protected CubicCurve2D() 
{

}

This is an abstract class that cannot be instantiated directly. Type-specific implementation subclasses are available for instantiation and provide a number of formats for storing the information necessary to satisfy the various accessor methods below.

Also see:

java.awt.geom.CubicCurve2D.Float
java.awt.geom.CubicCurve2D.Double
since: 1.2 -

 public Object clone() 
{
        try {
            return super.clone();
        } catch (CloneNotSupportedException e) {
            // this shouldn't happen, since we are Cloneable
            throw new InternalError();
        }
}

Creates a new object of the same class as this object.

 public boolean contains(Point2D p) 
{
        return contains(p.getX(), p.getY());
}

{@inheritDoc}

 public boolean contains(Rectangle2D r) 
{
        return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
}

{@inheritDoc}

 public boolean contains(double x,
    double y) 
{
        if (!(x * 0.0 + y * 0.0 == 0.0)) {
            /* Either x or y was infinite or NaN.
             * A NaN always produces a negative response to any test
             * and Infinity values cannot be "inside" any path so
             * they should return false as well.
             */
            return false;
        }
        // We count the "Y" crossings to determine if the point is
        // inside the curve bounded by its closing line.
        double x1 = getX1();
        double y1 = getY1();
        double x2 = getX2();
        double y2 = getY2();
        int crossings =
            (Curve.pointCrossingsForLine(x, y, x1, y1, x2, y2) +
             Curve.pointCrossingsForCubic(x, y,
                                          x1, y1,
                                          getCtrlX1(), getCtrlY1(),
                                          getCtrlX2(), getCtrlY2(),
                                          x2, y2, 0));
        return ((crossings & 1) == 1);
}

{@inheritDoc}

 public boolean contains(double x,
    double y,
    double w,
    double h) 
{
        if (w < = 0 || h < = 0) {
            return false;
        }
        // Assertion: Cubic curves closed by connecting their
        // endpoints form either one or two convex halves with
        // the closing line segment as an edge of both sides.
        if (!(contains(x, y) &&
              contains(x + w, y) &&
              contains(x + w, y + h) &&
              contains(x, y + h))) {
            return false;
        }
        // Either the rectangle is entirely inside one of the convex
        // halves or it crosses from one to the other, in which case
        // it must intersect the closing line segment.
        Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
        return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2());
}

{@inheritDoc}

 public Rectangle getBounds() 
{
        return getBounds2D().getBounds();
}

{@inheritDoc}

 abstract public Point2D getCtrlP1()
Returns the first control point.

 abstract public Point2D getCtrlP2()
Returns the second control point.

 abstract public double getCtrlX1()
Returns the X coordinate of the first control point in double precision.

 abstract public double getCtrlX2()
Returns the X coordinate of the second control point
in double precision.

 abstract public double getCtrlY1()
Returns the Y coordinate of the first control point in double precision.

 abstract public double getCtrlY2()
Returns the Y coordinate of the second control point
in double precision.

 public double getFlatness() 
{
        return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
                           getCtrlX2(), getCtrlY2(), getX2(), getY2());
}

Returns the flatness of this curve. The flatness is the maximum distance of a control point from the line connecting the end points.

 public static double getFlatness(double[] coords,
    int offset) 
{
        return getFlatness(coords[offset + 0], coords[offset + 1],
                           coords[offset + 2], coords[offset + 3],
                           coords[offset + 4], coords[offset + 5],
                           coords[offset + 6], coords[offset + 7]);
}

Returns the flatness of the cubic curve specified by the control points stored in the indicated array at the indicated index. The flatness is the maximum distance of a control point from the line connecting the end points.

 public static double getFlatness(double x1,
    double y1,
    double ctrlx1,
    double ctrly1,
    double ctrlx2,
    double ctrly2,
    double x2,
    double y2) 
{
        return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1,
                                       ctrlx2, ctrly2, x2, y2));
}

