From 554fd8c5195424bdbcabf5de30fdc183aba391bd Mon Sep 17 00:00:00 2001 From: upstream source tree Date: Sun, 15 Mar 2015 20:14:05 -0400 Subject: obtained gcc-4.6.4.tar.bz2 from upstream website; verified gcc-4.6.4.tar.bz2.sig; imported gcc-4.6.4 source tree from verified upstream tarball. downloading a git-generated archive based on the 'upstream' tag should provide you with a source tree that is binary identical to the one extracted from the above tarball. if you have obtained the source via the command 'git clone', however, do note that line-endings of files in your working directory might differ from line-endings of the respective files in the upstream repository. --- libjava/classpath/java/awt/geom/CubicCurve2D.java | 1724 +++++++++++++++++++++ 1 file changed, 1724 insertions(+) create mode 100644 libjava/classpath/java/awt/geom/CubicCurve2D.java (limited to 'libjava/classpath/java/awt/geom/CubicCurve2D.java') diff --git a/libjava/classpath/java/awt/geom/CubicCurve2D.java b/libjava/classpath/java/awt/geom/CubicCurve2D.java new file mode 100644 index 000000000..5cb11fe77 --- /dev/null +++ b/libjava/classpath/java/awt/geom/CubicCurve2D.java @@ -0,0 +1,1724 @@ +/* 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. + * + *

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 x coordinate of the curve’s start + * point. + */ + public abstract double getX1(); + + /** + * Returns the y coordinate of the curve’s start + * point. + */ + public abstract double getY1(); + + /** + * Returns the curve’s start point. + */ + public abstract Point2D getP1(); + + /** + * Returns the x coordinate of the curve’s first + * control point. + */ + public abstract double getCtrlX1(); + + /** + * Returns the y 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 x coordinate of the curve’s second + * control point. + */ + public abstract double getCtrlX2(); + + /** + * Returns the y 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 x coordinate of the curve’s end + * point. + */ + public abstract double getX2(); + + /** + * Returns the y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s new start + * point. + * + * @param y1 the y coordinate of the curve’s new start + * point. + * + * @param cx1 the x coordinate of the curve’s new + * first control point. + * + * @param cy1 the y coordinate of the curve’s new + * first control point. + * + * @param cx2 the x coordinate of the curve’s new + * second control point. + * + * @param cy2 the y coordinate of the curve’s new + * second control point. + * + * @param x2 the x coordinate of the curve’s new end + * point. + * + * @param y2 the y 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 + * x coordinate of the new start point is located at + * coords[offset], its y coordinate at + * coords[offset + 1]. The x coordinate of the + * new first control point is located at coords[offset + + * 2], its y coordinate at coords[offset + + * 3]. The x coordinate of the new second control + * point is located at coords[offset + 4], its y + * coordinate at coords[offset + 5]. The x + * coordinate of the new end point is located at coords[offset + * + 6], its y coordinate at coords[offset + + * 7]. + * + * @param offset the offset of the first coordinate value in + * coords. + */ + 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. + * + *

A drawing of a CubicCurve2D + * + *

The curve does not keep any reference to the passed point + * objects. Therefore, a later change to p1, + * c1, c2 or p2 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. + * + *

A drawing of a CubicCurve2D + * + *

The curve does not keep references to the passed point + * objects. Therefore, a later change to the pts 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 pts[offset], the new first control + * point at pts[offset + 1], the new second control + * point at pts[offset + 2], and the new end point + * at pts[offset + 3]. + * + * @param offset the offset of the start point in pts. + */ + 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. + * + *

A drawing that illustrates the flatness + * + *

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 x coordinate of the start point P1. + * @param y1 the y coordinate of the start point P1. + * @param cx1 the x coordinate of the first control point C1. + * @param cy1 the y coordinate of the first control point C1. + * @param cx2 the x coordinate of the second control point C2. + * @param cy2 the y coordinate of the second control point C2. + * @param x2 the x coordinate of the end point P2. + * @param y2 the y 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. + * + *

A drawing that illustrates the flatness + * + *

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 x coordinate of the start point P1. + * @param y1 the y coordinate of the start point P1. + * @param cx1 the x coordinate of the first control point C1. + * @param cy1 the y coordinate of the first control point C1. + * @param cx2 the x coordinate of the second control point C2. + * @param cy2 the y coordinate of the second control point C2. + * @param x2 the x coordinate of the end point P2. + * @param y2 the y 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. + * + *

