java.awt.geom

Class 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.

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

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.

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

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

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

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

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.

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.


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.

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.


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.

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.

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.

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

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.

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(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.

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.

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.

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.

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.

CubicCurve2D.java -- represents a parameterized cubic curve in 2-D space Copyright (C) 2002, 2003, 2004 Free Software Foundation This file is part of GNU Classpath. GNU Classpath is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version. GNU Classpath is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with GNU Classpath; see the file COPYING. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. Linking this library statically or dynamically with other modules is making a combined work based on this library. Thus, the terms and conditions of the GNU General Public License cover the whole combination. As a special exception, the copyright holders of this library give you permission to link this library with independent modules to produce an executable, regardless of the license terms of these independent modules, and to copy and distribute the resulting executable under terms of your choice, provided that you also meet, for each linked independent module, the terms and conditions of the license of that module. An independent module is a module which is not derived from or based on this library. If you modify this library, you may extend this exception to your version of the library, but you are not obligated to do so. If you do not wish to do so, delete this exception statement from your version.