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Diffstat (limited to 'libjava/classpath/java/awt/geom/CubicCurve2D.java')
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diff --git a/libjava/classpath/java/awt/geom/CubicCurve2D.java b/libjava/classpath/java/awt/geom/CubicCurve2D.java deleted file mode 100644 index 5cb11fe..0000000 --- a/libjava/classpath/java/awt/geom/CubicCurve2D.java +++ /dev/null @@ -1,1724 +0,0 @@ -/* CubicCurve2D.java -- represents a parameterized cubic 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 cubic - * function. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 CubicCurve2D 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 CubicCurve2D. Typical users will want to - * construct instances of a subclass, such as {@link - * CubicCurve2D.Float} or {@link CubicCurve2D.Double}. - */ - protected CubicCurve2D() - { - } - - /** - * 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 first - * control point. - */ - public abstract double getCtrlX1(); - - /** - * Returns the <i>y</i> coordinate of the curve’s first - * control point. - */ - public abstract double getCtrlY1(); - - /** - * Returns the curve’s first control point. - */ - public abstract Point2D getCtrlP1(); - - /** - * Returns the <i>x</i> coordinate of the curve’s second - * control point. - */ - public abstract double getCtrlX2(); - - /** - * Returns the <i>y</i> coordinate of the curve’s second - * control point. - */ - public abstract double getCtrlY2(); - - /** - * Returns the curve’s second control point. - */ - public abstract Point2D getCtrlP2(); - - /** - * 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. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s new - * first control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s new - * first control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s new - * second control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s new - * second 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 cx1, double cy1, - double cx2, double cy2, double x2, double y2); - - /** - * Changes the curve geometry, specifying 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 first 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 second control - * point is located at <code>coords[offset + 4]</code>, its <i>y</i> - * coordinate at <code>coords[offset + 5]</code>. The <i>x</i> - * coordinate of the new end point is located at <code>coords[offset - * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset + - * 7]</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++], - coords[offset++], coords[offset++]); - } - - /** - * Changes the curve geometry, specifying coordinate values in - * separate Point objects. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * <p>The curve does not keep any reference to the passed point - * objects. Therefore, a later change to <code>p1</code>, - * <code>c1</code>, <code>c2</code> or <code>p2</code> will not - * affect the curve geometry. - * - * @param p1 the new start point. - * @param c1 the new first control point. - * @param c2 the new second control point. - * @param p2 the new end point. - */ - public void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2) - { - setCurve(p1.getX(), p1.getY(), c1.getX(), c1.getY(), c2.getX(), c2.getY(), - p2.getX(), p2.getY()); - } - - /** - * Changes the curve geometry, specifying coordinate values in an - * array of Point objects. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * <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 first control - * point at <code>pts[offset + 1]</code>, the new second control - * point at <code>pts[offset + 2]</code>, and the new end point - * at <code>pts[offset + 3]</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].getX(), - pts[offset++].getY(), pts[offset].getX(), pts[offset++].getY(), - pts[offset].getX(), pts[offset++].getY()); - } - - /** - * Changes the curve geometry to that of another curve. - * - * @param c the curve whose coordinates will be copied. - */ - public void setCurve(CubicCurve2D c) - { - setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(), - c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2()); - } - - /** - * Calculates the squared flatness of a cubic curve, directly - * specifying each coordinate value. The flatness is the maximal - * distance of a control point to the line between start and end - * point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the square of the distance between C2 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 cx1 the <i>x</i> coordinate of the first control point C1. - * @param cy1 the <i>y</i> coordinate of the first control point C1. - * @param cx2 the <i>x</i> coordinate of the second control point C2. - * @param cy2 the <i>y</i> coordinate of the second control point C2. - * @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 cx1, - double cy1, double cx2, double cy2, - double x2, double