/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.geometry.euclidean.twod;
  
  import java.util.Arrays;
  import java.util.Comparator;
  import java.util.Iterator;
  import java.util.function.UnaryOperator;
  
  import org.apache.commons.geometry.core.internal.DoubleFunction2N;
  import org.apache.commons.geometry.core.internal.SimpleTupleFormat;
  import org.apache.commons.geometry.euclidean.EuclideanVectorSum;
  import org.apache.commons.geometry.euclidean.MultiDimensionalEuclideanVector;
  import org.apache.commons.geometry.euclidean.internal.Vectors;
  import org.apache.commons.numbers.core.Precision;
  
  /** This class represents vectors and points in two-dimensional Euclidean space.
   * Instances of this class are guaranteed to be immutable.
   */
  public class Vector2D extends MultiDimensionalEuclideanVector<Vector2D> {
  
      /** Zero vector (coordinates: 0, 0). */
      public static final Vector2D ZERO = new Vector2D(0, 0);
  
      /** A vector with all coordinates set to NaN. */
      public static final Vector2D NaN = new Vector2D(Double.NaN, Double.NaN);
  
      /** A vector with all coordinates set to positive infinity. */
      public static final Vector2D POSITIVE_INFINITY =
          new Vector2D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
  
      /** A vector with all coordinates set to negative infinity. */
      public static final Vector2D NEGATIVE_INFINITY =
          new Vector2D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);
  
      /** Comparator that sorts vectors in component-wise ascending order.
       * Vectors are only considered equal if their coordinates match exactly.
       * Null arguments are evaluated as being greater than non-null arguments.
       */
      public static final Comparator<Vector2D> COORDINATE_ASCENDING_ORDER = (a, b) -> {
          int cmp = 0;
  
          if (a != null && b != null) {
              cmp = Double.compare(a.getX(), b.getX());
              if (cmp == 0) {
                  cmp = Double.compare(a.getY(), b.getY());
              }
          } else if (a != null) {
              cmp = -1;
          } else if (b != null) {
              cmp = 1;
          }
  
          return cmp;
      };
  
      /** Abscissa (first coordinate). */
      private final double x;
  
      /** Ordinate (second coordinate). */
      private final double y;
  
      /** Simple constructor.
       * @param x abscissa (first coordinate)
       * @param y ordinate (second coordinate)
       */
      private Vector2D(final double x, final double y) {
          this.x = x;
          this.y = y;
      }
  
      /** Returns the abscissa (first coordinate value) of the instance.
       * @return the abscissa
       */
      public double getX() {
          return x;
      }
  
      /** Returns the ordinate (second coordinate value) of the instance.
       * @return the ordinate
       */
      public double getY() {
          return y;
      }
  
     /** Get the coordinates for this instance as a dimension 2 array.
      * @return coordinates for this instance
      */
     public double[] toArray() {
         return new double[]{x, y};
     }
 
     /** {@inheritDoc} */
     @Override
     public int getDimension() {
         return 2;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isNaN() {
         return Double.isNaN(x) || Double.isNaN(y);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isInfinite() {
         return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y));
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isFinite() {
         return Double.isFinite(x) && Double.isFinite(y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D vectorTo(final Vector2D v) {
         return v.subtract(this);
     }
 
     /** {@inheritDoc} */
     @Override
     public Unit directionTo(final Vector2D v) {
         return vectorTo(v).normalize();
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D lerp(final Vector2D p, final double t) {
         return Sum.create()
                 .addScaled(1.0 - t, this)
                 .addScaled(t, p).get();
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D getZero() {
         return ZERO;
     }
 
