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package com.sun.javafx.geom;

import com.sun.javafx.geom.transform.BaseTransform;

The QuadCurve2D class defines a quadratic parametric curve segment in (x,y) coordinate space. 

This class is only the abstract superclass for all objects that
store a 2D quadratic curve segment.
The actual storage representation of the coordinates is left to
the subclass.
Version:
    1.40, 05/05/07/**
 * The <code>QuadCurve2D</code> class defines a quadratic parametric curve
 * segment in {@code (x,y)} coordinate space.
 * <p>
 * This class is only the abstract superclass for all objects that
 * store a 2D quadratic curve segment.
 * The actual storage representation of the coordinates is left to
 * the subclass.
 *
 * @version     1.40, 05/05/07
 */
public class QuadCurve2D extends Shape {
    
The X coordinate of the start point of the quadratic curve
segment.
/**
     * The X coordinate of the start point of the quadratic curve
     * segment.
     */
    public float x1;

    
The Y coordinate of the start point of the quadratic curve
segment.
/**
     * The Y coordinate of the start point of the quadratic curve
     * segment.
     */
    public float y1;

    
The X coordinate of the control point of the quadratic curve
segment.
/**
     * The X coordinate of the control point of the quadratic curve
     * segment.
     */
    public float ctrlx;

    
The Y coordinate of the control point of the quadratic curve
segment.
/**
     * The Y coordinate of the control point of the quadratic curve
     * segment.
     */
    public float ctrly;

    
The X coordinate of the end point of the quadratic curve
segment.
/**
     * The X coordinate of the end point of the quadratic curve
     * segment.
     */
    public float x2;

    
The Y coordinate of the end point of the quadratic curve
segment.
/**
     * The Y coordinate of the end point of the quadratic curve
     * segment.
     */
    public float y2;

    
Constructs and initializes a QuadCurve2D with
coordinates (0, 0, 0, 0, 0, 0).
/**
     * Constructs and initializes a <code>QuadCurve2D</code> with
     * coordinates (0, 0, 0, 0, 0, 0).
     */
    public QuadCurve2D() { }

    
Constructs and initializes a QuadCurve2D from the specified float coordinates. 
Params:
x1 – the X coordinate of the start point
y1 – the Y coordinate of the start point
ctrlx – the X coordinate of the control point
ctrly – the Y coordinate of the control point
x2 – the X coordinate of the end point
y2 – the Y coordinate of the end point/**
     * Constructs and initializes a <code>QuadCurve2D</code> from the
     * specified {@code float} coordinates.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     */
    public QuadCurve2D(float x1, float y1,
             float ctrlx, float ctrly,
             float x2, float y2)
        {
        setCurve(x1, y1, ctrlx, ctrly, x2, y2);
    }

    
Sets the location of the end points and control point of this curve to the specified float coordinates. 
Params:
x1 – the X coordinate of the start point
y1 – the Y coordinate of the start point
ctrlx – the X coordinate of the control point
ctrly – the Y coordinate of the control point
x2 – the X coordinate of the end point
y2 – the Y coordinate of the end point/**
     * Sets the location of the end points and control point of this curve
     * to the specified {@code float} coordinates.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     */
    public void setCurve(float x1, float y1,
                 float ctrlx, float ctrly,
                 float x2, float y2)
    {
        this.x1    = x1;
        this.y1    = y1;
        this.ctrlx = ctrlx;
        this.ctrly = ctrly;
        this.x2    = x2;
        this.y2    = y2;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public RectBounds getBounds() {
        float left   = Math.min(Math.min(x1, x2), ctrlx);
        float top    = Math.min(Math.min(y1, y2), ctrly);
        float right  = Math.max(Math.max(x1, x2), ctrlx);
        float bottom = Math.max(Math.max(y1, y2), ctrly);
        return new RectBounds(left, top, right, bottom);
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public CubicCurve2D toCubic() {
        return new CubicCurve2D(x1, y1,
                               (x1 + 2 * ctrlx) / 3, (y1 + 2 * ctrly) / 3,
                               (2 * ctrlx + x2) / 3, (2 * ctrly + y2) / 3,
                               x2, y2);
    }

    
Sets the location of the end points and control points of this
QuadCurve2D to the double coordinates at
the specified offset in the specified array.
Params:
coords – the array containing coordinate values
offset – the index into the array from which to start
     getting the coordinate values and assigning them to this
     QuadCurve2D/**
     * Sets the location of the end points and control points of this
     * <code>QuadCurve2D</code> to the <code>double</code> coordinates at
     * the specified offset in the specified array.
     * @param coords the array containing coordinate values
     * @param offset the index into the array from which to start
     *      getting the coordinate values and assigning them to this
     *      <code>QuadCurve2D</code>
     */
    public void setCurve(float[] coords, int offset) {
        setCurve(coords[offset + 0], coords[offset + 1],
             coords[offset + 2], coords[offset + 3],
             coords[offset + 4], coords[offset + 5]);
    }

