Java tutorial
/* * Copyright (c) 1997, 2018, Oracle and/or its affiliates. All rights reserved. * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. * * This code is free software; you can redistribute it and/or modify it * under the terms of the GNU General Public License version 2 only, as * published by the Free Software Foundation. Oracle designates this * particular file as subject to the "Classpath" exception as provided * by Oracle in the LICENSE file that accompanied this code. * * This code 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 * version 2 for more details (a copy is included in the LICENSE file that * accompanied this code). * * You should have received a copy of the GNU General Public License version * 2 along with this work; if not, write to the Free Software Foundation, * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. * * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA * or visit www.oracle.com if you need additional information or have any * questions. */ package java.awt.geom; import java.awt.Shape; import java.awt.Rectangle; import java.io.Serializable; import sun.awt.geom.Curve; /** * The {@code QuadCurve2D} class defines a quadratic parametric curve * segment in {@code (x,y)} coordinate space. * <p> * This class is only the abstract superclass for all objects that * store a 2D quadratic curve segment. * The actual storage representation of the coordinates is left to * the subclass. * * @author Jim Graham * @since 1.2 */ public abstract class QuadCurve2D implements Shape, Cloneable { /** * A quadratic parametric curve segment specified with * {@code float} coordinates. * * @since 1.2 */ public static class Float extends QuadCurve2D implements Serializable { /** * The X coordinate of the start point of the quadratic curve * segment. * @since 1.2 * @serial */ public float x1; /** * The Y coordinate of the start point of the quadratic curve * segment. * @since 1.2 * @serial */ public float y1; /** * The X coordinate of the control point of the quadratic curve * segment. * @since 1.2 * @serial */ public float ctrlx; /** * The Y coordinate of the control point of the quadratic curve * segment. * @since 1.2 * @serial */ public float ctrly; /** * The X coordinate of the end point of the quadratic curve * segment. * @since 1.2 * @serial */ public float x2; /** * The Y coordinate of the end point of the quadratic curve * segment. * @since 1.2 * @serial */ public float y2; /** * Constructs and initializes a {@code QuadCurve2D} with * coordinates (0, 0, 0, 0, 0, 0). * @since 1.2 */ public Float() { } /** * Constructs and initializes a {@code QuadCurve2D} from the * specified {@code float} coordinates. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @since 1.2 */ public Float(float x1, float y1, float ctrlx, float ctrly, float x2, float y2) { setCurve(x1, y1, ctrlx, ctrly, x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public double getX1() { return (double) x1; } /** * {@inheritDoc} * @since 1.2 */ public double getY1() { return (double) y1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP1() { return new Point2D.Float(x1, y1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX() { return (double) ctrlx; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY() { return (double) ctrly; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlPt() { return new Point2D.Float(ctrlx, ctrly); } /** * {@inheritDoc} * @since 1.2 */ public double getX2() { return (double) x2; } /** * {@inheritDoc} * @since 1.2 */ public double getY2() { return (double) y2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP2() { return new Point2D.Float(x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public void setCurve(double x1, double y1, double ctrlx, double ctrly, double x2, double y2) { this.x1 = (float) x1; this.y1 = (float) y1; this.ctrlx = (float) ctrlx; this.ctrly = (float) ctrly; this.x2 = (float) x2; this.y2 = (float) y2; } /** * Sets the location of the end points and control point of this curve * to the specified {@code float} coordinates. