public abstract class CubicCurve2D extends Object implements Shape, Cloneable
CubicCurve2D
class defines a cubic parametric curve
segment in (x,y)
coordinate space.
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.
Modifier and Type  Class and Description 

static class 
CubicCurve2D.Double
A cubic parametric curve segment specified with
double coordinates. 
static class 
CubicCurve2D.Float
A cubic parametric curve segment specified with
float coordinates. 
Modifier  Constructor and Description 

protected 
CubicCurve2D()
This is an abstract class that cannot be instantiated directly.

Modifier and Type  Method and Description 

Object 
clone()
Creates a new object of the same class as this object.

boolean 
contains(double x,
double y)
Tests if the specified coordinates are inside the boundary of the
Shape , as described by the
definition of insideness. 
boolean 
contains(double x,
double y,
double w,
double h)
Tests if the interior of the
Shape entirely contains
the specified rectangular area. 
boolean 
contains(Point2D p)
Tests if a specified
Point2D is inside the boundary
of the Shape , as described by the
definition of insideness. 
boolean 
contains(Rectangle2D r)
Tests if the interior of the
Shape entirely contains the
specified Rectangle2D . 
Rectangle 
getBounds()
Returns an integer
Rectangle that completely encloses the
Shape . 
abstract Point2D 
getCtrlP1()
Returns the first control point.

abstract Point2D 
getCtrlP2()
Returns the second control point.

abstract double 
getCtrlX1()
Returns the X coordinate of the first control point in double precision.

abstract double 
getCtrlX2()
Returns the X coordinate of the second control point
in double precision.

abstract double 
getCtrlY1()
Returns the Y coordinate of the first control point in double precision.

abstract double 
getCtrlY2()
Returns the Y coordinate of the second control point
in double precision.

double 
getFlatness()
Returns the flatness of this curve.

static double 
getFlatness(double[] coords,
int offset)
Returns the flatness of the cubic curve specified
by the control points stored in the indicated array at the
indicated index.

static double 
getFlatness(double x1,
double y1,
double ctrlx1,
double ctrly1,
double ctrlx2,
double ctrly2,
double x2,
double y2)
Returns the flatness of the cubic curve specified
by the indicated control points.

double 
getFlatnessSq()
Returns the square of the flatness of this curve.

static double 
getFlatnessSq(double[] coords,
int offset)
Returns the square of the flatness of the cubic curve specified
by the control points stored in the indicated array at the
indicated index.

static double 
getFlatnessSq(double x1,
double y1,
double ctrlx1,
double ctrly1,
double ctrlx2,
double ctrly2,
double x2,
double y2)
Returns the square of the flatness of the cubic curve specified
by the indicated control points.

abstract Point2D 
getP1()
Returns the start point.

abstract Point2D 
getP2()
Returns the end point.

PathIterator 
getPathIterator(AffineTransform at)
Returns an iteration object that defines the boundary of the
shape.

PathIterator 
getPathIterator(AffineTransform at,
double flatness)
Return an iteration object that defines the boundary of the
flattened shape.

abstract double 
getX1()
Returns the X coordinate of the start point in double precision.

abstract double 
getX2()
Returns the X coordinate of the end point in double precision.

abstract double 
getY1()
Returns the Y coordinate of the start point in double precision.

abstract double 
getY2()
Returns the Y coordinate of the end point in double precision.

boolean 
intersects(double x,
double y,
double w,
double h)
Tests if the interior of the
Shape intersects the
interior of a specified rectangular area. 
boolean 
intersects(Rectangle2D r)
Tests if the interior of the
Shape intersects the
interior of a specified Rectangle2D . 
void 
setCurve(CubicCurve2D c)
Sets the location of the end points and control points of this curve
to the same as those in the specified
CubicCurve2D . 
void 
setCurve(double[] coords,
int offset)
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.

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 specified double coordinates.

void 
setCurve(Point2D[] pts,
int offset)
Sets the location of the end points and control points of this curve
to the coordinates of the
Point2D objects at the specified
offset in the specified array. 
void 
setCurve(Point2D p1,
Point2D cp1,
Point2D cp2,
Point2D p2)
Sets the location of the end points and control points of this curve
to the specified
Point2D coordinates. 
static int 
solveCubic(double[] eqn)
Solves the cubic whose coefficients are in the
eqn
array and places the noncomplex roots back into the same array,
returning the number of roots. 
static int 
solveCubic(double[] eqn,
double[] res)
Solve the cubic whose coefficients are in the
eqn
array and place the noncomplex roots into the res
array, returning the number of roots. 
void 
subdivide(CubicCurve2D left,
CubicCurve2D right)
Subdivides this cubic curve and stores the resulting two
subdivided curves into the left and right curve parameters.

