Vector2D.java
/*
* 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
*
* https://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.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.geometry.euclidean.twod;
import java.text.NumberFormat;
import org.hipparchus.exception.LocalizedCoreFormats;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.exception.MathRuntimeException;
import org.hipparchus.geometry.Point;
import org.hipparchus.geometry.Space;
import org.hipparchus.geometry.Vector;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.MathUtils;
/** This class represents a 2D vector.
* <p>Instances of this class are guaranteed to be immutable.</p>
*/
public class Vector2D implements Vector<Euclidean2D, Vector2D> {
/** Origin (coordinates: 0, 0). */
public static final Vector2D ZERO = new Vector2D(0, 0);
/** First canonical vector (coordinates: 1, 0).
* @since 1.6
*/
public static final Vector2D PLUS_I = new Vector2D(1, 0);
/** Opposite of the first canonical vector (coordinates: -1, 0).
* @since 1.6
*/
public static final Vector2D MINUS_I = new Vector2D(-1, 0);
/** Second canonical vector (coordinates: 0, 1).
* @since 1.6
*/
public static final Vector2D PLUS_J = new Vector2D(0, 1);
/** Opposite of the second canonical vector (coordinates: 0, -1).
* @since 1.6
*/
public static final Vector2D MINUS_J = new Vector2D(0, -1);
// 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 MathIllegalArgumentException if array does not have 2 elements
* @see #toArray()
*/
public Vector2D(double[] v) throws MathIllegalArgumentException {
if (v.length != 2) {
throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
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} */
@Override
public Space getSpace() {
return Euclidean2D.getInstance();
}
/** {@inheritDoc} */
@Override
public Vector2D getZero() {
return ZERO;
}
/** {@inheritDoc} */
@Override
public double getNorm1() {
return FastMath.abs(x) + FastMath.abs(y);
}
/** {@inheritDoc} */
@Override
public double getNorm() {
return FastMath.sqrt (x * x + y * y);
}
/** {@inheritDoc} */
@Override
public double getNormSq() {
return x * x + y * y;
}
/** {@inheritDoc} */
@Override
public double getNormInf() {
return FastMath.max(FastMath.abs(x), FastMath.abs(y));
}
/** {@inheritDoc} */
@Override
public Vector2D add(Vector<Euclidean2D, Vector2D> v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x + v2.getX(), y + v2.getY());
}
/** {@inheritDoc} */
@Override
public Vector2D add(double factor, Vector<Euclidean2D, Vector2D> v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x + factor * v2.getX(), y + factor * v2.getY());
}
/** {@inheritDoc} */
@Override
public Vector2D subtract(Vector<Euclidean2D, Vector2D> p) {
Vector2D p3 = (Vector2D) p;
return new Vector2D(x - p3.x, y - p3.y);
}
/** {@inheritDoc} */
@Override
public Vector2D subtract(double factor, Vector<Euclidean2D, Vector2D> v) {
Vector2D v2 = (Vector2D) v;
return new Vector2D(x - factor * v2.getX(), y - factor * v2.getY());
}
/** Compute the angular separation between two vectors.
* <p>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.</p>
* @param v1 first vector
* @param v2 second vector
* @return angular separation between v1 and v2
* @exception MathRuntimeException if either vector has a null norm
*/
public static double angle(Vector2D v1, Vector2D v2) throws MathRuntimeException {
double normProduct = v1.getNorm() * v2.getNorm();
if (normProduct == 0) {
throw new MathRuntimeException(LocalizedCoreFormats.ZERO_NORM);
}
double dot = v1.dotProduct(v2);
double threshold = normProduct * 0.9999;
if (FastMath.abs(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} */
@Override
public Vector2D negate() {
return new Vector2D(-x, -y);
}
/** {@inheritDoc} */
@Override
public Vector2D scalarMultiply(double a) {
return new Vector2D(a * x, a * y);
}
/** {@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 double distance1(Vector<Euclidean2D, Vector2D> 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} */
@Override
public double distance(Point<Euclidean2D> 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} */
@Override
public double distanceInf(Vector<Euclidean2D, Vector2D> 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} */
@Override
public double distanceSq(Vector<Euclidean2D, Vector2D> p) {
Vector2D p3 = (Vector2D) p;
final double dx = p3.x - x;
final double dy = p3.y - y;
return dx * dx + dy * dy;
}
/** {@inheritDoc} */
@Override
public double dotProduct(final Vector<Euclidean2D, Vector2D> 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.
