# Class CubicCurve2D

• `java.lang.Object`
• `java.awt.geom.CubicCurve2D`
Implemented Interfaces:
Cloneable, Shape
Known Direct 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.

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

`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 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.
`static double`
`getFlatness(double[] coords, int offset)`
Calculates the flatness of a cubic curve, specifying the coordinate values in an array.
` double`
`getFlatnessSq()`
Calculates the squared flatness of this curve.
`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.
`static double`
`getFlatnessSq(double[] coords, int offset)`
Calculates the squared flatness of a cubic curve, specifying the coordinate values in an array.
`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.
`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(double[] coords, int offset)`
Changes the curve geometry, specifying coordinate values in an array.
` void`
`setCurve(CubicCurve2D c)`
Changes the curve geometry to that of another curve.
` void`
`setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)`
Changes the curve geometry, specifying coordinate values in separate Point objects.
` void`
`setCurve(Point2D[] pts, int offset)`
Changes the curve geometry, specifying coordinate values in an array of 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.
`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.
` 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.

### Methods inherited from class java.lang.Object

`clone`, `equals`, `extends Object> getClass`, `finalize`, `hashCode`, `notify`, `notifyAll`, `toString`, `wait`, `wait`, `wait`

## Constructor Details

### 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 Details

### clone

`public Object clone()`
Create a new curve with the same contents as this one.
Overrides:
clone in interface Object
Returns:
the clone.

### 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.

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

Specified by:
contains in interface Shape

### 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.

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

Specified by:
contains in interface 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.

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

Specified by:
contains in interface Shape

### 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.

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

Specified by:
contains in interface Shape

### getBounds

`public Rectangle getBounds()`
Determines the smallest rectangle that encloses the curve’s start, end and control points.
Specified by:
getBounds in interface Shape

### getCtrlP1

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

### getCtrlP2

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

### getCtrlX1

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

### getCtrlX2

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

### getCtrlY1

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

### getCtrlY2

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

### 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.

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.

### 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.

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.

### 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.

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.

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.

### 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.

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.

### 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.

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`.

### getP1

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

### getP2

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

### getPathIterator

`public PathIterator getPathIterator(AffineTransform at)`
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:
Returns:
a new iterator over the boundary
Since:
1.2

### getPathIterator

```public PathIterator getPathIterator(AffineTransform at,
double flatness)```
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:
`flatness` - the maximum distance for deviation from the real boundary
Returns:
a new iterator over the boundary
Since:
1.2

### getX1

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

### getX2

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

### getY1

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

### getY2

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

### 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.

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

Specified by:
intersects in interface Shape

### 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

### 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.

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(CubicCurve2D c)`
Changes the curve geometry to that of another curve.
Parameters:
`c` - the curve whose coordinates will be copied.

### setCurve

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

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.

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`.

### 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).

### 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).

### 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.

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.

### subdivide

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

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.

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.