JDK8/Java8源码在线阅读
/*
* Copyright (c) 1997, 2011, 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
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*/
package java.awt.geom;
import java.awt.Shape;
import java.awt.Rectangle;
import java.util.Arrays;
import java.io.Serializable;
import sun.awt.geom.Curve;
import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.ulp;
/**
* The <code>CubicCurve2D</code> class defines a cubic parametric curve
* segment in {@code (x,y)} coordinate space.
* <p>
* This class is only the abstract superclass for all objects which
* store a 2D cubic curve segment.
* The actual storage representation of the coordinates is left to
* the subclass.
*
* @author Jim Graham
* @since 1.2
*/
public abstract class CubicCurve2D implements Shape, Cloneable {
/**
* A cubic parametric curve segment specified with
* {@code float} coordinates.
* @since 1.2
*/
public static class Float extends CubicCurve2D implements Serializable {
/**
* The X coordinate of the start point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float x1;
/**
* The Y coordinate of the start point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float y1;
/**
* The X coordinate of the first control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float ctrlx1;
/**
* The Y coordinate of the first control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float ctrly1;
/**
* The X coordinate of the second control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float ctrlx2;
/**
* The Y coordinate of the second control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float ctrly2;
/**
* The X coordinate of the end point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float x2;
/**
* The Y coordinate of the end point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public float y2;
/**
* Constructs and initializes a CubicCurve with coordinates
* (0, 0, 0, 0, 0, 0, 0, 0).
* @since 1.2
*/
public Float() {
}
/**
* Constructs and initializes a {@code CubicCurve2D} from
* the specified {@code float} coordinates.
*
* @param x1 the X coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param y1 the Y coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param ctrlx1 the X coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrly1 the Y coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrlx2 the X coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param ctrly2 the Y coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param x2 the X coordinate for the end point
* of the resulting {@code CubicCurve2D}
* @param y2 the Y coordinate for the end point
* of the resulting {@code CubicCurve2D}
* @since 1.2
*/
public Float(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2)
{
setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, 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 getCtrlX1() {
return (double) ctrlx1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlY1() {
return (double) ctrly1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Point2D getCtrlP1() {
return new Point2D.Float(ctrlx1, ctrly1);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlX2() {
return (double) ctrlx2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlY2() {
return (double) ctrly2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Point2D getCtrlP2() {
return new Point2D.Float(ctrlx2, ctrly2);
}
/**
* {@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 ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2)
{
this.x1 = (float) x1;
this.y1 = (float) y1;
this.ctrlx1 = (float) ctrlx1;
this.ctrly1 = (float) ctrly1;
this.ctrlx2 = (float) ctrlx2;
this.ctrly2 = (float) ctrly2;
this.x2 = (float) x2;
this.y2 = (float) y2;
}
/**
* Sets the location of the end points and control points
* of this curve to the specified {@code float} coordinates.
*
* @param x1 the X coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param y1 the Y coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param ctrlx1 the X coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrly1 the Y coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrlx2 the X coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param ctrly2 the Y coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param x2 the X coordinate used to set the end point
* of this {@code CubicCurve2D}
* @param y2 the Y coordinate used to set the end point
* of this {@code CubicCurve2D}
* @since 1.2
*/
public void setCurve(float x1, float y1,
float ctrlx1, float ctrly1,
float ctrlx2, float ctrly2,
float x2, float y2)
{
this.x1 = x1;
this.y1 = y1;
this.ctrlx1 = ctrlx1;
this.ctrly1 = ctrly1;
this.ctrlx2 = ctrlx2;
this.ctrly2 = ctrly2;
this.x2 = x2;
this.y2 = y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Rectangle2D getBounds2D() {
float left = Math.min(Math.min(x1, x2),
Math.min(ctrlx1, ctrlx2));
float top = Math.min(Math.min(y1, y2),
Math.min(ctrly1, ctrly2));
float right = Math.max(Math.max(x1, x2),
Math.max(ctrlx1, ctrlx2));
float bottom = Math.max(Math.max(y1, y2),
Math.max(ctrly1, ctrly2));
return new Rectangle2D.Float(left, top,
right - left, bottom - top);
}
/*
* JDK 1.6 serialVersionUID
*/
private static final long serialVersionUID = -1272015596714244385L;
}
/**
* A cubic parametric curve segment specified with
* {@code double} coordinates.