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @since 1.2 */ public void setCurve(float x1, float y1, float ctrlx, float ctrly, float x2, float y2) { this.x1 = x1; this.y1 = y1; this.ctrlx = ctrlx; this.ctrly = ctrly; this.x2 = x2; this.y2 = y2; } /** * {@inheritDoc} * @since 1.2 */ public Rectangle2D getBounds2D() { float left = Math.min(Math.min(x1, x2), ctrlx); float top = Math.min(Math.min(y1, y2), ctrly); float right = Math.max(Math.max(x1, x2), ctrlx); float bottom = Math.max(Math.max(y1, y2), ctrly); return new Rectangle2D.Float(left, top, right - left, bottom - top); } /* * JDK 1.6 serialVersionUID */ private static final long serialVersionUID = -8511188402130719609L; } /** * A quadratic parametric curve segment specified with * {@code double} coordinates. * * @since 1.2 */ public static class Double extends QuadCurve2D implements Serializable { /** * The X coordinate of the start point of the quadratic curve * segment. * @since 1.2 * @serial */ public double x1; /** * The Y coordinate of the start point of the quadratic curve * segment. * @since 1.2 * @serial */ public double y1; /** * The X coordinate of the control point of the quadratic curve * segment. * @since 1.2 * @serial */ public double ctrlx; /** * The Y coordinate of the control point of the quadratic curve * segment. * @since 1.2 * @serial */ public double ctrly; /** * The X coordinate of the end point of the quadratic curve * segment. * @since 1.2 * @serial */ public double x2; /** * The Y coordinate of the end point of the quadratic curve * segment. * @since 1.2 * @serial */ public double y2; /** * Constructs and initializes a {@code QuadCurve2D} with * coordinates (0, 0, 0, 0, 0, 0). * @since 1.2 */ public Double() { } /** * Constructs and initializes a {@code QuadCurve2D} from the * specified {@code double} coordinates. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @since 1.2 */ public Double(double x1, double y1, double ctrlx, double ctrly, double x2, double y2) { setCurve(x1, y1, ctrlx, ctrly, x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public double getX1() { return x1; } /** * {@inheritDoc} * @since 1.2 */ public double getY1() { return y1; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP1() { return new Point2D.Double(x1, y1); } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlX() { return ctrlx; } /** * {@inheritDoc} * @since 1.2 */ public double getCtrlY() { return ctrly; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getCtrlPt() { return new Point2D.Double(ctrlx, ctrly); } /** * {@inheritDoc} * @since 1.2 */ public double getX2() { return x2; } /** * {@inheritDoc} * @since 1.2 */ public double getY2() { return y2; } /** * {@inheritDoc} * @since 1.2 */ public Point2D getP2() { return new Point2D.Double(x2, y2); } /** * {@inheritDoc} * @since 1.2 */ public void setCurve(double x1, double y1, double ctrlx, double ctrly, double x2, double y2) { this.x1 = x1; this.y1 = y1; this.ctrlx = ctrlx; this.ctrly = ctrly; this.x2 = x2; this.y2 = y2; } /** * {@inheritDoc} * @since 1.2 */ public Rectangle2D getBounds2D() { double left = Math.min(Math.min(x1, x2), ctrlx); double top = Math.min(Math.min(y1, y2), ctrly); double right = Math.max(Math.max(x1, x2), ctrlx); double bottom = Math.max(Math.max(y1, y2), ctrly); return new Rectangle2D.Double(left, top, right - left, bottom - top); } /* * JDK 1.6 serialVersionUID */ private static final long serialVersionUID = 4217149928428559721L; } /** * This is an abstract class that cannot be instantiated directly. * Type-specific implementation subclasses are available for * instantiation and provide a number of formats for storing * the information necessary to satisfy the various accessor * methods below. * * @see java.awt.geom.QuadCurve2D.Float * @see java.awt.geom.QuadCurve2D.Double * @since 1.2 */ protected QuadCurve2D() { } /** * Returns the X coordinate of the start point in * {@code double} in precision. * @return the X coordinate of the start point. * @since 1.2 */ public abstract double getX1(); /** * Returns the Y coordinate of the start point in * {@code double} precision. * @return the Y coordinate of the start point. * @since 1.2 */ public abstract double getY1(); /** * Returns the start point. * @return a {@code Point2D} that is the start point of this * {@code QuadCurve2D}. * @since 1.2 */ public abstract Point2D getP1(); /** * Returns the X coordinate of the control point in * {@code double} precision. * @return X coordinate the control point * @since 1.2 */ public abstract double getCtrlX(); /** * Returns the Y coordinate of the control point in * {@code double} precision. * @return the Y coordinate of the control point. * @since 1.2 */ public abstract double getCtrlY(); /** * Returns the control point. * @return a {@code Point2D} that is the control point of this * {@code Point2D}. * @since 1.2 */ public abstract Point2D getCtrlPt(); /** * Returns the X coordinate of the end point in * {@code double} precision. * @return the x coordinate of the end point. * @since 1.2 */ public abstract double getX2(); /** * Returns the Y coordinate of the end point in * {@code double} precision. * @return the Y coordinate of the end point. * @since 1.2 */ public abstract double getY2(); /** * Returns the end point. * @return a {@code Point} object that is the end point * of this {@code Point2D}. * @since 1.2 */ public abstract Point2D getP2(); /** * Sets the location of the end points and control point of this curve * to the specified {@code double} coordinates. