Java example source code file (Vector3D.java)
The Vector3D.java Java example source code/*
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* 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
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*
* 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,
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* See the License for the specific language governing permissions and
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package org.apache.commons.math3.geometry.euclidean.threed;
import java.io.Serializable;
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 implements vectors in a three-dimensional space.
* <p>Instance of this class are guaranteed to be immutable.
* @since 1.2
*/
public class Vector3D implements Serializable, Vector<Euclidean3D> {
/** Null vector (coordinates: 0, 0, 0). */
public static final Vector3D ZERO = new Vector3D(0, 0, 0);
/** First canonical vector (coordinates: 1, 0, 0). */
public static final Vector3D PLUS_I = new Vector3D(1, 0, 0);
/** Opposite of the first canonical vector (coordinates: -1, 0, 0). */
public static final Vector3D MINUS_I = new Vector3D(-1, 0, 0);
/** Second canonical vector (coordinates: 0, 1, 0). */
public static final Vector3D PLUS_J = new Vector3D(0, 1, 0);
/** Opposite of the second canonical vector (coordinates: 0, -1, 0). */
public static final Vector3D MINUS_J = new Vector3D(0, -1, 0);
/** Third canonical vector (coordinates: 0, 0, 1). */
public static final Vector3D PLUS_K = new Vector3D(0, 0, 1);
/** Opposite of the third canonical vector (coordinates: 0, 0, -1). */
public static final Vector3D MINUS_K = new Vector3D(0, 0, -1);
// CHECKSTYLE: stop ConstantName
/** A vector with all coordinates set to NaN. */
public static final Vector3D NaN = new Vector3D(Double.NaN, Double.NaN, Double.NaN);
// CHECKSTYLE: resume ConstantName
/** A vector with all coordinates set to positive infinity. */
public static final Vector3D POSITIVE_INFINITY =
new Vector3D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
/** A vector with all coordinates set to negative infinity. */
public static final Vector3D NEGATIVE_INFINITY =
new Vector3D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);
/** Serializable version identifier. */
private static final long serialVersionUID = 1313493323784566947L;
/** Abscissa. */
private final double x;
/** Ordinate. */
private final double y;
/** Height. */
private final double z;
/** Simple constructor.
* Build a vector from its coordinates
* @param x abscissa
* @param y ordinate
* @param z height
* @see #getX()
* @see #getY()
* @see #getZ()
*/
public Vector3D(double x, double y, double z) {
this.x = x;
this.y = y;
this.z = z;
}
/** Simple constructor.
* Build a vector from its coordinates
* @param v coordinates array
* @exception DimensionMismatchException if array does not have 3 elements
* @see #toArray()
*/
public Vector3D(double[] v) throws DimensionMismatchException {
if (v.length != 3) {
throw new DimensionMismatchException(v.length, 3);
}
this.x = v[0];
this.y = v[1];
this.z = v[2];
}
/** Simple constructor.
* Build a vector from its azimuthal coordinates
* @param alpha azimuth (?) around Z
* (0 is +X, ?/2 is +Y, ? is -X and 3?/2 is -Y)
* @param delta elevation (?) above (XY) plane, from -?/2 to +?/2
* @see #getAlpha()
* @see #getDelta()
*/
public Vector3D(double alpha, double delta) {
double cosDelta = FastMath.cos(delta);
this.x = FastMath.cos(alpha) * cosDelta;
this.y = FastMath.sin(alpha) * cosDelta;
this.z = FastMath.sin(delta);
}
/** 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 Vector3D(double a, Vector3D u) {
this.x = a * u.x;
this.y = a * u.y;
this.z = a * u.z;
}
/** 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 Vector3D(double a1, Vector3D u1, double a2, Vector3D u2) {
this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x);
this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y);
this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z);
}
/** 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 Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, Vector3D u3) {
this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x);
this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y);
this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z);
}
/** 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 Vector3D(double a1, Vector3D u1, double a2, Vector3D u2,
double a3, Vector3D u3, double a4, Vector3D u4) {
this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x, a4, u4.x);
this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y, a4, u4.y);
this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z, a4, u4.z);
}
/** Get the abscissa of the vector.
* @return abscissa of the vector
* @see #Vector3D(double, double, double)
*/
public double getX() {
return x;
}
/** Get the ordinate of the vector.
* @return ordinate of the vector
* @see #Vector3D(double, double, double)
*/
public double getY() {
return y;
}
/** Get the height of the vector.
* @return height of the vector
* @see #Vector3D(double, double, double)
*/
public double getZ() {
return z;
}
/** Get the vector coordinates as a dimension 3 array.