* @since 1.2
*/
public static class Double extends CubicCurve2D implements Serializable {
/**
* The X coordinate of the start point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double x1;
/**
* The Y coordinate of the start point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double y1;
/**
* The X coordinate of the first control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double ctrlx1;
/**
* The Y coordinate of the first control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double ctrly1;
/**
* The X coordinate of the second control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double ctrlx2;
/**
* The Y coordinate of the second control point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double ctrly2;
/**
* The X coordinate of the end point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double x2;
/**
* The Y coordinate of the end point
* of the cubic curve segment.
* @since 1.2
* @serial
*/
public double y2;
/**
* Constructs and initializes a CubicCurve with coordinates
* (0, 0, 0, 0, 0, 0, 0, 0).
* @since 1.2
*/
public Double() {
}
/**
* Constructs and initializes a {@code CubicCurve2D} from
* the specified {@code double} coordinates.
*
* @param x1 the X coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param y1 the Y coordinate for the start point
* of the resulting {@code CubicCurve2D}
* @param ctrlx1 the X coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrly1 the Y coordinate for the first control point
* of the resulting {@code CubicCurve2D}
* @param ctrlx2 the X coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param ctrly2 the Y coordinate for the second control point
* of the resulting {@code CubicCurve2D}
* @param x2 the X coordinate for the end point
* of the resulting {@code CubicCurve2D}
* @param y2 the Y coordinate for the end point
* of the resulting {@code CubicCurve2D}
* @since 1.2
*/
public Double(double x1, double y1,
double ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2)
{
setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, 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 getCtrlX1() {
return ctrlx1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlY1() {
return ctrly1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Point2D getCtrlP1() {
return new Point2D.Double(ctrlx1, ctrly1);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlX2() {
return ctrlx2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double getCtrlY2() {
return ctrly2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Point2D getCtrlP2() {
return new Point2D.Double(ctrlx2, ctrly2);
}
/**
* {@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 ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2)
{
this.x1 = x1;
this.y1 = y1;
this.ctrlx1 = ctrlx1;
this.ctrly1 = ctrly1;
this.ctrlx2 = ctrlx2;
this.ctrly2 = ctrly2;
this.x2 = x2;
this.y2 = y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public Rectangle2D getBounds2D() {
double left = Math.min(Math.min(x1, x2),
Math.min(ctrlx1, ctrlx2));
double top = Math.min(Math.min(y1, y2),
Math.min(ctrly1, ctrly2));
double right = Math.max(Math.max(x1, x2),
Math.max(ctrlx1, ctrlx2));
double bottom = Math.max(Math.max(y1, y2),
Math.max(ctrly1, ctrly2));
return new Rectangle2D.Double(left, top,
right - left, bottom - top);
}
/*
* JDK 1.6 serialVersionUID
*/
private static final long serialVersionUID = -4202960122839707295L;
}
/**
* 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.CubicCurve2D.Float
* @see java.awt.geom.CubicCurve2D.Double
* @since 1.2
*/
protected CubicCurve2D() {
}
/**
* Returns the X coordinate of the start point in double precision.
* @return the X coordinate of the start point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getX1();
/**
* Returns the Y coordinate of the start point in double precision.
* @return the Y coordinate of the start point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getY1();
/**
* Returns the start point.
* @return a {@code Point2D} that is the start point of
* the {@code CubicCurve2D}.
* @since 1.2
*/
public abstract Point2D getP1();
/**
* Returns the X coordinate of the first control point in double precision.
* @return the X coordinate of the first control point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getCtrlX1();
/**
* Returns the Y coordinate of the first control point in double precision.
* @return the Y coordinate of the first control point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getCtrlY1();
/**
* Returns the first control point.