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @since 1.2 */ public abstract void setCurve(double x1, double y1, double ctrlx, double ctrly, double x2, double y2); /** * Sets the location of the end points and control points of this * {@code QuadCurve2D} to the {@code double} coordinates at * the specified offset in the specified array. * @param coords the array containing coordinate values * @param offset the index into the array from which to start * getting the coordinate values and assigning them to this * {@code QuadCurve2D} * @since 1.2 */ public void setCurve(double[] coords, int offset) { setCurve(coords[offset + 0], coords[offset + 1], coords[offset + 2], coords[offset + 3], coords[offset + 4], coords[offset + 5]); } /** * Sets the location of the end points and control point of this * {@code QuadCurve2D} to the specified {@code Point2D} * coordinates. * @param p1 the start point * @param cp the control point * @param p2 the end point * @since 1.2 */ public void setCurve(Point2D p1, Point2D cp, Point2D p2) { setCurve(p1.getX(), p1.getY(), cp.getX(), cp.getY(), p2.getX(), p2.getY()); } /** * Sets the location of the end points and control points of this * {@code QuadCurve2D} to the coordinates of the * {@code Point2D} objects at the specified offset in * the specified array. * @param pts an array containing {@code Point2D} that define * coordinate values * @param offset the index into {@code pts} from which to start * getting the coordinate values and assigning them to this * {@code QuadCurve2D} * @since 1.2 */ public void setCurve(Point2D[] pts, int offset) { setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(), pts[offset + 1].getX(), pts[offset + 1].getY(), pts[offset + 2].getX(), pts[offset + 2].getY()); } /** * Sets the location of the end points and control point of this * {@code QuadCurve2D} to the same as those in the specified * {@code QuadCurve2D}. * @param c the specified {@code QuadCurve2D} * @since 1.2 */ public void setCurve(QuadCurve2D c) { setCurve(c.getX1(), c.getY1(), c.getCtrlX(), c.getCtrlY(), c.getX2(), c.getY2()); } /** * Returns the square of the flatness, or maximum distance of a * control point from the line connecting the end points, of the * quadratic curve specified by the indicated control points. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @return the square of the flatness of the quadratic curve * defined by the specified coordinates. * @since 1.2 */ public static double getFlatnessSq(double x1, double y1, double ctrlx, double ctrly, double x2, double y2) { return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly); } /** * Returns the flatness, or maximum distance of a * control point from the line connecting the end points, of the * quadratic curve specified by the indicated control points. * * @param x1 the X coordinate of the start point * @param y1 the Y coordinate of the start point * @param ctrlx the X coordinate of the control point * @param ctrly the Y coordinate of the control point * @param x2 the X coordinate of the end point * @param y2 the Y coordinate of the end point * @return the flatness of the quadratic curve defined by the * specified coordinates. * @since 1.2 */ public static double getFlatness(double x1, double y1, double ctrlx, double ctrly, double x2, double y2) { return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly); } /** * Returns the square of the flatness, or maximum distance of a * control point from the line connecting the end points, of the * quadratic curve specified by the control points stored in the * indicated array at the indicated index. * @param coords an array containing coordinate values * @param offset the index into {@code coords} from which to * to start getting the values from the array * @return the flatness of the quadratic curve that is defined by the * values in the specified array at the specified index. * @since 1.2 */ public static double