* @return vector coordinates
* @see #Vector3D(double[])
*/
public double[] toArray() {
return new double[] { x, y, z };
}
/** {@inheritDoc} */
public Space getSpace() {
return Euclidean3D.getInstance();
}
/** {@inheritDoc} */
public Vector3D getZero() {
return ZERO;
}
/** {@inheritDoc} */
public double getNorm1() {
return FastMath.abs(x) + FastMath.abs(y) + FastMath.abs(z);
}
/** {@inheritDoc} */
public double getNorm() {
// there are no cancellation problems here, so we use the straightforward formula
return FastMath.sqrt (x * x + y * y + z * z);
}
/** {@inheritDoc} */
public double getNormSq() {
// there are no cancellation problems here, so we use the straightforward formula
return x * x + y * y + z * z;
}
/** {@inheritDoc} */
public double getNormInf() {
return FastMath.max(FastMath.max(FastMath.abs(x), FastMath.abs(y)), FastMath.abs(z));
}
/** Get the azimuth of the vector.
* @return azimuth (?) of the vector, between -? and +?
* @see #Vector3D(double, double)
*/
public double getAlpha() {
return FastMath.atan2(y, x);
}
/** Get the elevation of the vector.
* @return elevation (?) of the vector, between -?/2 and +?/2
* @see #Vector3D(double, double)
*/
public double getDelta() {
return FastMath.asin(z / getNorm());
}
/** {@inheritDoc} */
public Vector3D add(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
return new Vector3D(x + v3.x, y + v3.y, z + v3.z);
}
/** {@inheritDoc} */
public Vector3D add(double factor, final Vector<Euclidean3D> v) {
return new Vector3D(1, this, factor, (Vector3D) v);
}
/** {@inheritDoc} */
public Vector3D subtract(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
return new Vector3D(x - v3.x, y - v3.y, z - v3.z);
}
/** {@inheritDoc} */
public Vector3D subtract(final double factor, final Vector<Euclidean3D> v) {
return new Vector3D(1, this, -factor, (Vector3D) v);
}
/** {@inheritDoc} */
public Vector3D normalize() throws MathArithmeticException {
double s = getNorm();
if (s == 0) {
throw new MathArithmeticException(LocalizedFormats.CANNOT_NORMALIZE_A_ZERO_NORM_VECTOR);
}
return scalarMultiply(1 / s);
}
/** Get a vector orthogonal to the instance.
* <p>There are an infinite number of normalized vectors orthogonal
* to the instance. This method picks up one of them almost
* arbitrarily. It is useful when one needs to compute a reference
* frame with one of the axes in a predefined direction. The
* following example shows how to build a frame having the k axis
* aligned with the known vector u :
* <pre>
* @return a new normalized vector orthogonal to the instance
* @exception MathArithmeticException if the norm of the instance is null
*/
public Vector3D orthogonal() throws MathArithmeticException {
double threshold = 0.6 * getNorm();
if (threshold == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_NORM);
}
if (FastMath.abs(x) <= threshold) {
double inverse = 1 / FastMath.sqrt(y * y + z * z);
return new Vector3D(0, inverse * z, -inverse * y);
} else if (FastMath.abs(y) <= threshold) {
double inverse = 1 / FastMath.sqrt(x * x + z * z);
return new Vector3D(-inverse * z, 0, inverse * x);
}
double inverse = 1 / FastMath.sqrt(x * x + y * y);
return new Vector3D(inverse * y, -inverse * x, 0);
}
/** 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 MathArithmeticException if either vector has a null norm
*/
public static double angle(Vector3D v1, Vector3D 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
Vector3D v3 = crossProduct(v1, v2);
if (dot >= 0) {
return FastMath.asin(v3.getNorm() / normProduct);
}
return FastMath.PI - FastMath.asin(v3.getNorm() / normProduct);
}
// the vectors are sufficiently separated to use the cosine
return FastMath.acos(dot / normProduct);
}
/** {@inheritDoc} */
public Vector3D negate() {
return new Vector3D(-x, -y, -z);
}
/** {@inheritDoc} */
public Vector3D scalarMultiply(double a) {
return new Vector3D(a * x, a * y, a * z);
}
/** {@inheritDoc} */
public boolean isNaN() {
return Double.isNaN(x) || Double.isNaN(y) || Double.isNaN(z);
}
/** {@inheritDoc} */
public boolean isInfinite() {
return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y) || Double.isInfinite(z));
}
/**
* Test for the equality of two 3D vectors.
