/*
* Copyright (c) 1997, 2013, Oracle and/or its affiliates. All rights reserved.
* ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*/
package java.awt.geom;
import java.awt.
Shape;
import java.awt.
Rectangle;
import java.io.
Serializable;
import sun.awt.geom.
Curve;
/**
* The <code>QuadCurve2D</code> class defines a quadratic parametric curve
* segment in {@code (x,y)} coordinate space.
* <p>
* This class is only the abstract superclass for all objects that
* store a 2D quadratic curve segment.
* The actual storage representation of the coordinates is left to
* the subclass.
*
* @author Jim Graham
* @since 1.2
*/
public abstract class
QuadCurve2D implements
Shape,
Cloneable {
/**
* A quadratic parametric curve segment specified with
* {@code float} coordinates.
*
* @since 1.2
*/
public static class
Float extends
QuadCurve2D implements
Serializable {
/**
* The X coordinate of the start point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
x1;
/**
* The Y coordinate of the start point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
y1;
/**
* The X coordinate of the control point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
ctrlx;
/**
* The Y coordinate of the control point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
ctrly;
/**
* The X coordinate of the end point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
x2;
/**
* The Y coordinate of the end point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public float
y2;
/**
* Constructs and initializes a <code>QuadCurve2D</code> with
* coordinates (0, 0, 0, 0, 0, 0).
* @since 1.2
*/
public
Float() {
}
/**
* Constructs and initializes a <code>QuadCurve2D</code> from the
* specified {@code float} coordinates.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @since 1.2
*/
public
Float(float
x1, float
y1,
float
ctrlx, float
ctrly,
float
x2, float
y2)
{
setCurve(
x1,
y1,
ctrlx,
ctrly,
x2,
y2);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getX1() {
return (double)
x1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getY1() {
return (double)
y1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getP1() {
return new
Point2D.
Float(
x1,
y1);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getCtrlX() {
return (double)
ctrlx;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getCtrlY() {
return (double)
ctrly;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getCtrlPt() {
return new
Point2D.
Float(
ctrlx,
ctrly);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getX2() {
return (double)
x2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getY2() {
return (double)
y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getP2() {
return new
Point2D.
Float(
x2,
y2);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public void
setCurve(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2)
{
this.
x1 = (float)
x1;
this.
y1 = (float)
y1;
this.
ctrlx = (float)
ctrlx;
this.
ctrly = (float)
ctrly;
this.
x2 = (float)
x2;
this.
y2 = (float)
y2;
}
/**
* Sets the location of the end points and control point of this curve
* to the specified {@code float} coordinates.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @since 1.2
*/
public void
setCurve(float
x1, float
y1,
float
ctrlx, float
ctrly,
float
x2, float
y2)
{
this.
x1 =
x1;
this.
y1 =
y1;
this.
ctrlx =
ctrlx;
this.
ctrly =
ctrly;
this.
x2 =
x2;
this.
y2 =
y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Rectangle2D getBounds2D() {
float
left =
Math.
min(
Math.
min(
x1,
x2),
ctrlx);
float
top =
Math.
min(
Math.
min(
y1,
y2),
ctrly);
float
right =
Math.
max(
Math.
max(
x1,
x2),
ctrlx);
float
bottom =
Math.
max(
Math.
max(
y1,
y2),
ctrly);
return new
Rectangle2D.
Float(
left,
top,
right -
left,
bottom -
top);
}
/*
* JDK 1.6 serialVersionUID
*/
private static final long
serialVersionUID = -8511188402130719609L;
}
/**
* A quadratic parametric curve segment specified with
* {@code double} coordinates.
*
* @since 1.2
*/
public static class
Double extends
QuadCurve2D implements
Serializable {
/**
* The X coordinate of the start point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
x1;
/**
* The Y coordinate of the start point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
y1;
/**
* The X coordinate of the control point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
ctrlx;
/**
* The Y coordinate of the control point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
ctrly;
/**
* The X coordinate of the end point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
x2;
/**
* The Y coordinate of the end point of the quadratic curve
* segment.
* @since 1.2
* @serial
*/
public double
y2;
/**
* Constructs and initializes a <code>QuadCurve2D</code> with
* coordinates (0, 0, 0, 0, 0, 0).
* @since 1.2
*/
public
Double() {
}
/**
* Constructs and initializes a <code>QuadCurve2D</code> from the
* specified {@code double} coordinates.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @since 1.2
*/
public
Double(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2)
{
setCurve(
x1,
y1,
ctrlx,
ctrly,
x2,
y2);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getX1() {
return
x1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getY1() {
return
y1;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getP1() {
return new
Point2D.