getFlatnessSq(double[] coords, int offset) { return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1], coords[offset + 4], coords[offset + 5], coords[offset + 2], coords[offset + 3]); } /** * Returns the flatness, or maximum distance of a * control point from the line connecting the end points, of the * quadratic curve specified by the control points stored in the * indicated array at the indicated index. * @param coords an array containing coordinate values * @param offset the index into {@code coords} from which to * start getting the coordinate values * @return the flatness of a quadratic curve defined by the * specified array at the specified offset. * @since 1.2 */ public static double getFlatness(double[] coords, int offset) { return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1], coords[offset + 4], coords[offset + 5], coords[offset + 2], coords[offset + 3]); } /** * Returns the square of the flatness, or maximum distance of a * control point from the line connecting the end points, of this * {@code QuadCurve2D}. * @return the square of the flatness of this * {@code QuadCurve2D}. * @since 1.2 */ public double getFlatnessSq() { return Line2D.ptSegDistSq(getX1(), getY1(), getX2(), getY2(), getCtrlX(), getCtrlY()); } /** * Returns the flatness, or maximum distance of a * control point from the line connecting the end points, of this * {@code QuadCurve2D}. * @return the flatness of this {@code QuadCurve2D}. * @since 1.2 */ public double getFlatness() { return Line2D.ptSegDist(getX1(), getY1(), getX2(), getY2(), getCtrlX(), getCtrlY()); } /** * Subdivides this {@code QuadCurve2D} and stores the resulting * two subdivided curves into the {@code left} and * {@code right} curve parameters. * Either or both of the {@code left} and {@code right} * objects can be the same as this {@code QuadCurve2D} or * {@code null}. * @param left the {@code QuadCurve2D} object for storing the * left or first half of the subdivided curve * @param right the {@code QuadCurve2D} object for storing the * right or second half of the subdivided curve * @since 1.2 */ public void subdivide(QuadCurve2D left, QuadCurve2D right) { subdivide(this, left, right); } /** * Subdivides the quadratic curve specified by the {@code src} * parameter and stores the resulting two subdivided curves into the * {@code left} and {@code right} curve parameters. * Either or both of the {@code left} and {@code right} * objects can be the same as the {@code src} object or * {@code null}. * @param src the quadratic curve to be subdivided * @param left the {@code QuadCurve2D} object for storing the * left or first half of the subdivided curve * @param right the {@code QuadCurve2D} object for storing the * right or second half of the subdivided curve * @since 1.2 */ public static void subdivide(QuadCurve2D src, QuadCurve2D left, QuadCurve2D right) { double x1 = src.getX1(); double y1 = src.getY1(); double ctrlx = src.getCtrlX(); double ctrly = src.getCtrlY(); double x2 = src.getX2(); double y2 = src.getY2(); double ctrlx1 = (x1 + ctrlx) / 2.0; double ctrly1 = (y1 + ctrly) / 2.0; double ctrlx2 = (x2 + ctrlx) / 2.0; double ctrly2 = (y2 + ctrly) / 2.0; ctrlx = (ctrlx1 + ctrlx2) / 2.0; ctrly = (ctrly1 + ctrly2) / 2.0; if (left != null) { left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly); } if (right != null) { right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2); } } /** * Subdivides the quadratic curve specified by the coordinates * stored in the {@code src} array at indices * {@code srcoff} through {@code srcoff} + 5 * and stores the resulting two subdivided curves into the two * result arrays at the corresponding indices. * Either or both of the {@code left} and {@code right} * arrays can be {@code null} or a reference to the same array * and offset as the {@code src} array. * Note that the last point in the first subdivided curve is the * same as the first point in the second subdivided curve. Thus, * it is possible to pass the same array for {@code left} and * {@code right} and to use offsets such that * {@code rightoff} equals {@code leftoff} + 4 in order * to avoid allocating extra storage for this common point. * @param src the array holding the coordinates for the source curve * @param srcoff the offset into the array of the beginning of the * the 6 source coordinates * @param left the array for storing the coordinates for the first * half of the subdivided curve * @param leftoff the offset into the array of the beginning of the * the 6 