    
Sets the location of the end points and control point of this
QuadCurve2D to the specified Point2D
coordinates.
Params:
p1 – the start point
cp – the control point
p2 – the end point/**
     * Sets the location of the end points and control point of this
     * <code>QuadCurve2D</code> to the specified <code>Point2D</code>
     * coordinates.
     * @param p1 the start point
     * @param cp the control point
     * @param p2 the end point
     */
    public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
        setCurve(p1.x, p1.y, cp.x, cp.y, p2.x, p2.y);
    }

    
Sets the location of the end points and control points of this
QuadCurve2D to the coordinates of the
Point2D objects at the specified offset in
the specified array.
Params:
pts – an array containing Point2D that define
     coordinate values
offset – the index into pts from which to start
     getting the coordinate values and assigning them to this
     QuadCurve2D/**
     * Sets the location of the end points and control points of this
     * <code>QuadCurve2D</code> to the coordinates of the
     * <code>Point2D</code> objects at the specified offset in
     * the specified array.
     * @param pts an array containing <code>Point2D</code> that define
     *      coordinate values
     * @param offset the index into <code>pts</code> from which to start
     *      getting the coordinate values and assigning them to this
     *      <code>QuadCurve2D</code>
     */
    public void setCurve(Point2D[] pts, int offset) {
        setCurve(pts[offset + 0].x, pts[offset + 0].y,
             pts[offset + 1].x, pts[offset + 1].y,
             pts[offset + 2].x, pts[offset + 2].y);
    }

    
Sets the location of the end points and control point of this
QuadCurve2D to the same as those in the specified
QuadCurve2D.
Params:
c – the specified QuadCurve2D/**
     * Sets the location of the end points and control point of this
     * <code>QuadCurve2D</code> to the same as those in the specified
     * <code>QuadCurve2D</code>.
     * @param c the specified <code>QuadCurve2D</code>
     */
    public void setCurve(QuadCurve2D c) {
        setCurve(c.x1, c.y1, c.ctrlx, c.ctrly, c.x2, c.y2);
    }

    
Returns the square of the flatness, or maximum distance of a
control point from the line connecting the end points, of the
quadratic curve specified by the indicated control points.
Params:
x1 – the X coordinate of the start point
y1 – the Y coordinate of the start point
ctrlx – the X coordinate of the control point
ctrly – the Y coordinate of the control point
x2 – the X coordinate of the end point
y2 – the Y coordinate of the end point
Returns:
the square of the flatness of the quadratic curve
     defined by the specified coordinates./**
     * Returns the square of the flatness, or maximum distance of a
     * control point from the line connecting the end points, of the
     * quadratic curve specified by the indicated control points.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     * @return the square of the flatness of the quadratic curve
     *      defined by the specified coordinates.
     */
    public static float getFlatnessSq(float x1, float y1,
                       float ctrlx, float ctrly,
                       float x2, float y2) {
        return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
    }

    
Returns the flatness, or maximum distance of a
control point from the line connecting the end points, of the
quadratic curve specified by the indicated control points.
Params:
x1 – the X coordinate of the start point
y1 – the Y coordinate of the start point
ctrlx – the X coordinate of the control point
ctrly – the Y coordinate of the control point
x2 – the X coordinate of the end point
y2 – the Y coordinate of the end point
Returns:
the flatness of the quadratic curve defined by the
     specified coordinates./**
     * Returns the flatness, or maximum distance of a
     * control point from the line connecting the end points, of the
     * quadratic curve specified by the indicated control points.
     *
     * @param x1 the X coordinate of the start point
     * @param y1 the Y coordinate of the start point
     * @param ctrlx the X coordinate of the control point
     * @param ctrly the Y coordinate of the control point
     * @param x2 the X coordinate of the end point
     * @param y2 the Y coordinate of the end point
     * @return the flatness of the quadratic curve defined by the
     *      specified coordinates.
     */
    public static float getFlatness(float x1, float y1,
                     float ctrlx, float ctrly,
                     float x2, float y2) {
        return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
    }

    
Returns the square of the flatness, or maximum distance of a
control point from the line connecting the end points, of the
quadratic curve specified by the control points stored in the
indicated array at the indicated index.
Params:
coords – an array containing coordinate values
offset – the index into coords from which to
     to start getting the values from the array
Returns:
the flatness of the quadratic curve that is defined by the
     values in the specified array at the specified index./**
     * Returns the square of the flatness, or maximum distance of a
     * control point from the line connecting the end points, of the
     * quadratic curve specified by the control points stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> from which to
     *      to start getting the values from the array
     * @return the flatness of the quadratic curve that is defined by the
     *      values in the specified array at the specified index.
     */
    public static float getFlatnessSq(float coords[], int offset) {
        return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1],
                      coords[offset + 4], coords[offset + 5],
                      coords[offset + 2], coords[offset + 3]);
    }

