| /* 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., 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 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 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 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 = (float) Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2)); |
| float ny1 = (float) Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2)); |
| float nx2 = (float) Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2)); |
| float ny2 = (float) Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2)); |
| return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1); |
| } |
| } |
| } |