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/*
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* Copyright 1997-2006 Sun Microsystems, Inc. All Rights Reserved.
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation. Sun designates this
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* particular file as subject to the "Classpath" exception as provided
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* by Sun in the LICENSE file that accompanied this code.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
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* CA 95054 USA or visit www.sun.com if you need additional information or
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* have any questions.
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*/
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package java.awt.geom;
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import java.awt.Shape;
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import java.awt.Rectangle;
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import java.util.Arrays;
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import java.io.Serializable;
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import sun.awt.geom.Curve;
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/**
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* The <code>CubicCurve2D</code> class defines a cubic parametric curve
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* segment in {@code (x,y)} coordinate space.
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* <p>
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* This class is only the abstract superclass for all objects which
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* store a 2D cubic curve segment.
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* The actual storage representation of the coordinates is left to
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* the subclass.
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*
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* @author Jim Graham
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* @since 1.2
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*/
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public abstract class CubicCurve2D implements Shape, Cloneable {
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/**
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* A cubic parametric curve segment specified with
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* {@code float} coordinates.
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* @since 1.2
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*/
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public static class Float extends CubicCurve2D implements Serializable {
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/**
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* The X coordinate of the start point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float x1;
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/**
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* The Y coordinate of the start point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float y1;
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/**
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* The X coordinate of the first control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float ctrlx1;
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/**
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* The Y coordinate of the first control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float ctrly1;
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/**
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* The X coordinate of the second control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float ctrlx2;
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/**
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* The Y coordinate of the second control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float ctrly2;
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/**
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* The X coordinate of the end point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float x2;
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/**
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* The Y coordinate of the end point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public float y2;
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/**
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* Constructs and initializes a CubicCurve with coordinates
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* (0, 0, 0, 0, 0, 0, 0, 0).
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* @since 1.2
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*/
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public Float() {
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}
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/**
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* Constructs and initializes a {@code CubicCurve2D} from
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* the specified {@code float} coordinates.
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*
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* @param x1 the X coordinate for the start point
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* of the resulting {@code CubicCurve2D}
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* @param y1 the Y coordinate for the start point
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* of the resulting {@code CubicCurve2D}
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* @param ctrlx1 the X coordinate for the first control point
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* of the resulting {@code CubicCurve2D}
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* @param ctrly1 the Y coordinate for the first control point
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* of the resulting {@code CubicCurve2D}
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* @param ctrlx2 the X coordinate for the second control point
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* of the resulting {@code CubicCurve2D}
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* @param ctrly2 the Y coordinate for the second control point
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* of the resulting {@code CubicCurve2D}
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* @param x2 the X coordinate for the end point
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* of the resulting {@code CubicCurve2D}
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* @param y2 the Y coordinate for the end point
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* of the resulting {@code CubicCurve2D}
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* @since 1.2
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*/
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public Float(float x1, float y1,
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float ctrlx1, float ctrly1,
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float ctrlx2, float ctrly2,
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float x2, float y2)
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{
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setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX1() {
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return (double) x1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY1() {
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return (double) y1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP1() {
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return new Point2D.Float(x1, y1);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlX1() {
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return (double) ctrlx1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlY1() {
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return (double) ctrly1;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getCtrlP1() {
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return new Point2D.Float(ctrlx1, ctrly1);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlX2() {
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return (double) ctrlx2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getCtrlY2() {
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return (double) ctrly2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getCtrlP2() {
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return new Point2D.Float(ctrlx2, ctrly2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getX2() {
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return (double) x2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public double getY2() {
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return (double) y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Point2D getP2() {
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return new Point2D.Float(x2, y2);
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public void setCurve(double x1, double y1,
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double ctrlx1, double ctrly1,
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double ctrlx2, double ctrly2,
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double x2, double y2)
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{
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this.x1 = (float) x1;
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this.y1 = (float) y1;
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this.ctrlx1 = (float) ctrlx1;
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this.ctrly1 = (float) ctrly1;
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this.ctrlx2 = (float) ctrlx2;
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this.ctrly2 = (float) ctrly2;
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this.x2 = (float) x2;
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this.y2 = (float) y2;
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}
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/**
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* Sets the location of the end points and control points
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* of this curve to the specified {@code float} coordinates.
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*
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* @param x1 the X coordinate used to set the start point
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* of this {@code CubicCurve2D}
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* @param y1 the Y coordinate used to set the start point
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* of this {@code CubicCurve2D}
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* @param ctrlx1 the X coordinate used to set the first control point
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* of this {@code CubicCurve2D}
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* @param ctrly1 the Y coordinate used to set the first control point
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* of this {@code CubicCurve2D}
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* @param ctrlx2 the X coordinate used to set the second control point
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* of this {@code CubicCurve2D}
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* @param ctrly2 the Y coordinate used to set the second control point
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* of this {@code CubicCurve2D}
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* @param x2 the X coordinate used to set the end point
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* of this {@code CubicCurve2D}
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* @param y2 the Y coordinate used to set the end point
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* of this {@code CubicCurve2D}
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* @since 1.2
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*/
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public void setCurve(float x1, float y1,
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float ctrlx1, float ctrly1,
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float ctrlx2, float ctrly2,
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float x2, float y2)
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{
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this.x1 = x1;
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this.y1 = y1;
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this.ctrlx1 = ctrlx1;
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this.ctrly1 = ctrly1;
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this.ctrlx2 = ctrlx2;
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this.ctrly2 = ctrly2;
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this.x2 = x2;
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this.y2 = y2;
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}
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/**
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* {@inheritDoc}
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* @since 1.2
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*/
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public Rectangle2D getBounds2D() {
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float left = Math.min(Math.min(x1, x2),
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Math.min(ctrlx1, ctrlx2));
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float top = Math.min(Math.min(y1, y2),
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Math.min(ctrly1, ctrly2));
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float right = Math.max(Math.max(x1, x2),
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Math.max(ctrlx1, ctrlx2));
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float bottom = Math.max(Math.max(y1, y2),
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Math.max(ctrly1, ctrly2));
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return new Rectangle2D.Float(left, top,
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right - left, bottom - top);
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}
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/*
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* JDK 1.6 serialVersionUID
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*/
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private static final long serialVersionUID = -1272015596714244385L;
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}
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/**
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* A cubic parametric curve segment specified with
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* {@code double} coordinates.
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* @since 1.2
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*/
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public static class Double extends CubicCurve2D implements Serializable {
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/**
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* The X coordinate of the start point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double x1;
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/**
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* The Y coordinate of the start point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double y1;
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/**
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* The X coordinate of the first control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double ctrlx1;
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/**
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* The Y coordinate of the first control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double ctrly1;
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/**
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* The X coordinate of the second control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double ctrlx2;
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/**
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* The Y coordinate of the second control point
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* of the cubic curve segment.
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* @since 1.2
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* @serial
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*/
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public double ctrly2;
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/**
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* The X coordinate of the end point
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* of the cubic curve segment.
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|
388 |
* @since 1.2
|
|
|
389 |
* @serial
|
|
|
390 |
*/
|
|
|
391 |
public double x2;
|
|
|
392 |
|
|
|
393 |
/**
|
|
|
394 |
* The Y coordinate of the end point
|
|
|
395 |
* of the cubic curve segment.
|
|
|
396 |
* @since 1.2
|
|
|
397 |
* @serial
|
|
|
398 |
*/
|
|
|
399 |
public double y2;
|
|
|
400 |
|
|
|
401 |
/**
|
|
|
402 |
* Constructs and initializes a CubicCurve with coordinates
|
|
|
403 |
* (0, 0, 0, 0, 0, 0, 0, 0).
|
|
|
404 |
* @since 1.2
|
|
|
405 |
*/
|
|
|
406 |
public Double() {
|
|
|
407 |
}
|
|
|
408 |
|
|
|
409 |
/**
|
|
|
410 |
* Constructs and initializes a {@code CubicCurve2D} from
|
|
|
411 |
* the specified {@code double} coordinates.