    
Returns the flatness, or maximum distance of a
control point from the line connecting the end points, of the
quadratic curve specified by the control points stored in the
indicated array at the indicated index.
Params:
coords – an array containing coordinate values
offset – the index into coords from which to
     start getting the coordinate values
Returns:
the flatness of a quadratic curve defined by the
     specified array at the specified offset./**
     * Returns the flatness, or maximum distance of a
     * control point from the line connecting the end points, of the
     * quadratic curve specified by the control points stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> from which to
     *      start getting the coordinate values
     * @return the flatness of a quadratic curve defined by the
     *      specified array at the specified offset.
     */
    public static float getFlatness(float coords[], int offset) {
        return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1],
                    coords[offset + 4], coords[offset + 5],
                    coords[offset + 2], coords[offset + 3]);
    }

    
Returns the square of the flatness, or maximum distance of a
control point from the line connecting the end points, of this
QuadCurve2D.
Returns:
the square of the flatness of this
     QuadCurve2D./**
     * Returns the square of the flatness, or maximum distance of a
     * control point from the line connecting the end points, of this
     * <code>QuadCurve2D</code>.
     * @return the square of the flatness of this
     *      <code>QuadCurve2D</code>.
     */
    public float getFlatnessSq() {
        return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
    }

    
Returns the flatness, or maximum distance of a
control point from the line connecting the end points, of this
QuadCurve2D.
Returns:
the flatness of this QuadCurve2D./**
     * Returns the flatness, or maximum distance of a
     * control point from the line connecting the end points, of this
     * <code>QuadCurve2D</code>.
     * @return the flatness of this <code>QuadCurve2D</code>.
     */
    public float getFlatness() {
        return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
    }

    
Subdivides this QuadCurve2D and stores the resulting
two subdivided curves into the left and
right curve parameters.
Either or both of the left and right
objects can be the same as this QuadCurve2D or
null.
Params:
left – the QuadCurve2D object for storing the
left or first half of the subdivided curve
right – the QuadCurve2D object for storing the
right or second half of the subdivided curve/**
     * Subdivides this <code>QuadCurve2D</code> and stores the resulting
     * two subdivided curves into the <code>left</code> and
     * <code>right</code> curve parameters.
     * Either or both of the <code>left</code> and <code>right</code>
     * objects can be the same as this <code>QuadCurve2D</code> or
     * <code>null</code>.
     * @param left the <code>QuadCurve2D</code> object for storing the
     * left or first half of the subdivided curve
     * @param right the <code>QuadCurve2D</code> object for storing the
     * right or second half of the subdivided curve
     */
    public void subdivide(QuadCurve2D left, QuadCurve2D right) {
        subdivide(this, left, right);
    }

    
Subdivides the quadratic curve specified by the src
parameter and stores the resulting two subdivided curves into the
left and right curve parameters.
Either or both of the left and right
objects can be the same as the src object or
null.
Params:
src – the quadratic curve to be subdivided
left – the QuadCurve2D object for storing the
     left or first half of the subdivided curve
right – the QuadCurve2D object for storing the
     right or second half of the subdivided curve/**
     * Subdivides the quadratic curve specified by the <code>src</code>
     * parameter and stores the resulting two subdivided curves into the
     * <code>left</code> and <code>right</code> curve parameters.
     * Either or both of the <code>left</code> and <code>right</code>
     * objects can be the same as the <code>src</code> object or
     * <code>null</code>.
     * @param src the quadratic curve to be subdivided
     * @param left the <code>QuadCurve2D</code> object for storing the
     *      left or first half of the subdivided curve
     * @param right the <code>QuadCurve2D</code> object for storing the
     *      right or second half of the subdivided curve
     */
    public static void subdivide(QuadCurve2D src,
                 QuadCurve2D left,
                 QuadCurve2D right)
    {
        float x1 = src.x1;
        float y1 = src.y1;
        float ctrlx = src.ctrlx;
        float ctrly = src.ctrly;
        float x2 = src.x2;
        float y2 = src.y2;
        float ctrlx1 = (x1 + ctrlx) / 2f;
        float ctrly1 = (y1 + ctrly) / 2f;
        float ctrlx2 = (x2 + ctrlx) / 2f;
        float ctrly2 = (y2 + ctrly) / 2f;
        ctrlx = (ctrlx1 + ctrlx2) / 2f;
        ctrly = (ctrly1 + ctrly2) / 2f;
        if (left != null) {
            left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly);
        }
        if (right != null) {
            right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2);
        }
    }

