Class CubicCurve2D

public abstract class CubicCurve2D
extends Object
implements Shape, Cloneable

The 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.

Constructors

CubicCurve2D

protected CubicCurve2D()

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.

Since:

1.2

See Also:

CubicCurve2D.Float, CubicCurve2D.Double

Methods

getX1

public abstract double getX1()

Returns the X coordinate of the start point in double precision.

Returns:

the X coordinate of the start point of the CubicCurve2D.

Since:

1.2

getY1

public abstract double getY1()

Returns the Y coordinate of the start point in double precision.

Returns:

the Y coordinate of the start point of the CubicCurve2D.

Since:

1.2

getP1

public abstract Point2D getP1()

Returns the start point.

Returns:

a Point2D that is the start point of the CubicCurve2D.

Since:

1.2

getCtrlX1

public abstract double getCtrlX1()

Returns the X coordinate of the first control point in double precision.

Returns:

the X coordinate of the first control point of the CubicCurve2D.

Since:

1.2

getCtrlY1

public abstract double getCtrlY1()

Returns the Y coordinate of the first control point in double precision.

Returns:

the Y coordinate of the first control point of the CubicCurve2D.

Since:

1.2

getCtrlP1

public abstract Point2D getCtrlP1()

Returns the first control point.

Returns:

a Point2D that is the first control point of the CubicCurve2D.

Since:

1.2

getCtrlX2

public abstract double getCtrlX2()

Returns the X coordinate of the second control point in double precision.

Returns:

the X coordinate of the second control point of the CubicCurve2D.

Since:

1.2

getCtrlY2

public abstract double getCtrlY2()

Returns the Y coordinate of the second control point in double precision.

Returns:

the Y coordinate of the second control point of the CubicCurve2D.

Since:

1.2

getCtrlP2

public abstract Point2D getCtrlP2()

Returns the second control point.

Returns:

a Point2D that is the second control point of the CubicCurve2D.

Since:

1.2

getX2

public abstract double getX2()

Returns the X coordinate of the end point in double precision.

Returns:

the X coordinate of the end point of the CubicCurve2D.

Since:

1.2

getY2

public abstract double getY2()

Returns the Y coordinate of the end point in double precision.

Returns:

the Y coordinate of the end point of the CubicCurve2D.

Since:

1.2

getP2

public abstract Point2D getP2()

Returns the end point.

Returns:

a Point2D that is the end point of the CubicCurve2D.

Since:

1.2

setCurve

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 specified double coordinates.

Parameters:

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

Since:

1.2

setCurve

public 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.

Parameters:

coords - a double array containing coordinates

offset - the index of coords from which to begin setting the end points and control points of this curve to the coordinates contained in coords

Since:

1.2

setCurve

public 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.

Parameters:

p1 - the first specified Point2D used to set the start point of this curve

cp1 - the second specified Point2D used to set the first control point of this curve

cp2 - the third specified Point2D used to set the second control point of this curve

p2 - the fourth specified Point2D used to set the end point of this curve

Since:

1.2

setCurve

public 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.

Parameters:

pts - an array of Point2D objects

offset - the index of pts from which to begin setting the end points and control points of this curve to the points contained in pts

Since:

1.2

setCurve

public 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.

Parameters:

c - the specified CubicCurve2D

Since:

1.2

getFlatnessSq

public 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. The flatness is the maximum distance of a control point from the line connecting the end points.

Parameters:

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

Returns:

the square of the flatness of the CubicCurve2D represented by the specified coordinates.

Since:

1.2

getFlatness

public 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. The flatness is the maximum distance of a control point from the line connecting the end points.

Parameters:

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

Returns:

the flatness of the CubicCurve2D represented by the specified coordinates.

Since:

1.2

getFlatnessSq

public 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. The flatness is the maximum distance of a control point from the line connecting the end points.

Parameters:

coords - an array containing coordinates

offset - the index of coords from which to begin getting the end points and control points of the curve

Returns:

the square of the flatness of the CubicCurve2D specified by the coordinates in coords at the specified offset.

Since:

1.2

getFlatness

public 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. The flatness is the maximum distance of a control point from the line connecting the end points.

Parameters:

coords - an array containing coordinates

offset - the index of coords from which to begin getting the end points and control points of the curve

Returns:

the flatness of the CubicCurve2D specified by the coordinates in coords at the specified offset.

Since:

1.2

getFlatnessSq

public double getFlatnessSq()

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.

Returns:

the square of the flatness of this curve.

Since:

1.2

getFlatness

public double getFlatness()

Returns the flatness of this curve. The flatness is the maximum distance of a control point from the line connecting the end points.

Returns:

the flatness of this curve.

Since:

1.2

subdivide

public void subdivide(CubicCurve2D left,
                      CubicCurve2D right)

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.

Parameters:

left - the cubic curve object for storing for the left or first half of the subdivided curve

right - the cubic curve object for storing for the right or second half of the subdivided curve

Since:

1.2

subdivide

public 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. Either or both of the left and right objects may be the same as the src object or null.

Parameters:

src - the cubic curve to be subdivided

left - the cubic curve object for storing the left or first half of the subdivided curve

right - the cubic curve object for storing the right or second half of the subdivided curve

Since:

1.2

subdivide

public 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. 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.

