quadcurve2d.java

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    public abstract Point2D getP1();

    /**
     * Returns the x coordinate of the control point in 
     * <code>double</code> precision.
     * @return x coordinate the control point
     */
    public abstract double getCtrlX();

    /**
     * Returns the y coordinate of the control point in 
     * <code>double</code> precision.
     * @return the y coordinate of the control point.
     */
    public abstract double getCtrlY();

    /**
     * Returns the control point.
     * @return a <code>Point2D</code> that is the control point of this
     * 		<code>Point2D</code>.
     */
    public abstract Point2D getCtrlPt();

    /**
     * Returns the x coordinate of the end point in 
     * <code>double</code> precision.
     * @return the x coordiante of the end point.
     */
    public abstract double getX2();

    /**
     * Returns the y coordinate of the end point in 
     * <code>double</code> precision.
     * @return the y coordinate of the end point.
     */
    public abstract double getY2();

    /**
     * Returns the end point.
     * @return a <code>Point</code> object that is the end point
     * 		of this <code>Point2D</code>.
     */
    public abstract Point2D getP2();

    /**
     * Sets the location of the endpoints and controlpoint of this curve
     * to the specified <code>double</code> coordinates.
     * @param x1,&nbsp;y1 the coordinates of the starting point
     * @param ctrlx,&nbsp;ctrly the coordinates of the control point
     * @param x2,&nbsp;y2 the coordinates of the ending point
     */
    public abstract void setCurve(double x1, double y1,
				  double ctrlx, double ctrly,
				  double x2, double y2);

    /**
     * Sets the location of the endpoints and controlpoints 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(double[] 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 endpoints and controlpoint of this
     * <code>QuadCurve2D</code> to the specified <code>Point2D</code> 
     * coordinates.
     * @param p1 the starting point
     * @param cp the control point
     * @param p2 the ending point
     */
    public void setCurve(Point2D p1, Point2D cp, Point2D p2) {
	setCurve(p1.getX(), p1.getY(),
		 cp.getX(), cp.getY(),
		 p2.getX(), p2.getY());
    }

    /**
     * Sets the location of the endpoints and controlpoints 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> at 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].getX(), pts[offset + 0].getY(),
		 pts[offset + 1].getX(), pts[offset + 1].getY(),
		 pts[offset + 2].getX(), pts[offset + 2].getY());
    }

    /**
     * Sets the location of the endpoints and controlpoint 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.getX1(), c.getY1(),
		 c.getCtrlX(), c.getCtrlY(),
		 c.getX2(), c.getY2());
    }

    /**
     * Returns the square of the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the indicated controlpoints.
     * @param x1,&nbsp;y1 the coordinates of the starting point
     * @param ctrlx,&nbsp;ctrly the coordinates of the control point
     * @param x2,&nbsp;y2 the coordinates of the ending point
     * @return the square of the flatness of the quadratic curve
     *		defined by the specified coordinates.
     */
    public static double getFlatnessSq(double x1, double y1,
				       double ctrlx, double ctrly,
				       double x2, double y2) {
	return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly);
    }

    /**
     * Returns the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the indicated controlpoints.
     * @param x1,&nbsp;y1 the coordinates of the starting point
     * @param ctrlx,&nbsp;ctrly the coordinates of the control point
     * @param x2,&nbsp;y2 the coordinates of the ending point
     * @return the flatness of the quadratic curve defined by the 
     *		specified coordinates. 
     */
    public static double getFlatness(double x1, double y1,
				     double ctrlx, double ctrly,
				     double x2, double y2) {
	return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly);
    }

    /**
     * Returns the square of the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the controlpoints stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> at which to
     *		to start getting the values from the array and 
     *		assigning them to a quadratic curve
     * @return the flatness of the quadratic curve that is defined by the
     * 		values in the specified array at the specified index.
     */
    public static double getFlatnessSq(double 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
     * controlpoint from the line connecting the endpoints, of the
     * quadratic curve specified by the controlpoints stored in the
     * indicated array at the indicated index.
     * @param coords an array containing coordinate values
     * @param offset the index into <code>coords</code> at which to
     *		start getting the coordinate values and assigning 
     *		them to a quadratic curve
     * @return the flatness of a quadratic curve defined by the 
     *		specified array at the specified offset.
     */
    public static double getFlatness(double 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
     * controlpoint from the line connecting the endpoints, of this 
     * <code>QuadCurve2D</code>.
     * @return the square of the flatness of this
     *		<code>QuadCurve2D</code>.
     */
    public double getFlatnessSq() {
	return Line2D.ptSegDistSq(getX1(), getY1(),
				  getX2(), getY2(),
				  getCtrlX(), getCtrlY());
    }