y2) - { - return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, cx1, cy1), - Line2D.ptSegDistSq(x1, y1, x2, y2, cx2, cy2)); - } - - /** - * Calculates the flatness of a cubic curve, directly specifying - * each coordinate value. The flatness is the maximal distance of a - * control point to the line between start and end point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the distance between C2 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 cx1 the <i>x</i> coordinate of the first control point C1. - * @param cy1 the <i>y</i> coordinate of the first control point C1. - * @param cx2 the <i>x</i> coordinate of the second control point C2. - * @param cy2 the <i>y</i> coordinate of the second control point C2. - * @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 cx1, - double cy1, double cx2, double cy2, - double x2, double y2) - { - return Math.sqrt(getFlatnessSq(x1, y1, cx1, cy1, cx2, cy2, x2, y2)); - } - - /** - * Calculates the squared flatness of a cubic curve, specifying the - * coordinate values in an array. The flatness is the maximal - * distance of a control point to the line between start and end - * point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the square of the distance between C2 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 - * first control point C1 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 second control point C2 - * is located at <code>coords[offset + 4]</code>, its <i>y</i> - * coordinate at <code>coords[offset + 5]</code>. The <i>x</i> - * coordinate of the end point P2 is located at <code>coords[offset - * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset + - * 7]</code>. - * - * @param offset the offset of the first coordinate value in - * <code>coords</code>. - */ - public static double getFlatnessSq(double[] coords, int offset) - { - return getFlatnessSq(coords[offset++], coords[offset++], coords[offset++], - coords[offset++], coords[offset++], coords[offset++], - coords[offset++], coords[offset++]); - } - - /** - * Calculates the flatness of a cubic curve, specifying the - * coordinate values in an array. The flatness is the maximal - * distance of a control point to the line between start and end - * point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the distance between C2 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 - * first control point C1 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 second control point C2 - * is located at <code>coords[offset + 4]</code>, its <i>y</i> - * coordinate at <code>coords[offset + 5]</code>. The <i>x</i> - * coordinate of the end point P2 is located at <code>coords[offset - * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset + - * 7]</code>. - * - * @param offset the offset of the first coordinate value in - * <code>coords</code>. - */ - public static double getFlatness(double[] coords, int offset) - { - return Math.sqrt(getFlatnessSq(coords[offset++], coords[offset++], - coords[offset++], coords[offset++], - coords[offset++], coords[offset++], - coords[offset++], coords[offset++])); - } - - /** - * Calculates the squared flatness of this curve. The flatness is - * the maximal distance of a control point to the line between start - * and end point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the square of the distance between C2 and the - * gray line, i.e. the squared length of the red line. - */ - public double getFlatnessSq() - { - return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(), - getCtrlX2(), getCtrlY2(), getX2(), getY2()); - } - - /** - * Calculates the flatness of this curve. The flatness is the - * maximal distance of a control point to the line between start and - * end point. - * - * <p><img src="doc-files/CubicCurve2D-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. In comparison to C1, - * control point C2 is father away from the gray line. Therefore, - * the result will be the distance between C2 and the gray line, - * i.e. the length of the red line. - */ - public double getFlatness() - { - return Math.sqrt(getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(), - getCtrlX2(), getCtrlY2(), getX2(), getY2())); - } - - /** - * Subdivides this curve into two halves. - * - * <p><img src="doc-files/CubicCurve2D-3.png" width="700" - * height="180" alt="A drawing that illustrates the effects of - * subdividing a CubicCurve2D" /> - * - * @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(CubicCurve2D left, CubicCurve2D right) - { - // Use empty slots at end to share single array. - double[] d = new double[] - { - getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(), - getCtrlY2(), getX2(), getY2(), 0, 0, 0, 0, 0, 0 - }; - subdivide(d, 0, d, 0, d, 6); - if (left != null) - left.setCurve(d, 0); - if (right != null) - right.setCurve(d, 6); - } - - /** - * Subdivides a cubic curve into two halves. - * - * <p><img src="doc-files/CubicCurve2D-3.png" width="700" - * height="180" alt="A drawing that illustrates the effects of - * subdividing