     /** {@inheritDoc} */
     @Override
     public double norm() {
         return Vectors.norm(x, y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double normSq() {
         return Vectors.normSq(x, y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D withNorm(final double magnitude) {
         final double invNorm = 1.0 / getCheckedNorm();
 
         return new Vector2D(
                     magnitude * x * invNorm,
                     magnitude * y * invNorm
                 );
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D add(final Vector2D v) {
         return new Vector2D(x + v.x, y + v.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D add(final double factor, final Vector2D v) {
         return new Vector2D(x + (factor * v.x), y + (factor * v.y));
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D subtract(final Vector2D v) {
         return new Vector2D(x - v.x, y - v.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D subtract(final double factor, final Vector2D v) {
         return new Vector2D(x - (factor * v.x), y - (factor * v.y));
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D negate() {
         return new Vector2D(-x, -y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Unit normalize() {
         return Unit.from(x, y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Unit normalizeOrNull() {
         return Unit.tryCreateNormalized(x, y, false);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D multiply(final double a) {
         return new Vector2D(a * x, a * y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double distance(final Vector2D v) {
         return Vectors.norm(x - v.x, y - v.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double distanceSq(final Vector2D v) {
         return Vectors.normSq(x - v.x, y - v.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double dot(final Vector2D v) {
         return Vectors.linearCombination(x, v.x, y, v.y);
     }
 
     /** {@inheritDoc}
      * <p>This method computes the angular separation between the two
      * vectors using the dot product for well separated vectors and the
      * cross product for almost aligned vectors. This allows to have a
      * good accuracy in all cases, even for vectors very close to each
      * other.</p>
      */
     @Override
     public double angle(final Vector2D v) {
         final double normProduct = getCheckedNorm() * v.getCheckedNorm();
 
         final double dot = dot(v);
         final double threshold = normProduct * 0.9999;
         if ((dot < -threshold) || (dot > threshold)) {
             // the vectors are almost aligned, compute using the sine
             final double n = Math.abs(Vectors.linearCombination(x, v.y, -y, v.x));
             if (dot >= 0) {
                 return Math.asin(n / normProduct);
             }
             return Math.PI - Math.asin(n / normProduct);
         }
 
         // the vectors are sufficiently separated to use the cosine
         return Math.acos(dot / normProduct);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D project(final Vector2D base) {
         return getComponent(base, false, Vector2D::new);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D reject(final Vector2D base) {
         return getComponent(base, true, Vector2D::new);
     }
 
     /** {@inheritDoc}
      * The returned vector is computed by rotating the current instance {@code pi/2} radians
      * counterclockwise around the origin and normalizing. For example, if this method is
      * called on a vector pointing along the positive x-axis, then a unit vector representing
      * the positive y-axis is returned.
      * @return a unit vector orthogonal to the current instance
      * @throws IllegalArgumentException if the norm of the current instance is zero, NaN, or infinite
      */
     @Override
     public Vector2D.Unit orthogonal() {
         return Unit.from(-y, x);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D.Unit orthogonal(final Vector2D dir) {
         return dir.getComponent(this, true, Vector2D.Unit::from);
     }
 
     /** Compute the signed area of the parallelogram with sides formed by this instance
      * and the given vector.
      *
      * <p>The parallelogram in question can be visualized by taking the current instance as the
      * first side and placing {@code v} at the end of it to create the second. The other sides
      * are formed by lines parallel to these two vectors. If {@code v} points to the <em>left</em> of
      * the current instance (ie, the parallelogram is wound counter-clockwise), then the
      * returned area is positive. If {@code v} points to the <em>right</em> of the current instance,
      * (ie, the parallelogram is wound clockwise), then the returned area is negative. If
      * the vectors are collinear (ie, they lie on the same line), then 0 is returned. The area of
      * the triangle formed by the two vectors is exactly half of the returned value.
      * @param v vector representing the second side of the constructed parallelogram
      * @return the signed area of the parallelogram formed by this instance and the given vector
      */
     public double signedArea(final Vector2D v) {
         return Vectors.linearCombination(
                 x, v.y,
                 -y, v.x);
     }
 