static void 
subdivide(CubicCurve2D src,
CubicCurve2D left,
CubicCurve2D right)
Subdivides the cubic curve specified by the
src parameter
and stores the resulting two subdivided curves into the
left and right curve parameters. 
static void 
subdivide(double[] src,
int srcoff,
double[] left,
int leftoff,
double[] right,
int rightoff)
Subdivides the cubic curve specified by the coordinates
stored in the
src array at indices srcoff
through (srcoff + 7) and stores the
resulting two subdivided curves into the two result arrays at the
corresponding indices. 
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
getBounds2D
protected CubicCurve2D()
CubicCurve2D.Float
,
CubicCurve2D.Double
public abstract double getX1()
CubicCurve2D
.public abstract double getY1()
CubicCurve2D
.public abstract Point2D getP1()
Point2D
that is the start point of
the CubicCurve2D
.public abstract double getCtrlX1()
CubicCurve2D
.public abstract double getCtrlY1()
CubicCurve2D
.public abstract Point2D getCtrlP1()
Point2D
that is the first control point of
the CubicCurve2D
.public abstract double getCtrlX2()
CubicCurve2D
.public abstract double getCtrlY2()
CubicCurve2D
.public abstract Point2D getCtrlP2()
Point2D
that is the second control point of
the CubicCurve2D
.public abstract double getX2()
CubicCurve2D
.public abstract double getY2()
CubicCurve2D
.public abstract Point2D getP2()
Point2D
that is the end point of
the CubicCurve2D
.public abstract void setCurve(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)
x1
 the X coordinate used to set the start point
of this CubicCurve2D
y1
 the Y coordinate used to set the start point
of this CubicCurve2D
ctrlx1
 the X coordinate used to set the first control point
of this CubicCurve2D
ctrly1
 the Y coordinate used to set the first control point
of this CubicCurve2D
ctrlx2
 the X coordinate used to set the second control point
of this CubicCurve2D
ctrly2
 the Y coordinate used to set the second control point
of this CubicCurve2D
x2
 the X coordinate used to set the end point
of this CubicCurve2D
y2
 the Y coordinate used to set the end point
of this CubicCurve2D
public void setCurve(double[] coords, int offset)
coords
 a double array containing coordinatesoffset
 the index of coords
from which to begin
setting the end points and control points of this curve
to the coordinates contained in coords
public void setCurve(Point2D p1, Point2D cp1, Point2D cp2, Point2D p2)
Point2D
coordinates.p1
 the first specified Point2D
used to set the
start point of this curvecp1
 the second specified Point2D
used to set the
first control point of this curvecp2
 the third specified Point2D
used to set the
second control point of this curvep2
 the fourth specified Point2D
used to set the
end point of this curvepublic void setCurve(Point2D[] pts, int offset)
Point2D
objects at the specified
offset in the specified array.pts
 an array of Point2D
objectsoffset
 the index of pts
from which to begin setting
the end points and control points of this curve to the
points contained in pts
public void setCurve(CubicCurve2D c)
CubicCurve2D
.c
 the specified CubicCurve2D
public static double getFlatnessSq(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)
x1
 the X coordinate that specifies the start point
of a CubicCurve2D
y1
 the Y coordinate that specifies the start point
of a CubicCurve2D
ctrlx1
 the X coordinate that specifies the first control point
of a CubicCurve2D
ctrly1
 the Y coordinate that specifies the first control point
of a CubicCurve2D
ctrlx2
 the X coordinate that specifies the second control point
of a CubicCurve2D
ctrly2
 the Y coordinate that specifies the second control point
of a CubicCurve2D
x2
 the X coordinate that specifies the end point
of a CubicCurve2D
y2
 the Y coordinate that specifies the end point
of a CubicCurve2D
CubicCurve2D
represented by the specified coordinates.public static double getFlatness(double x1, double y1, double ctrlx1, double ctrly1, double ctrlx2, double ctrly2, double x2, double y2)
x1
 the X coordinate that specifies the start point
of a CubicCurve2D
y1
 the Y coordinate that specifies the start point
of a CubicCurve2D
ctrlx1
 the X coordinate that specifies the first control point
of a CubicCurve2D
ctrly1
 the Y coordinate that specifies the first control point
of a CubicCurve2D
ctrlx2
 the X coordinate that specifies the second control point
of a CubicCurve2D
ctrly2
 the Y coordinate that specifies the second control point
of a CubicCurve2D
x2
 the X coordinate that specifies the end point
of a CubicCurve2D
y2
 the Y coordinate that specifies the end point
of a CubicCurve2D
CubicCurve2D
represented by the specified coordinates.public static double getFlatnessSq(double[] coords, int offset)
coords
 an array containing coordinatesoffset
 the index of coords
from which to begin
getting the end points and control points of the curveCubicCurve2D
specified by the coordinates in coords
at