A drawing that illustrates the flatness + * + *

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 + * x coordinate of the start point P1 is located at + * coords[offset], its y coordinate at + * coords[offset + 1]. The x coordinate of the + * first control point C1 is located at coords[offset + + * 2], its y coordinate at coords[offset + + * 3]. The x coordinate of the second control point C2 + * is located at coords[offset + 4], its y + * coordinate at coords[offset + 5]. The x + * coordinate of the end point P2 is located at coords[offset + * + 6], its y coordinate at coords[offset + + * 7]. + * + * @param offset the offset of the first coordinate value in + * coords. + */ + 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. + * + *

A drawing that illustrates the flatness + * + *

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 + * x coordinate of the start point P1 is located at + * coords[offset], its y coordinate at + * coords[offset + 1]. The x coordinate of the + * first control point C1 is located at coords[offset + + * 2], its y coordinate at coords[offset + + * 3]. The x coordinate of the second control point C2 + * is located at coords[offset + 4], its y + * coordinate at coords[offset + 5]. The x + * coordinate of the end point P2 is located at coords[offset + * + 6], its y coordinate at coords[offset + + * 7]. + * + * @param offset the offset of the first coordinate value in + * coords. + */ + 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. + * + *

A drawing that illustrates the flatness + * + *

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. + * + *

A drawing that illustrates the flatness + * + *

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. + * + *

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 null 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 null 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. + * + *

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 src, or null if the caller is not + * interested in the left half. + * + * @param right a curve whose geometry will be set to the right half + * of src, or null 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. + * + *

A drawing that illustrates the effects of + * subdividing a CubicCurve2D + * + *

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 left and right, and + * set rightOff to leftOff + 6. + * + * @param src an array containing the coordinates of the curve to be + * subdivided. The x coordinate of the start point P1 is + * located at src[srcOff], its y at + * src[srcOff + 1]. The x coordinate of the + * first control point C1 is located at src[srcOff + + * 2], its y at src[srcOff + 3]. The + * x coordinate of the second control point C2 is located at + * src[srcOff + 4], its y at src[srcOff + + * 5]. The x coordinate of the end point is located at + * src[srcOff + 6], its y at src[srcOff + + * 7]. + * + * @param srcOff an offset into src, specifying + * the index of the start point’s x coordinate. + * + * @param left an array that will receive the coordinates of the + * left half of src. It is acceptable to pass + * src. A caller who is not interested in the left half + * can pass null. + * + * @param leftOff an offset into left, specifying the + * index where the start point’s x coordinate will be + * stored. + * + * @param right an array that will receive the coordinates of the + * right half of src. It is acceptable to pass + * src or left. A caller who is not + * interested in the right half can pass null. + * + * @param rightOff an offset into right, specifying the + * index where the start point’s x 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: + * + *

eqn[3] · x3 + * + eqn[2] · x2 + * + eqn[1] · x + * + eqn[0] + * = 0 + *
+ * + *

For some background about solving cubic equations, see the + * article “Cubic Formula” in PlanetMath. For an extensive + * library of numerical algorithms written in the C programming + * language, see the GNU + * Scientific Library, from which this implementation was + * adapted. + * + * @param eqn an array with the coefficients of the equation. When + * this procedure has returned, eqn 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 GNU Scientific Library) + * + * @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: + * + *

eqn[3] · x3 + * + eqn[2] · x2 + * + eqn[1] · x + * + eqn[0] + * = 0 + *
+ * + *

For some background about solving cubic equations, see the + * article “Cubic Formula” in PlanetMath. For an extensive + * library of numerical algorithms written in the C programming + * language, see the GNU + * Scientific Library, 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 eqn + * and res. + * + * @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 GNU Scientific Library) + * + * @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. + * + *

