java.awt.geom
Class CubicCurve2D

java.lang.Object
  extended by java.awt.geom.CubicCurve2D
All Implemented Interfaces:
Shape, Cloneable
Direct Known Subclasses:
CubicCurve2D.Double, CubicCurve2D.Float

public abstract class CubicCurve2D
extends Object
implements Shape, Cloneable

A two-dimensional curve that is parameterized with a cubic function.

A drawing of a CubicCurve2D

Since:
1.2

Nested Class Summary
static class CubicCurve2D.Double
          A two-dimensional curve that is parameterized with a cubic function and stores coordinate values in double-precision floating-point format.
static class CubicCurve2D.Float
          A two-dimensional curve that is parameterized with a cubic function and stores coordinate values in single-precision floating-point format.
 
Constructor Summary
protected CubicCurve2D()
          Constructs a new CubicCurve2D.
 
Method Summary
 Object clone()
          Create a new curve with the same contents as this one.
 boolean contains(double x, double y)
          Determines whether a position lies inside the area bounded by the curve and the straight line connecting its end points.
 boolean contains(double x, double y, double w, double h)
          Determine whether a rectangle is entirely inside the area that is bounded by the curve and the straight line connecting its end points.
 boolean contains(Point2D p)
          Determines whether a point lies inside the area bounded by the curve and the straight line connecting its end points.
 boolean contains(Rectangle2D r)
          Determine whether a Rectangle2D is entirely inside the area that is bounded by the curve and the straight line connecting its end points.
 Rectangle getBounds()
          Determines the smallest rectangle that encloses the curve’s start, end and control points.
abstract  Point2D getCtrlP1()
          Returns the curve’s first control point.
abstract  Point2D getCtrlP2()
          Returns the curve’s second control point.
abstract  double getCtrlX1()
          Returns the x coordinate of the curve’s first control point.
abstract  double getCtrlX2()
          Returns the x coordinate of the curve’s second control point.
abstract  double getCtrlY1()
          Returns the y coordinate of the curve’s first control point.
abstract  double getCtrlY2()
          Returns the y coordinate of the curve’s second control point.
 double getFlatness()
          Calculates the flatness of this curve.
static double getFlatness(double[] coords, int offset)
          Calculates the flatness of a cubic curve, specifying the coordinate values in an array.
static double getFlatness(double x1, double y1, double cx1, double cy1, double cx2, double cy2, double x2, double y2)
          Calculates the flatness of a cubic curve, directly specifying each coordinate value.
 double getFlatnessSq()
          Calculates the squared flatness of this curve.
static double getFlatnessSq(double[] coords, int offset)
          Calculates the squared flatness of a cubic curve, specifying the coordinate values in an array.
static double getFlatnessSq(double x1, double y1, double cx1, double cy1, double cx2, double cy2, double x2, double y2)
          Calculates the squared flatness of a cubic curve, directly specifying each coordinate value.
abstract  Point2D getP1()
          Returns the curve’s start point.
abstract  Point2D getP2()
          Returns the curve’s end point.
 PathIterator getPathIterator(AffineTransform at)
          Return an iterator along the shape boundary.
 PathIterator getPathIterator(AffineTransform at, double flatness)
          Return an iterator along the flattened version of the shape boundary.
abstract  double getX1()
          Returns the x coordinate of the curve’s start point.
abstract  double getX2()
          Returns the x coordinate of the curve’s end point.
abstract  double getY1()
          Returns the y coordinate of the curve’s start point.
abstract  double getY2()
          Returns the y coordinate of the curve’s end point.
 boolean intersects(double x, double y, double w, double h)
          Determines whether any part of a rectangle is inside the area bounded by the curve and the straight line connecting its end points.
 boolean intersects(Rectangle2D r)
          Determines whether any part of a Rectangle2D is inside the area bounded by the curve and the straight line connecting its end points.
 void setCurve(CubicCurve2D c)
          Changes the curve geometry to that of another curve.
 void setCurve(double[] coords, int offset)
          Changes the curve geometry, specifying coordinate values in an array.
abstract  void setCurve(double x1, double y1, double cx1, double cy1, double cx2, double cy2, double x2, double y2)
          Changes the curve geometry, separately specifying each coordinate value.
 void setCurve(Point2D[] pts, int offset)
          Changes the curve geometry, specifying coordinate values in an array of Point objects.
 void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
          Changes the curve geometry, specifying coordinate values in separate Point objects.
static int solveCubic(double[] eqn)
          Finds the non-complex roots of a cubic equation, placing the results into the same array as the equation coefficients.
static int solveCubic(double[] eqn, double[] res)
          Finds the non-complex roots of a cubic equation.
 void subdivide(CubicCurve2D left, CubicCurve2D right)
          Subdivides this curve into two halves.
static void subdivide(CubicCurve2D src, CubicCurve2D left, CubicCurve2D right)
          Subdivides a cubic curve into two halves.
static void subdivide(double[] src, int srcOff, double[] left, int leftOff, double[] right, int rightOff)
          Subdivides a cubic curve into two halves, passing all coordinates in an array.
 
Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 
Methods inherited from interface java.awt.Shape
getBounds2D
 

Constructor Detail

CubicCurve2D

protected CubicCurve2D()
Constructs a new CubicCurve2D. Typical users will want to construct instances of a subclass, such as CubicCurve2D.Float or CubicCurve2D.Double.

Method Detail

getX1

public abstract double getX1()
Returns the x coordinate of the curve’s start point.


getY1

public abstract double getY1()
Returns the y coordinate of the curve’s start point.


getP1

public abstract Point2D getP1()
Returns the curve’s start point.


getCtrlX1

public abstract double getCtrlX1()
Returns the x coordinate of the curve’s first control point.


getCtrlY1

public abstract double getCtrlY1()
Returns the y coordinate of the curve’s first control point.


getCtrlP1

public abstract Point2D getCtrlP1()
Returns the curve’s first control point.


getCtrlX2

public abstract double getCtrlX2()
Returns the x coordinate of the curve’s second control point.


getCtrlY2

public abstract double getCtrlY2()
Returns the y coordinate of the curve’s second control point.


getCtrlP2

public abstract Point2D getCtrlP2()
Returns the curve’s second control point.


getX2

public abstract double getX2()
Returns the x coordinate of the curve’s end point.


getY2

public abstract double getY2()
Returns the y coordinate of the curve’s end point.


getP2

public abstract Point2D getP2()
Returns the curve’s end point.


setCurve

public abstract void setCurve(double x1,
                              double y1,
                              double cx1,
                              double cy1,
                              double cx2,
                              double cy2,
                              double x2,
                              double y2)
Changes the curve geometry, separately specifying each coordinate value.

A drawing of a CubicCurve2D

Parameters:
x1 - the x coordinate of the curve’s new start point.
y1 - the y coordinate of the curve’s new start point.
cx1 - the x coordinate of the curve’s new first control point.
cy1 - the y coordinate of the curve’s new first control point.
cx2 - the x coordinate of the curve’s new second control point.
cy2 - the y coordinate of the curve’s new second control point.
x2 - the x coordinate of the curve’s new end point.
y2 - the y coordinate of the curve’s new end point.

setCurve

public void setCurve(double[] coords,
                     int offset)
Changes the curve geometry, specifying coordinate values in an array.

Parameters:
coords - an array containing the new coordinate values. The x coordinate of the new start point is located at coords[offset], its y coordinate at coords[offset + 1]. The x coordinate of the new first control point is located at coords[offset + 2], its y coordinate at coords[offset + 3]. The x coordinate of the new second control point is located at coords[offset + 4], its y coordinate at coords[offset + 5]. The x coordinate of the new end point is located at coords[offset + 6], its y coordinate at coords[offset + 7].
offset - the offset of the first coordinate value in coords.

setCurve

public void setCurve(Point2D p1,
                     Point2D c1,
                     Point2D c2,
                     Point2D p2)
Changes the curve geometry, specifying coordinate values in separate Point objects.

A drawing of a CubicCurve2D

The curve does not keep any reference to the passed point objects. Therefore, a later change to p1, c1, c2 or p2 will not affect the curve geometry.