Returns the flatness of the cubic curve specified by the indicated control points. The flatness is the maximum distance of a control point from the line connecting the end points.

 public double getFlatnessSq() 
{
        return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
                             getCtrlX2(), getCtrlY2(), getX2(), getY2());
}

Returns the square of the flatness of this curve. The flatness is the maximum distance of a control point from the line connecting the end points.

 public static double getFlatnessSq(double[] coords,
    int offset) 
{
        return getFlatnessSq(coords[offset + 0], coords[offset + 1],
                             coords[offset + 2], coords[offset + 3],
                             coords[offset + 4], coords[offset + 5],
                             coords[offset + 6], coords[offset + 7]);
}

Returns the square of the flatness of the cubic curve specified by the control points stored in the indicated array at the indicated index. The flatness is the maximum distance of a control point from the line connecting the end points.

 public static double getFlatnessSq(double x1,
    double y1,
    double ctrlx1,
    double ctrly1,
    double ctrlx2,
    double ctrly2,
    double x2,
    double y2) 
{
        return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1, ctrly1),
                        Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2, ctrly2));
}

Returns the square of the flatness of the cubic curve specified by the indicated control points. The flatness is the maximum distance of a control point from the line connecting the end points.

 abstract public Point2D getP1()
Returns the start point.

 abstract public Point2D getP2()
Returns the end point.

 public PathIterator getPathIterator(AffineTransform at) 
{
        return new CubicIterator(this, at);
}

Returns an iteration object that defines the boundary of the shape. The iterator for this class is not multi-threaded safe, which means that this CubicCurve2D class does not guarantee that modifications to the geometry of this CubicCurve2D object do not affect any iterations of that geometry that are already in process.

 public PathIterator getPathIterator(AffineTransform at,
    double flatness) 
{
        return new FlatteningPathIterator(getPathIterator(at), flatness);
}

Return an iteration object that defines the boundary of the flattened shape. The iterator for this class is not multi-threaded safe, which means that this CubicCurve2D class does not guarantee that modifications to the geometry of this CubicCurve2D object do not affect any iterations of that geometry that are already in process.

 abstract public double getX1()
Returns the X coordinate of the start point in double precision.

 abstract public double getX2()
Returns the X coordinate of the end point in double precision.

 abstract public double getY1()
Returns the Y coordinate of the start point in double precision.

 abstract public double getY2()
Returns the Y coordinate of the end point in double precision.

 public boolean intersects(Rectangle2D r) 
{
        return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
}