a CubicCurve2D" /> - * - * @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(CubicCurve2D src, CubicCurve2D left, - CubicCurve2D right) - { - src.subdivide(left, right); - } - - /** - * Subdivides a cubic curve into two halves, passing all coordinates - * in an array. - * - * <p><img src="doc-files/CubicCurve2D-3.png" width="700" - * height="180" alt="A drawing that illustrates the effects of - * subdividing a CubicCurve2D" /> - * - * <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 + 6</code>. - * - * @param src an array containing the coordinates of the curve to be - * subdivided. The <i>x</i> coordinate of the start point P1 is - * located at <code>src[srcOff]</code>, its <i>y</i> at - * <code>src[srcOff + 1]</code>. The <i>x</i> coordinate of the - * first control point C1 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 second control point C2 is located at - * <code>src[srcOff + 4]</code>, its <i>y</i> at <code>src[srcOff + - * 5]</code>. The <i>x</i> coordinate of the end point is located at - * <code>src[srcOff + 6]</code>, its <i>y</i> at <code>src[srcOff + - * 7]</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) - { - // To understand this code, please have a look at the image - // "CubicCurve2D-3.png" in the sub-directory "doc-files". - double src_C1_x; - double src_C1_y; - double src_C2_x; - double src_C2_y; - double left_P1_x; - double left_P1_y; - double left_C1_x; - double left_C1_y; - double left_C2_x; - double left_C2_y; - double right_C1_x; - double right_C1_y; - double right_C2_x; - double right_C2_y; - double right_P2_x; - double right_P2_y; - double Mid_x; // Mid = left.P2 = right.P1 - double Mid_y; // Mid = left.P2 = right.P1 - - left_P1_x = src[srcOff]; - left_P1_y = src[srcOff + 1]; - src_C1_x = src[srcOff + 2]; - src_C1_y = src[srcOff + 3]; - src_C2_x = src[srcOff + 4]; - src_C2_y = src[srcOff + 5]; - right_P2_x = src[srcOff + 6]; - right_P2_y = src[srcOff + 7]; - - left_C1_x = (left_P1_x + src_C1_x) / 2; - left_C1_y = (left_P1_y + src_C1_y) / 2; - right_C2_x = (right_P2_x + src_C2_x) / 2; - right_C2_y = (right_P2_y + src_C2_y) / 2; - Mid_x = (src_C1_x + src_C2_x) / 2; - Mid_y = (src_C1_y + src_C2_y) / 2; - left_C2_x = (left_C1_x + Mid_x) / 2; - left_C2_y = (left_C1_y + Mid_y) / 2; - right_C1_x = (Mid_x + right_C2_x) / 2; - right_C1_y = (Mid_y + right_C2_y) / 2; - Mid_x = (left_C2_x + right_C1_x) / 2; - Mid_y = (left_C2_y + right_C1_y) / 2; - - if (left != null) - { - left[leftOff] = left_P1_x; - left[leftOff + 1] = left_P1_y; - left[leftOff + 2] = left_C1_x; - left[leftOff + 3] = left_C1_y; - left[leftOff + 4] = left_C2_x; - left[leftOff + 5] = left_C2_y; - left[leftOff + 6] = Mid_x; - left[leftOff + 7] = Mid_y; - } - - if (right != null) - { - right[rightOff] = Mid_x; - right[rightOff + 1] = Mid_y; - right[rightOff + 2] = right_C1_x; - right[rightOff + 3] = right_C1_y; - right[rightOff + 4] = right_C2_x; - right[rightOff + 5] = right_C2_y; - right[rightOff + 6] = right_P2_x; - right[rightOff + 7] = right_P2_y; - } - } - - /** - * Finds the non-complex roots of a cubic equation, placing the - * results into the same array as the equation coefficients. The - * following equation is being solved: - * - * <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup> - * + <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 cubic equations, see the - * article <a - * href="http://planetmath.org/encyclopedia/CubicFormula.html" - * >“Cubic 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>, from which this implementation was - * adapted. - * - * @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). - * - * @see #solveCubic(double[], double[]) - * @see QuadCurve2D#solveQuadratic(double[],double[]) - * - * @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 solveCubic(double[] eqn) - { - return solveCubic(eqn, eqn); - } - - /** - * Finds the non-complex roots of a cubic equation. The following - * equation is being solved: - * - * <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup> - * + <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 cubic equations, see the - * article <a - * href="http://planetmath.org/encyclopedia/CubicFormula.html" - * >“Cubic 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>, from which this implementation was - * adapted. - * - * @see QuadCurve2D#solveQuadratic(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 solveCubic(double[] eqn, double[] res) - { - // Adapted from poly/solve_cubic.c in the GNU Scientific Library - // (GSL), 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 q; - double r; - double Q; - double R; - double c3; - double Q3; - double R2; - double CR2; - double CQ3; - - // If the cubic coefficient is zero, we have a quadratic equation. - c3 = eqn[3]; - if (c3 == 0) - return QuadCurve2D.solveQuadratic(eqn, res); - - // Divide the equation by the cubic coefficient. - c = eqn[0] / c3; - b = eqn[1] / c3; - a = eqn[2] / c3; - - // We now need to solve x^3 + ax^2 + bx + c = 0. - q = a * a - 3 * b; - r = 2 * a * a * a - 9 * a * b + 27 * c; - - Q = q / 9; - R = r / 54; - - Q3 = Q * Q * Q; - R2 = R * R; - - CR2 = 729 * r * r; - CQ3 = 2916 * q * q * q; - - if (R == 0 && Q == 0) - { - // The GNU Scientific Library would return three identical - // solutions in this case. - res[0] = -a / 3; - return 1; - } - - if (CR2 == CQ3) - { - /* this test is actually R2 == Q3, written in a form suitable - for exact computation with integers */ - /* Due to finite precision some double roots may be missed, and - considered to be a pair of complex roots z = x +/- epsilon i - close to the real axis. */ - double sqrtQ = Math.sqrt(Q); - - if (R > 0) - { - res[0] = -2 * sqrtQ - a / 3; - res[1] = sqrtQ - a / 3; - } - else - { - res[0] = -sqrtQ - a / 3; - res[1] = 2 * sqrtQ - a / 3; - } - return 2; - } - - if (CR2 < CQ3) /* equivalent to R2 < Q3 */ - { - double sqrtQ = Math.sqrt(Q); - double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ; - double theta = Math.acos(R / sqrtQ3); - double norm = -2 * sqrtQ; - res[0] = norm * Math.cos(theta / 3) - a / 3; - res[1] = norm * Math.cos((theta + 2.0 * Math.PI) / 3) - a / 3; - res[2] = norm * Math.cos((theta - 2.0 * Math.PI) / 3) - a / 3; - - // The GNU Scientific Library sorts the results. We don't. - return 3; - } - - double sgnR = (R >= 0 ? 1 : -1); - double A = -sgnR * Math.pow(Math.abs(R) + Math.sqrt(R2 - Q3), 1.0 / 3.0); - double B = Q / A; - res[0] = A + B - a / 3; - return 1; - } - - /** - * Determines whether a position lies inside the area bounded - * by the curve and the straight line connecting its end points. - * - * <p><img src="doc-files/CubicCurve2D-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 CubicCurve2D. - */ - 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 lies inside the area bounded - * by the curve and the straight line connecting its end points. - * - * <p><img src="doc-files/CubicCurve2D-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 CubicCurve2D. - */ - 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/CubicCurve2D-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. - * @see #contains(double, double) - */ - 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()); - } - - /** - * Determine whether a rectangle is entirely inside the area that is bounded - * by the curve and the straight line connecting its end points. - * - * <p><img src="doc-files/CubicCurve2D-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 CubicCurve2D. - * @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; - } - - /** - * Determine whether a Rectangle2D is entirely inside the area that is - * bounded by the curve and the straight line connecting its end points. - * - * <p><img src="doc-files/CubicCurve2D-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 CubicCurve2D. - * @see #contains(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 points. - */ - 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) getCtrlX1(); - coords[1] = (float) getCtrlY1(); - coords[2] = (float) getCtrlX2(); - coords[3] = (float) getCtrlY2(); - coords[4] = (float) getX2(); - coords[5] = (float) getY2(); - result = SEG_CUBICTO; - break; - default: - throw new NoSuchElementException("cubic iterator out of bounds"); - } - if (at != null) - at.transform(coords, 0, coords, 0, 3); - 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] = getCtrlX1(); - coords[1] = getCtrlY1(); - coords[2] = getCtrlX2(); - coords[3] = getCtrlY2(); - coords[4] = getX2(); - coords[5] = getY2(); - result = SEG_CUBICTO; - break; - default: - throw new NoSuchElementException("cubic iterator out of bounds"); - } - if (at != null) - at.transform(coords, 0, coords, 0, 3); - return result; - } - }; - } - - public PathIterator getPathIterator(AffineTransform at, double flatness) - { - return new FlatteningPathIterator(getPathIterator(at), flatness); - } - - /** - * Create 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, that - * returns the number of curve/line intersections on a given axis - * extending from a certain point. - * - * @param x x coordinate of the origin point - * @param y y coordinate of the origin point - * @param useYaxis axis used, 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/ - * - * A special-case not adressed in this code is self-intersections - * of the curve, e.g. if the axis intersects the self-itersection, - * the degenerate roots of the polynomial will erroneously count as - * a single intersection of the curve, and not two. - */ - private int getAxisIntersections(double x, double y, boolean useYaxis, - double distance) - { - int nCrossings = 0; - double a0; - double a1; - double a2; - double a3; - double b0; - double b1; - double b2; - double b3; - double[] r = new double[4]; - int nRoots; - - a0 = a3 = 0.0; - - if (useYaxis) - { - a0 = getY1() - y; - a1 = getCtrlY1() - y; - a2 = getCtrlY2() - y; - a3 = getY2() - y; - b0 = getX1() - x; - b1 = getCtrlX1() - x; - b2 = getCtrlX2() - x; - b3 = getX2() - x; - } - else - { - a0 = getX1() - x; - a1 = getCtrlX1() - x; - a2 = getCtrlX2() - x; - a3 = getX2() - x; - b0 = getY1() - y; - b1 = getCtrlY1() - y; - b2 = getCtrlY2() - y; - b3 = 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 || a3 == 0.0) - { - double small = getFlatness() * EPSILON; - if (a0 == 0.0) - a0 -= small; - if (a3 == 0.0) - a3 -= small; - } - - if (useYaxis) - { - if (Line2D.linesIntersect(b0, a0, b3, a3, EPSILON, 0.0, distance, 0.0)) - nCrossings++; - } - else - { - if (Line2D.linesIntersect(a0, b0, a3, b3, 0.0, EPSILON, 0.0, distance)) - nCrossings++; - } - - r[0] = a0; - r[1] = 3 * (a1 - a0); - r[2] = 3 * (a2 + a0 - 2 * a1); - r[3] = a3 - 3 * a2 + 3 * a1 - a0; - - if ((nRoots = solveCubic(r)) != 0) - for (int i = 0; i < nRoots; i++) - { - double t = r[i]; - if (t >= 0.0 && t <= 1.0) - { - double crossing = -(t * t * t) * (b0 - 3 * b1 + 3 * b2 - b3) - + 3 * t * t * (b0 - 2 * b1 + b2) - + 3 * t * (b1 - b0) + b0; - if (crossing > 0.0 && crossing <= distance) - nCrossings++; - } - } - - return (nCrossings); - } - - /** - * A two-dimensional curve that is parameterized with a cubic - * function and stores coordinate values in double-precision - * floating-point format. - * - * @see CubicCurve2D.Float - * - * @author Eric Blake (ebb9@email.byu.edu) - * @author Sascha Brawer (brawer@dandelis.ch) - */ - public static class Double extends CubicCurve2D - { - /** - * 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 first control point. - */ - public double ctrlx1; - - /** - * The <i>y</i> coordinate of the curve’s first control point. - */ - public double ctrly1; - - /** - * The <i>x</i> coordinate of the curve’s second control point. - */ - public double ctrlx2; - - /** - * The <i>y</i> coordinate of the curve’s second control point. - */ - public double ctrly2; - - /** - * 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 CubicCurve2D that stores its coordinate values - * in double-precision floating-point format. All points are - * initially at position (0, 0). - */ - public Double() - { - } - - /** - * Constructs a new CubicCurve2D that stores its coordinate values - * in double-precision floating-point format, specifying the - * initial position of each point. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s first - * control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s first - * control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s second - * control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s second - * 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 cx1, double cy1, double cx2, - double cy2, double x2, double y2) - { - this.x1 = x1; - this.y1 = y1; - ctrlx1 = cx1; - ctrly1 = cy1; - ctrlx2 = cx2; - ctrly2 = cy2; - 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 first - * control point. - */ - public double getCtrlX1() - { - return ctrlx1; - } - - /** - * Returns the <i>y</i> coordinate of the curve’s first - * control point. - */ - public double getCtrlY1() - { - return ctrly1; - } - - /** - * Returns the curve’s first control point. - */ - public Point2D getCtrlP1() - { - return new Point2D.Double(ctrlx1, ctrly1); - } - - /** - * Returns the <i>x</i> coordinate of the curve’s second - * control point. - */ - public double getCtrlX2() - { - return ctrlx2; - } - - /** - * Returns the <i>y</i> coordinate of the curve’s second - * control point. - */ - public double getCtrlY2() - { - return ctrly2; - } - - /** - * Returns the curve’s second control point. - */ - public Point2D getCtrlP2() - { - return new Point2D.Double(ctrlx2, ctrly2); - } - - /** - * 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 curve geometry, separately specifying each coordinate - * value. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s new - * first control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s new - * first control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s new - * second control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s new - * second 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 cx1, double cy1, - double cx2, double cy2, double x2, double y2) - { - this.x1 = x1; - this.y1 = y1; - ctrlx1 = cx1; - ctrly1 = cy1; - ctrlx2 = cx2; - ctrly2 = cy2; - this.x2 = x2; - this.y2 = y2; - } - - /** - * Determines the smallest rectangle that encloses the - * curve’s start, end and control points. As the - * illustration below shows, the invisible control points may cause - * the bounds to be much larger than the area that is actually - * covered by the curve. - * - * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180" - * alt="An illustration of the bounds of a CubicCurve2D" /> - */ - public Rectangle2D getBounds2D() - { - double nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2)); - double ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2)); - double nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2)); - double ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2)); - return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1); - } - } - - /** - * A