private PolynomialRoots()
    {
        // Do not instantiate
    }

    /**
     * Emulate the F77 sign function.
     * @param a the value to optionally sign invert
     * @param b the sign of which determines what to do
     * @return if b >= 0 then a; else -a
     */
    private static double sign(final double a, final double b)
    {
        return b >= 0 ? a : -a;
    }

    /**
     * LINEAR POLYNOMIAL ROOT SOLVER.
     * <p>
     * Calculates the root of the linear polynomial:<br>
     * q1 * x + q0<br>
     * Unlike the quadratic, cubic and quartic code, this is NOT derived from that Fortran90 code; it was added for completenes.
     * @param q1 coefficient of the x term
     * @param q0 independent coefficient
     * @return the roots of the equation
     */
    public static Complex[] linearRoots(final double q1, final double q0)
    {
        if (q1 == 0)
        {
            return new Complex[] {}; // No roots; return empty array
        }
        return linearRoots(q0 / q1);
    }

    /**
     * LINEAR POLYNOMIAL ROOT SOLVER.
     * <p>
     * Calculates the root of the linear polynomial:<br>
     * x + q0<br>
     * Unlike the quadratic, cubic and quartic code, this is NOT derived from that Fortran90 code; it was added for completenes.
     * @param q0 independent coefficient
     * @return the roots of the equation
     */
    public static Complex[] linearRoots(final double q0)
    {
        return new Complex[] { new Complex(-q0, 0) };
    }

    /**
     * QUADRATIC POLYNOMIAL ROOT SOLVER
     * <p>
     * Calculates all real + complex roots of the quadratic polynomial:<br>
     * q2 * x^2 + q1 * x + q0<br>
     * The code checks internally if rescaling of the coefficients is needed to avoid overflow.
     * <p>
     * The order of the roots is as follows:<br>
     * 1) For real roots, the order is according to their algebraic value on the number scale (largest positive first, largest
     * negative last).<br>
     * 2) Since there can be only one complex conjugate pair root, no order is necessary.<br>
     * q1 : coefficient of x term q0 : independent coefficient
     * @param q2 coefficient of the quadratic term
     * @param q1 coefficient of the x term
     * @param q0 independent coefficient
     * @return the roots of the equation
     */
    public static Complex[] quadraticRoots(final double q2, final double q1, final double q0)
    {
        if (q2 == 0)
        {
            return linearRoots(q1, q0);
        }
        return quadraticRoots(q1 / q2, q0 / q2);
    }

    /**
     * QUADRATIC POLYNOMIAL ROOT SOLVER
     * <p>
     * Calculates all real + complex roots of the quadratic polynomial:<br>
     * x^2 + q1 * x + q0<br>
     * The code checks internally if rescaling of the coefficients is needed to avoid overflow.
     * <p>
     * The order of the roots is as follows:<br>
     * 1) For real roots, the order is according to their algebraic value on the number scale (largest positive first, largest
     * negative last).<br>
     * 2) Since there can be only one complex conjugate pair root, no order is necessary.<br>
     * q1 : coefficient of x term q0 : independent coefficient
     * @param q1 coefficient of the x term
     * @param q0 independent coefficient
     * @return the roots of the equation
     */
    public static Complex[] quadraticRoots(final double q1, final double q0)
    {
        boolean rescale;

        double a0, a1;
        double k = 0, x, y, z;

        // Handle special cases.
        if (q0 == 0.0 && q1 == 0.0)
        {
            // Two real roots at 0,0
            return new Complex[] { Complex.ZERO, Complex.ZERO };
        }
        else if (q0 == 0.0)
        {
            // Two real roots; one of these is 0,0
            // x^2 + q1 * x == x * (x + q1)
            Complex nonZeroRoot = new Complex(-q1);
            return new Complex[] { q1 > 0 ? Complex.ZERO : nonZeroRoot, q1 <= 0 ? nonZeroRoot : Complex.ZERO };
        }
        else if (q1 == 0.0)
        {
            x = Math.sqrt(Math.abs(q0));

            if (q0 < 0.0)
            {
                // Two real roots, symmetrically around 0
                return new Complex[] { new Complex(x, 0), new Complex(-x, 0) };
            }
            else
            {
                // Two complex roots, symmetrically around 0
                return new Complex[] { new Complex(0, x), new Complex(0, -x) };
            }
        }
        else
        {
            // The general case. Do rescaling, if either squaring of q1/2 or evaluation of
            // (q1/2)^2 - q0 will lead to overflow. This is better than to have the solver
            // crashed. Note, that rescaling might lead to loss of accuracy, so we only
            // invoke it when absolutely necessary.
            final double sqrtLPN = Math.sqrt(Double.MAX_VALUE); // Square root of the Largest Positive Number
            rescale = (q1 > sqrtLPN + sqrtLPN); // this detects overflow of (q1/2)^2