{@inheritDoc}

 public boolean intersects(double x,
    double y,
    double w,
    double 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
        double x1 = getX1();
        double y1 = getY1();
        int x1tag = getTag(x1, x, x+w);
        int y1tag = getTag(y1, y, y+h);
        if (x1tag == INSIDE && y1tag == INSIDE) {
            return true;
        }
        double x2 = getX2();
        double y2 = getY2();
        int x2tag = getTag(x2, x, x+w);
        int y2tag = getTag(y2, y, y+h);
        if (x2tag == INSIDE && y2tag == INSIDE) {
            return true;
        }
        double ctrlx1 = getCtrlX1();
        double ctrly1 = getCtrlY1();
        double ctrlx2 = getCtrlX2();
        double ctrly2 = getCtrlY2();
        int ctrlx1tag = getTag(ctrlx1, x, x+w);
        int ctrly1tag = getTag(ctrly1, y, y+h);
        int ctrlx2tag = getTag(ctrlx2, x, x+w);
        int ctrly2tag = getTag(ctrly2, y, y+h);
        // Trivially reject if all points are entirely to one side of
        // the rectangle.
        if (x1tag <  INSIDE && x2tag <  INSIDE &&
            ctrlx1tag <  INSIDE && ctrlx2tag <  INSIDE)
        {
            return false;       // All points left
        }
        if (y1tag <  INSIDE && y2tag <  INSIDE &&
            ctrly1tag <  INSIDE && ctrly2tag <  INSIDE)
        {
            return false;       // All points above
        }
        if (x1tag  > INSIDE && x2tag  > INSIDE &&
            ctrlx1tag  > INSIDE && ctrlx2tag  > INSIDE)
        {
            return false;       // All points right
        }
        if (y1tag  > INSIDE && y2tag  > INSIDE &&
            ctrly1tag  > INSIDE && ctrly2tag  > 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, ctrlx1tag) &&
            inwards(y1tag, y2tag, ctrly1tag))
        {
            // First endpoint on border with either edge moving inside
            return true;
        }
        if (inwards(x2tag, x1tag, ctrlx2tag) &&
            inwards(y2tag, y1tag, ctrly2tag))
        {
            // 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 4 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.
        double[] eqn = new double[4];
        double[] res = new double[4];
        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, ctrly1, ctrly2, y2);
            int num = solveCubic(eqn, res);
            num = evalCubic(res, num, true, true, null,
                            x1, ctrlx1, ctrlx2, x2);
            // odd counts imply the crossing was out of [0,1] bounds
            // otherwise there is no way for that part of the curve to
            // "return" to meet its endpoint
            return (num == 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, ctrlx1, ctrlx2, x2);
            int num = solveCubic(eqn, res);
            num = evalCubic(res, num, true, true, null,
                            y1, ctrly1, ctrly2, y2);
            // odd counts imply the crossing was out of [0,1] bounds
            // otherwise there is no way for that part of the curve to
            // "return" to meet its endpoint
            return (num == 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
        double dx = x2 - x1;
        double dy = y2 - y1;
        double 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 may
        // get one or three intersections of the curve with the vertical
        // side of the rectangle.  This is because the endpoint segment
        // accounts for the other intersection in an even pairing.  Thus,
        // with the endpoint crossing we end up with 2 or 4 total crossings.
        //
        // (Remember there is overlap in both the X and Y ranges which
        //  means that the segment itself must cross at least one vertical
        //  edge of the rectangle - in particular, the "near vertical side"
        //  - leaving an odd number of intersections for the curve.)
        //
        // Now we calculate the y tags of all the intersections on the
        // "near vertical side" of the rectangle.  We will have one with
        // the endpoint segment, and one or three with the curve.  If
        // any pair of those 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);
        // Now we have to calculate an array of solutions of the curve
        // with the "near vertical side" of the rectangle.  Then we
        // need to sort the tags and do a pairwise range test to see
        // if either of the pairs of crossings spans the Y range of
        // the rectangle.
        //
        // Note that the c2tag can still tell us which vertical edge
        // to test against.
        fillEqn(eqn, (c2tag <  INSIDE ? x : x+w), x1, ctrlx1, ctrlx2, x2);
        int num = solveCubic(eqn, res);
        num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2, y2);
        // Now put all of the tags into a bucket and sort them.  There
        // is an intersection iff one of the pairs of tags "spans" the
        // Y range of the rectangle.
        int tags[] = new int[num+1];
        for (int i = 0; i <  num; i++) {
            tags[i] = getTag(res[i], y, y+h);
        }
        tags[num] = c1tag;
        Arrays.sort(tags);
        return ((num  >= 1 && tags[0] * tags[1] < = 0) ||
                (num  >= 3 && tags[2] * tags[3] < = 0));
}

{@inheritDoc}

 public  void setCurve(CubicCurve2D c) 
{
        setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
                 c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
}

Sets the location of the end points and control points of this curve to the same as those in the specified CubicCurve2D.

 public  void setCurve(double[] coords,
    int offset) 
{
        setCurve(coords[offset + 0], coords[offset + 1],
                 coords[offset + 2], coords[offset + 3],
                 coords[offset + 4], coords[offset + 5],
                 coords[offset + 6], coords[offset + 7]);
}