left coordinates * @param right the array for storing the coordinates for the second * half of the subdivided curve * @param rightoff the offset into the array of the beginning of the * the 6 right coordinates * @since 1.2 */ public static void subdivide(double[] src, int srcoff, double[] left, int leftoff, double[] right, int rightoff) { double x1 = src[srcoff + 0]; double y1 = src[srcoff + 1]; double ctrlx = src[srcoff + 2]; double ctrly = src[srcoff + 3]; double x2 = src[srcoff + 4]; double y2 = src[srcoff + 5]; if (left != null) { left[leftoff + 0] = x1; left[leftoff + 1] = y1; } if (right != null) { right[rightoff + 4] = x2; right[rightoff + 5] = y2; } x1 = (x1 + ctrlx) / 2.0; y1 = (y1 + ctrly) / 2.0; x2 = (x2 + ctrlx) / 2.0; y2 = (y2 + ctrly) / 2.0; ctrlx = (x1 + x2) / 2.0; ctrly = (y1 + y2) / 2.0; if (left != null) { left[leftoff + 2] = x1; left[leftoff + 3] = y1; left[leftoff + 4] = ctrlx; left[leftoff + 5] = ctrly; } if (right != null) { right[rightoff + 0] = ctrlx; right[rightoff + 1] = ctrly; right[rightoff + 2] = x2; right[rightoff + 3] = y2; } } /** * Solves the quadratic whose coefficients are in the {@code eqn} * array and places the non-complex roots back into the same array, * returning the number of roots. The quadratic solved is represented * by the equation: * <pre> * eqn = {C, B, A}; * ax^2 + bx + c = 0 * </pre> * A return value of {@code -1} is used to distinguish a constant * equation, which might be always 0 or never 0, from an equation that * has no zeroes. * @param eqn the array that contains the quadratic coefficients * @return the number of roots, or {@code -1} if the equation is * a constant * @since 1.2 */ public static int solveQuadratic(double[] eqn) { return solveQuadratic(eqn, eqn); } /** * Solves the quadratic whose coefficients are in the {@code eqn} * array and places the non-complex roots into the {@code res} * array, returning the number of roots. * The quadratic solved is represented by the equation: * <pre> * eqn = {C, B, A}; * ax^2 + bx + c = 0 * </pre> * A return value of {@code -1} is used to distinguish a constant * equation, which might be always 0 or never 0, from an equation that * has no zeroes. * @param eqn the specified array of coefficients to use to solve * the quadratic equation * @param res the array that contains the non-complex roots * resulting from the solution of the quadratic equation * @return the number of roots, or {@code -1} if the equation is * a constant. * @since 1.3 */ public static int solveQuadratic(double[] eqn, double[] res) { double a = eqn[2]; double b = eqn[1]; double c = eqn[0]; int roots = 0; if (a == 0.0) { // The quadratic parabola has degenerated to a line. if (b == 0.0) { // The line has degenerated to a constant. return -1; } res[roots++] = -c / b; } else { // From Numerical Recipes, 5.6, Quadratic and Cubic Equations double d = b * b - 4.0 * a * c; if (d < 0.0) { // If d < 0.0, then there are no roots return 0; } d = Math.sqrt(d); // For accuracy, calculate one root using: // (-b +/- d) / 2a // and the other using: // 2c / (-b +/- d) // Choose the sign of the +/- so that b+d gets larger in magnitude if (b < 0.0) { d = -d; } double q = (b + d) / -2.0; // We already tested a for being 0 above res[roots++] = q / a; if (q != 0.0) { res[roots++] = c / q; } } return roots; } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(double x, double y) { double x1 = getX1(); double y1 = getY1(); double xc = getCtrlX(); double yc = getCtrlY(); double x2 = getX2(); double y2 = getY2(); /* * We have a convex shape bounded by quad curve Pc(t) * and ine Pl(t). * * P1 = (x1, y1) - start point of curve * P2 = (x2, y2) - end point of curve * Pc = (xc, yc) - control point * * Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 = * = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1 * Pl(t) = P1*(1 - t) + P2*t * t = [0:1] * * P = (x, y) - point of interest * * Let's look at second derivative of quad curve equation: * * Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq'' * It's constant vector. * * Let's draw a line through P to be parallel to this * vector and find the intersection of the quad curve * and the line. * * Pq(t) is point of intersection if system of equations * below has the solution. * * L(s) = P + Pq''*s == Pq(t) * Pq''*s + (P - Pq(t)) == 0 * * | xq''*s + (x - xq(t)) == 0 * | yq''*s + (y - yq(t)) == 0 * * This system has the solution if rank of its matrix equals to 1. * That is, determinant of the matrix should be zero. * * (y - yq(t))*xq'' == (x - xq(t))*yq'' * * Let's solve this equation with 't' variable. * Also let kx = x1 - 2*xc + x2 * ky = y1 - 2*yc + y2 * * t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) / * ((xc - x1)*ky - (yc - y1)*kx) * * Let's do the same for our line Pl(t): * * t0l = ((x - x1)*ky - (y - y1)*kx) / * ((x2 - x1)*ky - (y2 - y1)*kx) * * It's easy to check that t0q == t0l. This fact means * we can compute t0 only one time. * * In case t0 < 0 or t0 > 1, we have an intersections outside * of shape bounds. So, P is definitely out of shape. * * In case t0 is inside [0:1], we should calculate Pq(t0) * and Pl(t0). We have three points for now, and all of them * lie on one line. So, we just need to detect, is our point * of interest between points of intersections or not. * * If the denominator in the t0q and t0l equations is * zero, then the points must be collinear and so the * curve is degenerate and encloses no area. Thus the * result is false. */ double kx = x1 - 2 * xc + x2; double ky = y1 - 2 * yc + y2; double dx = x - x1; double dy = y - y1; double dxl = x2 - x1; double dyl = y2 - y1; double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx); if (t0 < 0 || t0 > 1 || t0 != t0) { return false; } double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1; double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1; double xl = dxl * t0 + x1; double yl = dyl * t0 + y1; return (x >= xb && x < xl) || (x >= xl && x < xb) || (y >= yb && y < yl) || (y >= yl && y < yb); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(Point2D p) { return contains(p.getX(), p.getY()); } /** * Fill an array with the coefficients of the parametric equation * in t, ready for solving against val with solveQuadratic. * We currently have: * val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2 * = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2 * = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 * 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 * 0 = C + Bt + At^2 * C = C1 - val * B = 2*CP - 2*C1 * A = C1 - 2*CP + C2 */ private static void fillEqn(double[] eqn, double val, double c1, double cp, double c2) { eqn[0] = c1 - val; eqn[1] = cp + cp - c1 - c1; eqn[2] = c1 - cp - cp + c2; return; } /** * Evaluate the t values in the first num slots of the vals[] array * and place the evaluated values back into the same array. Only * evaluate t values that are within the range <0, 1>, including * the 0 and 1 ends of the range iff the include0 or include1 * booleans are true. If an "inflection" equation is handed in, * then any points which represent a point of inflection for that * quadratic equation are also ignored. */ private static int evalQuadratic(double[] vals, int num, boolean include0, boolean include1, double[] inflect, double c1, double ctrl, double c2) { int j = 0; for (int i = 0; i < num; i++) { double t = vals[i]; if ((include0 ? t >= 0 : t > 0) && (include1 ? t <= 1 : t < 1) && (inflect == null || inflect[1] + 2 * inflect[2] * t != 0)) { double u = 1 - t; vals[j++] = c1 * u * u + 2 * ctrl * t * u + c2 * t * t; } } return j; } private static final int BELOW = -2; private static final int LOWEDGE = -1; private static final int INSIDE = 0; private static final int HIGHEDGE = 1; private static final int ABOVE = 2; /** * Determine where coord lies with respect to the range from * low to high. It is assumed that low <= high. The return * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE, * or ABOVE. */ private static int getTag(double coord, double low, double high) { if (coord <= low) { return (coord < low ? BELOW : LOWEDGE); } if (coord >= high) { return (coord > high ? ABOVE : HIGHEDGE); } return INSIDE; } /** * Determine if the pttag represents a coordinate that is already * in its test range, or is on the border with either of the two * opttags representing another coordinate that is "towards the * inside" of that test range. In other words, are either of the * two "opt" points "drawing the pt inward"? */ private static boolean inwards(int pttag, int opt1tag, int opt2tag) { switch (pttag) { case BELOW: case ABOVE: default: return false; case LOWEDGE: return (opt1tag >= INSIDE || opt2tag >= INSIDE); case INSIDE: return true; case HIGHEDGE: return (opt1tag <= INSIDE || opt2tag <= INSIDE); } } /** * {@inheritDoc} * @since 1.2 */ public boolean intersects(double x, double y, double w, double h) { // Trivially reject non-existant rectangles if (w <= 0 || h <= 0) { return false; } // Trivially accept if either