|
|
|
412 |
*
|
|
|
413 |
* @param x1 the X coordinate for the start point
|
|
|
414 |
* of the resulting {@code CubicCurve2D}
|
|
|
415 |
* @param y1 the Y coordinate for the start point
|
|
|
416 |
* of the resulting {@code CubicCurve2D}
|
|
|
417 |
* @param ctrlx1 the X coordinate for the first control point
|
|
|
418 |
* of the resulting {@code CubicCurve2D}
|
|
|
419 |
* @param ctrly1 the Y coordinate for the first control point
|
|
|
420 |
* of the resulting {@code CubicCurve2D}
|
|
|
421 |
* @param ctrlx2 the X coordinate for the second control point
|
|
|
422 |
* of the resulting {@code CubicCurve2D}
|
|
|
423 |
* @param ctrly2 the Y coordinate for the second control point
|
|
|
424 |
* of the resulting {@code CubicCurve2D}
|
|
|
425 |
* @param x2 the X coordinate for the end point
|
|
|
426 |
* of the resulting {@code CubicCurve2D}
|
|
|
427 |
* @param y2 the Y coordinate for the end point
|
|
|
428 |
* of the resulting {@code CubicCurve2D}
|
|
|
429 |
* @since 1.2
|
|
|
430 |
*/
|
|
|
431 |
public Double(double x1, double y1,
|
|
|
432 |
double ctrlx1, double ctrly1,
|
|
|
433 |
double ctrlx2, double ctrly2,
|
|
|
434 |
double x2, double y2)
|
|
|
435 |
{
|
|
|
436 |
setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
|
|
|
437 |
}
|
|
|
438 |
|
|
|
439 |
/**
|
|
|
440 |
* {@inheritDoc}
|
|
|
441 |
* @since 1.2
|
|
|
442 |
*/
|
|
|
443 |
public double getX1() {
|
|
|
444 |
return x1;
|
|
|
445 |
}
|
|
|
446 |
|
|
|
447 |
/**
|
|
|
448 |
* {@inheritDoc}
|
|
|
449 |
* @since 1.2
|
|
|
450 |
*/
|
|
|
451 |
public double getY1() {
|
|
|
452 |
return y1;
|
|
|
453 |
}
|
|
|
454 |
|
|
|
455 |
/**
|
|
|
456 |
* {@inheritDoc}
|
|
|
457 |
* @since 1.2
|
|
|
458 |
*/
|
|
|
459 |
public Point2D getP1() {
|
|
|
460 |
return new Point2D.Double(x1, y1);
|
|
|
461 |
}
|
|
|
462 |
|
|
|
463 |
/**
|
|
|
464 |
* {@inheritDoc}
|
|
|
465 |
* @since 1.2
|
|
|
466 |
*/
|
|
|
467 |
public double getCtrlX1() {
|
|
|
468 |
return ctrlx1;
|
|
|
469 |
}
|
|
|
470 |
|
|
|
471 |
/**
|
|
|
472 |
* {@inheritDoc}
|
|
|
473 |
* @since 1.2
|
|
|
474 |
*/
|
|
|
475 |
public double getCtrlY1() {
|
|
|
476 |
return ctrly1;
|
|
|
477 |
}
|
|
|
478 |
|
|
|
479 |
/**
|
|
|
480 |
* {@inheritDoc}
|
|
|
481 |
* @since 1.2
|
|
|
482 |
*/
|
|
|
483 |
public Point2D getCtrlP1() {
|
|
|
484 |
return new Point2D.Double(ctrlx1, ctrly1);
|
|
|
485 |
}
|
|
|
486 |
|
|
|
487 |
/**
|
|
|
488 |
* {@inheritDoc}
|
|
|
489 |
* @since 1.2
|
|
|
490 |
*/
|
|
|
491 |
public double getCtrlX2() {
|
|
|
492 |
return ctrlx2;
|
|
|
493 |
}
|
|
|
494 |
|
|
|
495 |
/**
|
|
|
496 |
* {@inheritDoc}
|
|
|
497 |
* @since 1.2
|
|
|
498 |
*/
|
|
|
499 |
public double getCtrlY2() {
|
|
|
500 |
return ctrly2;
|
|
|
501 |
}
|
|
|
502 |
|
|
|
503 |
/**
|
|
|
504 |
* {@inheritDoc}
|
|
|
505 |
* @since 1.2
|
|
|
506 |
*/
|
|
|
507 |
public Point2D getCtrlP2() {
|
|
|
508 |
return new Point2D.Double(ctrlx2, ctrly2);
|
|
|
509 |
}
|
|
|
510 |
|
|
|
511 |
/**
|
|
|
512 |
* {@inheritDoc}
|
|
|
513 |
* @since 1.2
|
|
|
514 |
*/
|
|
|
515 |
public double getX2() {
|
|
|
516 |
return x2;
|
|
|
517 |
}
|
|
|
518 |
|
|
|
519 |
/**
|
|
|
520 |
* {@inheritDoc}
|
|
|
521 |
* @since 1.2
|
|
|
522 |
*/
|
|
|
523 |
public double getY2() {
|
|
|
524 |
return y2;
|
|
|
525 |
}
|
|
|
526 |
|
|
|
527 |
/**
|
|
|
528 |
* {@inheritDoc}
|
|
|
529 |
* @since 1.2
|
|
|
530 |
*/
|
|
|
531 |
public Point2D getP2() {
|
|
|
532 |
return new Point2D.Double(x2, y2);
|
|
|
533 |
}
|
|
|
534 |
|
|
|
535 |
/**
|
|
|
536 |
* {@inheritDoc}
|
|
|
537 |
* @since 1.2
|
|
|
538 |
*/
|
|
|
539 |
public void setCurve(double x1, double y1,
|
|
|
540 |
double ctrlx1, double ctrly1,
|
|
|
541 |
double ctrlx2, double ctrly2,
|
|
|
542 |
double x2, double y2)
|
|
|
543 |
{
|
|
|
544 |
this.x1 = x1;
|
|
|
545 |
this.y1 = y1;
|
|
|
546 |
this.ctrlx1 = ctrlx1;
|
|
|
547 |
this.ctrly1 = ctrly1;
|
|
|
548 |
this.ctrlx2 = ctrlx2;
|
|
|
549 |
this.ctrly2 = ctrly2;
|
|
|
550 |
this.x2 = x2;
|
|
|
551 |
this.y2 = y2;
|
|
|
552 |
}
|
|
|
553 |
|
|
|
554 |
/**
|
|
|
555 |
* {@inheritDoc}
|
|
|
556 |
* @since 1.2
|
|
|
557 |
*/
|
|
|
558 |
public Rectangle2D getBounds2D() {
|
|
|
559 |
double left = Math.min(Math.min(x1, x2),
|
|
|
560 |
Math.min(ctrlx1, ctrlx2));
|
|
|
561 |
double top = Math.min(Math.min(y1, y2),
|
|
|
562 |
Math.min(ctrly1, ctrly2));
|
|
|
563 |
double right = Math.max(Math.max(x1, x2),
|
|
|
564 |
Math.max(ctrlx1, ctrlx2));
|
|
|
565 |
double bottom = Math.max(Math.max(y1, y2),
|
|
|
566 |
Math.max(ctrly1, ctrly2));
|
|
|
567 |
return new Rectangle2D.Double(left, top,
|
|
|
568 |
right - left, bottom - top);
|
|
|
569 |
}
|
|
|
570 |
|
|
|
571 |
/*
|
|
|
572 |
* JDK 1.6 serialVersionUID
|
|
|
573 |
*/
|
|
|
574 |
private static final long serialVersionUID = -4202960122839707295L;
|
|
|
575 |
}
|
|
|
576 |
|
|
|
577 |
/**
|
|
|
578 |
* This is an abstract class that cannot be instantiated directly.
|
|
|
579 |
* Type-specific implementation subclasses are available for
|
|
|
580 |
* instantiation and provide a number of formats for storing
|
|
|
581 |
* the information necessary to satisfy the various accessor
|
|
|
582 |
* methods below.
|
|
|
583 |
*
|
|
|
584 |
* @see java.awt.geom.CubicCurve2D.Float
|
|
|
585 |
* @see java.awt.geom.CubicCurve2D.Double
|
|
|
586 |
* @since 1.2
|
|
|
587 |
*/
|
|
|
588 |
protected CubicCurve2D() {
|
|
|
589 |
}
|
|
|
590 |
|
|
|
591 |
/**
|
|
|
592 |
* Returns the X coordinate of the start point in double precision.
|
|
|
593 |
* @return the X coordinate of the start point of the
|
|
|
594 |
* {@code CubicCurve2D}.
|
|
|
595 |
* @since 1.2
|
|
|
596 |
*/
|
|
|
597 |
public abstract double getX1();
|
|
|
598 |
|
|
|
599 |
/**
|
|
|
600 |
* Returns the Y coordinate of the start point in double precision.
|
|
|
601 |
* @return the Y coordinate of the start point of the
|
|
|
602 |
* {@code CubicCurve2D}.
|
|
|
603 |
* @since 1.2
|
|
|
604 |
*/
|
|
|
605 |
public abstract double getY1();
|
|
|
606 |
|
|
|
607 |
/**
|
|
|
608 |
* Returns the start point.
|
|
|
609 |
* @return a {@code Point2D} that is the start point of
|
|
|
610 |
* the {@code CubicCurve2D}.
|
|
|
611 |
* @since 1.2
|
|
|
612 |
*/
|
|
|
613 |
public abstract Point2D getP1();
|
|
|
614 |
|
|
|
615 |
/**
|
|
|
616 |
* Returns the X coordinate of the first control point in double precision.
|
|
|
617 |
* @return the X coordinate of the first control point of the
|
|
|
618 |
* {@code CubicCurve2D}.
|
|
|
619 |
* @since 1.2
|
|
|
620 |
*/
|
|
|
621 |
public abstract double getCtrlX1();
|
|
|
622 |
|
|
|
623 |
/**
|
|
|
624 |
* Returns the Y coordinate of the first control point in double precision.
|
|
|
625 |
* @return the Y coordinate of the first control point of the
|
|
|
626 |
* {@code CubicCurve2D}.
|
|
|
627 |
* @since 1.2
|
|
|
628 |
*/
|
|
|
629 |
public abstract double getCtrlY1();
|
|
|
630 |
|
|
|
631 |
/**
|
|
|
632 |
* Returns the first control point.
|
|
|
633 |
* @return a {@code Point2D} that is the first control point of
|
|
|
634 |
* the {@code CubicCurve2D}.
|
|
|
635 |
* @since 1.2
|
|
|
636 |
*/
|
|
|
637 |
public abstract Point2D getCtrlP1();
|
|
|
638 |
|
|
|
639 |
/**
|
|
|
640 |
* Returns the X coordinate of the second control point
|
|
|
641 |
* in double precision.
|
|
|
642 |
* @return the X coordinate of the second control point of the
|
|
|
643 |
* {@code CubicCurve2D}.
|
|
|
644 |
* @since 1.2
|
|
|
645 |
*/
|
|
|
646 |
public abstract double getCtrlX2();
|
|
|
647 |
|
|
|
648 |
/**
|
|
|
649 |
* Returns the Y coordinate of the second control point
|
|
|
650 |
* in double precision.
|
|
|
651 |
* @return the Y coordinate of the second control point of the
|
|
|
652 |
* {@code CubicCurve2D}.
|
|
|
653 |
* @since 1.2
|
|
|
654 |
*/
|
|
|
655 |
public abstract double getCtrlY2();
|
|
|
656 |
|
|
|
657 |
/**
|
|
|
658 |
* Returns the second control point.
|
|
|
659 |
* @return a {@code Point2D} that is the second control point of
|
|
|
660 |
* the {@code CubicCurve2D}.
|
|
|
661 |
* @since 1.2
|
|
|
662 |
*/
|
|
|
663 |
public abstract Point2D getCtrlP2();
|
|
|
664 |
|
|
|
665 |
/**
|
|
|
666 |
* Returns the X coordinate of the end point in double precision.
|
|
|
667 |
* @return the X coordinate of the end point of the
|
|
|
668 |
* {@code CubicCurve2D}.