Sets the location of the end points and control points of this curve to the double coordinates at the specified offset in the specified array.

 public  void setCurve(Point2D[] pts,
    int offset) 
{
        setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
                 pts[offset + 1].getX(), pts[offset + 1].getY(),
                 pts[offset + 2].getX(), pts[offset + 2].getY(),
                 pts[offset + 3].getX(), pts[offset + 3].getY());
}

Sets the location of the end points and control points of this curve to the coordinates of the Point2D objects at the specified offset in the specified array.

 public  void setCurve(Point2D p1,
    Point2D cp1,
    Point2D cp2,
    Point2D p2) 
{
        setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(),
                 cp2.getX(), cp2.getY(), p2.getX(), p2.getY());
}

Sets the location of the end points and control points of this curve to the specified Point2D coordinates.

 abstract public  void setCurve(double x1,
    double y1,
    double ctrlx1,
    double ctrly1,
    double ctrlx2,
    double ctrly2,
    double x2,
    double y2)
Sets the location of the end points and control points of this curve
to the specified double coordinates.

 public static int solveCubic(double[] eqn) 
{
        return solveCubic(eqn, eqn);
}

Solves the cubic whose coefficients are in the eqn array and places the non-complex roots back into the same array, returning the number of roots. The solved cubic is represented by the equation:

eqn = {c, b, a, d}
dx^3 + ax^2 + bx + c = 0

A return value of -1 is used to distinguish a constant equation that might be always 0 or never 0 from an equation that has no zeroes.

 public static int solveCubic(double[] eqn,
    double[] res) 
{
        // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
        double d = eqn[3];
        if (d == 0.0) {
            // The cubic has degenerated to quadratic (or line or ...).
            return QuadCurve2D.solveQuadratic(eqn, res);
        }
        double a = eqn[2] / d;
        double b = eqn[1] / d;
        double c = eqn[0] / d;
        int roots = 0;
        double Q = (a * a - 3.0 * b) / 9.0;
        double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
        double R2 = R * R;
        double Q3 = Q * Q * Q;
        a = a / 3.0;
        if (R2 <  Q3) {
            double theta = Math.acos(R / Math.sqrt(Q3));
            Q = -2.0 * Math.sqrt(Q);
            if (res == eqn) {
                // Copy the eqn so that we don't clobber it with the
                // roots.  This is needed so that fixRoots can do its
                // work with the original equation.
                eqn = new double[4];
                System.arraycopy(res, 0, eqn, 0, 4);
            }
            res[roots++] = Q * Math.cos(theta / 3.0) - a;
            res[roots++] = Q * Math.cos((theta + Math.PI * 2.0)/ 3.0) - a;
            res[roots++] = Q * Math.cos((theta - Math.PI * 2.0)/ 3.0) - a;
            fixRoots(res, eqn);
        } else {
            boolean neg = (R <  0.0);
            double S = Math.sqrt(R2 - Q3);
            if (neg) {
                R = -R;
            }
            double A = Math.pow(R + S, 1.0 / 3.0);
            if (!neg) {
                A = -A;
            }
            double B = (A == 0.0) ? 0.0 : (Q / A);
            res[roots++] = (A + B) - a;
        }
        return roots;
}

Solve the cubic whose coefficients are in the eqn array and place the non-complex roots into the res array, returning the number of roots. The cubic solved is represented by the equation: eqn = {c, b, a, d} dx^3 + ax^2 + bx + c = 0 A return value of -1 is used to distinguish a constant equation, which may be always 0 or never 0, from an equation which has no zeroes.

 public  void subdivide(CubicCurve2D left,
    CubicCurve2D right) 
{
        subdivide(this, left, right);
}

Subdivides this cubic curve and stores the resulting two subdivided curves into the left and right curve parameters. Either or both of the left and right objects may be the same as this object or null.