* @return a {@code Point2D} that is the first control point of
* the {@code CubicCurve2D}.
* @since 1.2
*/
public abstract Point2D getCtrlP1();
/**
* Returns the X coordinate of the second control point
* in double precision.
* @return the X coordinate of the second control point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getCtrlX2();
/**
* Returns the Y coordinate of the second control point
* in double precision.
* @return the Y coordinate of the second control point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getCtrlY2();
/**
* Returns the second control point.
* @return a {@code Point2D} that is the second control point of
* the {@code CubicCurve2D}.
* @since 1.2
*/
public abstract Point2D getCtrlP2();
/**
* Returns the X coordinate of the end point in double precision.
* @return the X coordinate of the end point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getX2();
/**
* Returns the Y coordinate of the end point in double precision.
* @return the Y coordinate of the end point of the
* {@code CubicCurve2D}.
* @since 1.2
*/
public abstract double getY2();
/**
* Returns the end point.
* @return a {@code Point2D} that is the end point of
* the {@code CubicCurve2D}.
* @since 1.2
*/
public abstract Point2D getP2();
/**
* Sets the location of the end points and control points of this curve
* to the specified double coordinates.
*
* @param x1 the X coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param y1 the Y coordinate used to set the start point
* of this {@code CubicCurve2D}
* @param ctrlx1 the X coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrly1 the Y coordinate used to set the first control point
* of this {@code CubicCurve2D}
* @param ctrlx2 the X coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param ctrly2 the Y coordinate used to set the second control point
* of this {@code CubicCurve2D}
* @param x2 the X coordinate used to set the end point
* of this {@code CubicCurve2D}
* @param y2 the Y coordinate used to set the end point
* of this {@code CubicCurve2D}
* @since 1.2
*/
public abstract void setCurve(double x1, double y1,
double ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2);
/**
* Sets the location of the end points and control points of this curve
* to the double coordinates at the specified offset in the specified
* array.
* @param coords a double array containing coordinates
* @param offset the index of <code>coords</code> from which to begin
* setting the end points and control points of this curve
* to the coordinates contained in <code>coords</code>
* @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],
coords[offset + 6], coords[offset + 7]);
}
/**
* Sets the location of the end points and control points of this curve
* to the specified <code>Point2D</code> coordinates.
* @param p1 the first specified <code>Point2D</code> used to set the
* start point of this curve
* @param cp1 the second specified <code>Point2D</code> used to set the
* first control point of this curve
* @param cp2 the third specified <code>Point2D</code> used to set the
* second control point of this curve
* @param p2 the fourth specified <code>Point2D</code> used to set the
* end point of this curve
* @since 1.2
*/
public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2) {
setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
}
/**
* Sets the location of the end points and control points of this curve
* to the coordinates of the <code>Point2D</code> objects at the specified
* offset in the specified array.
* @param pts an array of <code>Point2D</code> objects
* @param offset the index of <code>pts</code> from which to begin setting
* the end points and control points of this curve to the
* points contained in <code>pts</code>
* @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(),
pts[offset + 3].getX(), pts[offset + 3].getY());
}
/**
* Sets the location of the end points and control points of this curve
* to the same as those in the specified <code>CubicCurve2D</code>.
* @param c the specified <code>CubicCurve2D</code>
* @since 1.2
*/
public void setCurve(CubicCurve2D c) {
setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
}
/**
* Returns the square of the flatness of the cubic curve specified
* by the indicated control points. The flatness is the maximum distance
* of a control point from the line connecting the end points.
*
* @param x1 the X coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param y1 the Y coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param ctrlx1 the X coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrly1 the Y coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrlx2 the X coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param ctrly2 the Y coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param x2 the X coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @param y2 the Y coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @return the square of the flatness of the {@code CubicCurve2D}
* represented by the specified coordinates.
* @since 1.2
*/
public static double getFlatnessSq(double x1, double y1,
double ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2) {
return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));
}
/**
* Returns the flatness of the cubic curve specified
* by the indicated control points. The flatness is the maximum distance
* of a control point from the line connecting the end points.