     /** Convenience method to apply a function to this vector. This
      * can be used to transform the vector inline with other methods.
      * @param fn the function to apply
      * @return the transformed vector
      */
     public Vector2D transform(final UnaryOperator<Vector2D> fn) {
         return fn.apply(this);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean eq(final Vector2D vec, final Precision.DoubleEquivalence precision) {
         return precision.eq(x, vec.x) &&
                 precision.eq(y, vec.y);
     }
 
     /**
      * Get a hashCode for the 2D coordinates.
      * <p>
      * All NaN values have the same hash code.</p>
      *
      * @return a hash code value for this object
      */
     @Override
     public int hashCode() {
         if (isNaN()) {
             return 542;
         }
         return 122 * (76 * Double.hashCode(x) + Double.hashCode(y));
     }
 
     /**
      * Test for the equality of two vector instances.
      * <p>
      * If all coordinates of two vectors are exactly the same, and none are
      * <code>Double.NaN</code>, the two instances are considered to be equal.
      * </p>
      * <p>
      * <code>NaN</code> coordinates are considered to globally affect the vector
      * and be equal to each other - i.e, if either (or all) coordinates of the
      * vector are equal to <code>Double.NaN</code>, the vector is equal to
      * {@link #NaN}.
      * </p>
      *
      * @param other Object to test for equality to this
      * @return true if two Vector2D objects are equal, false if
      *         object is null, not an instance of Vector2D, or
      *         not equal to this Vector2D instance
      *
      */
     @Override
     public boolean equals(final Object other) {
         if (this == other) {
             return true;
         }
         if (other instanceof Vector2D) {
             final Vector2D rhs = (Vector2D) other;
             if (rhs.isNaN()) {
                 return this.isNaN();
             }
 
             return Double.compare(x, rhs.x) == 0 &&
                     Double.compare(y, rhs.y) == 0;
         }
         return false;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString() {
         return SimpleTupleFormat.getDefault().format(x, y);
     }
 
     /** Returns a component of the current instance relative to the given base
      * vector. If {@code reject} is true, the vector rejection is returned; otherwise,
      * the projection is returned.
      * @param base The base vector
      * @param reject If true, the rejection of this instance from {@code base} is
      *      returned. If false, the projection of this instance onto {@code base}
      *      is returned.
      * @param factory factory function used to build the final vector
      * @param <T> Vector implementation type
      * @return The projection or rejection of this instance relative to {@code base},
      *      depending on the value of {@code reject}.
      * @throws IllegalArgumentException if {@code base} has a zero, NaN, or infinite norm
      */
     private <T extends Vector2D> T getComponent(final Vector2D base, final boolean reject,
             final DoubleFunction2N<T> factory) {
         final double aDotB = dot(base);
 
         // We need to check the norm value here to ensure that it's legal. However, we don't
         // want to incur the cost or floating point error of getting the actual norm and then
         // multiplying it again to get the square norm. So, we'll just check the squared norm
         // directly. This will produce the same error result as checking the actual norm since
         // Math.sqrt(0.0) == 0.0, Math.sqrt(Double.NaN) == Double.NaN and
         // Math.sqrt(Double.POSITIVE_INFINITY) == Double.POSITIVE_INFINITY.
         final double baseMagSq = Vectors.checkedNorm(base.normSq());
 
         final double scale = aDotB / baseMagSq;
 
         final double projX = scale * base.x;
         final double projY = scale * base.y;
 
         if (reject) {
             return factory.apply(x - projX, y - projY);
         }
 
         return factory.apply(projX, projY);
     }
 
     /** Returns a vector with the given coordinate values.
      * @param x abscissa (first coordinate value)
      * @param y abscissa (second coordinate value)
      * @return vector instance
      */
     public static Vector2D of(final double x, final double y) {
         return new Vector2D(x, y);
     }
 
     /** Creates a vector from the coordinates in the given 2-element array.
      * @param v coordinates array
      * @return new vector
      * @exception IllegalArgumentException if the array does not have 2 elements
      */
     public static Vector2D of(final double[] v) {
         if (v.length != 2) {
             throw new IllegalArgumentException("Dimension mismatch: " + v.length + " != 2");
         }
         return new Vector2D(v[0], v[1]);
     }
 