Double(
x1,
y1);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getCtrlX() {
return
ctrlx;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getCtrlY() {
return
ctrly;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getCtrlPt() {
return new
Point2D.
Double(
ctrlx,
ctrly);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getX2() {
return
x2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public double
getY2() {
return
y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Point2D getP2() {
return new
Point2D.
Double(
x2,
y2);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public void
setCurve(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2)
{
this.
x1 =
x1;
this.
y1 =
y1;
this.
ctrlx =
ctrlx;
this.
ctrly =
ctrly;
this.
x2 =
x2;
this.
y2 =
y2;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Rectangle2D getBounds2D() {
double
left =
Math.
min(
Math.
min(
x1,
x2),
ctrlx);
double
top =
Math.
min(
Math.
min(
y1,
y2),
ctrly);
double
right =
Math.
max(
Math.
max(
x1,
x2),
ctrlx);
double
bottom =
Math.
max(
Math.
max(
y1,
y2),
ctrly);
return new
Rectangle2D.
Double(
left,
top,
right -
left,
bottom -
top);
}
/*
* JDK 1.6 serialVersionUID
*/
private static final long
serialVersionUID = 4217149928428559721L;
}
/**
* This is an abstract class that cannot be instantiated directly.
* Type-specific implementation subclasses are available for
* instantiation and provide a number of formats for storing
* the information necessary to satisfy the various accessor
* methods below.
*
* @see java.awt.geom.QuadCurve2D.Float
* @see java.awt.geom.QuadCurve2D.Double
* @since 1.2
*/
protected
QuadCurve2D() {
}
/**
* Returns the X coordinate of the start point in
* <code>double</code> in precision.
* @return the X coordinate of the start point.
* @since 1.2
*/
public abstract double
getX1();
/**
* Returns the Y coordinate of the start point in
* <code>double</code> precision.
* @return the Y coordinate of the start point.
* @since 1.2
*/
public abstract double
getY1();
/**
* Returns the start point.
* @return a <code>Point2D</code> that is the start point of this
* <code>QuadCurve2D</code>.
* @since 1.2
*/
public abstract
Point2D getP1();
/**
* Returns the X coordinate of the control point in
* <code>double</code> precision.
* @return X coordinate the control point
* @since 1.2
*/
public abstract double
getCtrlX();
/**
* Returns the Y coordinate of the control point in
* <code>double</code> precision.
* @return the Y coordinate of the control point.
* @since 1.2
*/
public abstract double
getCtrlY();
/**
* Returns the control point.
* @return a <code>Point2D</code> that is the control point of this
* <code>Point2D</code>.
* @since 1.2
*/
public abstract
Point2D getCtrlPt();
/**
* Returns the X coordinate of the end point in
* <code>double</code> precision.
* @return the x coordinate of the end point.
* @since 1.2
*/
public abstract double
getX2();
/**
* Returns the Y coordinate of the end point in
* <code>double</code> precision.
* @return the Y coordinate of the end point.
* @since 1.2
*/
public abstract double
getY2();
/**
* Returns the end point.
* @return a <code>Point</code> object that is the end point
* of this <code>Point2D</code>.
* @since 1.2
*/
public abstract
Point2D getP2();
/**
* Sets the location of the end points and control point of this curve
* to the specified <code>double</code> coordinates.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @since 1.2
*/
public abstract void
setCurve(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2);
/**
* Sets the location of the end points and control points of this
* <code>QuadCurve2D</code> to the <code>double</code> coordinates at
* the specified offset in the specified array.
* @param coords the array containing coordinate values
* @param offset the index into the array from which to start
* getting the coordinate values and assigning them to this
* <code>QuadCurve2D</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]);
}
/**
* Sets the location of the end points and control point of this
* <code>QuadCurve2D</code> to the specified <code>Point2D</code>
* coordinates.
* @param p1 the start point
* @param cp the control point
* @param p2 the end point
* @since 1.2
*/
public void
setCurve(
Point2D p1,
Point2D cp,
Point2D p2) {
setCurve(
p1.
getX(),
p1.
getY(),
cp.
getX(),
cp.
getY(),
p2.
getX(),
p2.
getY());
}
/**
* Sets the location of the end points and control points of this
* <code>QuadCurve2D</code> to the coordinates of the
* <code>Point2D</code> objects at the specified offset in
* the specified array.