Parameters:

src - the array holding the coordinates for the source curve

srcoff - the offset into the array of the beginning of the the 6 source coordinates

left - the array for storing the coordinates for the first half of the subdivided curve

leftoff - the offset into the array of the beginning of the the 6 left coordinates

right - the array for storing the coordinates for the second half of the subdivided curve

rightoff - the offset into the array of the beginning of the the 6 right coordinates

Since:

1.2

solveCubic

public static int solveCubic(double[] eqn)

Solves the cubic whose coefficients are in the eqn 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:

eqn = {c, b, a, d}
     dx^3 + ax^2 + bx + c = 0

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.

Parameters:

eqn - an array containing coefficients for a cubic

Returns:

the number of roots, or -1 if the equation is a constant.

Since:

1.2

solveCubic

public static int solveCubic(double[] eqn,
                             double[] res)

Solve the cubic whose coefficients are in the eqn array and place the non-complex 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.

Parameters:

eqn - the specified array of coefficients to use to solve the cubic equation

res - the array that contains the non-complex roots resulting from the solution of the cubic equation

Returns:

the number of roots, or -1 if the equation is a constant

Since:

1.3

contains

public 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.

Specified by:

contains in interface Shape

Parameters:

x - the specified X coordinate to be tested

y - the specified Y coordinate to be tested

Returns:

true if the specified coordinates are inside the Shape boundary; false otherwise.

Since:

1.2

contains

public boolean contains(Point2D p)

Tests if a specified Point2D is inside the boundary of the Shape, as described by the definition of insideness.

Specified by:

contains in interface Shape

Parameters:

p - the specified Point2D to be tested

Returns:

true if the specified Point2D is inside the boundary of the Shape; false otherwise.

Since:

1.2

intersects

public boolean intersects(double x,
                          double y,
                          double w,
                          double h)

Specified by:

intersects in interface Shape

Parameters:

x - the X coordinate of the upper-left corner of the specified rectangular area

y - the Y coordinate of the upper-left corner of the specified rectangular area

w - the width of the specified rectangular area

h - the height of the specified rectangular area

Returns:

true 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.

Since:

1.2

See Also:

Area

intersects

public boolean intersects(Rectangle2D r)

Tests if the interior of the Shape intersects the interior of a specified Rectangle2D. The Shape.intersects() method allows a Shape implementation to conservatively return true when:

• there is a high probability that the Rectangle2D and the Shape intersect, but
• the calculations to accurately determine this intersection are prohibitively expensive.

This means that for some 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.

Specified by:

intersects in interface Shape

Parameters:

r - the specified Rectangle2D

Returns:

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.

Since:

1.2

See Also:

Shape.intersects(double, double, double, double)

contains

public boolean contains(double x,
                        double y,
                        double w,
                        double h)

Specified by:

contains in interface Shape

Parameters:

x - the X coordinate of the upper-left corner of the specified rectangular area

y - the Y coordinate of the upper-left corner of the specified rectangular area

w - the width of the specified rectangular area

h - the height of the specified rectangular area

Returns:

true 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.

Since:

1.2

See Also:

Area, Shape.intersects(double, double, double, double)

contains

public boolean contains(Rectangle2D r)

Tests if the interior of the Shape entirely contains the specified Rectangle2D. The Shape.contains() method allows a Shape implementation to conservatively return false when:

• the intersect method returns true and
• the calculations to determine whether or not the Shape entirely contains the Rectangle2D are prohibitively expensive.

This means that for some 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.

Specified by:

contains in interface Shape

Parameters:

r - The specified Rectangle2D

Returns:

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.

Since:

1.2

See Also:

Shape.contains(double, double, double, double)

getBounds

public Rectangle getBounds()

Specified by:

getBounds in interface Shape

Returns:

an integer Rectangle that completely encloses the Shape.

Since:

1.2

See Also:

Shape.getBounds2D()

getPathIterator

public PathIterator getPathIterator(AffineTransform at)

Returns an iteration object that defines the boundary of the shape. The iterator for this class is not multi-threaded safe, which means that this 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.

Specified by:

getPathIterator in interface Shape

Parameters:

at - an optional AffineTransform to be applied to the coordinates as they are returned in the iteration, or null if untransformed coordinates are desired

Returns:

the PathIterator object that returns the geometry of the outline of this CubicCurve2D, one segment at a time.

Since:

1.2

getPathIterator

public PathIterator getPathIterator(AffineTransform at,
                                    double flatness)

Return an iteration object that defines the boundary of the flattened shape. The iterator for this class is not multi-threaded safe, which means that this 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.

Specified by:

getPathIterator in interface Shape

Parameters:

at - an optional AffineTransform to be applied to the coordinates as they are returned in the iteration, or null if untransformed coordinates are desired

flatness - 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 points

Returns:

the PathIterator object that returns the geometry of the outline of this CubicCurve2D, one segment at a time.

Since:

1.2

clone

public Object clone()

Creates a new object of the same class as this object.

Overrides:

clone in class Object

Returns:

a clone of this instance.

Throws:

OutOfMemoryError - if there is not enough memory.

Since:

1.2

See Also:

Cloneable