|
|
|
669 |
* @since 1.2
|
|
|
670 |
*/
|
|
|
671 |
public abstract double getX2();
|
|
|
672 |
|
|
|
673 |
/**
|
|
|
674 |
* Returns the Y coordinate of the end point in double precision.
|
|
|
675 |
* @return the Y coordinate of the end point of the
|
|
|
676 |
* {@code CubicCurve2D}.
|
|
|
677 |
* @since 1.2
|
|
|
678 |
*/
|
|
|
679 |
public abstract double getY2();
|
|
|
680 |
|
|
|
681 |
/**
|
|
|
682 |
* Returns the end point.
|
|
|
683 |
* @return a {@code Point2D} that is the end point of
|
|
|
684 |
* the {@code CubicCurve2D}.
|
|
|
685 |
* @since 1.2
|
|
|
686 |
*/
|
|
|
687 |
public abstract Point2D getP2();
|
|
|
688 |
|
|
|
689 |
/**
|
|
|
690 |
* Sets the location of the end points and control points of this curve
|
|
|
691 |
* to the specified double coordinates.
|
|
|
692 |
*
|
|
|
693 |
* @param x1 the X coordinate used to set the start point
|
|
|
694 |
* of this {@code CubicCurve2D}
|
|
|
695 |
* @param y1 the Y coordinate used to set the start point
|
|
|
696 |
* of this {@code CubicCurve2D}
|
|
|
697 |
* @param ctrlx1 the X coordinate used to set the first control point
|
|
|
698 |
* of this {@code CubicCurve2D}
|
|
|
699 |
* @param ctrly1 the Y coordinate used to set the first control point
|
|
|
700 |
* of this {@code CubicCurve2D}
|
|
|
701 |
* @param ctrlx2 the X coordinate used to set the second control point
|
|
|
702 |
* of this {@code CubicCurve2D}
|
|
|
703 |
* @param ctrly2 the Y coordinate used to set the second control point
|
|
|
704 |
* of this {@code CubicCurve2D}
|
|
|
705 |
* @param x2 the X coordinate used to set the end point
|
|
|
706 |
* of this {@code CubicCurve2D}
|
|
|
707 |
* @param y2 the Y coordinate used to set the end point
|
|
|
708 |
* of this {@code CubicCurve2D}
|
|
|
709 |
* @since 1.2
|
|
|
710 |
*/
|
|
|
711 |
public abstract void setCurve(double x1, double y1,
|
|
|
712 |
double ctrlx1, double ctrly1,
|
|
|
713 |
double ctrlx2, double ctrly2,
|
|
|
714 |
double x2, double y2);
|
|
|
715 |
|
|
|
716 |
/**
|
|
|
717 |
* Sets the location of the end points and control points of this curve
|
|
|
718 |
* to the double coordinates at the specified offset in the specified
|
|
|
719 |
* array.
|
|
|
720 |
* @param coords a double array containing coordinates
|
|
|
721 |
* @param offset the index of <code>coords</code> from which to begin
|
|
|
722 |
* setting the end points and control points of this curve
|
|
|
723 |
* to the coordinates contained in <code>coords</code>
|
|
|
724 |
* @since 1.2
|
|
|
725 |
*/
|
|
|
726 |
public void setCurve(double[] coords, int offset) {
|
|
|
727 |
setCurve(coords[offset + 0], coords[offset + 1],
|
|
|
728 |
coords[offset + 2], coords[offset + 3],
|
|
|
729 |
coords[offset + 4], coords[offset + 5],
|
|
|
730 |
coords[offset + 6], coords[offset + 7]);
|
|
|
731 |
}
|
|
|
732 |
|
|
|
733 |
/**
|
|
|
734 |
* Sets the location of the end points and control points of this curve
|
|
|
735 |
* to the specified <code>Point2D</code> coordinates.
|
|
|
736 |
* @param p1 the first specified <code>Point2D</code> used to set the
|
|
|
737 |
* start point of this curve
|
|
|
738 |
* @param cp1 the second specified <code>Point2D</code> used to set the
|
|
|
739 |
* first control point of this curve
|
|
|
740 |
* @param cp2 the third specified <code>Point2D</code> used to set the
|
|
|
741 |
* second control point of this curve
|
|
|
742 |
* @param p2 the fourth specified <code>Point2D</code> used to set the
|
|
|
743 |
* end point of this curve
|
|
|
744 |
* @since 1.2
|
|
|
745 |
*/
|
|
|
746 |
public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
|
|
|
747 |
setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
|
|
|
748 |
cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
|
|
|
749 |
}
|
|
|
750 |
|
|
|
751 |
/**
|
|
|
752 |
* Sets the location of the end points and control points of this curve
|
|
|
753 |
* to the coordinates of the <code>Point2D</code> objects at the specified
|
|
|
754 |
* offset in the specified array.
|
|
|
755 |
* @param pts an array of <code>Point2D</code> objects
|
|
|
756 |
* @param offset the index of <code>pts</code> from which to begin setting
|
|
|
757 |
* the end points and control points of this curve to the
|
|
|
758 |
* points contained in <code>pts</code>
|
|
|
759 |
* @since 1.2
|
|
|
760 |
*/
|
|
|
761 |
public void setCurve(Point2D[] pts, int offset) {
|
|
|
762 |
setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
|
|
|
763 |
pts[offset + 1].getX(), pts[offset + 1].getY(),
|
|
|
764 |
pts[offset + 2].getX(), pts[offset + 2].getY(),
|
|
|
765 |
pts[offset + 3].getX(), pts[offset + 3].getY());
|
|
|
766 |
}
|
|
|
767 |
|
|
|
768 |
/**
|
|
|
769 |
* Sets the location of the end points and control points of this curve
|
|
|
770 |
* to the same as those in the specified <code>CubicCurve2D</code>.
|
|
|
771 |
* @param c the specified <code>CubicCurve2D</code>
|
|
|
772 |
* @since 1.2
|
|
|
773 |
*/
|
|
|
774 |
public void setCurve(CubicCurve2D c) {
|
|
|
775 |
setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
|
|
|
776 |
c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
|
|
|
777 |
}
|
|
|
778 |
|
|
|
779 |
/**
|
|
|
780 |
* Returns the square of the flatness of the cubic curve specified
|
|
|
781 |
* by the indicated control points. The flatness is the maximum distance
|
|
|
782 |
* of a control point from the line connecting the end points.
|
|
|
783 |
*
|
|
|
784 |
* @param x1 the X coordinate that specifies the start point
|
|
|
785 |
* of a {@code CubicCurve2D}
|
|
|
786 |
* @param y1 the Y coordinate that specifies the start point
|
|
|
787 |
* of a {@code CubicCurve2D}
|
|
|
788 |
* @param ctrlx1 the X coordinate that specifies the first control point
|
|
|
789 |
* of a {@code CubicCurve2D}
|
|
|
790 |
* @param ctrly1 the Y coordinate that specifies the first control point
|
|
|
791 |
* of a {@code CubicCurve2D}
|
|
|
792 |
* @param ctrlx2 the X coordinate that specifies the second control point
|
|
|
793 |
* of a {@code CubicCurve2D}
|
|
|
794 |
* @param ctrly2 the Y coordinate that specifies the second control point
|
|
|
795 |
* of a {@code CubicCurve2D}
|
|
|
796 |
* @param x2 the X coordinate that specifies the end point
|
|
|
797 |
* of a {@code CubicCurve2D}
|
|
|
798 |
* @param y2 the Y coordinate that specifies the end point
|
|
|
799 |
* of a {@code CubicCurve2D}
|
|
|
800 |
* @return the square of the flatness of the {@code CubicCurve2D}
|
|
|
801 |
* represented by the specified coordinates.
|
|
|
802 |
* @since 1.2
|
|
|
803 |
*/
|
|
|
804 |
public static double getFlatnessSq(double x1, double y1,
|
|
|
805 |
double ctrlx1, double ctrly1,
|
|
|
806 |
double ctrlx2, double ctrly2,
|
|
|
807 |
double x2, double y2) {
|
|
|
808 |
return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
|
|
|
809 |
Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));
|
|
|
810 |
|
|
|
811 |
}
|
|
|
812 |
|
|
|
813 |
/**
|
|
|
814 |
* Returns the flatness of the cubic curve specified
|
|
|
815 |
* by the indicated control points. The flatness is the maximum distance
|
|
|
816 |
* of a control point from the line connecting the end points.
|
|
|
817 |
*
|
|
|
818 |
* @param x1 the X coordinate that specifies the start point
|
|
|
819 |
* of a {@code CubicCurve2D}
|
|
|
820 |
* @param y1 the Y coordinate that specifies the start point
|
|
|
821 |
* of a {@code CubicCurve2D}
|
|
|
822 |
* @param ctrlx1 the X coordinate that specifies the first control point
|
|
|
823 |
* of a {@code CubicCurve2D}
|
|
|
824 |
* @param ctrly1 the Y coordinate that specifies the first control point
|
|
|
825 |
* of a {@code CubicCurve2D}
|
|
|
826 |
* @param ctrlx2 the X coordinate that specifies the second control point
|
|
|
827 |
* of a {@code CubicCurve2D}
|
|
|
828 |
* @param ctrly2 the Y coordinate that specifies the second control point
|
|
|
829 |
* of a {@code CubicCurve2D}
|
|
|
830 |
* @param x2 the X coordinate that specifies the end point
|
|
|
831 |
* of a {@code CubicCurve2D}
|
|
|
832 |
* @param y2 the Y coordinate that specifies the end point
|
|
|
833 |
* of a {@code CubicCurve2D}
|
|
|
834 |
* @return the flatness of the {@code CubicCurve2D}
|
|
|
835 |
* represented by the specified coordinates.
|
|
|
836 |
* @since 1.2
|
|
|
837 |
*/
|
|
|
838 |
public static double getFlatness(double x1, double y1,
|
|
|
839 |
double ctrlx1, double ctrly1,
|
|
|
840 |
double ctrlx2, double ctrly2,
|
|
|
841 |
double x2, double y2) {
|
|
|
842 |
return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
|
|
|
843 |
ctrlx2, ctrly2, x2, y2));
|
|
|
844 |
}
|
|
|
845 |
|
|
|
846 |
/**
|
|
|
847 |
* Returns the square of the flatness of the cubic curve specified
|
|
|
848 |
* by the control points stored in the indicated array at the
|
|
|
849 |
* indicated index. The flatness is the maximum distance
|
|
|
850 |
* of a control point from the line connecting the end points.