* @param pts an array containing <code>Point2D</code> that define
* coordinate values
* @param offset the index into <code>pts</code> from which to start
* getting the coordinate values and assigning them to this
* <code>QuadCurve2D</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());
}
/**
* Sets the location of the end points and control point of this
* <code>QuadCurve2D</code> to the same as those in the specified
* <code>QuadCurve2D</code>.
* @param c the specified <code>QuadCurve2D</code>
* @since 1.2
*/
public void
setCurve(
QuadCurve2D c) {
setCurve(
c.
getX1(),
c.
getY1(),
c.
getCtrlX(),
c.
getCtrlY(),
c.
getX2(),
c.
getY2());
}
/**
* Returns the square of the flatness, or maximum distance of a
* control point from the line connecting the end points, of the
* quadratic curve specified by the indicated control points.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @return the square of the flatness of the quadratic curve
* defined by the specified coordinates.
* @since 1.2
*/
public static double
getFlatnessSq(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2) {
return
Line2D.
ptSegDistSq(
x1,
y1,
x2,
y2,
ctrlx,
ctrly);
}
/**
* Returns the flatness, or maximum distance of a
* control point from the line connecting the end points, of the
* quadratic curve specified by the indicated control points.
*
* @param x1 the X coordinate of the start point
* @param y1 the Y coordinate of the start point
* @param ctrlx the X coordinate of the control point
* @param ctrly the Y coordinate of the control point
* @param x2 the X coordinate of the end point
* @param y2 the Y coordinate of the end point
* @return the flatness of the quadratic curve defined by the
* specified coordinates.
* @since 1.2
*/
public static double
getFlatness(double
x1, double
y1,
double
ctrlx, double
ctrly,
double
x2, double
y2) {
return
Line2D.
ptSegDist(
x1,
y1,
x2,
y2,
ctrlx,
ctrly);
}
/**
* Returns the square of the flatness, or maximum distance of a
* control point from the line connecting the end points, of the
* quadratic curve specified by the control points stored in the
* indicated array at the indicated index.
* @param coords an array containing coordinate values
* @param offset the index into <code>coords</code> from which to
* to start getting the values from the array
* @return the flatness of the quadratic curve that is defined by the
* values in the specified array at the specified index.
* @since 1.2
*/
public static double
getFlatnessSq(double
coords[], int
offset) {
return
Line2D.
ptSegDistSq(
coords[
offset + 0],
coords[
offset + 1],
coords[
offset + 4],
coords[
offset + 5],
coords[
offset + 2],
coords[
offset + 3]);
}
/**
* Returns the flatness, or maximum distance of a
* control point from the line connecting the end points, of the
* quadratic curve specified by the control points stored in the
* indicated array at the indicated index.
* @param coords an array containing coordinate values
* @param offset the index into <code>coords</code> from which to
* start getting the coordinate values
* @return the flatness of a quadratic curve defined by the
* specified array at the specified offset.
* @since 1.2
*/
public static double
getFlatness(double
coords[], int
offset) {
return
Line2D.
ptSegDist(
coords[
offset + 0],
coords[
offset + 1],
coords[
offset + 4],
coords[
offset + 5],
coords[
offset + 2],
coords[
offset + 3]);
}
/**
* Returns the square of the flatness, or maximum distance of a
* control point from the line connecting the end points, of this
* <code>QuadCurve2D</code>.
* @return the square of the flatness of this
* <code>QuadCurve2D</code>.
* @since 1.2
*/
public double
getFlatnessSq() {
return
Line2D.
ptSegDistSq(
getX1(),
getY1(),
getX2(),
getY2(),
getCtrlX(),
getCtrlY());
}
/**
* Returns the flatness, or maximum distance of a
* control point from the line connecting the end points, of this
* <code>QuadCurve2D</code>.
* @return the flatness of this <code>QuadCurve2D</code>.
* @since 1.2
*/
public double
getFlatness() {
return
Line2D.
ptSegDist(
getX1(),
getY1(),
getX2(),
getY2(),
getCtrlX(),
getCtrlY());
}
/**
* Subdivides this <code>QuadCurve2D</code> 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 can be the same as this <code>QuadCurve2D</code> or
* <code>null</code>.
* @param left the <code>QuadCurve2D</code> object for storing the
* left or first half of the subdivided curve
* @param right the <code>QuadCurve2D</code> object for storing the
* right or second half of the subdivided curve
* @since 1.2
*/
public void
subdivide(
QuadCurve2D left,
QuadCurve2D right) {
subdivide(this,
left,
right);
}
/**
* Subdivides the quadratic curve specified by the <code>src</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 can be the same as the <code>src</code> object or
* <code>null</code>.
