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`java.lang.Object`

`java.awt.geom.QuadCurve2D`

**Implemented Interfaces:**- Cloneable, Shape

**Known Direct Subclasses:**- QuadCurve2D.Double, QuadCurve2D.Float

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

**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

`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(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`

`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.

`double`

`getFlatness()`

- Calculates the flatness of this curve.

`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`

`getFlatnessSq()`

- Calculates the squared 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.

`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 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`

`void`

`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.

`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.

`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.

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

`clone`

,`equals`

,`extends Object> getClass`

,`finalize`

,`hashCode`

,`notify`

,`notifyAll`

,`toString`

,`wait`

,`wait`

,`wait`

protected QuadCurve2D()

Constructs a new QuadCurve2D. Typical users will want to construct instances of a subclass, such as`QuadCurve2D.Float`

or`QuadCurve2D.Double`

.

public Object clone()

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

Returns:- the clone.

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.

The above drawing illustrates in which area points are considered “inside” a QuadCurve2D.

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.

The above drawing illustrates in which area points are considered “inside” a QuadCurve2D.

See Also:`contains(double,double)`

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.

The above drawing illustrates in which area points are considered “inside” a QuadCurve2D.

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.

public Rectangle getBounds()

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.

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.

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.

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.

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`

- thexcoordinate of the start point P1.`y1`

- theycoordinate of the start point P1.`cx`

- thexcoordinate of the control point C.`cy`

- theycoordinate of the control point C.`x2`

- thexcoordinate of the end point P2.`y2`

- theycoordinate of the end point P2.

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.

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. Thexcoordinate of the start point P1 is located at`coords[offset]`

, itsycoordinate at`coords[offset + 1]`

. Thexcoordinate of the control point C is located at`coords[offset + 2]`

, itsycoordinate at`coords[offset + 3]`

. Thexcoordinate of the end point P2 is located at`coords[offset + 4]`

, itsycoordinate at`coords[offset + 5]`

.`offset`

- the offset of the first coordinate value in`coords`

.

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.

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.

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.

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.

Parameters:`x1`

- thexcoordinate of the start point P1.`y1`

- theycoordinate of the start point P1.`cx`

- thexcoordinate of the control point C.`cy`

- theycoordinate of the control point C.`x2`

- thexcoordinate of the end point P2.`y2`

- theycoordinate of the end point P2.

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.

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.

Parameters:`coords`

- an array containing the coordinate values. Thexcoordinate of the start point P1 is located at`coords[offset]`

, itsycoordinate at`coords[offset + 1]`

. Thexcoordinate of the control point C is located at`coords[offset + 2]`

, itsycoordinate at`coords[offset + 3]`

. Thexcoordinate of the end point P2 is located at`coords[offset + 4]`

, itsycoordinate at`coords[offset + 5]`

.`offset`

- the offset of the first coordinate value in`coords`

.

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

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

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

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

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`

- thexcoordinate of the curve’s new start point.`y1`

- theycoordinate of the curve’s new start point.`cx`

- thexcoordinate of the curve’s new control point.`cy`

- theycoordinate of the curve’s new control point.`x2`

- thexcoordinate of the curve’s new end point.`y2`

- theycoordinate of the curve’s new end point.

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. Thexcoordinate of the new start point is located at`coords[offset]`

, itsycoordinate at`coords[offset + 1]`

. Thexcoordinate of the new control point is located at`coords[offset + 2]`

, itsycoordinate at`coords[offset + 3]`

. Thexcoordinate of the new end point is located at`coords[offset + 4]`

, itsycoordinate at`coords[offset + 5]`

.`offset`

- the offset of the first coordinate value in`coords`

.

public void setCurve(Point2D p1, Point2D c, 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`

,`c`

`p2`

will not affect the curve geometry.

Parameters:`p1`

- the new start point.`c`

- the new control point.`p2`

- the new end point.

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 control point at`pts[offset + 1]`

, and the new end point at`pts[offset + 2]`

.`offset`

- the offset of the start point in`pts`

.

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.

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]`

·x^{2}+`eqn[1]`

·x+`eqn[0]`

= 0For 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).

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]`

·x^{2}+`eqn[1]`

·x+`eqn[0]`

= 0For 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.`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).

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.

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. Thexcoordinate of the start point is located at`src[srcOff]`

, itsyat`src[srcOff + 1]`

. Thexcoordinate of the control point is located at`src[srcOff + 2]`

, itsyat`src[srcOff + 3]`

. Thexcoordinate of the end point is located at`src[srcOff + 4]`

, itsyat`src[srcOff + 5]`

.`srcOff`

- an offset into`src`

, specifying the index of the start point’sxcoordinate.`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’sxcoordinate 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’sxcoordinate will be stored.

public void subdivide(QuadCurve2D left, QuadCurve2D 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.

public static void subdivide(QuadCurve2D src, QuadCurve2D left, QuadCurve2D right)

Subdivides a quadratic 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.

QuadCurve2D.java -- represents a parameterized quadratic curve in 2-D space
Copyright (C) 2002, 2003, 2004 Free Software Foundation
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