A drawing of the area spanned by the curve + * + *

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. + * + *

A drawing of the area spanned by the curve + * + *

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. + * + *

A drawing of the area spanned by the curve + * + *

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. + * + *

A drawing of the area spanned by the curve + * + *

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. + * + *

A drawing of the area spanned by the curve + * + *

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 x coordinate of the curve’s start point. + */ + public double x1; + + /** + * The y coordinate of the curve’s start point. + */ + public double y1; + + /** + * The x coordinate of the curve’s first control point. + */ + public double ctrlx1; + + /** + * The y coordinate of the curve’s first control point. + */ + public double ctrly1; + + /** + * The x coordinate of the curve’s second control point. + */ + public double ctrlx2; + + /** + * The y coordinate of the curve’s second control point. + */ + public double ctrly2; + + /** + * The x coordinate of the curve’s end point. + */ + public double x2; + + /** + * The y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s start + * point. + * + * @param y1 the y coordinate of the curve’s start + * point. + * + * @param cx1 the x coordinate of the curve’s first + * control point. + * + * @param cy1 the y coordinate of the curve’s first + * control point. + * + * @param cx2 the x coordinate of the curve’s second + * control point. + * + * @param cy2 the y coordinate of the curve’s second + * control point. + * + * @param x2 the x coordinate of the curve’s end + * point. + * + * @param y2 the y 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 x coordinate of the curve’s start + * point. + */ + public double getX1() + { + return x1; + } + + /** + * Returns the y 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 x coordinate of the curve’s first + * control point. + */ + public double getCtrlX1() + { + return ctrlx1; + } + + /** + * Returns the y 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 x coordinate of the curve’s second + * control point. + */ + public double getCtrlX2() + { + return ctrlx2; + } + + /** + * Returns the y 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 x coordinate of the curve’s end + * point. + */ + public double getX2() + { + return x2; + } + + /** + * Returns the y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s new start + * point. + * + * @param y1 the y coordinate of the curve’s new start + * point. + * + * @param cx1 the x coordinate of the curve’s new + * first control point. + * + * @param cy1 the y coordinate of the curve’s new + * first control point. + * + * @param cx2 the x coordinate of the curve’s new + * second control point. + * + * @param cy2 the y coordinate of the curve’s new + * second control point. + * + * @param x2 the x coordinate of the curve’s new end + * point. + * + * @param y2 the y 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. + * + *

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 x coordinate of the curve’s start point. + */ + public float x1; + + /** + * The y coordinate of the curve’s start point. + */ + public float y1; + + /** + * The x coordinate of the curve’s first control point. + */ + public float ctrlx1; + + /** + * The y coordinate of the curve’s first control point. + */ + public float ctrly1; + + /** + * The x coordinate of the curve’s second control point. + */ + public float ctrlx2; + + /** + * The y coordinate of the curve’s second control point. + */ + public float ctrly2; + + /** + * The x coordinate of the curve’s end point. + */ + public float x2; + + /** + * The y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s start + * point. + * + * @param y1 the y coordinate of the curve’s start + * point. + * + * @param cx1 the x coordinate of the curve’s first + * control point. + * + * @param cy1 the y coordinate of the curve’s first + * control point. + * + * @param cx2 the x coordinate of the curve’s second + * control point. + * + * @param cy2 the y coordinate of the curve’s second + * control point. + * + * @param x2 the x coordinate of the curve’s end + * point. + * + * @param y2 the y 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 x coordinate of the curve’s start + * point. + */ + public double getX1() + { + return x1; + } + + /** + * Returns the y 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 x coordinate of the curve’s first + * control point. + */ + public double getCtrlX1() + { + return ctrlx1; + } + + /** + * Returns the y 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 s coordinate of the curve’s second + * control point. + */ + public double getCtrlX2() + { + return ctrlx2; + } + + /** + * Returns the y 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 x coordinate of the curve’s end + * point. + */ + public double getX2() + { + return x2; + } + + /** + * Returns the y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s new start + * point. + * + * @param y1 the y coordinate of the curve’s new start + * point. + * + * @param cx1 the x coordinate of the curve’s new + * first control point. + * + * @param cy1 the y coordinate of the curve’s new + * first control point. + * + * @param cx2 the x coordinate of the curve’s new + * second control point. + * + * @param cy2 the y coordinate of the curve’s new + * second control point. + * + * @param x2 the x coordinate of the curve’s new end + * point. + * + * @param y2 the y 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. + * + *

A drawing of a CubicCurve2D + * + * @param x1 the x coordinate of the curve’s new start + * point. + * + * @param y1 the y coordinate of the curve’s new start + * point. + * + * @param cx1 the x coordinate of the curve’s new + * first control point. + * + * @param cy1 the y coordinate of the curve’s new + * first control point. + * + * @param cx2 the x coordinate of the curve’s new + * second control point. + * + * @param cy2 the y coordinate of the curve’s new + * second control point. + * + * @param x2 the x coordinate of the curve’s new end + * point. + * + * @param y2 the y 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. + * + *

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); + } + } +} -- cgit v1.2.3