* <p>
* If all coordinates of two 3D vectors are exactly the same, and none are
* <code>Double.NaN, the two 3D 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
* 3D vector are equal to <code>Double.NaN, the 3D vector is equal to
* {@link #NaN}.
* </p>
*
* @param other Object to test for equality to this
* @return true if two 3D vector objects are equal, false if
* object is null, not an instance of Vector3D, or
* not equal to this Vector3D instance
*
*/
@Override
public boolean equals(Object other) {
if (this == other) {
return true;
}
if (other instanceof Vector3D) {
final Vector3D rhs = (Vector3D)other;
if (rhs.isNaN()) {
return this.isNaN();
}
return (x == rhs.x) && (y == rhs.y) && (z == rhs.z);
}
return false;
}
/**
* Get a hashCode for the 3D 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 642;
}
return 643 * (164 * MathUtils.hash(x) + 3 * MathUtils.hash(y) + MathUtils.hash(z));
}
/** {@inheritDoc}
* <p>
* The implementation uses specific multiplication and addition
* algorithms to preserve accuracy and reduce cancellation effects.
* It should be very accurate even for nearly orthogonal vectors.
* </p>
* @see MathArrays#linearCombination(double, double, double, double, double, double)
*/
public double dotProduct(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
return MathArrays.linearCombination(x, v3.x, y, v3.y, z, v3.z);
}
/** Compute the cross-product of the instance with another vector.
* @param v other vector
* @return the cross product this ^ v as a new Vector3D
*/
public Vector3D crossProduct(final Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
return new Vector3D(MathArrays.linearCombination(y, v3.z, -z, v3.y),
MathArrays.linearCombination(z, v3.x, -x, v3.z),
MathArrays.linearCombination(x, v3.y, -y, v3.x));
}
/** {@inheritDoc} */
public double distance1(Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
final double dx = FastMath.abs(v3.x - x);
final double dy = FastMath.abs(v3.y - y);
final double dz = FastMath.abs(v3.z - z);
return dx + dy + dz;
}
/** {@inheritDoc} */
public double distance(Vector<Euclidean3D> v) {
return distance((Point<Euclidean3D>) v);
}
/** {@inheritDoc} */
public double distance(Point<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
final double dx = v3.x - x;
final double dy = v3.y - y;
final double dz = v3.z - z;
return FastMath.sqrt(dx * dx + dy * dy + dz * dz);
}
/** {@inheritDoc} */
public double distanceInf(Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
final double dx = FastMath.abs(v3.x - x);
final double dy = FastMath.abs(v3.y - y);
final double dz = FastMath.abs(v3.z - z);
return FastMath.max(FastMath.max(dx, dy), dz);
}
/** {@inheritDoc} */
public double distanceSq(Vector<Euclidean3D> v) {
final Vector3D v3 = (Vector3D) v;
final double dx = v3.x - x;
final double dy = v3.y - y;
final double dz = v3.z - z;
return dx * dx + dy * dy + dz * dz;
}
/** Compute the dot-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @return the dot product v1.v2
*/
public static double dotProduct(Vector3D v1, Vector3D v2) {
return v1.dotProduct(v2);
}
/** Compute the cross-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @return the cross product v1 ^ v2 as a new Vector
*/
public static Vector3D crossProduct(final Vector3D v1, final Vector3D v2) {
return v1.crossProduct(v2);
}
/** Compute the distance between two vectors according to the L<sub>1 norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm1() except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @return the distance between v1 and v2 according to the L<sub>1 norm
*/
public static double distance1(Vector3D v1, Vector3D v2) {
return v1.distance1(v2);
}
/** Compute the distance between two vectors according to the L<sub>2 norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm() except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @return the distance between v1 and v2 according to the L<sub>2 norm
*/
public static double distance(Vector3D v1, Vector3D v2) {
return v1.distance(v2);
}
/** Compute the distance between two vectors according to the L<sub>? norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormInf() except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @return the distance between v1 and v2 according to the L<sub>? norm
*/
public static double distanceInf(Vector3D v1, Vector3D v2) {
return v1.distanceInf(v2);
}
/** Compute the square of the distance between two vectors.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormSq() except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @return the square of the distance between v1 and v2
*/
public static double distanceSq(Vector3D v1, Vector3D v2) {
return v1.distanceSq(v2);
}
/** Get a string representation of this vector.
* @return a string representation of this vector
*/
@Override
public String toString() {
return Vector3DFormat.getInstance().format(this);
}
/** {@inheritDoc} */
public String toString(final NumberFormat format) {
return new Vector3DFormat(format).format(this);
}
}
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