|
|
|
851 |
* @param coords an array containing coordinates
|
|
|
852 |
* @param offset the index of <code>coords</code> from which to begin
|
|
|
853 |
* getting the end points and control points of the curve
|
|
|
854 |
* @return the square of the flatness of the <code>CubicCurve2D</code>
|
|
|
855 |
* specified by the coordinates in <code>coords</code> at
|
|
|
856 |
* the specified offset.
|
|
|
857 |
* @since 1.2
|
|
|
858 |
*/
|
|
|
859 |
public static double getFlatnessSq(double coords[], int offset) {
|
|
|
860 |
return getFlatnessSq(coords[offset + 0], coords[offset + 1],
|
|
|
861 |
coords[offset + 2], coords[offset + 3],
|
|
|
862 |
coords[offset + 4], coords[offset + 5],
|
|
|
863 |
coords[offset + 6], coords[offset + 7]);
|
|
|
864 |
}
|
|
|
865 |
|
|
|
866 |
/**
|
|
|
867 |
* Returns the flatness of the cubic curve specified
|
|
|
868 |
* by the control points stored in the indicated array at the
|
|
|
869 |
* indicated index. The flatness is the maximum distance
|
|
|
870 |
* of a control point from the line connecting the end points.
|
|
|
871 |
* @param coords an array containing coordinates
|
|
|
872 |
* @param offset the index of <code>coords</code> from which to begin
|
|
|
873 |
* getting the end points and control points of the curve
|
|
|
874 |
* @return the flatness of the <code>CubicCurve2D</code>
|
|
|
875 |
* specified by the coordinates in <code>coords</code> at
|
|
|
876 |
* the specified offset.
|
|
|
877 |
* @since 1.2
|
|
|
878 |
*/
|
|
|
879 |
public static double getFlatness(double coords[], int offset) {
|
|
|
880 |
return getFlatness(coords[offset + 0], coords[offset + 1],
|
|
|
881 |
coords[offset + 2], coords[offset + 3],
|
|
|
882 |
coords[offset + 4], coords[offset + 5],
|
|
|
883 |
coords[offset + 6], coords[offset + 7]);
|
|
|
884 |
}
|
|
|
885 |
|
|
|
886 |
/**
|
|
|
887 |
* Returns the square of the flatness of this curve. The flatness is the
|
|
|
888 |
* maximum distance of a control point from the line connecting the
|
|
|
889 |
* end points.
|
|
|
890 |
* @return the square of the flatness of this curve.
|
|
|
891 |
* @since 1.2
|
|
|
892 |
*/
|
|
|
893 |
public double getFlatnessSq() {
|
|
|
894 |
return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
|
|
|
895 |
getCtrlX2(), getCtrlY2(), getX2(), getY2());
|
|
|
896 |
}
|
|
|
897 |
|
|
|
898 |
/**
|
|
|
899 |
* Returns the flatness of this curve. The flatness is the
|
|
|
900 |
* maximum distance of a control point from the line connecting the
|
|
|
901 |
* end points.
|
|
|
902 |
* @return the flatness of this curve.
|
|
|
903 |
* @since 1.2
|
|
|
904 |
*/
|
|
|
905 |
public double getFlatness() {
|
|
|
906 |
return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
|
|
|
907 |
getCtrlX2(), getCtrlY2(), getX2(), getY2());
|
|
|
908 |
}
|
|
|
909 |
|
|
|
910 |
/**
|
|
|
911 |
* Subdivides this cubic curve and stores the resulting two
|
|
|
912 |
* subdivided curves into the left and right curve parameters.
|
|
|
913 |
* Either or both of the left and right objects may be the same
|
|
|
914 |
* as this object or null.
|
|
|
915 |
* @param left the cubic curve object for storing for the left or
|
|
|
916 |
* first half of the subdivided curve
|
|
|
917 |
* @param right the cubic curve object for storing for the right or
|
|
|
918 |
* second half of the subdivided curve
|
|
|
919 |
* @since 1.2
|
|
|
920 |
*/
|
|
|
921 |
public void subdivide(CubicCurve2D left, CubicCurve2D right) {
|
|
|
922 |
subdivide(this, left, right);
|
|
|
923 |
}
|
|
|
924 |
|
|
|
925 |
/**
|
|
|
926 |
* Subdivides the cubic curve specified by the <code>src</code> parameter
|
|
|
927 |
* and stores the resulting two subdivided curves into the
|
|
|
928 |
* <code>left</code> and <code>right</code> curve parameters.
|
|
|
929 |
* Either or both of the <code>left</code> and <code>right</code> objects
|
|
|
930 |
* may be the same as the <code>src</code> object or <code>null</code>.
|
|
|
931 |
* @param src the cubic curve to be subdivided
|
|
|
932 |
* @param left the cubic curve object for storing the left or
|
|
|
933 |
* first half of the subdivided curve
|
|
|
934 |
* @param right the cubic curve object for storing the right or
|
|
|
935 |
* second half of the subdivided curve
|
|
|
936 |
* @since 1.2
|
|
|
937 |
*/
|
|
|
938 |
public static void subdivide(CubicCurve2D src,
|
|
|
939 |
CubicCurve2D left,
|
|
|
940 |
CubicCurve2D right) {
|
|
|
941 |
double x1 = src.getX1();
|
|
|
942 |
double y1 = src.getY1();
|
|
|
943 |
double ctrlx1 = src.getCtrlX1();
|
|
|
944 |
double ctrly1 = src.getCtrlY1();
|
|
|
945 |
double ctrlx2 = src.getCtrlX2();
|
|
|
946 |
double ctrly2 = src.getCtrlY2();
|
|
|
947 |
double x2 = src.getX2();
|
|
|
948 |
double y2 = src.getY2();
|
|
|
949 |
double centerx = (ctrlx1 + ctrlx2) / 2.0;
|
|
|
950 |
double centery = (ctrly1 + ctrly2) / 2.0;
|
|
|
951 |
ctrlx1 = (x1 + ctrlx1) / 2.0;
|
|
|
952 |
ctrly1 = (y1 + ctrly1) / 2.0;
|
|
|
953 |
ctrlx2 = (x2 + ctrlx2) / 2.0;
|
|
|
954 |
ctrly2 = (y2 + ctrly2) / 2.0;
|
|
|
955 |
double ctrlx12 = (ctrlx1 + centerx) / 2.0;
|
|
|
956 |
double ctrly12 = (ctrly1 + centery) / 2.0;
|
|
|
957 |
double ctrlx21 = (ctrlx2 + centerx) / 2.0;
|
|
|
958 |
double ctrly21 = (ctrly2 + centery) / 2.0;
|
|
|
959 |
centerx = (ctrlx12 + ctrlx21) / 2.0;
|
|
|
960 |
centery = (ctrly12 + ctrly21) / 2.0;
|
|
|
961 |
if (left != null) {
|
|
|
962 |
left.setCurve(x1, y1, ctrlx1, ctrly1,
|
|
|
963 |
ctrlx12, ctrly12, centerx, centery);
|
|
|
964 |
}
|
|
|
965 |
if (right != null) {
|
|
|
966 |
right.setCurve(centerx, centery, ctrlx21, ctrly21,
|
|
|
967 |
ctrlx2, ctrly2, x2, y2);
|
|
|
968 |
}
|
|
|
969 |
}
|
|
|
970 |
|
|
|
971 |
/**
|
|
|
972 |
* Subdivides the cubic curve specified by the coordinates
|
|
|
973 |
* stored in the <code>src</code> array at indices <code>srcoff</code>
|
|
|
974 |
* through (<code>srcoff</code> + 7) and stores the
|
|
|
975 |
* resulting two subdivided curves into the two result arrays at the
|
|
|
976 |
* corresponding indices.
|
|
|
977 |
* Either or both of the <code>left</code> and <code>right</code>
|
|
|
978 |
* arrays may be <code>null</code> or a reference to the same array
|
|
|
979 |
* as the <code>src</code> array.
|
|
|
980 |
* Note that the last point in the first subdivided curve is the
|
|
|
981 |
* same as the first point in the second subdivided curve. Thus,
|
|
|
982 |
* it is possible to pass the same array for <code>left</code>
|
|
|
983 |
* and <code>right</code> and to use offsets, such as <code>rightoff</code>
|
|
|
984 |
* equals (<code>leftoff</code> + 6), in order
|
|
|
985 |
* to avoid allocating extra storage for this common point.