Parameters:
p1 - the new start point.
c1 - the new first control point.
c2 - the new second control point.
p2 - the new end point.

setCurve

public void setCurve(Point2D[] pts,
                     int offset)
Changes the curve geometry, specifying coordinate values in an array of Point objects.

A drawing of a CubicCurve2D

The curve does not keep references to the passed point objects. Therefore, a later change to the pts array or any of its elements will not affect the curve geometry.

Parameters:
pts - an array containing the points. The new start point is located at pts[offset], the new first control point at pts[offset + 1], the new second control point at pts[offset + 2], and the new end point at pts[offset + 3].
offset - the offset of the start point in pts.

setCurve

public void setCurve(CubicCurve2D c)
Changes the curve geometry to that of another curve.

Parameters:
c - the curve whose coordinates will be copied.

getFlatnessSq

public static double getFlatnessSq(double x1,
                                   double y1,
                                   double cx1,
                                   double cy1,
                                   double cx2,
                                   double cy2,
                                   double x2,
                                   double y2)
Calculates the squared flatness of a cubic curve, directly specifying each coordinate value. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the square of the distance between C2 and the gray line, i.e. the squared length of the red line.

Parameters:
x1 - the x coordinate of the start point P1.
y1 - the y coordinate of the start point P1.
cx1 - the x coordinate of the first control point C1.
cy1 - the y coordinate of the first control point C1.
cx2 - the x coordinate of the second control point C2.
cy2 - the y coordinate of the second control point C2.
x2 - the x coordinate of the end point P2.
y2 - the y coordinate of the end point P2.

getFlatness

public static double getFlatness(double x1,
                                 double y1,
                                 double cx1,
                                 double cy1,
                                 double cx2,
                                 double cy2,
                                 double x2,
                                 double y2)
Calculates the flatness of a cubic curve, directly specifying each coordinate value. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the distance between C2 and the gray line, i.e. the length of the red line.

Parameters:
x1 - the x coordinate of the start point P1.
y1 - the y coordinate of the start point P1.
cx1 - the x coordinate of the first control point C1.
cy1 - the y coordinate of the first control point C1.
cx2 - the x coordinate of the second control point C2.
cy2 - the y coordinate of the second control point C2.
x2 - the x coordinate of the end point P2.
y2 - the y coordinate of the end point P2.

getFlatnessSq

public static double getFlatnessSq(double[] coords,
                                   int offset)
Calculates the squared flatness of a cubic curve, specifying the coordinate values in an array. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the square of the distance between C2 and the gray line, i.e. the squared length of the red line.

Parameters:
coords - an array containing the coordinate values. The x coordinate of the start point P1 is located at coords[offset], its y coordinate at coords[offset + 1]. The x coordinate of the first control point C1 is located at coords[offset + 2], its y coordinate at coords[offset + 3]. The x coordinate of the second control point C2 is located at coords[offset + 4], its y coordinate at coords[offset + 5]. The x coordinate of the end point P2 is located at coords[offset + 6], its y coordinate at coords[offset + 7].
offset - the offset of the first coordinate value in coords.

getFlatness

public static double getFlatness(double[] coords,
                                 int offset)
Calculates the flatness of a cubic curve, specifying the coordinate values in an array. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the distance between C2 and the gray line, i.e. the length of the red line.

Parameters:
coords - an array containing the coordinate values. The x coordinate of the start point P1 is located at coords[offset], its y coordinate at coords[offset + 1]. The x coordinate of the first control point C1 is located at coords[offset + 2], its y coordinate at coords[offset + 3]. The x coordinate of the second control point C2 is located at coords[offset + 4], its y coordinate at coords[offset + 5]. The x coordinate of the end point P2 is located at coords[offset + 6], its y coordinate at coords[offset + 7].
offset - the offset of the first coordinate value in coords.

getFlatnessSq

public double getFlatnessSq()
Calculates the squared flatness of this curve. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the square of the distance between C2 and the gray line, i.e. the squared length of the red line.


getFlatness

public double getFlatness()
Calculates the flatness of this curve. The flatness is the maximal distance of a control point to the line between start and end point.