            if (!rescale)
            {
                x = q1 * 0.5; // we are sure here that x*x will not overflow
                rescale = (q0 < x * x - Double.MAX_VALUE); // this detects overflow of (q1/2)^2 - q0
            }

            if (rescale)
            {
                x = Math.abs(q1);
                y = Math.sqrt(Math.abs(q0));

                if (x > y)
                {
                    k = x;
                    z = 1.0 / x;
                    a1 = sign(1.0, q1);
                    a0 = (q0 * z) * z;
                }
                else
                {
                    k = y;
                    a1 = q1 / y;
                    a0 = sign(1.0, q0);
                }
            }
            else
            {
                a1 = q1;
                a0 = q0;
            }
            // Determine the roots of the quadratic. Note, that either a1 or a0 might
            // have become equal to zero due to underflow. But both cannot be zero.
            x = a1 * 0.5;
            y = x * x - a0;

            if (y >= 0.0)
            {
                // Two real roots
                y = Math.sqrt(y);

                if (x > 0.0)
                {
                    y = -x - y;
                }
                else
                {
                    y = -x + y;
                }

                if (rescale)
                {
                    y = y * k; // very important to convert to original
                    z = q0 / y; // root first, otherwise complete loss of
                }
                else // root due to possible a0 = 0 underflow
                {
                    z = a0 / y;
                }
                return new Complex[] { new Complex(Math.max(y, z), 0), new Complex(Math.min(y, z), 0) };
            }
            else
            {
                // Two complex roots (zero real roots)
                y = Math.sqrt(-y);

                if (rescale)
                {
                    x *= k;
                    y *= k;
                }
                return new Complex[] { new Complex(-x, y), new Complex(-x, -y) };
            }
        }
    }

    /**
     * CUBIC POLYNOMIAL ROOT SOLVER.
     * <p>
     * Calculates all (real and complex) roots of the cubic polynomial:<br>
     * c3 * x^3 + c2 * x^2 + c1 * x + c0<br>
     * The first real root (which always exists) is obtained using an optimized Newton-Raphson scheme. The other remaining roots
     * are obtained through composite deflation into a quadratic.
     * <P>
     * The cubic root solver can handle any size of cubic coefficients and there is no danger of overflow due to proper
     * rescaling of the cubic polynomial. The order of the roots is as follows: 1) For real roots, the order is according to
     * their algebraic value on the number scale (largest positive first, largest negative last). 2) Since there can be only one
     * complex conjugate pair root, no order is necessary. 3) All real roots precede the complex ones.
     * @param c3 coefficient of the cubic term
     * @param c2 coefficient of the quadratic term
     * @param c1 coefficient of the linear term
     * @param c0 coefficient of the independent term
     * @return array of Complex with all the roots
     */
    public static Complex[] cubicRoots(final double c3, final double c2, final double c1, final double c0)

Serializer[] serializers = TypedMessage.buildEncoderList(false, objectArray);
                    for (int i = 0; i < objectArray.length; i++)
                    {
                        buffer[pointer.getAndIncrement(1)] = serializers[i].fieldType();
                    }
                    for (int i = 0; i < objects.length; i++)
                    {
                        List<Object> row = objects[i].exportAsList();
                        Throw.when(row.size() != objectArray.length, SerializationException.class,
                                "List in row %d has %d elements which differs from the %d elements in row 0", i, row.size(),
                                objectArray.length);
                        for (int j = 0; j < row.size(); j++)
                        {
                            serializers[j].serialize(row.get(j), buffer, pointer, endianUtil);
                        }
                    }
                }