the specified offset.public static double getFlatness(double[] coords, int offset)
coords
 an array containing coordinatesoffset
 the index of coords
from which to begin
getting the end points and control points of the curveCubicCurve2D
specified by the coordinates in coords
at
the specified offset.public double getFlatnessSq()
public double getFlatness()
public void subdivide(CubicCurve2D left, CubicCurve2D right)
left
 the cubic curve object for storing for the left or
first half of the subdivided curveright
 the cubic curve object for storing for the right or
second half of the subdivided curvepublic static void subdivide(CubicCurve2D src, CubicCurve2D left, CubicCurve2D right)
src
parameter
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 the src
object or null
.src
 the cubic curve to be subdividedleft
 the cubic curve object for storing the left or
first half of the subdivided curveright
 the cubic curve object for storing the right or
second half of the subdivided curvepublic static void subdivide(double[] src, int srcoff, double[] left, int leftoff, double[] right, int rightoff)
src
array at indices srcoff
through (srcoff
+ 7) and stores the
resulting two subdivided curves into the two result arrays at the
corresponding indices.
Either or both of the left
and right
arrays may be null
or a reference to the same array
as the src
array.
Note that the last point in the first subdivided curve is the
same as the first point in the second subdivided curve. Thus,
it is possible to pass the same array for left
and right
and to use offsets, such as rightoff
equals (leftoff
+ 6), in order
to avoid allocating extra storage for this common point.src
 the array holding the coordinates for the source curvesrcoff
 the offset into the array of the beginning of the
the 6 source coordinatesleft
 the array for storing the coordinates for the first
half of the subdivided curveleftoff
 the offset into the array of the beginning of the
the 6 left coordinatesright
 the array for storing the coordinates for the second
half of the subdivided curverightoff
 the offset into the array of the beginning of the
the 6 right coordinatespublic static int solveCubic(double[] eqn)
eqn
array and places the noncomplex roots back into the same array,
returning the number of roots. The solved cubic is represented
by the equation:
eqn = {c, b, a, d} dx^3 + ax^2 + bx + c = 0A 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.
eqn
 an array containing coefficients for a cubicpublic static int solveCubic(double[] eqn, double[] res)
eqn
array and place the noncomplex roots into the res
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.eqn
 the specified array of coefficients to use to solve
the cubic equationres
 the array that contains the noncomplex roots
resulting from the solution of the cubic equationpublic boolean contains(double x, double y)
Shape
, as described by the
definition of insideness.public boolean contains(Point2D p)
Point2D
is inside the boundary
of the Shape
, as described by the
definition of insideness.public boolean intersects(double x, double y, double w, double h)
Shape
intersects the
interior of a specified rectangular area.
The rectangular area is considered to intersect the Shape
if any point is contained in both the interior of the
Shape
and the specified rectangular area.
The Shape.intersects()
method allows a Shape
implementation to conservatively return true
when:
Shape
intersect, but
Shapes
this method might
return true
even though the rectangular area does not
intersect the Shape
.
The Area
class performs
more accurate computations of geometric intersection than most
Shape
objects and therefore can be used if a more precise
answer is required.intersects
in interface Shape
x
 the X coordinate of the upperleft corner
of the specified rectangular areay
 the Y coordinate of the upperleft corner
of the specified rectangular areaw
 the width of the specified rectangular areah
 the height of the specified rectangular areatrue
if the interior of the Shape
and
the interior of the rectangular area intersect, or are
both highly likely to intersect and intersection calculations
would be too expensive to perform; false
otherwise.Area
public boolean intersects(Rectangle2D r)
Shape
intersects the
interior of a specified Rectangle2D
.
The Shape.intersects()
method allows a Shape
implementation to conservatively return true
when:
Rectangle2D
and the
Shape
intersect, but
Shapes
this method might
return true
even though the Rectangle2D
does not
intersect the Shape
.
The Area
class performs
more accurate computations of geometric intersection than most
Shape
objects and therefore can be used if a more precise
answer is required.intersects
in interface Shape
r
 the specified Rectangle2D
true
if the interior of the Shape
and
the interior of the specified Rectangle2D
intersect, or are both highly likely to intersect and intersection