A drawing that illustrates the flatness

In the above drawing, the straight line connecting start point P1 and end point P2 is depicted in gray. In comparison to C1, control point C2 is father away from the gray line. Therefore, the result will be the distance between C2 and the gray line, i.e. the length of the red line.


subdivide

public void subdivide(CubicCurve2D left,
                      CubicCurve2D right)
Subdivides this curve into two halves.

A drawing that illustrates the effects of
 subdividing a CubicCurve2D

Parameters:
left - a curve whose geometry will be set to the left half of this curve, or null if the caller is not interested in the left half.
right - a curve whose geometry will be set to the right half of this curve, or null if the caller is not interested in the right half.

subdivide

public static void subdivide(CubicCurve2D src,
                             CubicCurve2D left,
                             CubicCurve2D right)
Subdivides a cubic curve into two halves.

A drawing that illustrates the effects of
 subdividing a CubicCurve2D

Parameters:
src - the curve to be subdivided.
left - a curve whose geometry will be set to the left half of src, or null if the caller is not interested in the left half.
right - a curve whose geometry will be set to the right half of src, or null if the caller is not interested in the right half.

subdivide

public static void subdivide(double[] src,
                             int srcOff,
                             double[] left,
                             int leftOff,
                             double[] right,
                             int rightOff)
Subdivides a cubic curve into two halves, passing all coordinates in an array.

A drawing that illustrates the effects of
 subdividing a CubicCurve2D

The left end point and the right start point will always be identical. Memory-concious programmers thus may want to pass the same array for both left and right, and set rightOff to leftOff + 6.

Parameters:
src - an array containing the coordinates of the curve to be subdivided. The x coordinate of the start point P1 is located at src[srcOff], its y at src[srcOff + 1]. The x coordinate of the first control point C1 is located at src[srcOff + 2], its y at src[srcOff + 3]. The x coordinate of the second control point C2 is located at src[srcOff + 4], its y at src[srcOff + 5]. The x coordinate of the end point is located at src[srcOff + 6], its y at src[srcOff + 7].
srcOff - an offset into src, specifying the index of the start point’s x coordinate.
left - an array that will receive the coordinates of the left half of src. It is acceptable to pass src. A caller who is not interested in the left half can pass null.
leftOff - an offset into left, specifying the index where the start point’s x coordinate will be stored.
right - an array that will receive the coordinates of the right half of src. It is acceptable to pass src or left. A caller who is not interested in the right half can pass null.
rightOff - an offset into right, specifying the index where the start point’s x coordinate will be stored.

solveCubic

public static int solveCubic(double[] eqn)
Finds the non-complex roots of a cubic equation, placing the results into the same array as the equation coefficients. The following equation is being solved:
eqn[3] · x3 + eqn[2] · x2 + eqn[1] · x + eqn[0] = 0

For some background about solving cubic equations, see the article “Cubic Formula” in PlanetMath. For an extensive library of numerical algorithms written in the C programming language, see the GNU Scientific Library, from which this implementation was adapted.

Parameters:
eqn - an array with the coefficients of the equation. When this procedure has returned, eqn will contain the non-complex solutions of the equation, in no particular order.
Returns:
the number of non-complex solutions. A result of 0 indicates that the equation has no non-complex solutions. A result of -1 indicates that the equation is constant (i.e., always or never zero).
See Also:
solveCubic(double[], double[]), QuadCurve2D.solveQuadratic(double[],double[])

solveCubic

public static int solveCubic(double[] eqn,
                             double[] res)
Finds the non-complex roots of a cubic equation. The following equation is being solved:
eqn[3] · x3 + eqn[2] · x2 + eqn[1] · x + eqn[0] = 0

For some background about solving cubic equations, see the article “Cubic Formula” in PlanetMath. For an extensive library of numerical algorithms written in the C programming language, see the GNU Scientific Library, from which this implementation was adapted.

Parameters:
eqn - an array with the coefficients of the equation.
res - an array into which the non-complex roots will be stored. The results may be in an arbitrary order. It is safe to pass the same array object reference for both eqn and res.
Returns:
the number of non-complex solutions. A result of 0 indicates that the equation has no non-complex solutions. A result of -1 indicates that the equation is constant (i.e., always or never zero).
See Also:
QuadCurve2D.solveQuadratic(double[],double[])

contains

public boolean contains(double x,
                        double y)
Determines whether a position lies inside the area bounded by the curve and the straight line connecting its end points.