    
Subdivides the quadratic curve specified by the coordinates
stored in the src array at indices
srcoff through srcoff + 5
and stores the resulting two subdivided curves into the two
result arrays at the corresponding indices.
Either or both of the left and right
arrays can be null or a reference to the same array
and offset as the src array.
Note that the last point in the first subdivided curve is the
same as the first point in the second subdivided curve.  Thus,
it is possible to pass the same array for left and
right and to use offsets such that
rightoff equals leftoff + 4 in order
to avoid allocating extra storage for this common point.
Params:
src – the array holding the coordinates for the source curve
srcoff – the offset into the array of the beginning of the
the 6 source coordinates
left – the array for storing the coordinates for the first
half of the subdivided curve
leftoff – the offset into the array of the beginning of the
the 6 left coordinates
right – the array for storing the coordinates for the second
half of the subdivided curve
rightoff – the offset into the array of the beginning of the
the 6 right coordinates/**
     * Subdivides the quadratic curve specified by the coordinates
     * stored in the <code>src</code> array at indices
     * <code>srcoff</code> through <code>srcoff</code>&nbsp;+&nbsp;5
     * and stores the resulting two subdivided curves into the two
     * result arrays at the corresponding indices.
     * Either or both of the <code>left</code> and <code>right</code>
     * arrays can be <code>null</code> or a reference to the same array
     * and offset as the <code>src</code> array.
     * Note that the last point in the first subdivided curve is the
     * same as the first point in the second subdivided curve.  Thus,
     * it is possible to pass the same array for <code>left</code> and
     * <code>right</code> and to use offsets such that
     * <code>rightoff</code> equals <code>leftoff</code> + 4 in order
     * to avoid allocating extra storage for this common point.
     * @param src the array holding the coordinates for the source curve
     * @param srcoff the offset into the array of the beginning of the
     * the 6 source coordinates
     * @param left the array for storing the coordinates for the first
     * half of the subdivided curve
     * @param leftoff the offset into the array of the beginning of the
     * the 6 left coordinates
     * @param right the array for storing the coordinates for the second
     * half of the subdivided curve
     * @param rightoff the offset into the array of the beginning of the
     * the 6 right coordinates
     */
    public static void subdivide(float src[], int srcoff,
                 float left[], int leftoff,
                 float right[], int rightoff)
    {
        float x1 = src[srcoff + 0];
        float y1 = src[srcoff + 1];
        float ctrlx = src[srcoff + 2];
        float ctrly = src[srcoff + 3];
        float x2 = src[srcoff + 4];
        float y2 = src[srcoff + 5];
        if (left != null) {
            left[leftoff + 0] = x1;
            left[leftoff + 1] = y1;
        }
        if (right != null) {
            right[rightoff + 4] = x2;
            right[rightoff + 5] = y2;
        }
        x1 = (x1 + ctrlx) / 2f;
        y1 = (y1 + ctrly) / 2f;
        x2 = (x2 + ctrlx) / 2f;
        y2 = (y2 + ctrly) / 2f;
        ctrlx = (x1 + x2) / 2f;
        ctrly = (y1 + y2) / 2f;
        if (left != null) {
            left[leftoff + 2] = x1;
            left[leftoff + 3] = y1;
            left[leftoff + 4] = ctrlx;
            left[leftoff + 5] = ctrly;
        }
        if (right != null) {
            right[rightoff + 0] = ctrlx;
            right[rightoff + 1] = ctrly;
            right[rightoff + 2] = x2;
            right[rightoff + 3] = y2;
        }
    }

    
Solves the quadratic whose coefficients are in the eqn
array and places the non-complex roots back into the same array,
returning the number of roots.  The quadratic solved is represented
by the equation:
    eqn = {C, B, A};
    ax^2 + bx + c = 0

A return value of -1 is used to distinguish a constant
equation, which might be always 0 or never 0, from an equation that
has no zeroes.
Params:
eqn – the array that contains the quadratic coefficients
Returns:
the number of roots, or -1 if the equation is
     a constant/**
     * Solves the quadratic whose coefficients are in the <code>eqn</code>
     * array and places the non-complex roots back into the same array,
     * returning the number of roots.  The quadratic solved is represented
     * by the equation:
     * <pre>
     *     eqn = {C, B, A};
     *     ax^2 + bx + c = 0
     * </pre>
     * A return value of <code>-1</code> is used to distinguish a constant
     * equation, which might be always 0 or never 0, from an equation that
     * has no zeroes.
     * @param eqn the array that contains the quadratic coefficients
     * @return the number of roots, or <code>-1</code> if the equation is
     *      a constant
     */
    public static int solveQuadratic(float eqn[]) {
        return solveQuadratic(eqn, eqn);
    }

    
Solves the quadratic whose coefficients are in the eqn
array and places the non-complex roots into the res
array, returning the number of roots.
The quadratic solved is represented by the equation:
    eqn = {C, B, A};
    ax^2 + bx + c = 0