                @Override
                public SerializableObject<?>[] deSerialize(final byte[] buffer, final Pointer pointer,
                        final EndianUtil endianUtil) throws SerializationException
                {
                    int arraySize = endianUtil.decodeInt(buffer, pointer.getAndIncrement(4));
                    int fieldCount = endianUtil.decodeInt(buffer, pointer.getAndIncrement(4));
                    Serializer<?>[] deSerializers = new Serializer[fieldCount];
                    for (int i = 0; i < fieldCount; i++)
                    {
                        Byte key = buffer[pointer.getAndIncrement(1)];
                        Serializer<?> deSerializer = PRIMITIVE_DATA_DECODERS.get(key);
                        Throw.whenNull(SerializationException.class, "No decoder for %d", key);
                        deSerializers[i] = deSerializer;
                    }
                    MinimalSerializableObject[] result = new MinimalSerializableObject[arraySize];
                    for (int i = 0; i < arraySize; i++)
                    {
                        List<Object> element = new ArrayList<>();
                        for (int j = 0; j < fieldCount; j++)
                        {
                            element.add(deSerializers[j].deSerialize(buffer, pointer, endianUtil));
                        }
                        result[i] = new MinimalSerializableObject(element);
                    }
                    return result;
                }
            };

    /** Converter for array of SerializebleObject using UTF8 for strings and characters. */
    protected static final Serializer<SerializableObject<?>[]> COMPOUND_ARRAY_SERIALIZER_UTF8 =

public class DoubleScalarSerializer<U extends Unit<U>, S extends DoubleScalar<U, S>> implements TextSerializer<S>
{
    /** cache of the retrieved valueOf(String) methods for scalars based on the stored string. */
    private static Map<String, Method> valueOfMethodCache = new LinkedHashMap<>();

    /** cache of the retrieved unit instances based on the unit string. */
    private static Map<String, Unit<?>> unitCache = new LinkedHashMap<>();

    /**
     * Serialize an Scalar value to text in such a way that it can be deserialized with the corresponding deserializer.
     * @param value the scalar to serialize
     * @return a string representation of the value that can later be deserialized
     */
    @SuppressWarnings("unchecked")
    @Override
    public String serialize(final S value, final String unitString)
    {
        if (value == null)
        {
            return null;
        }

        String key = value.getClass().getSimpleName() + "_" + unitString;
        Unit<?> unit = unitCache.get(key);
        if (unit == null)
        {
            unit = value.getDisplayUnit().getQuantity().of(unitString);
            unitCache.put(key, unit);
        }
        return String.valueOf(value.getInUnit((U) unit));
    }

    /**
     * Deserialize a String to the correct Scalar value. The method caches the valueOf(String) method for repeated use.
     * @param text the text to deserialize
     * @return the reconstructed scalar
     */
    @SuppressWarnings("unchecked")
    @Override
    public S deserialize(final Class<S> type, final String text, final String unit)
    {
        if (text == null || text.isEmpty())
        {
            return null;
        }
        try
        {
            Method valueOfMethod = valueOfMethodCache.get(type.getName());
            if (valueOfMethod == null)
            {
                valueOfMethod = type.getDeclaredMethod("valueOf", String.class);
                valueOfMethodCache.put(type.getName(), valueOfMethod);
            }
            return (S) valueOfMethod.invoke(null, text + unit);
        }
        catch (IllegalAccessException | IllegalArgumentException | InvocationTargetException | NoSuchMethodException
                | SecurityException exception)
        {
            throw new RuntimeException(exception);
        }
    }

}

this.maxAngle = maxAngle;
        }

        @Override
        public PolyLine2d flatten(final OffsetCurve2d curve, final ContinuousPiecewiseLinearFunction of)
        {
            Throw.whenNull(curve, "curve");
            Flattener.FlattableCurve<Point2d, Double> fc = makeFlattableCurve(curve, of);
            NavigableMap<Double, Point2d> result = new TreeMap<>();
            loadKnots(result, curve, of);
            Map<Double, Double> directions = new LinkedHashMap<>();
            directions.put(0.0, curve.getDirection(0.0, of)); // directions can't do ULP before 0.0
            Set<Double> knots = new HashSet<>();
            for (double knot : result.keySet())
            {
                if (knot > 0)
                {
                    directions.put(knot, curve.getDirection(knot - Math.ulp(knot), of));
                }
                if (knot != 0.0 && knot != 1.0)
                {
                    knots.add(knot);
                }
            }

            // Walk along all point pairs and see if additional points need to be inserted
            double prevT = result.firstKey();
            Point2d prevPoint = result.get(prevT);
            Map.Entry<Double, Point2d> entry;
            int iterationsAtSinglePoint = 0;
            while ((entry = result.higherEntry(prevT)) != null)
            {
                double nextT = entry.getKey();
                Point2d nextPoint = entry.getValue();
                double medianT = (prevT + nextT) / 2;

