350" height="180" |
| * alt="An illustration of the bounds of a QuadCurve2D" /> |
| */ |
| public Rectangle2D getBounds2D() |
| { |
| float nx1 = (float) Math.min(Math.min(x1, ctrlx), x2); |
| float ny1 = (float) Math.min(Math.min(y1, ctrly), y2); |
| float nx2 = (float) Math.max(Math.max(x1, ctrlx), x2); |
| float ny2 = (float) Math.max(Math.max(y1, ctrly), y2); |
| return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1); |
| } |
| } |
| } |