|
|
|
986 |
* @param src the array holding the coordinates for the source curve
|
|
|
987 |
* @param srcoff the offset into the array of the beginning of the
|
|
|
988 |
* the 6 source coordinates
|
|
|
989 |
* @param left the array for storing the coordinates for the first
|
|
|
990 |
* half of the subdivided curve
|
|
|
991 |
* @param leftoff the offset into the array of the beginning of the
|
|
|
992 |
* the 6 left coordinates
|
|
|
993 |
* @param right the array for storing the coordinates for the second
|
|
|
994 |
* half of the subdivided curve
|
|
|
995 |
* @param rightoff the offset into the array of the beginning of the
|
|
|
996 |
* the 6 right coordinates
|
|
|
997 |
* @since 1.2
|
|
|
998 |
*/
|
|
|
999 |
public static void subdivide(double src[], int srcoff,
|
|
|
1000 |
double left[], int leftoff,
|
|
|
1001 |
double right[], int rightoff) {
|
|
|
1002 |
double x1 = src[srcoff + 0];
|
|
|
1003 |
double y1 = src[srcoff + 1];
|
|
|
1004 |
double ctrlx1 = src[srcoff + 2];
|
|
|
1005 |
double ctrly1 = src[srcoff + 3];
|
|
|
1006 |
double ctrlx2 = src[srcoff + 4];
|
|
|
1007 |
double ctrly2 = src[srcoff + 5];
|
|
|
1008 |
double x2 = src[srcoff + 6];
|
|
|
1009 |
double y2 = src[srcoff + 7];
|
|
|
1010 |
if (left != null) {
|
|
|
1011 |
left[leftoff + 0] = x1;
|
|
|
1012 |
left[leftoff + 1] = y1;
|
|
|
1013 |
}
|
|
|
1014 |
if (right != null) {
|
|
|
1015 |
right[rightoff + 6] = x2;
|
|
|
1016 |
right[rightoff + 7] = y2;
|
|
|
1017 |
}
|
|
|
1018 |
x1 = (x1 + ctrlx1) / 2.0;
|
|
|
1019 |
y1 = (y1 + ctrly1) / 2.0;
|
|
|
1020 |
x2 = (x2 + ctrlx2) / 2.0;
|
|
|
1021 |
y2 = (y2 + ctrly2) / 2.0;
|
|
|
1022 |
double centerx = (ctrlx1 + ctrlx2) / 2.0;
|
|
|
1023 |
double centery = (ctrly1 + ctrly2) / 2.0;
|
|
|
1024 |
ctrlx1 = (x1 + centerx) / 2.0;
|
|
|
1025 |
ctrly1 = (y1 + centery) / 2.0;
|
|
|
1026 |
ctrlx2 = (x2 + centerx) / 2.0;
|
|
|
1027 |
ctrly2 = (y2 + centery) / 2.0;
|
|
|
1028 |
centerx = (ctrlx1 + ctrlx2) / 2.0;
|
|
|
1029 |
centery = (ctrly1 + ctrly2) / 2.0;
|
|
|
1030 |
if (left != null) {
|
|
|
1031 |
left[leftoff + 2] = x1;
|
|
|
1032 |
left[leftoff + 3] = y1;
|
|
|
1033 |
left[leftoff + 4] = ctrlx1;
|
|
|
1034 |
left[leftoff + 5] = ctrly1;
|
|
|
1035 |
left[leftoff + 6] = centerx;
|
|
|
1036 |
left[leftoff + 7] = centery;
|
|
|
1037 |
}
|
|
|
1038 |
if (right != null) {
|
|
|
1039 |
right[rightoff + 0] = centerx;
|
|
|
1040 |
right[rightoff + 1] = centery;
|
|
|
1041 |
right[rightoff + 2] = ctrlx2;
|
|
|
1042 |
right[rightoff + 3] = ctrly2;
|
|
|
1043 |
right[rightoff + 4] = x2;
|
|
|
1044 |
right[rightoff + 5] = y2;
|
|
|
1045 |
}
|
|
|
1046 |
}
|
|
|
1047 |
|
|
|
1048 |
/**
|
|
|
1049 |
* Solves the cubic whose coefficients are in the <code>eqn</code>
|
|
|
1050 |
* array and places the non-complex roots back into the same array,
|
|
|
1051 |
* returning the number of roots. The solved cubic is represented
|
|
|
1052 |
* by the equation:
|
|
|
1053 |
* <pre>
|
|
|
1054 |
* eqn = {c, b, a, d}
|
|
|
1055 |
* dx^3 + ax^2 + bx + c = 0
|
|
|
1056 |
* </pre>
|
|
|
1057 |
* A return value of -1 is used to distinguish a constant equation
|
|
|
1058 |
* that might be always 0 or never 0 from an equation that has no
|
|
|
1059 |
* zeroes.
|
|
|
1060 |
* @param eqn an array containing coefficients for a cubic
|
|
|
1061 |
* @return the number of roots, or -1 if the equation is a constant.
|
|
|
1062 |
* @since 1.2
|
|
|
1063 |
*/
|
|
|
1064 |
public static int solveCubic(double eqn[]) {
|
|
|
1065 |
return solveCubic(eqn, eqn);
|
|
|
1066 |
}
|
|
|
1067 |
|
|
|
1068 |
/**
|
|
|
1069 |
* Solve the cubic whose coefficients are in the <code>eqn</code>
|
|
|
1070 |
* array and place the non-complex roots into the <code>res</code>
|
|
|
1071 |
* array, returning the number of roots.
|
|
|
1072 |
* The cubic solved is represented by the equation:
|
|
|
1073 |
* eqn = {c, b, a, d}
|
|
|
1074 |
* dx^3 + ax^2 + bx + c = 0
|
|
|
1075 |
* A return value of -1 is used to distinguish a constant equation,
|
|
|
1076 |
* which may be always 0 or never 0, from an equation which has no
|
|
|
1077 |
* zeroes.
|
|
|
1078 |
* @param eqn the specified array of coefficients to use to solve
|
|
|
1079 |
* the cubic equation
|
|
|
1080 |
* @param res the array that contains the non-complex roots
|
|
|
1081 |
* resulting from the solution of the cubic equation
|
|
|
1082 |
* @return the number of roots, or -1 if the equation is a constant
|
|
|
1083 |
* @since 1.3
|
|
|
1084 |
*/
|
|
|
1085 |
public static int solveCubic(double eqn[], double res[]) {
|
|
|
1086 |
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
|
|
|
1087 |
double d = eqn[3];
|
|
|
1088 |
if (d == 0.0) {
|
|
|
1089 |
// The cubic has degenerated to quadratic (or line or ...).
|
|
|
1090 |
return QuadCurve2D.solveQuadratic(eqn, res);
|
|
|
1091 |
}
|
|
|
1092 |
double a = eqn[2] / d;
|
|
|
1093 |
double b = eqn[1] / d;
|
|
|
1094 |
double c = eqn[0] / d;
|
|
|
1095 |
int roots = 0;
|
|
|
1096 |
double Q = (a * a - 3.0 * b) / 9.0;
|
|
|
1097 |
double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
|
|
|
1098 |
double R2 = R * R;
|
|
|
1099 |
double Q3 = Q * Q * Q;
|
|
|
1100 |
a = a / 3.0;
|
|
|
1101 |
if (R2 < Q3) {
|
|
|
1102 |
double theta = Math.acos(R / Math.sqrt(Q3));
|
|
|
1103 |
Q = -2.0 * Math.sqrt(Q);
|
|
|
1104 |
if (res == eqn) {
|
|
|
1105 |
// Copy the eqn so that we don't clobber it with the
|
|
|
1106 |
// roots. This is needed so that fixRoots can do its
|
|
|
1107 |
// work with the original equation.
|
|
|
1108 |
eqn = new double[4];
|
|
|
1109 |
System.arraycopy(res, 0, eqn, 0, 4);
|
|
|
1110 |
}
|
|
|
1111 |
res[roots++] = Q * Math.cos(theta / 3.0) - a;
|
|
|
1112 |
res[roots++] = Q * Math.cos((theta + Math.PI * 2.0)/ 3.0) - a;
|
|
|
1113 |
res[roots++] = Q * Math.cos((theta - Math.PI * 2.0)/ 3.0) - a;
|
|
|
1114 |
fixRoots(res, eqn);
|
|
|
1115 |
} else {
|
|
|
1116 |
boolean neg = (R < 0.0);
|
|
|
1117 |
double S = Math.sqrt(R2 - Q3);
|
|
|
1118 |
if (neg) {
|
|
|
1119 |
R = -R;
|
|
|
1120 |
}
|
|
|
1121 |
double A = Math.pow(R + S, 1.0 / 3.0);
|
|
|
1122 |
if (!neg) {
|
|
|
1123 |
A = -A;
|
|
|
1124 |
}
|
|
|
1125 |
double B = (A == 0.0) ? 0.0 : (Q / A);
|
|
|
1126 |
res[roots++] = (A + B) - a;
|
|
|
1127 |
}
|
|
|
1128 |
return roots;
|
|
|
1129 |
}
|
|
|
1130 |
|
|
|
1131 |
/*
|
|
|
1132 |
* This pruning step is necessary since solveCubic uses the
|
|
|
1133 |
* cosine function to calculate the roots when there are 3
|
|
|
1134 |
* of them. Since the cosine method can have an error of
|
|
|
1135 |
* +/- 1E-14 we need to make sure that we don't make any
|
|
|
1136 |
* bad decisions due to an error.
|
|
|
1137 |
*
|
|
|
1138 |
* If the root is not near one of the endpoints, then we will
|
|
|
1139 |
* only have a slight inaccuracy in calculating the x intercept
|
|
|
1140 |
* which will only cause a slightly wrong answer for some
|
|
|
1141 |
* points very close to the curve. While the results in that
|
|
|
1142 |
* case are not as accurate as they could be, they are not
|
|
|
1143 |
* disastrously inaccurate either.
|
|
|
1144 |
*
|
|
|
1145 |
* On the other hand, if the error happens near one end of
|
|
|
1146 |
* the curve, then our processing to reject values outside
|
|
|
1147 |
* of the t=[0,1] range will fail and the results of that
|
|
|
1148 |
* failure will be disastrous since for an entire horizontal
|
|
|
1149 |
* range of test points, we will either overcount or undercount
|
|
|
1150 |
* the crossings and get a wrong answer for all of them, even
|
|
|
1151 |
* when they are clearly and obviously inside or outside the
|
|
|
1152 |
* curve.
|
|
|
1153 |
*
|
|
|
1154 |
* To work around this problem, we try a couple of Newton-Raphson
|
|
|
1155 |
* iterations to see if the true root is closer to the endpoint
|
|
|
1156 |
* or further away. If it is further away, then we can stop
|
|
|
1157 |
* since we know we are on the right side of the endpoint. If
|
|
|
1158 |
* we change direction, then either we are now being dragged away
|
|
|
1159 |
* from the endpoint in which case the first condition will cause
|
|
|
1160 |
* us to stop, or we have passed the endpoint and are headed back.
|
|
|
1161 |
* In the second case, we simply evaluate the slope at the
|
|
|
1162 |
* endpoint itself and place ourselves on the appropriate side
|
|
|
1163 |
* of it or on it depending on that result.