endpoint is inside the rectangle // (not on its border since it may end there and not go inside) // Record where they lie with respect to the rectangle. // -1 => left, 0 => inside, 1 => right double x1 = getX1(); double y1 = getY1(); int x1tag = getTag(x1, x, x + w); int y1tag = getTag(y1, y, y + h); if (x1tag == INSIDE && y1tag == INSIDE) { return true; } double x2 = getX2(); double y2 = getY2(); int x2tag = getTag(x2, x, x + w); int y2tag = getTag(y2, y, y + h); if (x2tag == INSIDE && y2tag == INSIDE) { return true; } double ctrlx = getCtrlX(); double ctrly = getCtrlY(); int ctrlxtag = getTag(ctrlx, x, x + w); int ctrlytag = getTag(ctrly, y, y + h); // Trivially reject if all points are entirely to one side of // the rectangle. if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) { return false; // All points left } if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) { return false; // All points above } if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) { return false; // All points right } if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) { return false; // All points below } // Test for endpoints on the edge where either the segment // or the curve is headed "inwards" from them // Note: These tests are a superset of the fast endpoint tests // above and thus repeat those tests, but take more time // and cover more cases if (inwards(x1tag, x2tag, ctrlxtag) && inwards(y1tag, y2tag, ctrlytag)) { // First endpoint on border with either edge moving inside return true; } if (inwards(x2tag, x1tag, ctrlxtag) && inwards(y2tag, y1tag, ctrlytag)) { // Second endpoint on border with either edge moving inside return true; } // Trivially accept if endpoints span directly across the rectangle boolean xoverlap = (x1tag * x2tag <= 0); boolean yoverlap = (y1tag * y2tag <= 0); if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) { return true; } if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) { return true; } // We now know that both endpoints are outside the rectangle // but the 3 points are not all on one side of the rectangle. // Therefore the curve cannot be contained inside the rectangle, // but the rectangle might be contained inside the curve, or // the curve might intersect the boundary of the rectangle. double[] eqn = new double[3]; double[] res = new double[3]; if (!yoverlap) { // Both Y coordinates for the closing segment are above or // below the rectangle which means that we can only intersect // if the curve crosses the top (or bottom) of the rectangle // in more than one place and if those crossing locations // span the horizontal range of the rectangle. fillEqn(eqn, (y1tag < INSIDE ? y : y + h), y1, ctrly, y2); return (solveQuadratic(eqn, res) == 2 && evalQuadratic(res, 2, true, true, null, x1, ctrlx, x2) == 2 && getTag(res[0], x, x + w) * getTag(res[1], x, x + w) <= 0); } // Y ranges overlap. Now we examine the X ranges if (!xoverlap) { // Both X coordinates for the closing segment are left of // or right of the rectangle which means that we can only // intersect if the curve crosses the left (or right) edge // of the rectangle in more than one place and if those // crossing locations span the vertical range of the rectangle. fillEqn(eqn, (x1tag < INSIDE ? x : x + w), x1, ctrlx, x2); return (solveQuadratic(eqn, res) == 2 && evalQuadratic(res, 2, true, true, null, y1, ctrly, y2) == 2 && getTag(res[0], y, y + h) * getTag(res[1], y, y + h) <= 0); } // The X and Y ranges of the endpoints overlap the X and Y // ranges of the rectangle, now find out how the endpoint // line segment intersects the Y range of the rectangle double dx = x2 - x1; double dy = y2 - y1; double k = y2 * x1 - x2 * y1; int c1tag, c2tag; if (y1tag == INSIDE) { c1tag = x1tag; } else { c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y + h)) / dy, x, x + w); } if (y2tag == INSIDE) { c2tag = x2tag; } else { c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y + h)) / dy, x, x + w); } // If the part of the line segment that intersects the Y range // of the rectangle crosses it horizontally - trivially accept if (c1tag * c2tag <= 0) { return true; } // Now we know that both the X and Y ranges intersect and that // the endpoint line segment does not directly cross the rectangle. // // We can almost treat this case like one of the cases above // where both endpoints are to one side, except that we will // only get one intersection of the curve with the vertical // side of the rectangle. This is because the endpoint