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(NO_FILTER, pointList);

0.9999999999999999, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, 0.9999999999999999, /* 8.20 - 8.24 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.25 - 8.29 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.30 - 8.34 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.35 - 8.39 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.40 - 8.44 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.45 - 8.49 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.50 - 8.54 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.55 - 8.59 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.60 - 8.64 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.65 - 8.69 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.70 - 8.74 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.75 - 8.79 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.80 - 8.84 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.85 - 8.89 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.90 - 8.94 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 8.95 - 8.99 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 9.00 - 9.04 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 9.05 - 9.09 */
            1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, 1.0000000000000000, /* 9.10 - 9.14 */

1, -0.5).scaleBy(this.omega);
        if (this.chain == null)
        {
            return myDerivative.simplify();
        }
        return new Product(myDerivative.simplify(), this.chain.getDerivative()).simplify();
    }

    @Override
    public MathFunction simplify()
    {
        if (this.omega == 0.0)
        {
            return Constant.ZERO;
        }
        if (this.chain != null && this.chain instanceof Constant)
        {
            return new Constant(get(0)).simplify();
        }
        return this;
    }

    @Override
    public double getScale()
    {
        return this.omega;
    }

    @Override
    public MathFunction scaleBy(final double scaleFactor)
    {
        if (scaleFactor == 0.0)
        {
            return Constant.ZERO;
        }
        if (scaleFactor == 1.0)
        {
            return this;
        }
        return new ArcSine(this.chain, scaleFactor * this.omega, this.shift);
    }

    @Override
    public int sortPriority()
    {
        return 5;

Table table;
            Consumer<Object[]> unserializableTable;
            if (tableProperties[2].equals(ListTable.class.getName()))
            {
                ListTable listTable = new ListTable(tableProperties[0], tableProperties[1], columns);
                table = listTable;
                unserializableTable = (
                        data
                ) -> listTable.addRow(data);
            }
            else
            {
                // fallback
                ListTable listTable = new ListTable(tableProperties[0], tableProperties[1], columns);
                table = listTable;
                unserializableTable = (
                        data
                ) -> listTable.addRow(data);
            }

            // obtain the serializers
            TextSerializer<?>[] serializers = new TextSerializer[table.getNumberOfColumns()];
            for (int i = 0; i < table.getNumberOfColumns(); i++)
            {
                serializers[i] = TextSerializer.resolve(columns.get(i).getValueType());
            }

Serializer[] serializers = TypedMessage.buildEncoderList(false, objectArray);
                    result += serializers.length;
                    for (int i = 0; i < objectArray.length; i++)
                    {
                        result += objects.length * serializers[i].size(objectArray[i]);
                    }
                    return result;
                }

                @SuppressWarnings({"unchecked", "rawtypes"})
                @Override
                public void serialize(final SerializableObject<?>[] objects, final byte[] buffer, final Pointer pointer,
                        final EndianUtil endianUtil) throws SerializationException
                {
                    SerializableObject<?> so = objects[0];
                    Object[] objectArray = so.exportAsList().toArray();
                    endianUtil.encodeInt(objects.length, buffer, pointer.getAndIncrement(4));
                    endianUtil.encodeInt(objectArray.length, buffer, pointer.getAndIncrement(4));
                    Serializer[] serializers = TypedMessage.buildEncoderList(false, objectArray);

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]);

message[p++] = (byte) ((v >> 24) & 0xFF);
            message[p++] = (byte) ((v >> 16) & 0xFF);
            message[p++] = (byte) ((v >> 8) & 0xFF);
            message[p++] = (byte) (v & 0xFF);
        }
        else
        {
            message[p++] = (byte) (v & 0xFF);
            message[p++] = (byte) ((v >> 8) & 0xFF);
            message[p++] = (byte) ((v >> 16) & 0xFF);
            message[p++] = (byte) ((v >> 24) & 0xFF);

}

    /**
     * Code a unit.
     * @param unit the unit to code in the byte array
     * @param message the byte array
     * @param pointer the start pointer in the byte array
     * @param endianUtil encoder to use for multi-byte values
     */
    protected void encodeUnit(final U unit, final byte[] message, final Pointer pointer, final EndianUtil endianUtil)
    {
        SerializationUnits unitType = SerializationUnits.getUnitType(unit);
        message[pointer.getAndIncrement(1)] = unitType.getCode();
        DisplayType displayType = DisplayType.getDisplayType(unit);
        message[pointer.getAndIncrement(1)] = displayType.getByteCode();
    }