* @param src the quadratic curve to be subdivided
* @param left the <code>QuadCurve2D</code> object for storing the
* left or first half of the subdivided curve
* @param right the <code>QuadCurve2D</code> object for storing the
* right or second half of the subdivided curve
* @since 1.2
*/
public static void
subdivide(
QuadCurve2D src,
QuadCurve2D left,
QuadCurve2D right) {
double
x1 =
src.
getX1();
double
y1 =
src.
getY1();
double
ctrlx =
src.
getCtrlX();
double
ctrly =
src.
getCtrlY();
double
x2 =
src.
getX2();
double
y2 =
src.
getY2();
double
ctrlx1 = (
x1 +
ctrlx) / 2.0;
double
ctrly1 = (
y1 +
ctrly) / 2.0;
double
ctrlx2 = (
x2 +
ctrlx) / 2.0;
double
ctrly2 = (
y2 +
ctrly) / 2.0;
ctrlx = (
ctrlx1 +
ctrlx2) / 2.0;
ctrly = (
ctrly1 +
ctrly2) / 2.0;
if (
left != null) {
left.
setCurve(
x1,
y1,
ctrlx1,
ctrly1,
ctrlx,
ctrly);
}
if (
right != null) {
right.
setCurve(
ctrlx,
ctrly,
ctrlx2,
ctrly2,
x2,
y2);
}
}
/**
* Subdivides the quadratic curve specified by the coordinates
* stored in the <code>src</code> array at indices
* <code>srcoff</code> through <code>srcoff</code> + 5
* 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 can be <code>null</code> or a reference to the same array
* and offset 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 that
* <code>rightoff</code> equals <code>leftoff</code> + 4 in order
* to avoid allocating extra storage for this common point.
* @param src the array holding the coordinates for the source curve
* @param srcoff the offset into the array of the beginning of the
* the 6 source coordinates
* @param left the array for storing the coordinates for the first
* half of the subdivided curve
* @param leftoff the offset into the array of the beginning of the
* the 6 left coordinates
* @param right the array for storing the coordinates for the second
* half of the subdivided curve
* @param rightoff the offset into the array of the beginning of the
* the 6 right coordinates
* @since 1.2
*/
public static void
subdivide(double
src[], int
srcoff,
double
left[], int
leftoff,
double
right[], int
rightoff) {
double
x1 =
src[
srcoff + 0];
double
y1 =
src[
srcoff + 1];
double
ctrlx =
src[
srcoff + 2];
double
ctrly =
src[
srcoff + 3];
double
x2 =
src[
srcoff + 4];
double
y2 =
src[
srcoff + 5];
if (
left != null) {
left[
leftoff + 0] =
x1;
left[
leftoff + 1] =
y1;
}
if (
right != null) {
right[
rightoff + 4] =
x2;
right[
rightoff + 5] =
y2;
}
x1 = (
x1 +
ctrlx) / 2.0;
y1 = (
y1 +
ctrly) / 2.0;
x2 = (
x2 +
ctrlx) / 2.0;
y2 = (
y2 +
ctrly) / 2.0;
ctrlx = (
x1 +
x2) / 2.0;
ctrly = (
y1 +
y2) / 2.0;
if (
left != null) {
left[
leftoff + 2] =
x1;
left[
leftoff + 3] =
y1;
left[
leftoff + 4] =
ctrlx;
left[
leftoff + 5] =
ctrly;
}
if (
right != null) {
right[
rightoff + 0] =
ctrlx;
right[
rightoff + 1] =
ctrly;
right[
rightoff + 2] =
x2;
right[
rightoff + 3] =
y2;
}
}
/**
* Solves the quadratic whose coefficients are in the <code>eqn</code>
* array and places the non-complex roots back into the same array,
* returning the number of roots. The quadratic solved is represented
* by the equation:
* <pre>
* eqn = {C, B, A};
* ax^2 + bx + c = 0
* </pre>
* A return value of <code>-1</code> is used to distinguish a constant
* equation, which might be always 0 or never 0, from an equation that
* has no zeroes.
* @param eqn the array that contains the quadratic coefficients
* @return the number of roots, or <code>-1</code> if the equation is
* a constant
* @since 1.2
*/
public static int
solveQuadratic(double
eqn[]) {
return
solveQuadratic(
eqn,
eqn);
}
/**
* Solves the quadratic whose coefficients are in the <code>eqn</code>
* array and places the non-complex roots into the <code>res</code>
* array, returning the number of roots.