A return value of -1 is used to distinguish a constant
equation, which might be always 0 or never 0, from an equation that
has no zeroes.
Params:
eqn – the specified array of coefficients to use to solve
       the quadratic equation
res – the array that contains the non-complex roots
       resulting from the solution of the quadratic equation
Returns:
the number of roots, or -1 if the equation is
 a constant./**
     * Solves the quadratic whose coefficients are in the <code>eqn</code>
     * array and places the non-complex roots into the <code>res</code>
     * array, returning the number of roots.
     * The quadratic solved is represented by the equation:
     * <pre>
     *     eqn = {C, B, A};
     *     ax^2 + bx + c = 0
     * </pre>
     * A return value of <code>-1</code> is used to distinguish a constant
     * equation, which might be always 0 or never 0, from an equation that
     * has no zeroes.
     * @param eqn the specified array of coefficients to use to solve
     *        the quadratic equation
     * @param res the array that contains the non-complex roots
     *        resulting from the solution of the quadratic equation
     * @return the number of roots, or <code>-1</code> if the equation is
     *  a constant.
     */
    public static int solveQuadratic(float eqn[], float res[]) {
        float a = eqn[2];
        float b = eqn[1];
        float c = eqn[0];
        int roots = 0;
        if (a == 0f) {
            // The quadratic parabola has degenerated to a line.
            if (b == 0f) {
                // The line has degenerated to a constant.
                return -1;
            }
            res[roots++] = -c / b;
        } else {
            // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
            float d = b * b - 4f * a * c;
            if (d < 0f) {
                // If d < 0.0, then there are no roots
                return 0;
            }
            d = (float) Math.sqrt(d);
            // For accuracy, calculate one root using:
            //     (-b +/- d) / 2a
            // and the other using:
            //     2c / (-b +/- d)
            // Choose the sign of the +/- so that b+d gets larger in magnitude
            if (b < 0f) {
                d = -d;
            }
            float q = (b + d) / -2f;
            // We already tested a for being 0 above
            res[roots++] = q / a;
            if (q != 0f) {
                res[roots++] = c / q;
            }
        }
        return roots;
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public boolean contains(float x, float y) {
        float x1 = this.x1;
        float y1 = this.y1;
        float xc = this.ctrlx;
        float yc = this.ctrly;
        float x2 = this.x2;
        float y2 = this.y2;

        /*
         * We have a convex shape bounded by quad curve Pc(t)
         * and ine Pl(t).
         *
         *     P1 = (x1, y1) - start point of curve
         *     P2 = (x2, y2) - end point of curve
         *     Pc = (xc, yc) - control point
         *
         *     Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 =
         *           = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1
         *     Pl(t) = P1*(1 - t) + P2*t
         *     t = [0:1]
         *
         *     P = (x, y) - point of interest
         *
         * Let's look at second derivative of quad curve equation:
         *
         *     Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq''
         *     It's constant vector.
         *
         * Let's draw a line through P to be parallel to this
         * vector and find the intersection of the quad curve
         * and the line.
         *
         * Pq(t) is point of intersection if system of equations
         * below has the solution.
         *
         *     L(s) = P + Pq''*s == Pq(t)
         *     Pq''*s + (P - Pq(t)) == 0
         *
         *     | xq''*s + (x - xq(t)) == 0
         *     | yq''*s + (y - yq(t)) == 0
         *
         * This system has the solution if rank of its matrix equals to 1.
         * That is, determinant of the matrix should be zero.
         *
         *     (y - yq(t))*xq'' == (x - xq(t))*yq''
         *
         * Let's solve this equation with 't' variable.
         * Also let kx = x1 - 2*xc + x2
         *          ky = y1 - 2*yc + y2
         *
         *     t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) /
         *                 ((xc - x1)*ky - (yc - y1)*kx)
         *
         * Let's do the same for our line Pl(t):
         *
         *     t0l = ((x - x1)*ky - (y - y1)*kx) /
         *           ((x2 - x1)*ky - (y2 - y1)*kx)
         *
         * It's easy to check that t0q == t0l. This fact means
         * we can compute t0 only one time.
         *
         * In case t0 < 0 or t0 > 1, we have an intersections outside
         * of shape bounds. So, P is definitely out of shape.
         *
         * In case t0 is inside [0:1], we should calculate Pq(t0)
         * and Pl(t0). We have three points for now, and all of them
         * lie on one line. So, we just need to detect, is our point
         * of interest between points of intersections or not.
         *
         * If the denominator in the t0q and t0l equations is
         * zero, then the points must be collinear and so the
         * curve is degenerate and encloses no area.  Thus the
         * result is false.
         */
        float kx = x1 - 2 * xc + x2;
        float ky = y1 - 2 * yc + y2;
        float dx = x - x1;
        float dy = y - y1;
        float dxl = x2 - x1;
        float dyl = y2 - y1;

        float t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx);
        if (t0 < 0 || t0 > 1 || t0 != t0) {
            return false;
        }

        float xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1;
        float yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1;
        float xl = dxl * t0 + x1;
        float yl = dyl * t0 + y1;

        return (x >= xb && x < xl) ||
               (x >= xl && x < xb) ||
               (y >= yb && y < yl) ||
               (y >= yl && y < yb);
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public boolean contains(Point2D p) {
        return contains(p.x, p.y);
    }

