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With inspiration from other libraries
/*
* 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.math3.geometry.euclidean.twod;
import java.text.NumberFormat;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Space;
import org.apache.commons.math3.geometry.Vector;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MathUtils;
/** This class represents a 2D vector.
* Instances of this class are guaranteed to be immutable.
* @since 3.0
*/
public class Vector2D implements Vector {
/** Origin (coordinates: 0, 0). */
public static final Vector2D ZERO = new Vector2D(0, 0);
// CHECKSTYLE: stop ConstantName
/** A vector with all coordinates set to NaN. */
public static final Vector2D NaN = new Vector2D(Double.NaN, Double.NaN);
// CHECKSTYLE: resume ConstantName
/** 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);
/** Serializable UID. */
private static final long serialVersionUID = 266938651998679754L;
/** Abscissa. */
private final double x;
/** Ordinate. */
private final double y;
/** Simple constructor.
* Build a vector from its coordinates
* @param x abscissa
* @param y ordinate
* @see #getX()
* @see #getY()
*/
public Vector2D(double x, double y) {
this.x = x;
this.y = y;
}
/** Simple constructor.
* Build a vector from its coordinates
* @param v coordinates array
* @exception DimensionMismatchException if array does not have 2 elements
* @see #toArray()
*/
public Vector2D(double[] v) throws DimensionMismatchException {
if (v.length != 2) {
throw new DimensionMismatchException(v.length, 2);
}
this.x = v[0];
this.y = v[1];
}
/** Multiplicative constructor
* Build a vector from another one and a scale factor.
* The vector built will be a * u
* @param a scale factor
* @param u base (unscaled) vector
*/
public Vector2D(double a, Vector2D u) {
this.x = a * u.x;
this.y = a * u.y;
}
/** Linear constructor
* Build a vector from two other ones and corresponding scale factors.
* The vector built will be a1 * u1 + a2 * u2
* @param a1 first scale factor
* @param u1 first base (unscaled) vector
* @param a2 second scale factor
* @param u2 second base (unscaled) vector
*/
public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2) {
this.x = a1 * u1.x + a2 * u2.x;
this.y = a1 * u1.y + a2 * u2.y;
}
/** Linear constructor
* Build a vector from three other ones and corresponding scale factors.
* The vector built will be a1 * u1 + a2 * u2 + a3 * u3
* @param a1 first scale factor
* @param u1 first base (unscaled) vector
* @param a2 second scale factor
* @param u2 second base (unscaled) vector
* @param a3 third scale factor
* @param u3 third base (unscaled) vector
*/
public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2,
double a3, Vector2D u3) {
this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x;
this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y;
}
/** Linear constructor
* Build a vector from four other ones and corresponding scale factors.
* The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4
* @param a1 first scale factor
* @param u1 first base (unscaled) vector
* @param a2 second scale factor
* @param u2 second base (unscaled) vector
* @param a3 third scale factor
* @param u3 third base (unscaled) vector
* @param a4 fourth scale factor
* @param u4 fourth base (unscaled) vector
*/
public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2,
double a3, Vector2D u3, double a4, Vector2D u4) {
this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x + a4 * u4.x;
this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y + a4 * u4.y;
}
/** Get the abscissa of the vector.
* @return abscissa of the vector
* @see #Vector2D(double, double)
*/
public double getX() {
return x;
}
/** Get the ordinate of the vector.
* @return ordinate of the vector
* @see #Vector2D(double, double)
*/
public double getY() {
return y;
}
/** Get the vector coordinates as a dimension 2 array.
* @return vector coordinates
* @see #Vector2D(double[])
*/
public double[] toArray() {
return new double[] { x, y };
}
/** {@inheritDoc} */
public Space getSpace() {
return Euclidean2D.getInstance();
}
/** {@inheritDoc} */
public Vector2D getZero() {
return ZERO;
}
/** {@inheritDoc} */
public double getNorm1() {
return FastMath.abs(x) + FastMath.abs(y);
}
/** {@inheritDoc} */
public double getNorm() {
return FastMath.sqrt (x * x + y * y);
}
/** {@inheritDoc} */
public double getNormSq() {
return x * x + y * y;
}
/** {@inheritDoc} */
public double getNormInf() {
return FastMath.max(FastMath.abs(x), FastMath.abs(y));
}
/** {@inheritDoc} */
public Vector2D add(Vector v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x + v2.getX(), y + v2.getY());
}
/** {@inheritDoc} */
public Vector2D add(double factor, Vector v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x + factor * v2.getX(), y + factor * v2.getY());
}
/** {@inheritDoc} */
public Vector2D subtract(Vector p) {
Vector2D p3 = (Vector2D) p;
return new Vector2D(x - p3.x, y - p3.y);
}
/** {@inheritDoc} */
public Vector2D subtract(double factor, Vector v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x - factor * v2.getX(), y - factor * v2.getY());
}
/** {@inheritDoc} */
public Vector2D normalize() throws MathArithmeticException {
double s = getNorm();
if (s == 0) {
throw new MathArithmeticException(LocalizedFormats.CANNOT_NORMALIZE_A_ZERO_NORM_VECTOR);
}
return scalarMultiply(1 / s);
}
/** Compute the angular separation between two vectors.
* This method computes the angular separation between 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.