*
* @param x1 the X coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param y1 the Y coordinate that specifies the start point
* of a {@code CubicCurve2D}
* @param ctrlx1 the X coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrly1 the Y coordinate that specifies the first control point
* of a {@code CubicCurve2D}
* @param ctrlx2 the X coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param ctrly2 the Y coordinate that specifies the second control point
* of a {@code CubicCurve2D}
* @param x2 the X coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @param y2 the Y coordinate that specifies the end point
* of a {@code CubicCurve2D}
* @return the flatness of the {@code CubicCurve2D}
* represented by the specified coordinates.
* @since 1.2
*/
public static double getFlatness(double x1, double y1,
double ctrlx1, double ctrly1,
double ctrlx2, double ctrly2,
double x2, double y2) {
return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
ctrlx2, ctrly2, x2, y2));
}
/**
* Returns the square of the flatness of the cubic curve specified
* by the control points stored in the indicated array at the
* indicated index. The flatness is the maximum distance
* of a control point from the line connecting the end points.
* @param coords an array containing coordinates
* @param offset the index of <code>coords</code> from which to begin
* getting the end points and control points of the curve
* @return the square of the flatness of the <code>CubicCurve2D</code>
* specified by the coordinates in <code>coords</code> at
* the specified offset.
* @since 1.2
*/
public static double getFlatnessSq(double coords[], int offset) {
return getFlatnessSq(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
}
/**
* Returns the flatness of the cubic curve specified
* by the control points stored in the indicated array at the
* indicated index. The flatness is the maximum distance
* of a control point from the line connecting the end points.
* @param coords an array containing coordinates
* @param offset the index of <code>coords</code> from which to begin
* getting the end points and control points of the curve
* @return the flatness of the <code>CubicCurve2D</code>
* specified by the coordinates in <code>coords</code> at
* the specified offset.
* @since 1.2
*/
public static double getFlatness(double coords[], int offset) {
return getFlatness(coords[offset + 0], coords[offset + 1],
coords[offset + 2], coords[offset + 3],
coords[offset + 4], coords[offset + 5],
coords[offset + 6], coords[offset + 7]);
}
/**
* Returns the square of the flatness of this curve. The flatness is the
* maximum distance of a control point from the line connecting the
* end points.
* @return the square of the flatness of this curve.
* @since 1.2
*/
public double getFlatnessSq() {
return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
getCtrlX2(), getCtrlY2(), getX2(), getY2());
}
/**
* Returns the flatness of this curve. The flatness is the
* maximum distance of a control point from the line connecting the
* end points.
* @return the flatness of this curve.
* @since 1.2
*/
public double getFlatness() {
return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
getCtrlX2(), getCtrlY2(), getX2(), getY2());
}
/**
* Subdivides this cubic curve and stores the resulting two
* subdivided curves into the left and right curve parameters.
* Either or both of the left and right objects may be the same
* as this object or null.
* @param left the cubic curve object for storing for the left or
* first half of the subdivided curve
* @param right the cubic curve object for storing for the right or
* second half of the subdivided curve
* @since 1.2
*/
public void subdivide(CubicCurve2D left, CubicCurve2D right) {
subdivide(this, left, right);
}
/**
* Subdivides the cubic curve specified by the <code>src</code> parameter
* and stores the resulting two subdivided curves into the
* <code>left</code> and <code>right</code> curve parameters.
* Either or both of the <code>left</code> and <code>right</code> objects
* may be the same as the <code>src</code> object or <code>null</code>.