* The quadratic solved is represented by the equation:
* <pre>
* eqn = {C, B, A};
* ax^2 + bx + c = 0
* </pre>
* A return value of <code>-1</code> is used to distinguish a constant
* equation, which might be always 0 or never 0, from an equation that
* has no zeroes.
* @param eqn the specified array of coefficients to use to solve
* the quadratic equation
* @param res the array that contains the non-complex roots
* resulting from the solution of the quadratic equation
* @return the number of roots, or <code>-1</code> if the equation is
* a constant.
* @since 1.3
*/
public static int
solveQuadratic(double
eqn[], double
res[]) {
double
a =
eqn[2];
double
b =
eqn[1];
double
c =
eqn[0];
int
roots = 0;
if (
a == 0.0) {
// The quadratic parabola has degenerated to a line.
if (
b == 0.0) {
// The line has degenerated to a constant.
return -1;
}
res[
roots++] = -
c /
b;
} else {
// From Numerical Recipes, 5.6, Quadratic and Cubic Equations
double
d =
b *
b - 4.0 *
a *
c;
if (
d < 0.0) {
// If d < 0.0, then there are no roots
return 0;
}
d =
Math.
sqrt(
d);
// For accuracy, calculate one root using:
// (-b +/- d) / 2a
// and the other using:
// 2c / (-b +/- d)
// Choose the sign of the +/- so that b+d gets larger in magnitude
if (
b < 0.0) {
d = -
d;
}
double
q = (
b +
d) / -2.0;
// We already tested a for being 0 above
res[
roots++] =
q /
a;
if (
q != 0.0) {
res[
roots++] =
c /
q;
}
}
return
roots;
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
contains(double
x, double
y) {
double
x1 =
getX1();
double
y1 =
getY1();
double
xc =
getCtrlX();
double
yc =
getCtrlY();
double
x2 =
getX2();
double
y2 =
getY2();
/*
* We have a convex shape bounded by quad curve Pc(t)
* and ine Pl(t).
*
* P1 = (x1, y1) - start point of curve
* P2 = (x2, y2) - end point of curve
* Pc = (xc, yc) - control point
*
* Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 =
* = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1
* Pl(t) = P1*(1 - t) + P2*t
* t = [0:1]
*
* P = (x, y) - point of interest
*
* Let's look at second derivative of quad curve equation:
*
* Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
* It's constant vector.
*
* Let's draw a line through P to be parallel to this
* vector and find the intersection of the quad curve
* and the line.
*
* Pq(t) is point of intersection if system of equations
* below has the solution.
*
* L(s) = P + Pq''*s == Pq(t)
* Pq''*s + (P - Pq(t)) == 0
*
* | xq''*s + (x - xq(t)) == 0
* | yq''*s + (y - yq(t)) == 0
*
* This system has the solution if rank of its matrix equals to 1.
* That is, determinant of the matrix should be zero.
*
* (y - yq(t))*xq'' == (x - xq(t))*yq''
*
* Let's solve this equation with 't' variable.
* Also let kx = x1 - 2*xc + x2
* ky = y1 - 2*yc + y2
*
* t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) /
* ((xc - x1)*ky - (yc - y1)*kx)
*
* Let's do the same for our line Pl(t):
*
* t0l = ((x - x1)*ky - (y - y1)*kx) /
* ((x2 - x1)*ky - (y2 - y1)*kx)
*
* It's easy to check that t0q == t0l. This fact means
* we can compute t0 only one time.
*
* In case t0 < 0 or t0 > 1, we have an intersections outside
* of shape bounds. So, P is definitely out of shape.
*
* In case t0 is inside [0:1], we should calculate Pq(t0)
* and Pl(t0). We have three points for now, and all of them
* lie on one line. So, we just need to detect, is our point
* of interest between points of intersections or not.
*
* If the denominator in the t0q and t0l equations is
* zero, then the points must be collinear and so the
* curve is degenerate and encloses no area. Thus the
* result is false.
*/
double
kx =
x1 - 2 *
xc +
x2;
double
ky =
y1 - 2 *
yc +
y2;
double
dx =
x -
x1;
double
dy =
y -
y1;
double
dxl =
x2 -
x1;
double
dyl =
y2 -
y1;
double
t0 = (
dx *
ky -
dy *
kx) / (
dxl *
ky -
dyl *
kx);
if (
t0 < 0 ||
t0 > 1 ||
t0 !=
t0) {
return false;
}
double
xb =
kx *
t0 *
t0 + 2 * (
xc -
x1) *
t0 +
x1;
double
yb =
ky *
t0 *
t0 + 2 * (
yc -
y1) *
t0 +
y1;
double
xl =
dxl *
t0 +
x1;
double
yl =
dyl *
t0 +
y1;
return (
x >=
xb &&
x <
xl) ||
(
x >=
xl &&
x <
xb) ||
(
y >=
yb &&
y <
yl) ||
(
y >=
yl &&
y <
yb);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
contains(
Point2D p) {
return
contains(
p.
getX(),
p.
getY());
}
/**
* Fill an array with the coefficients of the parametric equation
* in t, ready for solving against val with solveQuadratic.