|
|
|
1164 |
*/
|
|
|
1165 |
private static void fixRoots(double res[], double eqn[]) {
|
|
|
1166 |
final double EPSILON = 1E-5;
|
|
|
1167 |
for (int i = 0; i < 3; i++) {
|
|
|
1168 |
double t = res[i];
|
|
|
1169 |
if (Math.abs(t) < EPSILON) {
|
|
|
1170 |
res[i] = findZero(t, 0, eqn);
|
|
|
1171 |
} else if (Math.abs(t - 1) < EPSILON) {
|
|
|
1172 |
res[i] = findZero(t, 1, eqn);
|
|
|
1173 |
}
|
|
|
1174 |
}
|
|
|
1175 |
}
|
|
|
1176 |
|
|
|
1177 |
private static double solveEqn(double eqn[], int order, double t) {
|
|
|
1178 |
double v = eqn[order];
|
|
|
1179 |
while (--order >= 0) {
|
|
|
1180 |
v = v * t + eqn[order];
|
|
|
1181 |
}
|
|
|
1182 |
return v;
|
|
|
1183 |
}
|
|
|
1184 |
|
|
|
1185 |
private static double findZero(double t, double target, double eqn[]) {
|
|
|
1186 |
double slopeqn[] = {eqn[1], 2*eqn[2], 3*eqn[3]};
|
|
|
1187 |
double slope;
|
|
|
1188 |
double origdelta = 0;
|
|
|
1189 |
double origt = t;
|
|
|
1190 |
while (true) {
|
|
|
1191 |
slope = solveEqn(slopeqn, 2, t);
|
|
|
1192 |
if (slope == 0) {
|
|
|
1193 |
// At a local minima - must return
|
|
|
1194 |
return t;
|
|
|
1195 |
}
|
|
|
1196 |
double y = solveEqn(eqn, 3, t);
|
|
|
1197 |
if (y == 0) {
|
|
|
1198 |
// Found it! - return it
|
|
|
1199 |
return t;
|
|
|
1200 |
}
|
|
|
1201 |
// assert(slope != 0 && y != 0);
|
|
|
1202 |
double delta = - (y / slope);
|
|
|
1203 |
// assert(delta != 0);
|
|
|
1204 |
if (origdelta == 0) {
|
|
|
1205 |
origdelta = delta;
|
|
|
1206 |
}
|
|
|
1207 |
if (t < target) {
|
|
|
1208 |
if (delta < 0) return t;
|
|
|
1209 |
} else if (t > target) {
|
|
|
1210 |
if (delta > 0) return t;
|
|
|
1211 |
} else { /* t == target */
|
|
|
1212 |
return (delta > 0
|
|
|
1213 |
? (target + java.lang.Double.MIN_VALUE)
|
|
|
1214 |
: (target - java.lang.Double.MIN_VALUE));
|
|
|
1215 |
}
|
|
|
1216 |
double newt = t + delta;
|
|
|
1217 |
if (t == newt) {
|
|
|
1218 |
// The deltas are so small that we aren't moving...
|
|
|
1219 |
return t;
|
|
|
1220 |
}
|
|
|
1221 |
if (delta * origdelta < 0) {
|
|
|
1222 |
// We have reversed our path.
|
|
|
1223 |
int tag = (origt < t
|
|
|
1224 |
? getTag(target, origt, t)
|
|
|
1225 |
: getTag(target, t, origt));
|
|
|
1226 |
if (tag != INSIDE) {
|
|
|
1227 |
// Local minima found away from target - return the middle
|
|
|
1228 |
return (origt + t) / 2;
|
|
|
1229 |
}
|
|
|
1230 |
// Local minima somewhere near target - move to target
|
|
|
1231 |
// and let the slope determine the resulting t.
|
|
|
1232 |
t = target;
|
|
|
1233 |
} else {
|
|
|
1234 |
t = newt;
|
|
|
1235 |
}
|
|
|
1236 |
}
|
|
|
1237 |
}
|
|
|
1238 |
|
|
|
1239 |
/**
|
|
|
1240 |
* {@inheritDoc}
|
|
|
1241 |
* @since 1.2
|
|
|
1242 |
*/
|
|
|
1243 |
public boolean contains(double x, double y) {
|
|
|
1244 |
if (!(x * 0.0 + y * 0.0 == 0.0)) {
|
|
|
1245 |
/* Either x or y was infinite or NaN.
|
|
|
1246 |
* A NaN always produces a negative response to any test
|
|
|
1247 |
* and Infinity values cannot be "inside" any path so
|
|
|
1248 |
* they should return false as well.
|
|
|
1249 |
*/
|
|
|
1250 |
return false;
|
|
|
1251 |
}
|
|
|
1252 |
// We count the "Y" crossings to determine if the point is
|
|
|
1253 |
// inside the curve bounded by its closing line.
|
|
|
1254 |
double x1 = getX1();
|
|
|
1255 |
double y1 = getY1();
|
|
|
1256 |
double x2 = getX2();
|
|
|
1257 |
double y2 = getY2();
|
|
|
1258 |
int crossings =
|
|
|
1259 |
(Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
|
|
|
1260 |
Curve.pointCrossingsForCubic(x, y,
|
|
|
1261 |
x1, y1,
|
|
|
1262 |
getCtrlX1(), getCtrlY1(),
|
|
|
1263 |
getCtrlX2(), getCtrlY2(),
|
|
|
1264 |
x2, y2, 0));
|
|
|
1265 |
return ((crossings & 1) == 1);
|
|
|
1266 |
}
|
|
|
1267 |
|
|
|
1268 |
/**
|
|
|
1269 |
* {@inheritDoc}
|
|
|
1270 |
* @since 1.2
|
|
|
1271 |
*/
|
|
|
1272 |
public boolean contains(Point2D p) {
|
|
|
1273 |
return contains(p.getX(), p.getY());
|
|
|
1274 |
}
|
|
|
1275 |
|
|
|
1276 |
/*
|
|
|
1277 |
* Fill an array with the coefficients of the parametric equation
|
|
|
1278 |
* in t, ready for solving against val with solveCubic.
|
|
|
1279 |
* We currently have:
|
|
|
1280 |
* <pre>
|
|
|
1281 |
* val = P(t) = C1(1-t)^3 + 3CP1 t(1-t)^2 + 3CP2 t^2(1-t) + C2 t^3
|
|
|
1282 |
* = C1 - 3C1t + 3C1t^2 - C1t^3 +
|
|
|
1283 |
* 3CP1t - 6CP1t^2 + 3CP1t^3 +
|
|
|
1284 |
* 3CP2t^2 - 3CP2t^3 +
|
|
|
1285 |
* C2t^3
|
|
|
1286 |
* 0 = (C1 - val) +
|
|
|
1287 |
* (3CP1 - 3C1) t +
|
|
|
1288 |
* (3C1 - 6CP1 + 3CP2) t^2 +
|
|
|
1289 |
* (C2 - 3CP2 + 3CP1 - C1) t^3
|
|
|
1290 |
* 0 = C + Bt + At^2 + Dt^3
|
|
|
1291 |
* C = C1 - val
|
|
|
1292 |
* B = 3*CP1 - 3*C1
|
|
|
1293 |
* A = 3*CP2 - 6*CP1 + 3*C1
|
|
|
1294 |
* D = C2 - 3*CP2 + 3*CP1 - C1
|
|
|
1295 |
* </pre>
|
|
|
1296 |
*/
|
|
|
1297 |
private static void fillEqn(double eqn[], double val,
|
|
|
1298 |
double c1, double cp1, double cp2, double c2) {
|
|
|
1299 |
eqn[0] = c1 - val;
|
|
|
1300 |
eqn[1] = (cp1 - c1) * 3.0;
|
|
|
1301 |
eqn[2] = (cp2 - cp1 - cp1 + c1) * 3.0;
|
|
|
1302 |
eqn[3] = c2 + (cp1 - cp2) * 3.0 - c1;
|
|
|
1303 |
return;
|
|
|
1304 |
}
|
|
|
1305 |
|
|
|
1306 |
/*
|
|
|
1307 |
* Evaluate the t values in the first num slots of the vals[] array
|
|
|
1308 |
* and place the evaluated values back into the same array. Only
|
|
|
1309 |
* evaluate t values that are within the range <0, 1>, including
|
|
|
1310 |
* the 0 and 1 ends of the range iff the include0 or include1
|
|
|
1311 |
* booleans are true. If an "inflection" equation is handed in,
|
|
|
1312 |
* then any points which represent a point of inflection for that
|
|
|
1313 |
* cubic equation are also ignored.
|
|
|
1314 |
*/
|
|
|
1315 |
private static int evalCubic(double vals[], int num,
|
|
|
1316 |
boolean include0,
|
|
|
1317 |
boolean include1,
|
|
|
1318 |
double inflect[],
|
|
|
1319 |
double c1, double cp1,
|
|
|
1320 |
double cp2, double c2) {
|
|
|
1321 |
int j = 0;
|
|
|
1322 |
for (int i = 0; i < num; i++) {
|
|
|
1323 |
double t = vals[i];
|
|
|
1324 |
if ((include0 ? t >= 0 : t > 0) &&
|
|
|
1325 |
(include1 ? t <= 1 : t < 1) &&
|
|
|
1326 |
(inflect == null ||
|
|
|
1327 |
inflect[1] + (2*inflect[2] + 3*inflect[3]*t)*t != 0))
|
|
|
1328 |
{
|
|
|
1329 |
double u = 1 - t;
|
|
|
1330 |
vals[j++] = c1*u*u*u + 3*cp1*t*u*u + 3*cp2*t*t*u + c2*t*t*t;
|
|
|
1331 |
}
|
|
|
1332 |
}
|
|
|
1333 |
return j;
|
|
|
1334 |
}
|
|
|
1335 |
|
|
|
1336 |
private static final int BELOW = -2;
|
|
|
1337 |
private static final int LOWEDGE = -1;
|
|
|
1338 |
private static final int INSIDE = 0;
|
|
|
1339 |
private static final int HIGHEDGE = 1;
|
|
|
1340 |
private static final int ABOVE = 2;
|
|
|
1341 |
|
|
|
1342 |
/*
|
|
|
1343 |
* Determine where coord lies with respect to the range from
|
|
|
1344 |
* low to high. It is assumed that low <= high. The return
|
|
|
1345 |
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
|
|
|
1346 |
* or ABOVE.