    
Fill an array with the coefficients of the parametric equation
in t, ready for solving against val with solveQuadratic.
We currently have:
    val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
                = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
                = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
              0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
              0 = C + Bt + At^2
    C = C1 - val
    B = 2*CP - 2*C1
    A = C1 - 2*CP + C2
/**
     * Fill an array with the coefficients of the parametric equation
     * in t, ready for solving against val with solveQuadratic.
     * We currently have:
     *     val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2
     *                 = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2
     *                 = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
     *               0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2
     *               0 = C + Bt + At^2
     *     C = C1 - val
     *     B = 2*CP - 2*C1
     *     A = C1 - 2*CP + C2
     */
    private static void fillEqn(float eqn[], float val,
                float c1, float cp, float c2) {
        eqn[0] = c1 - val;
        eqn[1] = cp + cp - c1 - c1;
        eqn[2] = c1 - cp - cp + c2;
    }

    
Evaluate the t values in the first num slots of the vals[] array
and place the evaluated values back into the same array.  Only
evaluate t values that are within the range <0, 1>, including
the 0 and 1 ends of the range iff the include0 or include1
booleans are true.  If an "inflection" equation is handed in,
then any points which represent a point of inflection for that
quadratic equation are also ignored.
/**
     * Evaluate the t values in the first num slots of the vals[] array
     * and place the evaluated values back into the same array.  Only
     * evaluate t values that are within the range <0, 1>, including
     * the 0 and 1 ends of the range iff the include0 or include1
     * booleans are true.  If an "inflection" equation is handed in,
     * then any points which represent a point of inflection for that
     * quadratic equation are also ignored.
     */
    private static int evalQuadratic(float vals[], int num,
                     boolean include0,
                     boolean include1,
                     float inflect[],
                     float c1, float ctrl, float c2) {
        int j = 0;
        for (int i = 0; i < num; i++) {
            float t = vals[i];
            if ((include0 ? t >= 0 : t > 0) &&
            (include1 ? t <= 1 : t < 1) &&
            (inflect == null ||
             inflect[1] + 2*inflect[2]*t != 0))
            {
                float u = 1 - t;
                vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t;
            }
        }
        return j;
    }

    private static final int BELOW = -2;
    private static final int LOWEDGE = -1;
    private static final int INSIDE = 0;
    private static final int HIGHEDGE = 1;
    private static final int ABOVE = 2;

    
Determine where coord lies with respect to the range from
low to high.  It is assumed that low <= high.  The return
value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
or ABOVE.
/**
     * Determine where coord lies with respect to the range from
     * low to high.  It is assumed that low <= high.  The return
     * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
     * or ABOVE.
     */
    private static int getTag(float coord, float low, float high) {
        if (coord <= low) {
            return (coord < low ? BELOW : LOWEDGE);
        }
        if (coord >= high) {
            return (coord > high ? ABOVE : HIGHEDGE);
        }
        return INSIDE;
    }

    
Determine if the pttag represents a coordinate that is already
in its test range, or is on the border with either of the two
opttags representing another coordinate that is "towards the
inside" of that test range.  In other words, are either of the
two "opt" points "drawing the pt inward"?
/**
     * Determine if the pttag represents a coordinate that is already
     * in its test range, or is on the border with either of the two
     * opttags representing another coordinate that is "towards the
     * inside" of that test range.  In other words, are either of the
     * two "opt" points "drawing the pt inward"?
     */
    private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
        switch (pttag) {
            case BELOW:
            case ABOVE:
            default:
                return false;
            case LOWEDGE:
                return (opt1tag >= INSIDE || opt2tag >= INSIDE);
            case INSIDE:
                return true;
            case HIGHEDGE:
                return (opt1tag <= INSIDE || opt2tag <= INSIDE);
        }
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public boolean intersects(float x, float y, float w, float h) {
        // Trivially reject non-existant rectangles
        if (w <= 0 || h <= 0) {
            return false;
        }

        // Trivially accept if either endpoint is inside the rectangle
        // (not on its border since it may end there and not go inside)
        // Record where they lie with respect to the rectangle.
        //     -1 => left, 0 => inside, 1 => right
        float x1 = this.x1;
        float y1 = this.y1;
        int x1tag = getTag(x1, x, x + w);
        int y1tag = getTag(y1, y, y + h);
        if (x1tag == INSIDE && y1tag == INSIDE) {
            return true;
        }
        float x2 = this.x2;
        float y2 = this.y2;
        int x2tag = getTag(x2, x, x + w);
        int y2tag = getTag(y2, y, y + h);
        if (x2tag == INSIDE && y2tag == INSIDE) {
            return true;
        }
        float ctrlx = this.ctrlx;
        float ctrly = this.ctrly;
        int ctrlxtag = getTag(ctrlx, x, x + w);
        int ctrlytag = getTag(ctrly, y, y + h);