* We currently have:
* val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
* = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
* = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
* 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
* 0 = C + Bt + At^2
* C = C1 - val
* B = 2*CP - 2*C1
* A = C1 - 2*CP + C2
*/
private static void
fillEqn(double
eqn[], double
val,
double
c1, double
cp, double
c2) {
eqn[0] =
c1 -
val;
eqn[1] =
cp +
cp -
c1 -
c1;
eqn[2] =
c1 -
cp -
cp +
c2;
return;
}
/**
* Evaluate the t values in the first num slots of the vals[] array
* and place the evaluated values back into the same array. Only
* evaluate t values that are within the range <0, 1>, including
* the 0 and 1 ends of the range iff the include0 or include1
* booleans are true. If an "inflection" equation is handed in,
* then any points which represent a point of inflection for that
* quadratic equation are also ignored.
*/
private static int
evalQuadratic(double
vals[], int
num,
boolean
include0,
boolean
include1,
double
inflect[],
double
c1, double
ctrl, double
c2) {
int
j = 0;
for (int
i = 0;
i <
num;
i++) {
double
t =
vals[
i];
if ((
include0 ?
t >= 0 :
t > 0) &&
(
include1 ?
t <= 1 :
t < 1) &&
(
inflect == null ||
inflect[1] + 2*
inflect[2]*
t != 0))
{
double
u = 1 -
t;
vals[
j++] =
c1*
u*
u + 2*
ctrl*
t*
u +
c2*
t*
t;
}
}
return
j;
}
private static final int
BELOW = -2;
private static final int
LOWEDGE = -1;
private static final int
INSIDE = 0;
private static final int
HIGHEDGE = 1;
private static final int
ABOVE = 2;
/**
* Determine where coord lies with respect to the range from
* low to high. It is assumed that low <= high. The return
* value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
* or ABOVE.
*/
private static int
getTag(double
coord, double
low, double
high) {
if (
coord <=
low) {
return (
coord <
low ?
BELOW :
LOWEDGE);
}
if (
coord >=
high) {
return (
coord >
high ?
ABOVE :
HIGHEDGE);
}
return
INSIDE;
}
/**
* Determine if the pttag represents a coordinate that is already
* in its test range, or is on the border with either of the two
* opttags representing another coordinate that is "towards the
* inside" of that test range. In other words, are either of the
* two "opt" points "drawing the pt inward"?
*/
private static boolean
inwards(int
pttag, int
opt1tag, int
opt2tag) {
switch (
pttag) {
case
BELOW:
case
ABOVE:
default:
return false;
case
LOWEDGE:
return (
opt1tag >=
INSIDE ||
opt2tag >=
INSIDE);
case
INSIDE:
return true;
case
HIGHEDGE:
return (
opt1tag <=
INSIDE ||
opt2tag <=
INSIDE);
}
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
intersects(double
x, double
y, double
w, double
h) {
// Trivially reject non-existant rectangles
if (
w <= 0 ||
h <= 0) {
return false;
}
// Trivially accept if either endpoint is inside the rectangle
// (not on its border since it may end there and not go inside)
// Record where they lie with respect to the rectangle.
// -1 => left, 0 => inside, 1 => right
double
x1 =
getX1();
double
y1 =
getY1();
int
x1tag =
getTag(
x1,
x,
x+
w);
int
y1tag =
getTag(
y1,
y,
y+
h);
if (
x1tag ==
INSIDE &&
y1tag ==
INSIDE) {
return true;
}
double
x2 =
getX2();
double
y2 =
getY2();
int
x2tag =
getTag(
x2,
x,
x+
w);
int
y2tag =
getTag(
y2,
y,
y+
h);
if (
x2tag ==
INSIDE &&
y2tag ==
INSIDE) {
return true;
}
double
ctrlx =
getCtrlX();
double
ctrly =
getCtrlY();
int
ctrlxtag =
getTag(
ctrlx,
x,
x+
w);
int
ctrlytag =
getTag(
ctrly,
y,
y+
h);
// Trivially reject if all points are entirely to one side of
// the rectangle.