* @param src the cubic curve to be subdivided
* @param left the cubic curve object for storing the left or
* first half of the subdivided curve
* @param right the cubic curve object for storing the right or
* second half of the subdivided curve
* @since 1.2
*/
public static void subdivide(CubicCurve2D src,
CubicCurve2D left,
CubicCurve2D right) {
double x1 = src.getX1();
double y1 = src.getY1();
double ctrlx1 = src.getCtrlX1();
double ctrly1 = src.getCtrlY1();
double ctrlx2 = src.getCtrlX2();
double ctrly2 = src.getCtrlY2();
double x2 = src.getX2();
double y2 = src.getY2();
double centerx = (ctrlx1 + ctrlx2) / 2.0;
double centery = (ctrly1 + ctrly2) / 2.0;
ctrlx1 = (x1 + ctrlx1) / 2.0;
ctrly1 = (y1 + ctrly1) / 2.0;
ctrlx2 = (x2 + ctrlx2) / 2.0;
ctrly2 = (y2 + ctrly2) / 2.0;
double ctrlx12 = (ctrlx1 + centerx) / 2.0;
double ctrly12 = (ctrly1 + centery) / 2.0;
double ctrlx21 = (ctrlx2 + centerx) / 2.0;
double ctrly21 = (ctrly2 + centery) / 2.0;
centerx = (ctrlx12 + ctrlx21) / 2.0;
centery = (ctrly12 + ctrly21) / 2.0;
if (left != null) {
left.setCurve(x1, y1, ctrlx1, ctrly1,
ctrlx12, ctrly12, centerx, centery);
}
if (right != null) {
right.setCurve(centerx, centery, ctrlx21, ctrly21,
ctrlx2, ctrly2, x2, y2);
}
}
/**
* Subdivides the cubic curve specified by the coordinates
* stored in the <code>src</code> array at indices <code>srcoff</code>
* through (<code>srcoff</code> + 7) and stores the
* resulting two subdivided curves into the two result arrays at the
* corresponding indices.
* Either or both of the <code>left</code> and <code>right</code>
* arrays may be <code>null</code> or a reference to the same array
* as the <code>src</code> 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</code>
* and <code>right</code> and to use offsets, such as <code>rightoff</code>
* equals (<code>leftoff</code> + 6), 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 ctrlx1 = src[srcoff + 2];
double ctrly1 = src[srcoff + 3];
double ctrlx2 = src[srcoff + 4];
double ctrly2 = src[srcoff + 5];
double x2 = src[srcoff + 6];
double y2 = src[srcoff + 7];
if (left != null) {
left[leftoff + 0] = x1;
left[leftoff + 1] = y1;
}
if (right != null) {
right[rightoff + 6] = x2;
right[rightoff + 7] = y2;
}
x1 = (x1 + ctrlx1) / 2.0;
y1 = (y1 + ctrly1) / 2.0;
x2 = (x2 + ctrlx2) / 2.0;
y2 = (y2 + ctrly2) / 2.0;
double centerx = (ctrlx1 + ctrlx2) / 2.0;
double centery = (ctrly1 + ctrly2) / 2.0;
ctrlx1 = (x1 + centerx) / 2.0;
ctrly1 = (y1 + centery) / 2.0;
ctrlx2 = (x2 + centerx) / 2.0;
ctrly2 = (y2 + centery) / 2.0;
centerx = (ctrlx1 + ctrlx2) / 2.0;
centery = (ctrly1 + ctrly2) / 2.0;
if (left != null) {
left[leftoff + 2] = x1;
left[leftoff + 3] = y1;
left[leftoff + 4] = ctrlx1;
left[leftoff + 5] = ctrly1;
left[leftoff + 6] = centerx;
left[leftoff + 7] = centery;
}
if (right != null) {
right[rightoff + 0] = centerx;
right[rightoff + 1] = centery;
right[rightoff + 2] = ctrlx2;
right[rightoff + 3] = ctrly2;
right[rightoff + 4] = x2;
right[rightoff + 5] = y2;
}
}
/**
* Solves the cubic whose coefficients are in the <code>eqn</code>
* array and places the non-complex roots back into the same array,
* returning the number of roots. The solved cubic is represented
* by the equation:
* <pre>
* eqn = {c, b, a, d}
* dx^3 + ax^2 + bx + c = 0
* </pre>
* A return value of -1 is used to distinguish a constant equation
* that might be always 0 or never 0 from an equation that has no
* zeroes.
* @param eqn an array containing coefficients for a cubic
* @return the number of roots, or -1 if the equation is a constant.