    /**
     * Retrieve and decode a DJUNITS unit.
     * @param buffer the encoded data
     * @param pointer position in the encoded data where the unit is to be decoded from
     * @param endianUtil decoder for multi-byte values
     * @return Unit
     */
    @SuppressWarnings("unchecked")
    protected U getUnit(final byte[] buffer, final Pointer pointer, final EndianUtil endianUtil)
    {
        SerializationUnits unitType = SerializationUnits.getUnitType(buffer[pointer.getAndIncrement(1)]);
        DisplayType displayType = DisplayType.getDisplayType(unitType, 0 + buffer[pointer.getAndIncrement(1)]);
        return (U) displayType.getDjunitsType();
    }

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.append("asin(");
        result.append(this.chain == null ? "x" : this.chain.toString());
        if (this.shift != 0.0)
        {
            if (this.shift > 0)
            {
                result.append("+");
            }
            result.append(printValue(this.shift));
        }
        result.append(")");
        return result.toString();
    }

    @Override
    public int hashCode()
    {
        return Objects.hash(this.chain, this.omega, this.shift);
    }

    @SuppressWarnings("checkstyle:needbraces")
    @Override
    public boolean equals(final Object obj)
    {
        if (this == obj)
            return true;
        if (obj == null)
            return false;
        if (getClass() != obj.getClass())
            return false;

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 IllegalArgumentException(
                        "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;
        }

directions.put(knot, curve.getDirection(knot - Math.ulp(knot)));
                }
                if (knot != 0.0 && knot != 1.0)
                {
                    knots.add(knot);
                }
            }

            // Walk along all point pairs and see if additional points need to be inserted
            double prevT = result.firstKey();
            Point2d prevPoint = result.get(prevT);
            Map.Entry<Double, Point2d> entry;
            int iterationsAtSinglePoint = 0;
            while ((entry = result.higherEntry(prevT)) != null)
            {
                double nextT = entry.getKey();
                Point2d nextPoint = entry.getValue();
                double medianT = (prevT + nextT) / 2;

                // Check max angle
                if (checkDirectionError(prevPoint.directionTo(nextPoint), directions.get(prevT), directions.get(nextT),
                        this.maxAngle))
                {
                    // We need to insert another point
                    Point2d medianPoint = curve.getPoint(medianT);

size += 4 + string.getBytes(UTF8).length;
                        }
                    }
                    return size;
                }

                @Override
                public void serialize(final String[][] stringMatrix, final byte[] buffer, final Pointer pointer,
                        final EndianUtil endianUtil) throws SerializationException
                {
                    int height = stringMatrix.length;
                    int width = stringMatrix[0].length;
                    endianUtil.encodeInt(height, buffer, pointer.getAndIncrement(4));
                    endianUtil.encodeInt(width, buffer, pointer.getAndIncrement(4));
                    for (int i = 0; i < height; i++)
                    {
                        Throw.when(stringMatrix[i].length != width, SerializationException.class,
                                "Jagged matrix is not allowed");
                        for (int j = 0; j < width; j++)
                        {

public void serialize(final byte[][] matrix, final byte[] buffer, final Pointer pointer,
                        final EndianUtil endianUtil) throws SerializationException
                {
                    int height = matrix.length;
                    int width = matrix[0].length;
                    endianUtil.encodeInt(height, buffer, pointer.getAndIncrement(4));
                    endianUtil.encodeInt(width, buffer, pointer.getAndIncrement(4));
                    for (int i = 0; i < height; i++)
                    {
                        Throw.when(matrix[i].length != width, SerializationException.class, "Jagged matrix is not allowed");
                        for (int j = 0; j < width; j++)
                        {
                            buffer[pointer.getAndIncrement(getElementSize())] = matrix[i][j];

return result;
    }

    @Override
    public void serialize(final V[] adva, final byte[] buffer, final Pointer pointer, final EndianUtil endianUtil)
            throws SerializationException
    {
        int width = adva.length;
        int height = adva[0].size();
        endianUtil.encodeInt(height, buffer, pointer.getAndIncrement(4));
        endianUtil.encodeInt(adva.length, buffer, pointer.getAndIncrement(4));
        for (int i = 0; i < width; i++)
        {
            V adv = adva[i];
            Throw.when(adv.size() != height, SerializationException.class,

