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authorupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
committerupstream source tree <ports@midipix.org>2015-03-15 20:14:05 -0400
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tree976dc5ab7fddf506dadce60ae936f43f58787092 /libjava/classpath/java/awt/geom/QuadCurve2D.java
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+/* 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., 51 Franklin Street, Fifth Floor, Boston, MA
+02110-1301 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&#x2019;s start
+ * point.
+ */
+ public abstract double getX1();
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s start
+ * point.
+ */
+ public abstract double getY1();
+
+ /**
+ * Returns the curve&#x2019;s start point.
+ */
+ public abstract Point2D getP1();
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public abstract double getCtrlX();
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public abstract double getCtrlY();
+
+ /**
+ * Returns the curve&#x2019;s control point.
+ */
+ public abstract Point2D getCtrlPt();
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public abstract double getX2();
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public abstract double getY2();
+
+ /**
+ * Returns the curve&#x2019;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&#x2019;s new start
+ * point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
+ * point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
+ * point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;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&#x2019;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&#x2019;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> &#xb7; <i>x</i><sup>2</sup>
+ * + <code>eqn[1]</code> &#xb7; <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"
+ * >&#x201c;Quadratic Formula&#x201d;</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 Brian Gough (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> &#xb7; <i>x</i><sup>2</sup>
+ * + <code>eqn[1]</code> &#xb7; <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"
+ * >&#x201c;Quadratic Formula&#x201d;</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 Gough (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 &#x201c;inside&#x201d; 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 &#x201c;inside&#x201d; 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 &#x201c;inside&#x201d; 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 &#x201c;inside&#x201d; 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&#x2019;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&#x2019;s start point.
+ */
+ public double x1;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;s start point.
+ */
+ public double y1;
+
+ /**
+ * The <i>x</i> coordinate of the curve&#x2019;s control point.
+ */
+ public double ctrlx;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;s control point.
+ */
+ public double ctrly;
+
+ /**
+ * The <i>x</i> coordinate of the curve&#x2019;s end point.
+ */
+ public double x2;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;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&#x2019;s start
+ * point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
+ * point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s control
+ * point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s control
+ * point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
+ * point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;s start
+ * point.
+ */
+ public double getX1()
+ {
+ return x1;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s start
+ * point.
+ */
+ public double getY1()
+ {
+ return y1;
+ }
+
+ /**
+ * Returns the curve&#x2019;s start point.
+ */
+ public Point2D getP1()
+ {
+ return new Point2D.Double(x1, y1);
+ }
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public double getCtrlX()
+ {
+ return ctrlx;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public double getCtrlY()
+ {
+ return ctrly;
+ }
+
+ /**
+ * Returns the curve&#x2019;s control point.
+ */
+ public Point2D getCtrlPt()
+ {
+ return new Point2D.Double(ctrlx, ctrly);
+ }
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public double getX2()
+ {
+ return x2;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public double getY2()
+ {
+ return y2;
+ }
+
+ /**
+ * Returns the curve&#x2019;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&#x2019;s new
+ * start point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
+ * start point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
+ * end point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;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&#x2019;s start point.
+ */
+ public float x1;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;s start point.
+ */
+ public float y1;
+
+ /**
+ * The <i>x</i> coordinate of the curve&#x2019;s control point.
+ */
+ public float ctrlx;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;s control point.
+ */
+ public float ctrly;
+
+ /**
+ * The <i>x</i> coordinate of the curve&#x2019;s end point.
+ */
+ public float x2;
+
+ /**
+ * The <i>y</i> coordinate of the curve&#x2019;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&#x2019;s start
+ * point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
+ * point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s control
+ * point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s control
+ * point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
+ * point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;s start
+ * point.
+ */
+ public double getX1()
+ {
+ return x1;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s start
+ * point.
+ */
+ public double getY1()
+ {
+ return y1;
+ }
+
+ /**
+ * Returns the curve&#x2019;s start point.
+ */
+ public Point2D getP1()
+ {
+ return new Point2D.Float(x1, y1);
+ }
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public double getCtrlX()
+ {
+ return ctrlx;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s control
+ * point.
+ */
+ public double getCtrlY()
+ {
+ return ctrly;
+ }
+
+ /**
+ * Returns the curve&#x2019;s control point.
+ */
+ public Point2D getCtrlPt()
+ {
+ return new Point2D.Float(ctrlx, ctrly);
+ }
+
+ /**
+ * Returns the <i>x</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public double getX2()
+ {
+ return x2;
+ }
+
+ /**
+ * Returns the <i>y</i> coordinate of the curve&#x2019;s end
+ * point.
+ */
+ public double getY2()
+ {
+ return y2;
+ }
+
+ /**
+ * Returns the curve&#x2019;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&#x2019;s new
+ * start point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
+ * start point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
+ * end point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;s new
+ * start point.
+ *
+ * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new
+ * start point.
+ *
+ * @param cx the <i>x</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param cy the <i>y</i> coordinate of the curve&#x2019;s new
+ * control point.
+ *
+ * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new
+ * end point.
+ *
+ * @param y2 the <i>y</i> coordinate of the curve&#x2019;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&#x2019;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 = Math.min(Math.min(x1, ctrlx), x2);
+ float ny1 = Math.min(Math.min(y1, ctrly), y2);
+ float nx2 = Math.max(Math.max(x1, ctrlx), x2);
+ float ny2 = Math.max(Math.max(y1, ctrly), y2);
+ return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
+ }
+ }
+}