    /**
     * Returns the flatness, or maximum distance of a
     * controlpoint from the line connecting the endpoints, of this
     * <code>QuadCurve2D</code>.
     * @return the flatness of this <code>QuadCurve2D</code>.
     */
    public double getFlatness() {
	return Line2D.ptSegDist(getX1(), getY1(),
				getX2(), getY2(),
				getCtrlX(), getCtrlY());
    }

    /**
     * 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 <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) {
	double x1 = src.getX1();
	double y1 = src.getY1();
	double ctrlx = src.getCtrlX();
	double ctrly = src.getCtrlY();
	double x2 = src.getX2();
	double y2 = src.getY2();
	double ctrlx1 = (x1 + ctrlx) / 2.0;
	double ctrly1 = (y1 + ctrly) / 2.0;
	double ctrlx2 = (x2 + ctrlx) / 2.0;
	double ctrly2 = (y2 + ctrly) / 2.0;
	ctrlx = (ctrlx1 + ctrlx2) / 2.0;
	ctrly = (ctrly1 + ctrly2) / 2.0;
	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 <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(double src[], int srcoff,
				 double left[], int leftoff,
				 double right[], int rightoff) {
	double x1 = src[srcoff + 0];
	double y1 = src[srcoff + 1];
	double ctrlx = src[srcoff + 2];
	double ctrly = src[srcoff + 3];
	double x2 = src[srcoff + 4];
	double 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) / 2.0;
	y1 = (y1 + ctrly) / 2.0;
	x2 = (x2 + ctrlx) / 2.0;
	y2 = (y2 + ctrly) / 2.0;
	ctrlx = (x1 + x2) / 2.0;
	ctrly = (y1 + y2) / 2.0;
	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 <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(double eqn[]) {
	return solveQuadratic(eqn, eqn);
    }

    /**
     * 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(double eqn[], double res[]) {
	double a = eqn[2];
	double b = eqn[1];
	double c = eqn[0];
	int roots = 0;
	if (a == 0.0) {
	    // The quadratic parabola has degenerated to a line.
	    if (b == 0.0) {
		// The line has degenerated to a constant.
		return -1;
	    } 
	    res[roots++] = -c / b;
	} else {
	    // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
	    double d = b * b - 4.0 * a * c;
	    if (d < 0.0) {
		// If d < 0.0, then there are no roots
		return 0;
	    }
	    d = 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 < 0.0) {
		d = -d;
	    }
	    double q = (b + d) / -2.0;
	    // We already tested a for being 0 above
	    res[roots++] = q / a;
	    if (q != 0.0) {
		res[roots++] = c / q;
	    }
	}
	return roots;
    }

    /**
     * Tests if a specified coordinate is inside the boundary of the
     * shape of this <code>QuadCurve2D</code>.
     * @param x,&nbsp;y the specified coordinates
     * @return <code>true</code> if the specified coordinate is inside
     *		the boundary of the shape of this
     *		<code>QuadCurve2D</code>; <code>false</code> otherwise.
     */
    public boolean contains(double x, double y) {
	// We count the "Y" crossings to determine if the point is
	// inside the curve bounded by its closing line.
	int crossings = 0;
	double x1 = getX1();
	double y1 = getY1();
	double x2 = getX2();
	double y2 = getY2();
	// First check for a crossing of the line connecting the endpoints
	double dy = y2 - y1;
	if ((dy > 0.0 && y >= y1 && y <= y2) ||
	    (dy < 0.0 && y <= y1 && y >= y2))
	{
	    if (x <= x1 + (y - y1) * (x2 - x1) / dy) {
		crossings++;
	    }
	}
	// Solve the Y parametric equation for intersections with y
	double ctrlx = getCtrlX();
	double ctrly = getCtrlY();
	boolean include0 = ((y2 - y1) * (ctrly - y1) >= 0);