     /** Parses the given string and returns a new vector instance. The expected string
      * format is the same as that returned by {@link #toString()}.
      * @param str the string to parse
      * @return vector instance represented by the string
      * @throws IllegalArgumentException if the given string has an invalid format
      */
     public static Vector2D parse(final String str) {
         return SimpleTupleFormat.getDefault().parse(str, Vector2D::new);
     }
 
     /** Return a vector containing the maximum component values from all input vectors.
      * @param first first vector
      * @param more additional vectors
      * @return a vector containing the maximum component values from all input vectors
      */
     public static Vector2D max(final Vector2D first, final Vector2D... more) {
         return computeMax(first, Arrays.asList(more).iterator());
     }
 
     /** Return a vector containing the maximum component values from all input vectors.
      * @param vecs input vectors
      * @return a vector containing the maximum component values from all input vectors
      * @throws IllegalArgumentException if the argument does not contain any vectors
      */
     public static Vector2D max(final Iterable<Vector2D> vecs) {
         final Iterator<Vector2D> it = vecs.iterator();
         if (!it.hasNext()) {
             throw new IllegalArgumentException("Cannot compute vector max: no vectors given");
         }
 
         return computeMax(it.next(), it);
     }
 
     /** Internal method for computing a max vector.
      * @param first first vector
      * @param more iterator with additional vectors
      * @return vector containing the maximum component values of all input vectors
      */
     private static Vector2D computeMax(final Vector2D first, final Iterator<? extends Vector2D> more) {
         double x = first.getX();
         double y = first.getY();
 
         Vector2D vec;
         while (more.hasNext()) {
             vec = more.next();
 
             x = Math.max(x, vec.getX());
             y = Math.max(y, vec.getY());
         }
 
         return Vector2D.of(x, y);
     }
 
     /** Return a vector containing the minimum component values from all input vectors.
      * @param first first vector
      * @param more more vectors
      * @return a vector containing the minimum component values from all input vectors
      */
     public static Vector2D min(final Vector2D first, final Vector2D... more) {
         return computeMin(first, Arrays.asList(more).iterator());
     }
 
     /** Return a vector containing the minimum component values from all input vectors.
      * @param vecs input vectors
      * @return a vector containing the minimum component values from all input vectors
      * @throws IllegalArgumentException if the argument does not contain any vectors
      */
     public static Vector2D min(final Iterable<Vector2D> vecs) {
         final Iterator<Vector2D> it = vecs.iterator();
         if (!it.hasNext()) {
             throw new IllegalArgumentException("Cannot compute vector min: no vectors given");
         }
 
         return computeMin(it.next(), it);
     }
 
     /** Internal method for computing a min vector.
      * @param first first vector
      * @param more iterator with additional vectors
      * @return vector containing the minimum component values of all input vectors
      */
     private static Vector2D computeMin(final Vector2D first, final Iterator<? extends Vector2D> more) {
         double x = first.getX();
         double y = first.getY();
 
         Vector2D vec;
         while (more.hasNext()) {
             vec = more.next();
 
             x = Math.min(x, vec.getX());
             y = Math.min(y, vec.getY());
         }
 
         return Vector2D.of(x, y);
     }
 
     /** Compute the centroid of the given points. The centroid is the arithmetic mean position of a set
      * of points.
      * @param first first point
      * @param more additional points
      * @return the centroid of the given points
      */
     public static Vector2D centroid(final Vector2D first, final Vector2D... more) {
         return computeCentroid(first, Arrays.asList(more).iterator());
     }
 
