double dx = x1 - x0;
        double dy = y1 - y0;
        double r = Math.hypot(dx, dy);
        double phi = Math.atan2(dy, dx);

        double phi0 = theta0 - phi;
        double phi1 = theta1 - phi;

        phi0 -= m_2pi * Math.rint(phi0 / m_2pi);
        phi1 -= m_2pi * Math.rint(phi1 / m_2pi);

        if (phi0 > m_pi)
        {
            phi0 -= m_2pi;
        }
        if (phi0 < -m_pi)
        {
            phi0 += m_2pi;
        }
        if (phi1 > m_pi)
        {
            phi1 -= m_2pi;
        }
        if (phi1 < -m_pi)
        {
            phi1 += m_2pi;
        }

        double delta = phi1 - phi0;

        // punto iniziale
        double x = phi0 * m_1_pi;
        double y = phi1 * m_1_pi;
        double xy = x * y;
        y *= y;
        x *= x;
        double a =
                (phi0 + phi1) * (CF[0] + xy * (CF[1] + xy * CF[2]) + (CF[3] + xy * CF[4]) * (x + y) + CF[5] * (x * x + y * y));

        // newton
        double g = 0;
        double dg;
        double[] intC = new double[3];
        double[] intS = new double[3];
        int niter = 0;
        do
        {
            GeneralizedFresnelCS(3, 2 * a, delta - a, phi0, intC, intS);
            g = intS[0];
            dg = intC[2] - intC[1];
            a -= g / dg;
        }
        while (++niter <= 10 && Math.abs(g) > 1E-12);

        Throw.when(Math.abs(g) > 1E-8, DrawRuntimeException.class, "Newton did not converge, g = " + g + " niter = " + niter);

Point2d projectedPoint = medianPoint.closestPointOnSegment(prevPoint, nextPoint);
            double errorPosition = medianPoint.distance(projectedPoint);
            if (errorPosition >= epsilon)
            {
                // We need to insert another point
                result.put(medianT, medianPoint);
                continue;
            }
            if (prevPoint.distance(nextPoint) > epsilon)
            {
                // Check for an inflection point by creating additional points at one quarter and three quarters. If these
                // are on opposite sides of the line from prevPoint to nextPoint; there must be an inflection point.
                // https://stackoverflow.com/questions/1560492/how-to-tell-whether-a-point-is-to-the-right-or-left-side-of-a-line
                double quarterT = (prevT + medianT) / 2;
                double quarterX = Bn(quarterT, px);
                double quarterY = Bn(quarterT, py);
                int sign1 = (int) Math.signum((nextPoint.x - prevPoint.x) * (quarterY - prevPoint.y)
                        - (nextPoint.y - prevPoint.y) * (quarterX - prevPoint.x));
                double threeQuarterT = (nextT + medianT) / 2;
                double threeQuarterX = Bn(threeQuarterT, px);
                double threeQuarterY = Bn(threeQuarterT, py);
                int sign2 = (int) Math.signum((nextPoint.x - prevPoint.x) * (threeQuarterY - prevPoint.y)
                        - (nextPoint.y - prevPoint.y) * (threeQuarterX - prevPoint.x));
                if (sign1 != sign2)
                {

List<Point2d> pointList = new ArrayList<>();
        int indexInStart = 0;
        int indexInEnd = 0;
        while (indexInStart < this.size() && indexInEnd < endLine.size())
        {
            double fractionInStart = lengthAtIndex(indexInStart) / this.length;
            double fractionInEnd = endLine.lengthAtIndex(indexInEnd) / endLine.length;
            if (fractionInStart < fractionInEnd)
            {
                pointList.add(get(indexInStart).interpolate(endLine.getLocation(fractionInStart * endLine.length),
                        transition.function(fractionInStart)));
                indexInStart++;
            }
            else if (fractionInStart > fractionInEnd)
            {
                pointList.add(this.getLocation(fractionInEnd * this.length).interpolate(endLine.get(indexInEnd),
                        transition.function(fractionInEnd)));
                indexInEnd++;
            }
            else
            {
                pointList.add(this.get(indexInStart).interpolate(endLine.getLocation(fractionInEnd * endLine.length),
                        transition.function(fractionInStart)));
                indexInStart++;
                indexInEnd++;
            }
        }
        return new PolyLine2d(true, pointList);