* @param v1 first vector
* @param v2 second vector
* @return angular separation between v1 and v2
* @exception MathArithmeticException if either vector has a null norm
*/
public static double angle(Vector2D v1, Vector2D v2) throws MathArithmeticException {
double normProduct = v1.getNorm() * v2.getNorm();
if (normProduct == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_NORM);
}
double dot = v1.dotProduct(v2);
double threshold = normProduct * 0.9999;
if ((dot < -threshold) || (dot > threshold)) {
// the vectors are almost aligned, compute using the sine
final double n = FastMath.abs(MathArrays.linearCombination(v1.x, v2.y, -v1.y, v2.x));
if (dot >= 0) {
return FastMath.asin(n / normProduct);
}
return FastMath.PI - FastMath.asin(n / normProduct);
}
// the vectors are sufficiently separated to use the cosine
return FastMath.acos(dot / normProduct);
}
/** {@inheritDoc} */
public Vector2D negate() {
return new Vector2D(-x, -y);
}
/** {@inheritDoc} */
public Vector2D scalarMultiply(double a) {
return new Vector2D(a * x, a * y);
}
/** {@inheritDoc} */
public boolean isNaN() {
return Double.isNaN(x) || Double.isNaN(y);
}
/** {@inheritDoc} */
public boolean isInfinite() {
return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y));
}
/** {@inheritDoc} */
public double distance1(Vector p) {
Vector2D p3 = (Vector2D) p;
final double dx = FastMath.abs(p3.x - x);
final double dy = FastMath.abs(p3.y - y);
return dx + dy;
}
/** {@inheritDoc}
*/
public double distance(Vector p) {
return distance((Point) p);
}
/** {@inheritDoc} */
public double distance(Point p) {
Vector2D p3 = (Vector2D) p;
final double dx = p3.x - x;
final double dy = p3.y - y;
return FastMath.sqrt(dx * dx + dy * dy);
}
/** {@inheritDoc} */
public double distanceInf(Vector p) {
Vector2D p3 = (Vector2D) p;
final double dx = FastMath.abs(p3.x - x);
final double dy = FastMath.abs(p3.y - y);
return FastMath.max(dx, dy);
}
/** {@inheritDoc} */
public double distanceSq(Vector p) {
Vector2D p3 = (Vector2D) p;
final double dx = p3.x - x;
final double dy = p3.y - y;
return dx * dx + dy * dy;
}
/** {@inheritDoc} */
public double dotProduct(final Vector v) {
final Vector2D v2 = (Vector2D) v;
return MathArrays.linearCombination(x, v2.x, y, v2.y);
}
/**
* Compute the cross-product of the instance and the given points.
*
* The cross product can be used to determine the location of a point
* with regard to the line formed by (p1, p2) and is calculated as:
* \[
* P = (x_2 - x_1)(y_3 - y_1) - (y_2 - y_1)(x_3 - x_1)
* \]
* with \(p3 = (x_3, y_3)\) being this instance.
*
* If the result is 0, the points are collinear, i.e. lie on a single straight line L;
* if it is positive, this point lies to the left, otherwise to the right of the line
* formed by (p1, p2).
*
* @param p1 first point of the line
* @param p2 second point of the line
* @return the cross-product
*
* @see Cross product (Wikipedia)
*/
public double crossProduct(final Vector2D p1, final Vector2D p2) {
final double x1 = p2.getX() - p1.getX();
final double y1 = getY() - p1.getY();
final double x2 = getX() - p1.getX();
final double y2 = p2.getY() - p1.getY();
return MathArrays.linearCombination(x1, y1, -x2, y2);
}
/** Compute the distance between two vectors according to the L2 norm.
*
Calling this method is equivalent to calling:
* p1.subtract(p2).getNorm() except that no intermediate
* vector is built
* @param p1 first vector
* @param p2 second vector
* @return the distance between p1 and p2 according to the L2 norm
*/
public static double distance(Vector2D p1, Vector2D p2) {
return p1.distance(p2);
}
/** Compute the distance between two vectors according to the L∞ norm.
* Calling this method is equivalent to calling:
* p1.subtract(p2).getNormInf() except that no intermediate
* vector is built
* @param p1 first vector
* @param p2 second vector
* @return the distance between p1 and p2 according to the L∞ norm
*/
public static double distanceInf(Vector2D p1, Vector2D p2) {
return p1.distanceInf(p2);
}
/** Compute the square of the distance between two vectors.
* Calling this method is equivalent to calling:
* p1.subtract(p2).getNormSq() except that no intermediate
* vector is built
* @param p1 first vector
* @param p2 second vector
* @return the square of the distance between p1 and p2
*/
public static double distanceSq(Vector2D p1, Vector2D p2) {
return p1.distanceSq(p2);
}
/**
* Test for the equality of two 2D vectors.
*
* If all coordinates of two 2D vectors are exactly the same, and none are
* Double.NaN, the two 2D vectors are considered to be equal.
*
*
* NaN coordinates are considered to affect globally the vector
* and be equals to each other - i.e, if either (or all) coordinates of the
* 2D vector are equal to Double.NaN, the 2D vector is equal to
* {@link #NaN}.
*
*
* @param other Object to test for equality to this
* @return true if two 2D vector objects are equal, false if
* object is null, not an instance of Vector2D, or
* not equal to this Vector2D instance
*
*/
@Override
public boolean equals(Object other) {
if (this == other) {
return true;
}
if (other instanceof Vector2D) {
final Vector2D rhs = (Vector2D)other;
if (rhs.isNaN()) {
return this.isNaN();
}
return (x == rhs.x) && (y == rhs.y);
}
return false;
}
/**
* Get a hashCode for the 2D vector.
*
* All NaN values have the same hash code.
*
* @return a hash code value for this object
*/
@Override
public int hashCode() {
if (isNaN()) {
return 542;
}
return 122 * (76 * MathUtils.hash(x) + MathUtils.hash(y));
}
/** Get a string representation of this vector.
* @return a string representation of this vector
*/
@Override
public String toString() {
return Vector2DFormat.getInstance().format(this);
}
/** {@inheritDoc} */
public String toString(final NumberFormat format) {
return new Vector2DFormat(format).format(this);
}
}