     /** Compute the centroid of the given points. The centroid is the arithmetic mean position of a set
      * of points.
      * @param pts the points to compute the centroid of
      * @return the centroid of the given points
      * @throws IllegalArgumentException if the argument contains no points
      */
     public static Vector2D centroid(final Iterable<Vector2D> pts) {
         final Iterator<Vector2D> it = pts.iterator();
         if (!it.hasNext()) {
             throw new IllegalArgumentException("Cannot compute centroid: no points given");
         }
 
         return computeCentroid(it.next(), it);
     }
 
     /** Internal method for computing the centroid of a set of points.
      * @param first first point
      * @param more iterator with additional points
      * @return the centroid of the point set
      */
     private static Vector2D computeCentroid(final Vector2D first, final Iterator<? extends Vector2D> more) {
         final Sum sum = Sum.of(first);
         int count = 1;
 
         while (more.hasNext()) {
             sum.add(more.next());
             ++count;
         }
 
         return sum.get().multiply(1.0 / count);
     }
 
     /**
      * Represents unit vectors.
      * This allows optimizations for certain operations.
      */
     public static final class Unit extends Vector2D {
         /** Unit vector (coordinates: 1, 0). */
         public static final Unit PLUS_X  = new Unit(1d, 0d);
         /** Negation of unit vector (coordinates: -1, 0). */
         public static final Unit MINUS_X = new Unit(-1d, 0d);
         /** Unit vector (coordinates: 0, 1). */
         public static final Unit PLUS_Y  = new Unit(0d, 1d);
         /** Negation of unit vector (coordinates: 0, -1). */
         public static final Unit MINUS_Y = new Unit(0d, -1d);
 
         /** Maximum coordinate value for computing normalized vectors
          * with raw, unscaled values.
          */
         private static final double UNSCALED_MAX = 0x1.0p+500;
 
         /** Factor used to scale up coordinate values in order to produce
          * normalized coordinates without overflow or underflow.
          */
         private static final double SCALE_UP_FACTOR = 0x1.0p+600;
 
         /** Factor used to scale down coordinate values in order to produce
          * normalized coordinates without overflow or underflow.
          */
         private static final double SCALE_DOWN_FACTOR = 0x1.0p-600;
 
         /** Simple constructor. Callers are responsible for ensuring that the given
          * values represent a normalized vector.
          * @param x abscissa (first coordinate value)
          * @param y abscissa (second coordinate value)
          */
         private Unit(final double x, final double y) {
             super(x, y);
         }
 
         /** {@inheritDoc} */
         @Override
         public double norm() {
             return 1;
         }
 
         /** {@inheritDoc} */
         @Override
         public double normSq() {
             return 1;
         }
 
         /** {@inheritDoc} */
         @Override
         public Unit normalize() {
             return this;
         }
 
         /** {@inheritDoc} */
         @Override
         public Unit normalizeOrNull() {
             return this;
         }
 
         /** {@inheritDoc} */
         @Override
         public Vector2D.Unit orthogonal() {
             return new Unit(-getY(), getX());
         }
 
         /** {@inheritDoc} */
         @Override
         public Vector2D withNorm(final double mag) {
             return multiply(mag);
         }
 
         /** {@inheritDoc} */
         @Override
         public Unit negate() {
             return new Unit(-getX(), -getY());
         }
 
         /** Create a normalized vector.
          * @param x Vector coordinate.
          * @param y Vector coordinate.
          * @return a vector whose norm is 1.
          * @throws IllegalArgumentException if the norm of the given value is zero, NaN,
          *      or infinite
          */
         public static Unit from(final double x, final double y) {
             return tryCreateNormalized(x, y, true);
         }
 
         /** Create a normalized vector.
          * @param v Vector.
          * @return a vector whose norm is 1.
          * @throws IllegalArgumentException if the norm of the given value is zero, NaN,
          *      or infinite
          */
         public static Unit from(final Vector2D v) {
             return v instanceof Unit ?
                 (Unit) v :
                 from(v.getX(), v.getY());
         }
 