* <p>
* 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.
* <p>
* 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 <a href="http://en.wikipedia.org/wiki/Cross_product">Cross product (Wikipedia)</a>
*/
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 L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>p1.subtract(p2).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param p1 first vector
* @param p2 second vector
* @return the distance between p1 and p2 according to the L<sub>1</sub> norm
* @since 1.6
*/
public static double distance1(Vector2D p1, Vector2D p2) {
return p1.distance1(p2);
}
/** Compute the distance between two vectors according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>p1.subtract(p2).getNorm()</code> except that no intermediate
* vector is built</p>
* @param p1 first vector
* @param p2 second vector
* @return the distance between p1 and p2 according to the L<sub>2</sub> norm
*/
public static double distance(Vector2D p1, Vector2D p2) {
return p1.distance(p2);
}
/** Compute the distance between two vectors according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>p1.subtract(p2).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param p1 first vector
* @param p2 second vector
* @return the distance between p1 and p2 according to the L<sub>∞</sub> norm
*/
public static double distanceInf(Vector2D p1, Vector2D p2) {
return p1.distanceInf(p2);
}
/** Compute the square of the distance between two vectors.
* <p>Calling this method is equivalent to calling:
* <code>p1.subtract(p2).getNormSq()</code> except that no intermediate
* vector is built</p>
* @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);
}
/** Compute the orientation of a triplet of points.
* @param p first vector of the triplet
* @param q second vector of the triplet
* @param r third vector of the triplet
* @return a positive value if (p, q, r) defines a counterclockwise oriented
* triangle, a negative value if (p, q, r) defines a clockwise oriented
* triangle, and 0 if (p, q, r) are collinear or some points are equal
* @since 1.2
*/
public static double orientation(final Vector2D p, final Vector2D q, final Vector2D r) {
return MathArrays.linearCombination(new double[] {
p.getX(), -p.getX(), q.getX(), -q.getX(), r.getX(), -r.getX()
}, new double[] {
q.getY(), r.getY(), r.getY(), p.getY(), p.getY(), q.getY()
});
}
/**
* Test for the equality of two 2D vectors.
* <p>
* If all coordinates of two 2D vectors are exactly the same, and none are
* {@code Double.NaN}, the two 2D vectors are considered to be equal.
* </p>
* <p>
* {@code 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 {@code Double.NaN}, the 2D vector is equal to
* {@link #NaN}.
* </p>
*
* @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;
return x == rhs.x && y == rhs.y || isNaN() && rhs.isNaN();
}
return false;
}
/**
* Test for the equality of two 2D vectors.
* <p>
* If all coordinates of two 2D vectors are exactly the same, and none are
* {@code NaN}, the two 2D vectors are considered to be equal.
* </p>
* <p>
* In compliance with IEEE754 handling, if any coordinates of any of the
* two vectors are {@code NaN}, then the vectors are considered different.
* This implies that {@link #NaN Vector2D.NaN}.equals({@link #NaN Vector2D.NaN})
* returns {@code false} despite the instance is checked against itself.
* </p>
*
* @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
* @since 2.1
*/
public boolean equalsIeee754(Object other) {
if (this == other && !isNaN()) {
return true;
}
if (other instanceof Vector2D) {
final Vector2D rhs = (Vector2D) other;
return x == rhs.x && y == rhs.y;
}
return false;
}
/**
* Get a hashCode for the 2D vector.
* <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 * 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.getVector2DFormat().format(this);
}
/** {@inheritDoc} */
@Override
public String toString(final NumberFormat format) {
return new Vector2DFormat(format).format(this);
}
}