* @since 1.2
*/
public static int solveCubic(double eqn[]) {
return solveCubic(eqn, eqn);
}
/**
* Solve the cubic whose coefficients are in the <code>eqn</code>
* array and place the non-complex roots into the <code>res</code>
* array, returning the number of roots.
* The cubic solved is represented by the equation:
* eqn = {c, b, a, d}
* dx^3 + ax^2 + bx + c = 0
* A return value of -1 is used to distinguish a constant equation,
* which may be always 0 or never 0, from an equation which has no
* zeroes.
* @param eqn the specified array of coefficients to use to solve
* the cubic equation
* @param res the array that contains the non-complex roots
* resulting from the solution of the cubic equation
* @return the number of roots, or -1 if the equation is a constant
* @since 1.3
*/
public static int solveCubic(double eqn[], double res[]) {
// From Graphics Gems:
// http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
final double d = eqn[3];
if (d == 0) {
return QuadCurve2D.solveQuadratic(eqn, res);
}
/* normal form: x^3 + Ax^2 + Bx + C = 0 */
final double A = eqn[2] / d;
final double B = eqn[1] / d;
final double C = eqn[0] / d;
// substitute x = y - A/3 to eliminate quadratic term:
// x^3 +Px + Q = 0
//
// Since we actually need P/3 and Q/2 for all of the
// calculations that follow, we will calculate
// p = P/3
// q = Q/2
// instead and use those values for simplicity of the code.
double sq_A = A * A;
double p = 1.0/3 * (-1.0/3 * sq_A + B);
double q = 1.0/2 * (2.0/27 * A * sq_A - 1.0/3 * A * B + C);
/* use Cardano's formula */
double cb_p = p * p * p;
double D = q * q + cb_p;
final double sub = 1.0/3 * A;
int num;
if (D < 0) { /* Casus irreducibilis: three real solutions */
// see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
double phi = 1.0/3 * Math.acos(-q / Math.sqrt(-cb_p));
double t = 2 * Math.sqrt(-p);
if (res == eqn) {
eqn = Arrays.copyOf(eqn, 4);
}
res[ 0 ] = ( t * Math.cos(phi));
res[ 1 ] = (-t * Math.cos(phi + Math.PI / 3));
res[ 2 ] = (-t * Math.cos(phi - Math.PI / 3));
num = 3;
for (int i = 0; i < num; ++i) {
res[ i ] -= sub;
}
} else {
// Please see the comment in fixRoots marked 'XXX' before changing
// any of the code in this case.
double sqrt_D = Math.sqrt(D);
double u = Math.cbrt(sqrt_D - q);
double v = - Math.cbrt(sqrt_D + q);
double uv = u+v;
num = 1;
double err = 1200000000*ulp(abs(uv) + abs(sub));
if (iszero(D, err) || within(u, v, err)) {
if (res == eqn) {
eqn = Arrays.copyOf(eqn, 4);
}
res[1] = -(uv / 2) - sub;
num = 2;
}
// this must be done after the potential Arrays.copyOf
res[ 0 ] = uv - sub;
}
if (num > 1) { // num == 3 || num == 2
num = fixRoots(eqn, res, num);
}
if (num > 2 && (res[2] == res[1] || res[2] == res[0])) {
num--;
}
if (num > 1 && res[1] == res[0]) {
res[1] = res[--num]; // Copies res[2] to res[1] if needed
}
return num;
}
// preconditions: eqn != res && eqn[3] != 0 && num > 1
// This method tries to improve the accuracy of the roots of eqn (which
// should be in res). It also might eliminate roots in res if it decideds
// that they're not real roots. It will not check for roots that the
// computation of res might have missed, so this method should only be
// used when the roots in res have been computed using an algorithm
// that never underestimates the number of roots (such as solveCubic above)
private static int fixRoots(double[] eqn, double[] res, int num) {
double[] intervals = {eqn[1], 2*eqn[2], 3*eqn[3]};
int critCount = QuadCurve2D.solveQuadratic(intervals, intervals);
if (critCount == 2 && intervals[0] == intervals[1]) {
critCount--;
}
if (critCount == 2 && intervals[0] > intervals[1]) {
double tmp = intervals[0];
intervals[0] = intervals[1];
intervals[1] = tmp;
}
// below we use critCount to possibly filter out roots that shouldn't
// have been computed. We require that eqn[3] != 0, so eqn is a proper
// cubic, which means that its limits at -/+inf are -/+inf or +/-inf.