public static PolyLine2d concatenate(final double tolerance, final PolyLine2d... lines) throws DrawRuntimeException
    {
        if (0 == lines.length)
        {
            throw new DrawRuntimeException("Empty argument list");
        }
        else if (1 == lines.length)
        {
            return lines[0];
        }
        int size = lines[0].size();
        for (int i = 1; i < lines.length; i++)
        {
            if (lines[i - 1].getLast().distance(lines[i].getFirst()) > tolerance)
            {
                throw new DrawRuntimeException(
                        "Lines are not connected: " + lines[i - 1].getLast() + " to " + lines[i].getFirst() + " distance is "
                                + lines[i - 1].getLast().distance(lines[i].getFirst()) + " > " + tolerance);
            }
            size += lines[i].size() - 1;
        }

point.y - (this.y[index - 1] + fraction * (this.y[index] - this.y[index - 1])));
            if (distance < bestDistanceExtended && (fraction >= 0.0 && fraction <= 1.0 || (fraction < 0.0 && index == 1)
                    || fraction > 1.0 && index == this.size() - 1))
            {
                bestDistanceExtended = distance;
            }
            if (distance < bestDistance && (fraction >= 0.0 || index == 1 && limitHandling != null && !limitHandling)
                    && (fraction <= 1.0 || index == this.size() - 1 && limitHandling != null && !limitHandling))
            {
                bestDistance = distance;
                result = lengthAtIndex(index - 1) + fraction * (lengthAtIndex(index) - lengthAtIndex(index - 1));
            }
            else if (fraction < 0.0 && limitHandling != null && limitHandling)
            {
                distance = Math.hypot(point.x - this.x[index - 1], point.y - this.y[index - 1]);

Point2d currentPoint = get(index);
            if (null != prevPoint && prevPoint.distance(currentPoint) < noiseLevel)
            {
                if (index == this.size() - 1)
                {
                    if (list.size() > 1)
                    {
                        // Replace the last point of the result by the last point of this PolyLine2d
                        list.set(list.size() - 1, currentPoint);
                    }
                    else
                    {
                        // Append the last point of this even though it is close to the first point than the noise value to
                        // comply with the requirement that first and last point of this are ALWAYS included in the result.
                        list.add(currentPoint);
                    }
                }
                continue; // Do not replace prevPoint by currentPoint
            }
            list.add(currentPoint);
            prevPoint = currentPoint;
        }
        if (list.size() == this.x.length)
        {
            return this;
        }
        if (list.size() == 2 && list.get(0).equals(list.get(1)))
        {
            // Insert point 1 of this; it MUST be different from point 0; so we don't have to test for anything.
            list.add(1, get(1));
        }
        return new PolyLine2d(list);

result = new Ray2d(getLocation(0.0)).projectOrthogonalFractionalExtended(point);
            if (null == limitHandling)
            {
                return result == 0.0 ? 0.0 : Double.NaN;
            }
            // limitHandling is false
            if (result == 0.0)
            {
                return 0.0;
            }
            return result > 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY;
        }
        double bestDistance = Double.POSITIVE_INFINITY;
        double bestDistanceExtended = Double.POSITIVE_INFINITY;
        for (int index = 1; index < this.size(); index++)
        {
            double fraction = point.fractionalPositionOnLine(this.x[index - 1], this.y[index - 1], this.x[index], this.y[index],

Point2d toPoint = get(index);
            segmentLength = fromPoint.distance(toPoint);
            cumulativeLength = nextCumulativeLength;
            nextCumulativeLength = cumulativeLength + segmentLength;
            if (nextCumulativeLength >= start)
            {
                break;
            }
        }
        if (start == nextCumulativeLength)
        {
            pointList.add(get(index));
        }
        else
        {
            pointList.add(get(index - 1).interpolate(get(index), (start - cumulativeLength) / segmentLength));
            if (end > nextCumulativeLength)
            {
                pointList.add(get(index));
            }
        }
        while (end > nextCumulativeLength)
        {

if (firstPoint.x == lastPoint.x && firstPoint.y == lastPoint.y)
        {
            if (doNotModifyList)
            {
                result = new ArrayList<>(points.size() - 1);
                for (int i = 0; i < points.size() - 1; i++)
                {
                    result.add(points.get(i));
                }
            }
            else
            {
                result.remove(points.size() - 1);
            }
            lastPoint = result.get(result.size() - 1);
        }
        Throw.when(firstPoint.x == lastPoint.x && firstPoint.y == lastPoint.y, DrawRuntimeException.class,