|
|
|
1347 |
*/
|
|
|
1348 |
private static int getTag(double coord, double low, double high) {
|
|
|
1349 |
if (coord <= low) {
|
|
|
1350 |
return (coord < low ? BELOW : LOWEDGE);
|
|
|
1351 |
}
|
|
|
1352 |
if (coord >= high) {
|
|
|
1353 |
return (coord > high ? ABOVE : HIGHEDGE);
|
|
|
1354 |
}
|
|
|
1355 |
return INSIDE;
|
|
|
1356 |
}
|
|
|
1357 |
|
|
|
1358 |
/*
|
|
|
1359 |
* Determine if the pttag represents a coordinate that is already
|
|
|
1360 |
* in its test range, or is on the border with either of the two
|
|
|
1361 |
* opttags representing another coordinate that is "towards the
|
|
|
1362 |
* inside" of that test range. In other words, are either of the
|
|
|
1363 |
* two "opt" points "drawing the pt inward"?
|
|
|
1364 |
*/
|
|
|
1365 |
private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
|
|
|
1366 |
switch (pttag) {
|
|
|
1367 |
case BELOW:
|
|
|
1368 |
case ABOVE:
|
|
|
1369 |
default:
|
|
|
1370 |
return false;
|
|
|
1371 |
case LOWEDGE:
|
|
|
1372 |
return (opt1tag >= INSIDE || opt2tag >= INSIDE);
|
|
|
1373 |
case INSIDE:
|
|
|
1374 |
return true;
|
|
|
1375 |
case HIGHEDGE:
|
|
|
1376 |
return (opt1tag <= INSIDE || opt2tag <= INSIDE);
|
|
|
1377 |
}
|
|
|
1378 |
}
|
|
|
1379 |
|
|
|
1380 |
/**
|
|
|
1381 |
* {@inheritDoc}
|
|
|
1382 |
* @since 1.2
|
|
|
1383 |
*/
|
|
|
1384 |
public boolean intersects(double x, double y, double w, double h) {
|
|
|
1385 |
// Trivially reject non-existant rectangles
|
|
|
1386 |
if (w <= 0 || h <= 0) {
|
|
|
1387 |
return false;
|
|
|
1388 |
}
|
|
|
1389 |
|
|
|
1390 |
// Trivially accept if either endpoint is inside the rectangle
|
|
|
1391 |
// (not on its border since it may end there and not go inside)
|
|
|
1392 |
// Record where they lie with respect to the rectangle.
|
|
|
1393 |
// -1 => left, 0 => inside, 1 => right
|
|
|
1394 |
double x1 = getX1();
|
|
|
1395 |
double y1 = getY1();
|
|
|
1396 |
int x1tag = getTag(x1, x, x+w);
|
|
|
1397 |
int y1tag = getTag(y1, y, y+h);
|
|
|
1398 |
if (x1tag == INSIDE && y1tag == INSIDE) {
|
|
|
1399 |
return true;
|
|
|
1400 |
}
|
|
|
1401 |
double x2 = getX2();
|
|
|
1402 |
double y2 = getY2();
|
|
|
1403 |
int x2tag = getTag(x2, x, x+w);
|
|
|
1404 |
int y2tag = getTag(y2, y, y+h);
|
|
|
1405 |
if (x2tag == INSIDE && y2tag == INSIDE) {
|
|
|
1406 |
return true;
|
|
|
1407 |
}
|
|
|
1408 |
|
|
|
1409 |
double ctrlx1 = getCtrlX1();
|
|
|
1410 |
double ctrly1 = getCtrlY1();
|
|
|
1411 |
double ctrlx2 = getCtrlX2();
|
|
|
1412 |
double ctrly2 = getCtrlY2();
|
|
|
1413 |
int ctrlx1tag = getTag(ctrlx1, x, x+w);
|
|
|
1414 |
int ctrly1tag = getTag(ctrly1, y, y+h);
|
|
|
1415 |
int ctrlx2tag = getTag(ctrlx2, x, x+w);
|
|
|
1416 |
int ctrly2tag = getTag(ctrly2, y, y+h);
|
|
|
1417 |
|
|
|
1418 |
// Trivially reject if all points are entirely to one side of
|
|
|
1419 |
// the rectangle.
|
|
|
1420 |
if (x1tag < INSIDE && x2tag < INSIDE &&
|
|
|
1421 |
ctrlx1tag < INSIDE && ctrlx2tag < INSIDE)
|
|
|
1422 |
{
|
|
|
1423 |
return false; // All points left
|
|
|
1424 |
}
|
|
|
1425 |
if (y1tag < INSIDE && y2tag < INSIDE &&
|
|
|
1426 |
ctrly1tag < INSIDE && ctrly2tag < INSIDE)
|
|
|
1427 |
{
|
|
|
1428 |
return false; // All points above
|
|
|
1429 |
}
|
|
|
1430 |
if (x1tag > INSIDE && x2tag > INSIDE &&
|
|
|
1431 |
ctrlx1tag > INSIDE && ctrlx2tag > INSIDE)
|
|
|
1432 |
{
|
|
|
1433 |
return false; // All points right
|
|
|
1434 |
}
|
|
|
1435 |
if (y1tag > INSIDE && y2tag > INSIDE &&
|
|
|
1436 |
ctrly1tag > INSIDE && ctrly2tag > INSIDE)
|
|
|
1437 |
{
|
|
|
1438 |
return false; // All points below
|
|
|
1439 |
}
|
|
|
1440 |
|
|
|
1441 |
// Test for endpoints on the edge where either the segment
|
|
|
1442 |
// or the curve is headed "inwards" from them
|
|
|
1443 |
// Note: These tests are a superset of the fast endpoint tests
|
|
|
1444 |
// above and thus repeat those tests, but take more time
|
|
|
1445 |
// and cover more cases
|
|
|
1446 |
if (inwards(x1tag, x2tag, ctrlx1tag) &&
|
|
|
1447 |
inwards(y1tag, y2tag, ctrly1tag))
|
|
|
1448 |
{
|
|
|
1449 |
// First endpoint on border with either edge moving inside
|
|
|
1450 |
return true;
|
|
|
1451 |
}
|
|
|
1452 |
if (inwards(x2tag, x1tag, ctrlx2tag) &&
|
|
|
1453 |
inwards(y2tag, y1tag, ctrly2tag))
|
|
|
1454 |
{
|
|
|
1455 |
// Second endpoint on border with either edge moving inside
|
|
|
1456 |
return true;
|
|
|
1457 |
}
|
|
|
1458 |
|
|
|
1459 |
// Trivially accept if endpoints span directly across the rectangle
|
|
|
1460 |
boolean xoverlap = (x1tag * x2tag <= 0);
|
|
|
1461 |
boolean yoverlap = (y1tag * y2tag <= 0);
|
|
|
1462 |
if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
|
|
|
1463 |
return true;
|
|
|
1464 |
}
|
|
|
1465 |
if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
|
|
|
1466 |
return true;
|
|
|
1467 |
}
|
|
|
1468 |
|
|
|
1469 |
// We now know that both endpoints are outside the rectangle
|
|
|
1470 |
// but the 4 points are not all on one side of the rectangle.
|
|
|
1471 |
// Therefore the curve cannot be contained inside the rectangle,
|
|
|
1472 |
// but the rectangle might be contained inside the curve, or
|
|
|
1473 |
// the curve might intersect the boundary of the rectangle.
|
|
|
1474 |
|
|
|
1475 |
double[] eqn = new double[4];
|
|
|
1476 |
double[] res = new double[4];
|
|
|
1477 |
if (!yoverlap) {
|
|
|
1478 |
// Both y coordinates for the closing segment are above or
|
|
|
1479 |
// below the rectangle which means that we can only intersect
|
|
|
1480 |
// if the curve crosses the top (or bottom) of the rectangle
|
|
|
1481 |
// in more than one place and if those crossing locations
|
|
|
1482 |
// span the horizontal range of the rectangle.
|
|
|
1483 |
fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly1, ctrly2, y2);
|
|
|
1484 |
int num = solveCubic(eqn, res);
|
|
|
1485 |
num = evalCubic(res, num, true, true, null,
|
|
|
1486 |
x1, ctrlx1, ctrlx2, x2);
|
|
|
1487 |
// odd counts imply the crossing was out of [0,1] bounds
|
|
|
1488 |
// otherwise there is no way for that part of the curve to
|
|
|
1489 |
// "return" to meet its endpoint
|
|
|
1490 |
return (num == 2 &&
|
|
|
1491 |
getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
|
|
|
1492 |
}
|
|
|
1493 |
|
|
|
1494 |
// Y ranges overlap. Now we examine the X ranges
|
|
|
1495 |
if (!xoverlap) {
|
|
|
1496 |
// Both x coordinates for the closing segment are left of
|
|
|
1497 |
// or right of the rectangle which means that we can only
|
|
|
1498 |
// intersect if the curve crosses the left (or right) edge
|
|
|
1499 |
// of the rectangle in more than one place and if those
|
|
|
1500 |
// crossing locations span the vertical range of the rectangle.
|
|
|
1501 |
fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
|
|
|
1502 |
int num = solveCubic(eqn, res);
|
|
|
1503 |
num = evalCubic(res, num, true, true, null,
|
|
|
1504 |
y1, ctrly1, ctrly2, y2);
|
|
|
1505 |
// odd counts imply the crossing was out of [0,1] bounds
|
|
|
1506 |
// otherwise there is no way for that part of the curve to
|
|
|
1507 |
// "return" to meet its endpoint
|
|
|
1508 |
return (num == 2 &&
|
|
|
1509 |
getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
|
|
|
1510 |
}
|
|
|
1511 |
|
|
|
1512 |
// The X and Y ranges of the endpoints overlap the X and Y
|
|
|
1513 |
// ranges of the rectangle, now find out how the endpoint
|
|
|
1514 |
// line segment intersects the Y range of the rectangle
|
|
|
1515 |
double dx = x2 - x1;
|
|
|
1516 |
double dy = y2 - y1;
|
|
|
1517 |
double k = y2 * x1 - x2 * y1;
|
|
|
1518 |
int c1tag, c2tag;
|
|
|
1519 |
if (y1tag == INSIDE) {
|
|
|
1520 |
c1tag = x1tag;
|
|
|
1521 |
} else {
|
|
|
1522 |
c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
|
|
|
1523 |
}
|
|
|
1524 |
if (y2tag == INSIDE) {
|
|
|
1525 |
c2tag = x2tag;
|
|
|
1526 |
} else {
|
|
|
1527 |
c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
|
|
|
1528 |
}
|
|
|
1529 |
// If the part of the line segment that intersects the Y range
|
|
|
1530 |
// of the rectangle crosses it horizontally - trivially accept
|
|
|
1531 |
if (c1tag * c2tag <= 0) {
|
|
|
1532 |
return true;
|
|
|
1533 |
}
|
|
|
1534 |
|
|
|
1535 |
// Now we know that both the X and Y ranges intersect and that
|
|
|
1536 |
// the endpoint line segment does not directly cross the rectangle.