two-dimensional curve that is parameterized with a cubic - * function and stores coordinate values in single-precision - * floating-point format. - * - * @see CubicCurve2D.Float - * - * @author Eric Blake (ebb9@email.byu.edu) - * @author Sascha Brawer (brawer@dandelis.ch) - */ - public static class Float extends CubicCurve2D - { - /** - * 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 first control point. - */ - public float ctrlx1; - - /** - * The <i>y</i> coordinate of the curve’s first control point. - */ - public float ctrly1; - - /** - * The <i>x</i> coordinate of the curve’s second control point. - */ - public float ctrlx2; - - /** - * The <i>y</i> coordinate of the curve’s second control point. - */ - public float ctrly2; - - /** - * 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 CubicCurve2D that stores its coordinate values - * in single-precision floating-point format. All points are - * initially at position (0, 0). - */ - public Float() - { - } - - /** - * Constructs a new CubicCurve2D that stores its coordinate values - * in single-precision floating-point format, specifying the - * initial position of each point. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s first - * control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s first - * control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s second - * control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s second - * 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 cx1, float cy1, float cx2, - float cy2, float x2, float y2) - { - this.x1 = x1; - this.y1 = y1; - ctrlx1 = cx1; - ctrly1 = cy1; - ctrlx2 = cx2; - ctrly2 = cy2; - 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 first - * control point. - */ - public double getCtrlX1() - { - return ctrlx1; - } - - /** - * Returns the <i>y</i> coordinate of the curve’s first - * control point. - */ - public double getCtrlY1() - { - return ctrly1; - } - - /** - * Returns the curve’s first control point. - */ - public Point2D getCtrlP1() - { - return new Point2D.Float(ctrlx1, ctrly1); - } - - /** - * Returns the <i>s</i> coordinate of the curve’s second - * control point. - */ - public double getCtrlX2() - { - return ctrlx2; - } - - /** - * Returns the <i>y</i> coordinate of the curve’s second - * control point. - */ - public double getCtrlY2() - { - return ctrly2; - } - - /** - * Returns the curve’s second control point. - */ - public Point2D getCtrlP2() - { - return new Point2D.Float(ctrlx2, ctrly2); - } - - /** - * 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 curve geometry, separately specifying each coordinate - * value as a double-precision floating-point number. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s new - * first control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s new - * first control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s new - * second control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s new - * second 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 cx1, double cy1, - double cx2, double cy2, double x2, double y2) - { - this.x1 = (float) x1; - this.y1 = (float) y1; - ctrlx1 = (float) cx1; - ctrly1 = (float) cy1; - ctrlx2 = (float) cx2; - ctrly2 = (float) cy2; - this.x2 = (float) x2; - this.y2 = (float) y2; - } - - /** - * Changes the curve geometry, separately specifying each coordinate - * value as a single-precision floating-point number. - * - * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180" - * alt="A drawing of a CubicCurve2D" /> - * - * @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 cx1 the <i>x</i> coordinate of the curve’s new - * first control point. - * - * @param cy1 the <i>y</i> coordinate of the curve’s new - * first control point. - * - * @param cx2 the <i>x</i> coordinate of the curve’s new - * second control point. - * - * @param cy2 the <i>y</i> coordinate of the curve’s new - * second 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 cx1, float cy1, float cx2, - float cy2, float x2, float y2) - { - this.x1 = x1; - this.y1 = y1; - ctrlx1 = cx1; - ctrly1 = cy1; - ctrlx2 = cx2; - ctrly2 = cy2; - this.x2 = x2; - this.y2 = y2; - } - - /** - * Determines the smallest rectangle that encloses the - * curve’s start, end and control points. As the - * illustration below shows, the invisible control points may cause - * the bounds to be much larger than the area that is actually - * covered by the curve. - * - * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180" - * alt="An illustration of the bounds of a CubicCurve2D" /> - */ - public Rectangle2D getBounds2D() - { - float nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2)); - float ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2)); - float nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2)); - float ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2)); - return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1); - } - } -} |