         /** Attempt to create a normalized vector from the given coordinate values. If {@code throwOnFailure}
          * is true, an exception is thrown if a normalized vector cannot be created. Otherwise, null
          * is returned.
          * @param x x coordinate
          * @param y y coordinate
          * @param throwOnFailure if true, an exception will be thrown if a normalized vector cannot be created
          * @return normalized vector or null if one cannot be created and {@code throwOnFailure}
          *      is false
          * @throws IllegalArgumentException if the computed norm is zero, NaN, or infinite
          */
         private static Unit tryCreateNormalized(final double x, final double y, final boolean throwOnFailure) {
 
             // Compute the inverse norm directly. If the result is a non-zero real number,
             // then we can go ahead and construct the unit vector immediately. If not,
             // we'll do some extra work for edge cases.
             final double norm = Vectors.norm(x, y);
             final double normInv = 1.0 / norm;
             if (Vectors.isRealNonZero(normInv)) {
                 return new Unit(
                         x * normInv,
                         y * normInv);
             }
 
             // Direct computation did not work. Try scaled versions of the coordinates
             // to handle overflow and underflow.
             final double scaledX;
             final double scaledY;
 
             final double maxCoord = Math.max(Math.abs(x), Math.abs(y));
             if (maxCoord > UNSCALED_MAX) {
                 scaledX = x * SCALE_DOWN_FACTOR;
                 scaledY = y * SCALE_DOWN_FACTOR;
             } else {
                 scaledX = x * SCALE_UP_FACTOR;
                 scaledY = y * SCALE_UP_FACTOR;
             }
 
             final double scaledNormInv = 1.0 / Vectors.norm(scaledX, scaledY);
 
             if (Vectors.isRealNonZero(scaledNormInv)) {
                 return new Unit(
                         scaledX * scaledNormInv,
                         scaledY * scaledNormInv);
             } else if (throwOnFailure) {
                 throw Vectors.illegalNorm(norm);
             }
             return null;
         }
     }
 
     /** Class used to create high-accuracy sums of vectors. Each vector component is
      * summed using an instance of {@link org.apache.commons.numbers.core.Sum}.
      *
      * <p>This class is mutable and not thread-safe.
      * @see org.apache.commons.numbers.core.Sum
      */
     public static final class Sum extends EuclideanVectorSum<Vector2D> {
         /** X component sum. */
         private final org.apache.commons.numbers.core.Sum xsum;
         /** Y component sum. */
         private final org.apache.commons.numbers.core.Sum ysum;
 
         /** Construct a new instance with the given initial value.
          * @param initial initial value
          */
         Sum(final Vector2D initial) {
             this.xsum = org.apache.commons.numbers.core.Sum.of(initial.x);
             this.ysum = org.apache.commons.numbers.core.Sum.of(initial.y);
         }
 
         /** {@inheritDoc} */
         @Override
         public Sum add(final Vector2D vec) {
             xsum.add(vec.x);
             ysum.add(vec.y);
             return this;
         }
 
         /** {@inheritDoc} */
         @Override
         public Sum addScaled(final double scale, final Vector2D vec) {
             xsum.addProduct(scale, vec.x);
             ysum.addProduct(scale, vec.y);
             return this;
         }
 
         /** {@inheritDoc} */
         @Override
         public Vector2D get() {
             return Vector2D.of(
                     xsum.getAsDouble(),
                     ysum.getAsDouble());
         }
 
         /** Create a new instance with an initial value set to the {@link Vector2D#ZERO zero vector}.
          * @return new instance set to zero
          */
         public static Sum create() {
             return new Sum(Vector2D.ZERO);
         }
 
         /** Construct a new instance with an initial value set to the argument.
          * @param initial initial sum value
          * @return new instance
          */
         public static Sum of(final Vector2D initial) {
             return new Sum(initial);
         }
 
         /** Construct a new instance from multiple values.
          * @param first first vector
          * @param more additional vectors
          * @return new instance
          */
         public static Sum of(final Vector2D first, final Vector2D... more) {
             final Sum s = new Sum(first);
             for (final Vector2D v : more) {
                 s.add(v);
             }
             return s;
         }
     }
 }