// Therefore, if critCount==2, the curve is shaped like a sideways S,
// and it could have 1-3 roots. If critCount==0 it is monotonic, and
// if critCount==1 it is monotonic with a single point where it is
// flat. In the last 2 cases there can only be 1 root. So in cases
// where num > 1 but critCount < 2, we eliminate all roots in res
// except one.
if (num == 3) {
double xe = getRootUpperBound(eqn);
double x0 = -xe;
Arrays.sort(res, 0, num);
if (critCount == 2) {
// this just tries to improve the accuracy of the computed
// roots using Newton's method.
res[0] = refineRootWithHint(eqn, x0, intervals[0], res[0]);
res[1] = refineRootWithHint(eqn, intervals[0], intervals[1], res[1]);
res[2] = refineRootWithHint(eqn, intervals[1], xe, res[2]);
return 3;
} else if (critCount == 1) {
// we only need fx0 and fxe for the sign of the polynomial
// at -inf and +inf respectively, so we don't need to do
// fx0 = solveEqn(eqn, 3, x0); fxe = solveEqn(eqn, 3, xe)
double fxe = eqn[3];
double fx0 = -fxe;
double x1 = intervals[0];
double fx1 = solveEqn(eqn, 3, x1);
// if critCount == 1 or critCount == 0, but num == 3 then
// something has gone wrong. This branch and the one below
// would ideally never execute, but if they do we can't know
// which of the computed roots is closest to the real root;
// therefore, we can't use refineRootWithHint. But even if
// we did know, being here most likely means that the
// curve is very flat close to two of the computed roots
// (or maybe even all three). This might make Newton's method
// fail altogether, which would be a pain to detect and fix.
// This is why we use a very stable bisection method.
if (oppositeSigns(fx0, fx1)) {
res[0] = bisectRootWithHint(eqn, x0, x1, res[0]);
} else if (oppositeSigns(fx1, fxe)) {
res[0] = bisectRootWithHint(eqn, x1, xe, res[2]);
} else /* fx1 must be 0 */ {
res[0] = x1;
}
// return 1
} else if (critCount == 0) {
res[0] = bisectRootWithHint(eqn, x0, xe, res[1]);
// return 1
}
} else if (num == 2 && critCount == 2) {
// XXX: here we assume that res[0] has better accuracy than res[1].
// This is true because this method is only used from solveCubic
// which puts in res[0] the root that it would compute anyway even
// if num==1. If this method is ever used from any other method, or
// if the solveCubic implementation changes, this assumption should
// be reevaluated, and the choice of goodRoot might have to become
// goodRoot = (abs(eqn'(res[0])) > abs(eqn'(res[1]))) ? res[0] : res[1]
// where eqn' is the derivative of eqn.
double goodRoot = res[0];
double badRoot = res[1];
double x1 = intervals[0];
double x2 = intervals[1];
// If a cubic curve really has 2 roots, one of those roots must be
// at a critical point. That can't be goodRoot, so we compute x to
// be the farthest critical point from goodRoot. If there are two
// roots, x must be the second one, so we evaluate eqn at x, and if
// it is zero (or close enough) we put x in res[1] (or badRoot, if
// |solveEqn(eqn, 3, badRoot)| < |solveEqn(eqn, 3, x)| but this
// shouldn't happen often).
double x = abs(x1 - goodRoot) > abs(x2 - goodRoot) ? x1 : x2;
double fx = solveEqn(eqn, 3, x);
if (iszero(fx, 10000000*ulp(x))) {
double badRootVal = solveEqn(eqn, 3, badRoot);
res[1] = abs(badRootVal) < abs(fx) ? badRoot : x;
return 2;
}
} // else there can only be one root - goodRoot, and it is already in res[0]
return 1;
}
// use newton's method.
