java.awt.geom

Class QuadCurve2D

public abstract class QuadCurve2D extends Object implements Shape, Cloneable

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

A drawing of a QuadCurve2D

Since: 1.2

Nested Class Summary
static class	QuadCurve2D.Double A two-dimensional curve that is parameterized with a quadratic function and stores coordinate values in double-precision floating-point format.
static class	QuadCurve2D.Float A two-dimensional curve that is parameterized with a quadratic function and stores coordinate values in single-precision floating-point format.

Constructor Summary
protected	QuadCurve2D() Constructs a new QuadCurve2D.

Method Summary
Object	clone() Creates a new curve with the same contents as this one.
boolean	contains(double x, double y) Determines whether a point is inside the area bounded by the curve and the straight line connecting its end points.
boolean	contains(Point2D p) Determines whether a point is 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) Determines whether a rectangle is entirely inside the area bounded by the curve and the straight line connecting its end points.
boolean	contains(Rectangle2D r) Determines 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 point.
abstract Point2D	getCtrlPt() Returns the curve’s control point.
abstract double	getCtrlX() Returns the x coordinate of the curve’s control point.
abstract double	getCtrlY() Returns the y coordinate of the curve’s control point.
static double	getFlatness(double x1, double y1, double cx, double cy, double x2, double y2) Calculates the flatness of a quadratic curve, directly specifying each coordinate value.
static double	getFlatness(double[] coords, int offset) Calculates the flatness of a quadratic curve, specifying the coordinate values in an array.
double	getFlatness() Calculates the flatness of this curve.
static double	getFlatnessSq(double x1, double y1, double cx, double cy, double x2, double y2) Calculates the squared flatness of a quadratic curve, directly specifying each coordinate value.
static double	getFlatnessSq(double[] coords, int offset) Calculates the squared flatness of a quadratic curve, specifying the coordinate values in an array.
double	getFlatnessSq() Calculates the squared flatness of this curve.
abstract Point2D	getP1() Returns the curve’s start point.
abstract Point2D	getP2() Returns the curve’s end point.
PathIterator	getPathIterator(AffineTransform at)
PathIterator	getPathIterator(AffineTransform at, double flatness)
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 cx, double cy, double x2, double y2) Changes the curve geometry, separately specifying each coordinate value.
void	setCurve(double[] coords, int offset) Changes the curve geometry, passing coordinate values in an array.
void	setCurve(Point2D p1, Point2D c, 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.
void	setCurve(QuadCurve2D c) Changes the geometry of the curve to that of another curve.
static int	solveQuadratic(double[] eqn) Finds the non-complex roots of a quadratic equation, placing the results into the same array as the equation coefficients.
static int	solveQuadratic(double[] eqn, double[] res) Finds the non-complex roots of a quadratic equation.
void	subdivide(QuadCurve2D left, QuadCurve2D right) Subdivides this curve into two halves.
static void	subdivide(QuadCurve2D src, QuadCurve2D left, QuadCurve2D right) Subdivides a quadratic curve into two halves.
static void	subdivide(double[] src, int srcOff, double[] left, int leftOff, double[] right, int rightOff) Subdivides a quadratic curve into two halves, passing all coordinates in an array.

Constructor Detail

QuadCurve2D

protected QuadCurve2D()

Constructs a new QuadCurve2D. Typical users will want to construct instances of a subclass, such as {@link QuadCurve2D.Float} or {@link QuadCurve2D.Double}.

Method Detail

clone

public Object clone()

Creates a new curve with the same contents as this one.

Returns: the clone.

contains

public boolean contains(double x, double y)

Determines whether a point 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” a QuadCurve2D.

contains

public boolean contains(Point2D p)

Determines whether a point 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” a QuadCurve2D.

contains

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

Determines whether a rectangle is entirely 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 QuadCurve2D.

contains

public boolean contains(Rectangle2D r)

Determines whether a Rectangle2D is entirely inside the area that is bounded by the curve and the straight line connecting its end points.

Determines the smallest rectangle that encloses the curve’s start, end and control point. As the illustration below shows, the invisible control point may cause the bounds to be much larger than the area that is actually covered by the curve.