if (
x1tag <
INSIDE &&
x2tag <
INSIDE &&
ctrlxtag <
INSIDE) {
return false; // All points left
}
if (
y1tag <
INSIDE &&
y2tag <
INSIDE &&
ctrlytag <
INSIDE) {
return false; // All points above
}
if (
x1tag >
INSIDE &&
x2tag >
INSIDE &&
ctrlxtag >
INSIDE) {
return false; // All points right
}
if (
y1tag >
INSIDE &&
y2tag >
INSIDE &&
ctrlytag >
INSIDE) {
return false; // All points below
}
// Test for endpoints on the edge where either the segment
// or the curve is headed "inwards" from them
// Note: These tests are a superset of the fast endpoint tests
// above and thus repeat those tests, but take more time
// and cover more cases
if (
inwards(
x1tag,
x2tag,
ctrlxtag) &&
inwards(
y1tag,
y2tag,
ctrlytag))
{
// First endpoint on border with either edge moving inside
return true;
}
if (
inwards(
x2tag,
x1tag,
ctrlxtag) &&
inwards(
y2tag,
y1tag,
ctrlytag))
{
// Second endpoint on border with either edge moving inside
return true;
}
// Trivially accept if endpoints span directly across the rectangle
boolean
xoverlap = (
x1tag *
x2tag <= 0);
boolean
yoverlap = (
y1tag *
y2tag <= 0);
if (
x1tag ==
INSIDE &&
x2tag ==
INSIDE &&
yoverlap) {
return true;
}
if (
y1tag ==
INSIDE &&
y2tag ==
INSIDE &&
xoverlap) {
return true;
}
// We now know that both endpoints are outside the rectangle
// but the 3 points are not all on one side of the rectangle.
// Therefore the curve cannot be contained inside the rectangle,
// but the rectangle might be contained inside the curve, or
// the curve might intersect the boundary of the rectangle.
double[]
eqn = new double[3];
double[]
res = new double[3];
if (!
yoverlap) {
// Both Y coordinates for the closing segment are above or
// below the rectangle which means that we can only intersect
// if the curve crosses the top (or bottom) of the rectangle
// in more than one place and if those crossing locations
// span the horizontal range of the rectangle.
fillEqn(
eqn, (
y1tag <
INSIDE ?
y :
y+
h),
y1,
ctrly,
y2);
return (
solveQuadratic(
eqn,
res) == 2 &&
evalQuadratic(
res, 2, true, true, null,
x1,
ctrlx,
x2) == 2 &&
getTag(
res[0],
x,
x+
w) *
getTag(
res[1],
x,
x+
w) <= 0);
}
// Y ranges overlap. Now we examine the X ranges
if (!
xoverlap) {
// Both X coordinates for the closing segment are left of
// or right of the rectangle which means that we can only
// intersect if the curve crosses the left (or right) edge
// of the rectangle in more than one place and if those
// crossing locations span the vertical range of the rectangle.
fillEqn(
eqn, (
x1tag <
INSIDE ?
x :
x+
w),
x1,
ctrlx,
x2);
return (
solveQuadratic(
eqn,
res) == 2 &&
evalQuadratic(
res, 2, true, true, null,
y1,
ctrly,
y2) == 2 &&
getTag(
res[0],
y,
y+
h) *
getTag(
res[1],
y,
y+
h) <= 0);
}
// The X and Y ranges of the endpoints overlap the X and Y
// ranges of the rectangle, now find out how the endpoint
// line segment intersects the Y range of the rectangle
double
dx =
x2 -
x1;
double
dy =
y2 -
y1;
double
k =
y2 *
x1 -
x2 *
y1;
int
c1tag,
c2tag;
if (
y1tag ==
INSIDE) {
c1tag =
x1tag;
} else {
c1tag =
getTag((
k +
dx * (
y1tag <
INSIDE ?
y :
y+
h)) /
dy,
x,
x+
w);
}
if (
y2tag ==
INSIDE) {
c2tag =
x2tag;
} else {
c2tag =
getTag((
k +
dx * (
y2tag <
INSIDE ?
y :
y+
h)) /
dy,
x,
x+
w);
}
// If the part of the line segment that intersects the Y range
// of the rectangle crosses it horizontally - trivially accept
if (
c1tag *
c2tag <= 0) {
return true;
}
// Now we know that both the X and Y ranges intersect and that
// the endpoint line segment does not directly cross the rectangle.
//
// We can almost treat this case like one of the cases above
// where both endpoints are to one side, except that we will
// only get one intersection of the curve with the vertical
// side of the rectangle. This is because the endpoint segment
// accounts for the other intersection.