private static double refineRootWithHint(double[] eqn, double min, double max, double t) {
if (!inInterval(t, min, max)) {
return t;
}
double[] deriv = {eqn[1], 2*eqn[2], 3*eqn[3]};
double origt = t;
for (int i = 0; i < 3; i++) {
double slope = solveEqn(deriv, 2, t);
double y = solveEqn(eqn, 3, t);
double delta = - (y / slope);
double newt = t + delta;
if (slope == 0 || y == 0 || t == newt) {
break;
}
t = newt;
}
if (within(t, origt, 1000*ulp(origt)) && inInterval(t, min, max)) {
return t;
}
return origt;
}
private static double bisectRootWithHint(double[] eqn, double x0, double xe, double hint) {
double delta1 = Math.min(abs(hint - x0) / 64, 0.0625);
double delta2 = Math.min(abs(hint - xe) / 64, 0.0625);
double x02 = hint - delta1;
double xe2 = hint + delta2;
double fx02 = solveEqn(eqn, 3, x02);
double fxe2 = solveEqn(eqn, 3, xe2);
while (oppositeSigns(fx02, fxe2)) {
if (x02 >= xe2) {
return x02;
}
x0 = x02;
xe = xe2;
delta1 /= 64;
delta2 /= 64;
x02 = hint - delta1;
xe2 = hint + delta2;
fx02 = solveEqn(eqn, 3, x02);
fxe2 = solveEqn(eqn, 3, xe2);
}
if (fx02 == 0) {
return x02;
}
if (fxe2 == 0) {
return xe2;
}
return bisectRoot(eqn, x0, xe);
}
private static double bisectRoot(double[] eqn, double x0, double xe) {
double fx0 = solveEqn(eqn, 3, x0);
double m = x0 + (xe - x0) / 2;
while (m != x0 && m != xe) {
double fm = solveEqn(eqn, 3, m);
if (fm == 0) {
return m;
}
if (oppositeSigns(fx0, fm)) {
xe = m;
} else {
fx0 = fm;
x0 = m;
}
m = x0 + (xe-x0)/2;
}
return m;
}
private static boolean inInterval(double t, double min, double max) {
return min <= t && t <= max;
}
private static boolean within(double x, double y, double err) {
double d = y - x;
return (d <= err && d >= -err);
}
private static boolean iszero(double x, double err) {
return within(x, 0, err);
}
private static boolean oppositeSigns(double x1, double x2) {
return (x1 < 0 && x2 > 0) || (x1 > 0 && x2 < 0);
}
private static double solveEqn(double eqn[], int order, double t) {
double v = eqn[order];
while (--order >= 0) {
v = v * t + eqn[order];
}
return v;
}
/*
* Computes M+1 where M is an upper bound for all the roots in of eqn.
* See: http://en.wikipedia.org/wiki/Sturm%27s_theorem#Applications.
* The above link doesn't contain a proof, but I [dlila] proved it myself
* so the result is reliable. The proof isn't difficult, but it's a bit
* long to include here.
* Precondition: eqn must represent a cubic polynomial
*/
private static double getRootUpperBound(double[] eqn) {
double d = eqn[3];
double a = eqn[2];
double b = eqn[1];
double c = eqn[0];
double M = 1 + max(max(abs(a), abs(b)), abs(c)) / abs(d);
M += ulp(M) + 1;
return M;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean contains(double x, double y) {
if (!(x * 0.0 + y * 0.0 == 0.0)) {
/* Either x or y was infinite or NaN.
* A NaN always produces a negative response to any test
* and Infinity values cannot be "inside" any path so
* they should return false as well.
*/
return false;
}
// We count the "Y" crossings to determine if the point is
// inside the curve bounded by its closing line.
double x1 = getX1();
double y1 = getY1();
double x2 = getX2();
double y2 = getY2();
int crossings =
(Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
Curve.pointCrossingsForCubic(x, y,
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