An illustration of the bounds of a QuadCurve2D

getCtrlPt

public abstract Point2D getCtrlPt()

Returns the curve’s control point.

getCtrlX

public abstract double getCtrlX()

Returns the x coordinate of the curve’s control point.

getCtrlY

public abstract double getCtrlY()

Returns the y coordinate of the curve’s control point.

getFlatness

public static double getFlatness(double x1, double y1, double cx, double cy, double x2, double y2)

Calculates the flatness of a quadratic curve, directly specifying each coordinate value. The flatness is the distance of the 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. The result will be the the distance between C 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. cx the x coordinate of the control point C. cy the y coordinate of the control point C. 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 quadratic curve, specifying the coordinate values in an array. The flatness is the distance of the 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. The result will be the the the distance between C 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 control point C is located at coords[offset + 2], its y coordinate at coords[offset + 3]. The x coordinate of the end point P2 is located at coords[offset + 4], its y coordinate at coords[offset + 5]. offset the offset of the first coordinate value in coords.

getFlatness

public double getFlatness()

Calculates the flatness of this curve. The flatness is the distance of the control point to the line between start and end point.

A drawing that illustrates the flatness

getFlatnessSq

public static double getFlatnessSq(double x1, double y1, double cx, double cy, double x2, double y2)

Calculates the squared flatness of a quadratic curve, directly specifying each coordinate value. The flatness is the distance of the 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. The result will be the the square of the distance between C and the gray line, i.e. the squared length of the red line.

getFlatnessSq

public static double getFlatnessSq(double[] coords, int offset)

Calculates the squared flatness of a quadratic curve, specifying the coordinate values in an array. The flatness is the distance of the control point to the line between start and end point.

A drawing that illustrates the flatness

getFlatnessSq

public double getFlatnessSq()

Calculates the squared flatness of this curve. The flatness is the distance of the control point to the line between start and end point.

A drawing that illustrates the flatness

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)

getPathIterator

public PathIterator getPathIterator(AffineTransform at, double flatness)

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.

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.

setCurve

public abstract void setCurve(double x1, double y1, double cx, double cy, 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. cx the x coordinate of the curve’s new control point. cy the y coordinate of the curve’s new 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, passing 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 control point is located at coords[offset + 2], its y coordinate at coords[offset + 3]. The x coordinate of the new end point is located at coords[offset + 4], its y coordinate at coords[offset + 5]. offset the offset of the first coordinate value in coords.

setCurve

public void setCurve(Point2D p1, Point2D c, Point2D p2)

Changes the curve geometry, specifying coordinate values in separate Point objects.

A drawing of a QuadCurve2D

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

Parameters: p1 the new start point. c the new 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 QuadCurve2D

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 control point at pts[offset + 1], and the new end point at pts[offset + 2]. offset the offset of the start point in pts.

setCurve

public void setCurve(QuadCurve2D c)

Changes the geometry of the curve to that of another curve.

Parameters: c the curve whose coordinates will be copied.

solveQuadratic

public static int solveQuadratic(double[] eqn)

Finds the non-complex roots of a quadratic equation, placing the results into the same array as the equation coefficients. The following equation is being solved:

eqn[2] · x² + eqn[1] · x + eqn[0] = 0

For some background about solving quadratic equations, see the article “Quadratic Formula” in PlanetMath. For an extensive library of numerical algorithms written in the C programming language, see the GNU Scientific Library.

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).

solveQuadratic

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

Finds the non-complex roots of a quadratic equation. The following equation is being solved:

eqn[2] · x² + eqn[1] · x + eqn[0] = 0

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.

subdivide

public void subdivide(QuadCurve2D left, QuadCurve2D right)

Subdivides this curve into two halves.

A drawing that illustrates the effects of
subdividing a QuadCurve2D

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(QuadCurve2D src, QuadCurve2D left, QuadCurve2D right)

Subdivides a quadratic curve into two halves.

A drawing that illustrates the effects of
subdividing a QuadCurve2D

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 quadratic curve into two halves, passing all coordinates in an array.

A drawing that illustrates the effects of
subdividing a QuadCurve2D

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 + 4.

Parameters: src an array containing the coordinates of the curve to be subdivided. The x coordinate of the start point is located at src[srcOff], its y at src[srcOff + 1]. The x coordinate of the control point is located at src[srcOff + 2], its y at src[srcOff + 3]. The x coordinate of the end point is located at src[srcOff + 4], its y at src[srcOff + 5]. 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.