A drawing of the area spanned by the curve

The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.

Specified by:
contains in interface Shape
Parameters:
x - the x coordinate
y - the y coordinate
Returns:
true if (x,y) lies inside the shape

contains

public boolean contains(Point2D p)
Determines whether a point lies inside the area bounded by the curve and the straight line connecting its end points.

A drawing of the area spanned by the curve

The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.

Specified by:
contains in interface Shape
Parameters:
p - the high-precision point
Returns:
true if p lies inside the shape

intersects

public boolean intersects(double x,
                          double y,
                          double w,
                          double h)
Determines whether any part of a rectangle is inside the area bounded by the curve and the straight line connecting its end points.

A drawing of the area spanned by the curve

The above drawing illustrates in which area points are considered “inside” in a CubicCurve2D.

Specified by:
intersects in interface Shape
Parameters:
x - the x coordinate of the rectangle
y - the y coordinate of the rectangle
w - the width of the rectangle, undefined results if negative
h - the height of the rectangle, undefined results if negative
Returns:
true if the rectangle intersects this shape
See Also:
contains(double, double)

intersects

public boolean intersects(Rectangle2D r)
Determines whether any part of a Rectangle2D is inside the area bounded by the curve and the straight line connecting its end points.

Specified by:
intersects in interface Shape
Parameters:
r - the rectangle
Returns:
true if the rectangle intersects this shape
See Also:
intersects(double, double, double, double)

contains

public boolean contains(double x,
                        double y,
                        double w,
                        double h)
Determine whether a rectangle is entirely inside the area that is bounded by the curve and the straight line connecting its end points.

A drawing of the area spanned by the curve

The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.

Specified by:
contains in interface Shape
Parameters:
x - the x coordinate of the rectangle
y - the y coordinate of the rectangle
w - the width of the rectangle, undefined results if negative
h - the height of the rectangle, undefined results if negative
Returns:
true if the rectangle is contained in this shape
See Also:
contains(double, double)

contains

public boolean contains(Rectangle2D r)
Determine whether a Rectangle2D is entirely inside the area that is bounded by the curve and the straight line connecting its end points.

A drawing of the area spanned by the curve

The above drawing illustrates in which area points are considered “inside” a CubicCurve2D.

Specified by:
contains in interface Shape
Parameters:
r - the rectangle
Returns:
true if the rectangle is contained in this shape
See Also:
contains(double, double)

getBounds

public Rectangle getBounds()
Determines the smallest rectangle that encloses the curve’s start, end and control points.

Specified by:
getBounds in interface Shape
Returns:
the shape's bounding box
See Also:
Shape.getBounds2D()

getPathIterator

public PathIterator getPathIterator(AffineTransform at)
Description copied from interface: Shape
Return an iterator along the shape boundary. If the optional transform is provided, the iterator is transformed accordingly. Each call returns a new object, independent from others in use. It is recommended, but not required, that the Shape isolate iterations from future changes to the boundary, and document this fact.

Specified by:
getPathIterator in interface Shape
Parameters:
at - an optional transform to apply to the iterator (null permitted).
Returns:
a new iterator over the boundary

getPathIterator

public PathIterator getPathIterator(AffineTransform at,
                                    double flatness)
Description copied from interface: Shape
Return an iterator along the flattened version of the shape boundary. Only SEG_MOVETO, SEG_LINETO, and SEG_CLOSE points are returned in the iterator. The flatness parameter controls how far points are allowed to differ from the real curve; although a limit on accuracy may cause this parameter to be enlarged if needed.

If the optional transform is provided, the iterator is transformed accordingly. Each call returns a new object, independent from others in use. It is recommended, but not required, that the Shape isolate iterations from future changes to the boundary, and document this fact.

Specified by:
getPathIterator in interface Shape
Parameters:
at - an optional transform to apply to the iterator (null permitted).
flatness - the maximum distance for deviation from the real boundary
Returns:
a new iterator over the boundary

clone

public Object clone()
Create a new curve with the same contents as this one.

Overrides:
clone in class Object
Returns:
the clone.
See Also:
Cloneable