Point2d medianPoint = curve.getPoint(medianT);
                // Check max deviation
                if (checkPositionError(medianPoint, prevPoint, nextPoint, this.maxDeviation))
                {
                    // We need to insert another point
                    result.put(medianT, medianPoint);
                    directions.put(medianT, curve.getDirection(medianT));
                    continue;
                }
                // Check max angle
                if (checkDirectionError(prevPoint.directionTo(nextPoint), directions.get(prevT), directions.get(nextT),
                        this.maxAngle))
                {
                    // We need to insert another point
                    result.put(medianT, medianPoint);
                    directions.put(medianT, curve.getDirection(medianT));
                    iterationsAtSinglePoint++;
                    Throw.when(iterationsAtSinglePoint == 50, IllegalArgumentException.class,
                            "Required a new point 50 times "
                                    + "around the same point (t=%f). Likely there is an (unreported) knot in the Curve2d.",

Point2d medianPoint = curve.getPoint(medianT);
                // Check max deviation
                if (checkPositionError(medianPoint, prevPoint, nextPoint, this.maxDeviation))
                {
                    // We need to insert another point
                    result.put(medianT, medianPoint);
                    continue;
                }
                if (prevPoint.distance(nextPoint) > this.maxDeviation
                        && checkInflectionPoint(curve, prevT, medianT, nextT, prevPoint, nextPoint))
                {
                    // There is an inflection point, inserting the halfway point should take care of this
                    result.put(medianT, medianPoint);
                    continue;
                }
                if (checkLoopBack(curve.getDirection(prevT), curve.getDirection(nextT)))
                {
                    // The curve loops back onto itself. Inserting the halfway point should prevent missing out a major detour
                    // This check is NOT needed in the MaxDeviationAndAngle flattener.
                    result.put(medianT, medianPoint);
                    continue;
                }
                prevT = nextT;
                prevPoint = nextPoint;
            }
            return new PolyLine2d(result.values().iterator());

public static Complex[] rootsDurandKerner(final Complex[] a)
    {
        int n = a.length - 1;
        double radius = 1 + maxAbs(a);

        // initialize the initial values, not as a real number and not as a root of unity
        Complex[] p = new Complex[n];
        p[0] = new Complex(Math.sqrt(radius), Math.cbrt(radius));
        double rot = 350.123 / n;
        for (int i = 1; i < n; i++)
        {
            p[i] = p[0].rotate(rot * i);
        }

        double maxError = 1.0;
        int count = 0;
        while (maxError > 0 && count < MAX_STEPS_DURAND_KERNER)

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],

if (Integer.valueOf(columnProperties[0]).intValue() != index)
                {
                    throw new IOException("column nr not ok");
                }
                String type = columnProperties[3];
                Class<?> valueClass = Primitive.forName(type);
                if (valueClass == null)
                {
                    try
                    {
                        valueClass = Class.forName(type);
                    }
                    catch (ClassNotFoundException exception)
                    {
                        throw new IOException("Could not find class " + type, exception);
                    }
                }
                Column<?> column = new Column<>(columnProperties[1], columnProperties[2], valueClass, columnProperties[4]);

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, IllegalArgumentException.class,

Map<Double, Double> directions = new LinkedHashMap<>();
            directions.put(0.0, curve.getDirection(0.0)); // directions can't do ULP before 0.0
            Set<Double> knots = new HashSet<>();
            for (double knot : result.keySet())
            {
                if (knot > 0)
                {
                    directions.put(knot, curve.getDirection(knot - Math.ulp(knot)));
                }
                if (knot != 0.0 && knot != 1.0)
                {
                    knots.add(knot);
                }
            }

            // Walk along all point pairs and see if additional points need to be inserted
            double prevT = result.firstKey();

+ "around the same point (t=%f). Likely there is an (unreported) knot in the Curve2d.",
                            medianT);
                    continue;
                }
                iterationsAtSinglePoint = 0;
                if (prevPoint.distance(nextPoint) > this.maxDeviation
                        && checkInflectionPoint(curve, prevT, medianT, nextT, prevPoint, nextPoint))
                {
                    // There is an inflection point, inserting the halfway point should take care of this
                    result.put(medianT, medianPoint);
                    directions.put(medianT, curve.getDirection(medianT));
                    continue;
                }
                prevT = nextT;
                prevPoint = nextPoint;
                if (knots.contains(prevT))
                {
                    directions.put(prevT, curve.getDirection(prevT + Math.ulp(prevT)));
                }
            }
            return new PolyLine2d(result.values().iterator());