calculations would be too expensive to perform; false
otherwise.Shape.intersects(double, double, double, double)
public boolean contains(double x, double y, double w, double h)
Shape
entirely contains
the specified rectangular area. All coordinates that lie inside
the rectangular area must lie within the Shape
for the
entire rectangular area to be considered contained within the
Shape
.
The Shape.contains()
method allows a Shape
implementation to conservatively return false
when:
intersect
method returns true
and
Shape
entirely contains the rectangular area are
prohibitively expensive.
Shapes
this method might
return false
even though the Shape
contains
the rectangular area.
The Area
class performs
more accurate geometric computations than most
Shape
objects and therefore can be used if a more precise
answer is required.contains
in interface Shape
x
 the X coordinate of the upperleft corner
of the specified rectangular areay
 the Y coordinate of the upperleft corner
of the specified rectangular areaw
 the width of the specified rectangular areah
 the height of the specified rectangular areatrue
if the interior of the Shape
entirely contains the specified rectangular area;
false
otherwise or, if the Shape
contains the rectangular area and the
intersects
method returns true
and the containment calculations would be too expensive to
perform.Area
,
Shape.intersects(double, double, double, double)
public boolean contains(Rectangle2D r)
Shape
entirely contains the
specified Rectangle2D
.
The Shape.contains()
method allows a Shape
implementation to conservatively return false
when:
intersect
method returns true
and
Shape
entirely contains the Rectangle2D
are prohibitively expensive.
Shapes
this method might
return false
even though the Shape
contains
the Rectangle2D
.
The Area
class performs
more accurate geometric computations than most
Shape
objects and therefore can be used if a more precise
answer is required.contains
in interface Shape
r
 The specified Rectangle2D
true
if the interior of the Shape
entirely contains the Rectangle2D
;
false
otherwise or, if the Shape
contains the Rectangle2D
and the
intersects
method returns true
and the containment calculations would be too expensive to
perform.Shape.contains(double, double, double, double)
public Rectangle getBounds()
Rectangle
that completely encloses the
Shape
. Note that there is no guarantee that the
returned Rectangle
is the smallest bounding box that
encloses the Shape
, only that the Shape
lies entirely within the indicated Rectangle
. The
returned Rectangle
might also fail to completely
enclose the Shape
if the Shape
overflows
the limited range of the integer data type. The
getBounds2D
method generally returns a
tighter bounding box due to its greater flexibility in
representation.
Note that the
definition of insideness can lead to situations where points
on the defining outline of the shape
may not be considered
contained in the returned bounds
object, but only in cases
where those points are also not considered contained in the original
shape
.
If a point
is inside the shape
according to the
contains(point)
method, then
it must be inside the returned Rectangle
bounds object
according to the contains(point)
method of the bounds
. Specifically:
shape.contains(x,y)
requires bounds.contains(x,y)
If a point
is not inside the shape
, then it might
still be contained in the bounds
object:
bounds.contains(x,y)
does not imply shape.contains(x,y)
getBounds
in interface Shape
Rectangle
that completely encloses
the Shape
.Shape.getBounds2D()
public PathIterator getPathIterator(AffineTransform at)
CubicCurve2D
class does not
guarantee that modifications to the geometry of this
CubicCurve2D
object do not affect any iterations of
that geometry that are already in process.getPathIterator
in interface Shape
at
 an optional AffineTransform
to be applied to the
coordinates as they are returned in the iteration, or null
if untransformed coordinates are desiredPathIterator
object that returns the
geometry of the outline of this CubicCurve2D
, one
segment at a time.public PathIterator getPathIterator(AffineTransform at, double flatness)
CubicCurve2D
class does not
guarantee that modifications to the geometry of this
CubicCurve2D
object do not affect any iterations of
that geometry that are already in process.getPathIterator
in interface Shape
at
 an optional AffineTransform
to be applied to the
coordinates as they are returned in the iteration, or null
if untransformed coordinates are desiredflatness
 the maximum amount that the control points
for a given curve can vary from colinear before a subdivided
curve is replaced by a straight line connecting the end pointsPathIterator
object that returns the
geometry of the outline of this CubicCurve2D
,
one segment at a time.public Object clone()
clone
in class Object
OutOfMemoryError
 if there is not enough memory.Cloneable
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