|
|
|
1537 |
//
|
|
|
1538 |
// We can almost treat this case like one of the cases above
|
|
|
1539 |
// where both endpoints are to one side, except that we may
|
|
|
1540 |
// get one or three intersections of the curve with the vertical
|
|
|
1541 |
// side of the rectangle. This is because the endpoint segment
|
|
|
1542 |
// accounts for the other intersection in an even pairing. Thus,
|
|
|
1543 |
// with the endpoint crossing we end up with 2 or 4 total crossings.
|
|
|
1544 |
//
|
|
|
1545 |
// (Remember there is overlap in both the X and Y ranges which
|
|
|
1546 |
// means that the segment itself must cross at least one vertical
|
|
|
1547 |
// edge of the rectangle - in particular, the "near vertical side"
|
|
|
1548 |
// - leaving an odd number of intersections for the curve.)
|
|
|
1549 |
//
|
|
|
1550 |
// Now we calculate the y tags of all the intersections on the
|
|
|
1551 |
// "near vertical side" of the rectangle. We will have one with
|
|
|
1552 |
// the endpoint segment, and one or three with the curve. If
|
|
|
1553 |
// any pair of those vertical intersections overlap the Y range
|
|
|
1554 |
// of the rectangle, we have an intersection. Otherwise, we don't.
|
|
|
1555 |
|
|
|
1556 |
// c1tag = vertical intersection class of the endpoint segment
|
|
|
1557 |
//
|
|
|
1558 |
// Choose the y tag of the endpoint that was not on the same
|
|
|
1559 |
// side of the rectangle as the subsegment calculated above.
|
|
|
1560 |
// Note that we can "steal" the existing Y tag of that endpoint
|
|
|
1561 |
// since it will be provably the same as the vertical intersection.
|
|
|
1562 |
c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
|
|
|
1563 |
|
|
|
1564 |
// Now we have to calculate an array of solutions of the curve
|
|
|
1565 |
// with the "near vertical side" of the rectangle. Then we
|
|
|
1566 |
// need to sort the tags and do a pairwise range test to see
|
|
|
1567 |
// if either of the pairs of crossings spans the Y range of
|
|
|
1568 |
// the rectangle.
|
|
|
1569 |
//
|
|
|
1570 |
// Note that the c2tag can still tell us which vertical edge
|
|
|
1571 |
// to test against.
|
|
|
1572 |
fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
|
|
|
1573 |
int num = solveCubic(eqn, res);
|
|
|
1574 |
num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);
|
|
|
1575 |
|
|
|
1576 |
// Now put all of the tags into a bucket and sort them. There
|
|
|
1577 |
// is an intersection iff one of the pairs of tags "spans" the
|
|
|
1578 |
// Y range of the rectangle.
|
|
|
1579 |
int tags[] = new int[num+1];
|
|
|
1580 |
for (int i = 0; i < num; i++) {
|
|
|
1581 |
tags[i] = getTag(res[i], y, y+h);
|
|
|
1582 |
}
|
|
|
1583 |
tags[num] = c1tag;
|
|
|
1584 |
Arrays.sort(tags);
|
|
|
1585 |
return ((num >= 1 && tags[0] * tags[1] <= 0) ||
|
|
|
1586 |
(num >= 3 && tags[2] * tags[3] <= 0));
|
|
|
1587 |
}
|
|
|
1588 |
|
|
|
1589 |
/**
|
|
|
1590 |
* {@inheritDoc}
|
|
|
1591 |
* @since 1.2
|
|
|
1592 |
*/
|
|
|
1593 |
public boolean intersects(Rectangle2D r) {
|
|
|
1594 |
return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
|
1595 |
}
|
|
|
1596 |
|
|
|
1597 |
/**
|
|
|
1598 |
* {@inheritDoc}
|
|
|
1599 |
* @since 1.2
|
|
|
1600 |
*/
|
|
|
1601 |
public boolean contains(double x, double y, double w, double h) {
|
|
|
1602 |
if (w <= 0 || h <= 0) {
|
|
|
1603 |
return false;
|
|
|
1604 |
}
|
|
|
1605 |
// Assertion: Cubic curves closed by connecting their
|
|
|
1606 |
// endpoints form either one or two convex halves with
|
|
|
1607 |
// the closing line segment as an edge of both sides.
|
|
|
1608 |
if (!(contains(x, y) &&
|
|
|
1609 |
contains(x + w, y) &&
|
|
|
1610 |
contains(x + w, y + h) &&
|
|
|
1611 |
contains(x, y + h))) {
|
|
|
1612 |
return false;
|
|
|
1613 |
}
|
|
|
1614 |
// Either the rectangle is entirely inside one of the convex
|
|
|
1615 |
// halves or it crosses from one to the other, in which case
|
|
|
1616 |
// it must intersect the closing line segment.
|
|
|
1617 |
Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
|
|
|
1618 |
return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2());
|
|
|
1619 |
}
|
|
|
1620 |
|
|
|
1621 |
/**
|
|
|
1622 |
* {@inheritDoc}
|
|
|
1623 |
* @since 1.2
|
|
|
1624 |
*/
|
|
|
1625 |
public boolean contains(Rectangle2D r) {
|
|
|
1626 |
return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
|
|
|
1627 |
}
|
|
|
1628 |
|
|
|
1629 |
/**
|
|
|
1630 |
* {@inheritDoc}
|
|
|
1631 |
* @since 1.2
|
|
|
1632 |
*/
|
|
|
1633 |
public Rectangle getBounds() {
|
|
|
1634 |
return getBounds2D().getBounds();
|
|
|
1635 |
}
|
|
|
1636 |
|
|
|
1637 |
/**
|
|
|
1638 |
* Returns an iteration object that defines the boundary of the
|
|
|
1639 |
* shape.
|
|
|
1640 |
* The iterator for this class is not multi-threaded safe,
|
|
|
1641 |
* which means that this <code>CubicCurve2D</code> class does not
|
|
|
1642 |
* guarantee that modifications to the geometry of this
|
|
|
1643 |
* <code>CubicCurve2D</code> object do not affect any iterations of
|
|
|
1644 |
* that geometry that are already in process.
|
|
|
1645 |
* @param at an optional <code>AffineTransform</code> to be applied to the
|
|
|
1646 |
* coordinates as they are returned in the iteration, or <code>null</code>
|
|
|
1647 |
* if untransformed coordinates are desired
|
|
|
1648 |
* @return the <code>PathIterator</code> object that returns the
|
|
|
1649 |
* geometry of the outline of this <code>CubicCurve2D</code>, one
|
|
|
1650 |
* segment at a time.
|
|
|
1651 |
* @since 1.2
|
|
|
1652 |
*/
|
|
|
1653 |
public PathIterator getPathIterator(AffineTransform at) {
|
|
|
1654 |
return new CubicIterator(this, at);
|
|
|
1655 |
}
|
|
|
1656 |
|
|
|
1657 |
/**
|
|
|
1658 |
* Return an iteration object that defines the boundary of the
|
|
|
1659 |
* flattened shape.
|
|
|
1660 |
* The iterator for this class is not multi-threaded safe,
|
|
|
1661 |
* which means that this <code>CubicCurve2D</code> class does not
|
|
|
1662 |
* guarantee that modifications to the geometry of this
|
|
|
1663 |
* <code>CubicCurve2D</code> object do not affect any iterations of
|
|
|
1664 |
* that geometry that are already in process.
|
|
|
1665 |
* @param at an optional <code>AffineTransform</code> to be applied to the
|
|
|
1666 |
* coordinates as they are returned in the iteration, or <code>null</code>
|
|
|
1667 |
* if untransformed coordinates are desired
|
|
|
1668 |
* @param flatness the maximum amount that the control points
|
|
|
1669 |
* for a given curve can vary from colinear before a subdivided
|
|
|
1670 |
* curve is replaced by a straight line connecting the end points
|
|
|
1671 |
* @return the <code>PathIterator</code> object that returns the
|
|
|
1672 |
* geometry of the outline of this <code>CubicCurve2D</code>,
|
|
|
1673 |
* one segment at a time.
|
|
|
1674 |
* @since 1.2
|
|
|
1675 |
*/
|
|
|
1676 |
public PathIterator getPathIterator(AffineTransform at, double flatness) {
|
|
|
1677 |
return new FlatteningPathIterator(getPathIterator(at), flatness);
|
|
|
1678 |
}
|
|
|
1679 |
|
|
|
1680 |
/**
|
|
|
1681 |
* Creates a new object of the same class as this object.
|
|
|
1682 |
*
|
|
|
1683 |
* @return a clone of this instance.
|
|
|
1684 |
* @exception OutOfMemoryError if there is not enough memory.
|
|
|
1685 |
* @see java.lang.Cloneable
|
|
|
1686 |
* @since 1.2
|
|
|
1687 |
*/
|
|
|
1688 |
public Object clone() {
|
|
|
1689 |
try {
|
|
|
1690 |
return super.clone();
|
|
|
1691 |
} catch (CloneNotSupportedException e) {
|
|
|
1692 |
// this shouldn't happen, since we are Cloneable
|
|
|
1693 |
throw new InternalError();
|
|
|
1694 |
}
|
|
|
1695 |
}
|
|
|
1696 |
}
|