//
// (Remember there is overlap in both the X and Y ranges which
// means that the segment must cross at least one vertical edge
// of the rectangle - in particular, the "near vertical side" -
// leaving only one intersection for the curve.)
//
// Now we calculate the y tags of the two intersections on the
// "near vertical side" of the rectangle. We will have one with
// the endpoint segment, and one with the curve. If those two
// vertical intersections overlap the Y range of the rectangle,
// we have an intersection. Otherwise, we don't.
// c1tag = vertical intersection class of the endpoint segment
//
// Choose the y tag of the endpoint that was not on the same
// side of the rectangle as the subsegment calculated above.
// Note that we can "steal" the existing Y tag of that endpoint
// since it will be provably the same as the vertical intersection.
c1tag = ((
c1tag *
x1tag <= 0) ?
y1tag :
y2tag);
// c2tag = vertical intersection class of the curve
//
// We have to calculate this one the straightforward way.
// Note that the c2tag can still tell us which vertical edge
// to test against.
fillEqn(
eqn, (
c2tag <
INSIDE ?
x :
x+
w),
x1,
ctrlx,
x2);
int
num =
solveQuadratic(
eqn,
res);
// Note: We should be able to assert(num == 2); since the
// X range "crosses" (not touches) the vertical boundary,
// but we pass num to evalQuadratic for completeness.
evalQuadratic(
res,
num, true, true, null,
y1,
ctrly,
y2);
// Note: We can assert(num evals == 1); since one of the
// 2 crossings will be out of the [0,1] range.
c2tag =
getTag(
res[0],
y,
y+
h);
// Finally, we have an intersection if the two crossings
// overlap the Y range of the rectangle.
return (
c1tag *
c2tag <= 0);
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
intersects(
Rectangle2D r) {
return
intersects(
r.
getX(),
r.
getY(),
r.
getWidth(),
r.
getHeight());
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
contains(double
x, double
y, double
w, double
h) {
if (
w <= 0 ||
h <= 0) {
return false;
}
// Assertion: Quadratic curves closed by connecting their
// endpoints are always convex.
return (
contains(
x,
y) &&
contains(
x +
w,
y) &&
contains(
x +
w,
y +
h) &&
contains(
x,
y +
h));
}
/**
* {@inheritDoc}
* @since 1.2
*/
public boolean
contains(
Rectangle2D r) {
return
contains(
r.
getX(),
r.
getY(),
r.
getWidth(),
r.
getHeight());
}
/**
* {@inheritDoc}
* @since 1.2
*/
public
Rectangle getBounds() {
return
getBounds2D().
getBounds();
}
/**
* Returns an iteration object that defines the boundary of the
* shape of this <code>QuadCurve2D</code>.
* The iterator for this class is not multi-threaded safe,
* which means that this <code>QuadCurve2D</code> class does not
* guarantee that modifications to the geometry of this
* <code>QuadCurve2D</code> object do not affect any iterations of
* that geometry that are already in process.
* @param at an optional {@link AffineTransform} to apply to the
* shape boundary
* @return a {@link PathIterator} object that defines the boundary
* of the shape.
* @since 1.2
*/
public
PathIterator getPathIterator(
AffineTransform at) {
return new
QuadIterator(this,
at);
}
/**
* Returns an iteration object that defines the boundary of the
* flattened shape of this <code>QuadCurve2D</code>.
* The iterator for this class is not multi-threaded safe,
* which means that this <code>QuadCurve2D</code> class does not
* guarantee that modifications to the geometry of this
* <code>QuadCurve2D</code> object do not affect any iterations of
* that geometry that are already in process.
* @param at an optional <code>AffineTransform</code> to apply
* to the boundary of the shape
* @param flatness the maximum distance that the control points for a
* subdivided curve can be with respect to a line connecting
* the end points of this curve before this curve is
* replaced by a straight line connecting the end points.
* @return a <code>PathIterator</code> object that defines the
* flattened boundary of the shape.
* @since 1.2
*/
public
PathIterator getPathIterator(
AffineTransform at, double
flatness) {
return new
FlatteningPathIterator(
getPathIterator(
at),
flatness);
}
/**
* Creates a new object of the same class and with the same contents
* as this object.
*
* @return a clone of this instance.
* @exception OutOfMemoryError if there is not enough memory.
* @see java.lang.Cloneable
* @since 1.2
*/
public
Object clone() {
try {
return super.clone();
} catch (
CloneNotSupportedException e) {
// this shouldn't happen, since we are Cloneable
throw new
InternalError(
e);
}
}
}