        // Trivially reject if all points are entirely to one side of
        // the rectangle.
        if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) {
            return false;   // All points left
        }
        if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) {
            return false;   // All points above
        }
        if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) {
            return false;   // All points right
        }
        if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) {
            return false;   // All points below
        }

        // Test for endpoints on the edge where either the segment
        // or the curve is headed "inwards" from them
        // Note: These tests are a superset of the fast endpoint tests
        //       above and thus repeat those tests, but take more time
        //       and cover more cases
        if (inwards(x1tag, x2tag, ctrlxtag) &&
            inwards(y1tag, y2tag, ctrlytag))
        {
            // First endpoint on border with either edge moving inside
            return true;
        }
        if (inwards(x2tag, x1tag, ctrlxtag) &&
            inwards(y2tag, y1tag, ctrlytag))
        {
            // Second endpoint on border with either edge moving inside
            return true;
        }

        // Trivially accept if endpoints span directly across the rectangle
        boolean xoverlap = (x1tag * x2tag <= 0);
        boolean yoverlap = (y1tag * y2tag <= 0);
        if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
            return true;
        }
        if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
            return true;
        }

        // We now know that both endpoints are outside the rectangle
        // but the 3 points are not all on one side of the rectangle.
        // Therefore the curve cannot be contained inside the rectangle,
        // but the rectangle might be contained inside the curve, or
        // the curve might intersect the boundary of the rectangle.

        float[] eqn = new float[3];
        float[] res = new float[3];
        if (!yoverlap) {
                // Both Y coordinates for the closing segment are above or
            // below the rectangle which means that we can only intersect
            // if the curve crosses the top (or bottom) of the rectangle
            // in more than one place and if those crossing locations
            // span the horizontal range of the rectangle.
            fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2);
            return (solveQuadratic(eqn, res) == 2 &&
                evalQuadratic(res, 2, true, true, null,
                      x1, ctrlx, x2) == 2 &&
                getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0);
        }

        // Y ranges overlap.  Now we examine the X ranges
        if (!xoverlap) {
                // Both X coordinates for the closing segment are left of
            // or right of the rectangle which means that we can only
            // intersect if the curve crosses the left (or right) edge
            // of the rectangle in more than one place and if those
            // crossing locations span the vertical range of the rectangle.
            fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2);
            return (solveQuadratic(eqn, res) == 2 &&
                evalQuadratic(res, 2, true, true, null,
                      y1, ctrly, y2) == 2 &&
                getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0);
        }

        // The X and Y ranges of the endpoints overlap the X and Y
        // ranges of the rectangle, now find out how the endpoint
        // line segment intersects the Y range of the rectangle
        float dx = x2 - x1;
        float dy = y2 - y1;
        float k = y2 * x1 - x2 * y1;
        int c1tag, c2tag;
        if (y1tag == INSIDE) {
            c1tag = x1tag;
        } else {
            c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w);
        }
        if (y2tag == INSIDE) {
            c2tag = x2tag;
        } else {
            c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w);
        }
        // If the part of the line segment that intersects the Y range
        // of the rectangle crosses it horizontally - trivially accept
        if (c1tag * c2tag <= 0) {
            return true;
        }

        // Now we know that both the X and Y ranges intersect and that
        // the endpoint line segment does not directly cross the rectangle.
        //
        // We can almost treat this case like one of the cases above
        // where both endpoints are to one side, except that we will
        // only get one intersection of the curve with the vertical
        // side of the rectangle.  This is because the endpoint segment
        // accounts for the other intersection.
        //
        // (Remember there is overlap in both the X and Y ranges which
        //  means that the segment must cross at least one vertical edge
        //  of the rectangle - in particular, the "near vertical side" -
        //  leaving only one intersection for the curve.)
        //
        // Now we calculate the y tags of the two intersections on the
        // "near vertical side" of the rectangle.  We will have one with
        // the endpoint segment, and one with the curve.  If those two
        // vertical intersections overlap the Y range of the rectangle,
        // we have an intersection.  Otherwise, we don't.