segment // accounts for the other intersection. // // (Remember there is overlap in both the X and Y ranges which // means that the segment must cross at least one vertical edge // of the rectangle - in particular, the "near vertical side" - // leaving only one intersection for the curve.) // // Now we calculate the y tags of the two intersections on the // "near vertical side" of the rectangle. We will have one with // the endpoint segment, and one with the curve. If those two // vertical intersections overlap the Y range of the rectangle, // we have an intersection. Otherwise, we don't. // c1tag = vertical intersection class of the endpoint segment // // Choose the y tag of the endpoint that was not on the same // side of the rectangle as the subsegment calculated above. // Note that we can "steal" the existing Y tag of that endpoint // since it will be provably the same as the vertical intersection. c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag); // c2tag = vertical intersection class of the curve // // We have to calculate this one the straightforward way. // Note that the c2tag can still tell us which vertical edge // to test against. fillEqn(eqn, (c2tag < INSIDE ? x : x + w), x1, ctrlx, x2); int num = solveQuadratic(eqn, res); // Note: We should be able to assert(num == 2); since the // X range "crosses" (not touches) the vertical boundary, // but we pass num to evalQuadratic for completeness. evalQuadratic(res, num, true, true, null, y1, ctrly, y2); // Note: We can assert(num evals == 1); since one of the // 2 crossings will be out of the [0,1] range. c2tag = getTag(res[0], y, y + h); // Finally, we have an intersection if the two crossings // overlap the Y range of the rectangle. return (c1tag * c2tag <= 0); } /** * {@inheritDoc} * @since 1.2 */ public boolean intersects(Rectangle2D r) { return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight()); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(double x, double y, double w, double h) { if (w <= 0 || h <= 0) { return false; } // Assertion: Quadratic curves closed by connecting their // endpoints are always convex. return (contains(x, y) && contains(x + w, y) && contains(x + w, y + h) && contains(x, y + h)); } /** * {@inheritDoc} * @since 1.2 */ public boolean contains(Rectangle2D r) { return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); } /** * {@inheritDoc} * @since 1.2 */ public Rectangle getBounds() { return getBounds2D().getBounds(); } /** * Returns an iteration object that defines the boundary of the * shape of this {@code QuadCurve2D}. * The iterator for this class is not multi-threaded safe, * which means that this {@code QuadCurve2D} class does not * guarantee that modifications to the geometry of this * {@code QuadCurve2D} object do not affect any iterations of * that geometry that are already in process. * @param at an optional {@link AffineTransform} to apply to the * shape boundary * @return a {@link PathIterator} object that defines the boundary * of the shape. * @since 1.2 */ public PathIterator getPathIterator(AffineTransform at) { return new QuadIterator(this, at); } /** * Returns an iteration object that defines the boundary of the * flattened shape of this {@code QuadCurve2D}. * The iterator for this class is not multi-threaded safe, * which means that this {@code QuadCurve2D} class does not * guarantee that modifications to the geometry of this * {@code QuadCurve2D} object do not affect any iterations of * that geometry that are already in process. * @param at an optional {@code AffineTransform} to apply * to the boundary of the shape * @param flatness the maximum distance that the control points for a * subdivided curve can be with respect to a line connecting * the end points of this curve before this curve is * replaced by a straight line connecting the end points. * @return a {@code PathIterator} object that defines the * flattened boundary of the shape. * @since 1.2 */ public PathIterator getPathIterator(AffineTransform at, double flatness) { return new FlatteningPathIterator(getPathIterator(at), flatness); } /** * Creates a new object of the same class and with the same contents * as this object. * * @return a clone of this instance. * @exception OutOfMemoryError if there is not enough memory. * @see java.lang.Cloneable * @since 1.2 */ public Object clone() { try { return super.clone(); } catch (CloneNotSupportedException e) { // this shouldn't happen, since we are Cloneable throw new InternalError(e); } } }