 public static  void subdivide(CubicCurve2D src,
    CubicCurve2D left,
    CubicCurve2D right) 
{
        double x1 = src.getX1();
        double y1 = src.getY1();
        double ctrlx1 = src.getCtrlX1();
        double ctrly1 = src.getCtrlY1();
        double ctrlx2 = src.getCtrlX2();
        double ctrly2 = src.getCtrlY2();
        double x2 = src.getX2();
        double y2 = src.getY2();
        double centerx = (ctrlx1 + ctrlx2) / 2.0;
        double centery = (ctrly1 + ctrly2) / 2.0;
        ctrlx1 = (x1 + ctrlx1) / 2.0;
        ctrly1 = (y1 + ctrly1) / 2.0;
        ctrlx2 = (x2 + ctrlx2) / 2.0;
        ctrly2 = (y2 + ctrly2) / 2.0;
        double ctrlx12 = (ctrlx1 + centerx) / 2.0;
        double ctrly12 = (ctrly1 + centery) / 2.0;
        double ctrlx21 = (ctrlx2 + centerx) / 2.0;
        double ctrly21 = (ctrly2 + centery) / 2.0;
        centerx = (ctrlx12 + ctrlx21) / 2.0;
        centery = (ctrly12 + ctrly21) / 2.0;
        if (left != null) {
            left.setCurve(x1, y1, ctrlx1, ctrly1,
                          ctrlx12, ctrly12, centerx, centery);
        }
        if (right != null) {
            right.setCurve(centerx, centery, ctrlx21, ctrly21,
                           ctrlx2, ctrly2, x2, y2);
        }
}

Subdivides the cubic 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 may be the same as the src object or null.

 public static  void subdivide(double[] src,
    int srcoff,
    double[] left,
    int leftoff,
    double[] right,
    int rightoff) 
{
        double x1 = src[srcoff + 0];
        double y1 = src[srcoff + 1];
        double ctrlx1 = src[srcoff + 2];
        double ctrly1 = src[srcoff + 3];
        double ctrlx2 = src[srcoff + 4];
        double ctrly2 = src[srcoff + 5];
        double x2 = src[srcoff + 6];
        double y2 = src[srcoff + 7];
        if (left != null) {
            left[leftoff + 0] = x1;
            left[leftoff + 1] = y1;
        }
        if (right != null) {
            right[rightoff + 6] = x2;
            right[rightoff + 7] = y2;
        }
        x1 = (x1 + ctrlx1) / 2.0;
        y1 = (y1 + ctrly1) / 2.0;
        x2 = (x2 + ctrlx2) / 2.0;
        y2 = (y2 + ctrly2) / 2.0;
        double centerx = (ctrlx1 + ctrlx2) / 2.0;
        double centery = (ctrly1 + ctrly2) / 2.0;
        ctrlx1 = (x1 + centerx) / 2.0;
        ctrly1 = (y1 + centery) / 2.0;
        ctrlx2 = (x2 + centerx) / 2.0;
        ctrly2 = (y2 + centery) / 2.0;
        centerx = (ctrlx1 + ctrlx2) / 2.0;
        centery = (ctrly1 + ctrly2) / 2.0;
        if (left != null) {
            left[leftoff + 2] = x1;
            left[leftoff + 3] = y1;
            left[leftoff + 4] = ctrlx1;
            left[leftoff + 5] = ctrly1;
            left[leftoff + 6] = centerx;
            left[leftoff + 7] = centery;
        }
        if (right != null) {
            right[rightoff + 0] = centerx;
            right[rightoff + 1] = centery;
            right[rightoff + 2] = ctrlx2;
            right[rightoff + 3] = ctrly2;
            right[rightoff + 4] = x2;
            right[rightoff + 5] = y2;
        }
}

Subdivides the cubic curve specified by the coordinates stored in the src array at indices srcoff through (srcoff + 7) 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 may be null or a reference to the same array 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 as rightoff equals (leftoff + 6), in order to avoid allocating extra storage for this common point.