        // c1tag = vertical intersection class of the endpoint segment
        //
        // Choose the y tag of the endpoint that was not on the same
        // side of the rectangle as the subsegment calculated above.
        // Note that we can "steal" the existing Y tag of that endpoint
        // since it will be provably the same as the vertical intersection.
        c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);

        // c2tag = vertical intersection class of the curve
        //
        // We have to calculate this one the straightforward way.
        // Note that the c2tag can still tell us which vertical edge
        // to test against.
        fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2);
        int num = solveQuadratic(eqn, res);

        // Note: We should be able to assert(num == 2); since the
        // X range "crosses" (not touches) the vertical boundary,
        // but we pass num to evalQuadratic for completeness.
        evalQuadratic(res, num, true, true, null, y1, ctrly, y2);

        // Note: We can assert(num evals == 1); since one of the
        // 2 crossings will be out of the [0,1] range.
        c2tag = getTag(res[0], y, y+h);

        // Finally, we have an intersection if the two crossings
        // overlap the Y range of the rectangle.
        return (c1tag * c2tag <= 0);
    }

    
{@inheritDoc}
/**
     * {@inheritDoc}
     */
    public boolean contains(float x, float y, float w, float h) {
        if (w <= 0 || h <= 0) {
            return false;
        }
        // Assertion: Quadratic curves closed by connecting their
        // endpoints are always convex.
        return (contains(x, y) &&
            contains(x + w, y) &&
            contains(x + w, y + h) &&
            contains(x, y + h));
    }

    
Returns an iteration object that defines the boundary of the
shape of this QuadCurve2D.
The iterator for this class is not multi-threaded safe,
which means that this QuadCurve2D class does not
guarantee that modifications to the geometry of this
QuadCurve2D object do not affect any iterations of
that geometry that are already in process.
Params:
tx – an optional BaseTransform to apply to the shape boundary
Returns:
a PathIterator object that defines the boundary of the shape./**
     * Returns an iteration object that defines the boundary of the
     * shape of this <code>QuadCurve2D</code>.
     * The iterator for this class is not multi-threaded safe,
     * which means that this <code>QuadCurve2D</code> class does not
     * guarantee that modifications to the geometry of this
     * <code>QuadCurve2D</code> object do not affect any iterations of
     * that geometry that are already in process.
     * @param tx an optional {@link BaseTransform} to apply to the
     *      shape boundary
     * @return a {@link PathIterator} object that defines the boundary
     *      of the shape.
     */
    public PathIterator getPathIterator(BaseTransform tx) {
        return new QuadIterator(this, tx);
    }

    
Returns an iteration object that defines the boundary of the
flattened shape of this QuadCurve2D.
The iterator for this class is not multi-threaded safe,
which means that this QuadCurve2D class does not
guarantee that modifications to the geometry of this
QuadCurve2D object do not affect any iterations of
that geometry that are already in process.
Params:
tx – an optional BaseTransform to apply
     to the boundary of the shape
flatness – the maximum distance that the control points for a
     subdivided curve can be with respect to a line connecting
     the end points of this curve before this curve is
     replaced by a straight line connecting the end points.
Returns:
a PathIterator object that defines the
     flattened boundary of the shape./**
     * Returns an iteration object that defines the boundary of the
     * flattened shape of this <code>QuadCurve2D</code>.
     * The iterator for this class is not multi-threaded safe,
     * which means that this <code>QuadCurve2D</code> class does not
     * guarantee that modifications to the geometry of this
     * <code>QuadCurve2D</code> object do not affect any iterations of
     * that geometry that are already in process.
     * @param tx an optional <code>BaseTransform</code> to apply
     *      to the boundary of the shape
     * @param flatness the maximum distance that the control points for a
     *      subdivided curve can be with respect to a line connecting
     *      the end points of this curve before this curve is
     *      replaced by a straight line connecting the end points.
     * @return a <code>PathIterator</code> object that defines the
     *      flattened boundary of the shape.
     */
    public PathIterator getPathIterator(BaseTransform tx, float flatness) {
        return new FlatteningPathIterator(getPathIterator(tx), flatness);
    }

    @Override
    public QuadCurve2D copy() {
        return new QuadCurve2D(x1, y1, ctrlx, ctrly, x2, y2);
    }

    @Override
    public int hashCode() {
        int bits = java.lang.Float.floatToIntBits(x1);
        bits += java.lang.Float.floatToIntBits(y1) * 37;
        bits += java.lang.Float.floatToIntBits(x2) * 43;
        bits += java.lang.Float.floatToIntBits(y2) * 47;
        bits += java.lang.Float.floatToIntBits(ctrlx) * 53;
        bits += java.lang.Float.floatToIntBits(ctrly) * 59;
        return bits;
    }

    @Override
    public boolean equals(Object obj) {
        if (obj == this) {
            return true;
        }
        if (obj instanceof QuadCurve2D) {
            QuadCurve2D curve = (QuadCurve2D) obj;
            return ((x1 == curve.x1) && (y1 == curve.y1) &&
                    (x2 == curve.x2) && (y2 == curve.y2) &&
                    (ctrlx == curve.ctrlx) && (ctrly == curve.ctrly));
        }
        return false;
    }
}