/*
* 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.threed;
import java.io.Serializable;
import java.text.NumberFormat;
import org.apache.commons.math3.RealFieldElement;
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.util.FastMath;
import org.apache.commons.math3.util.MathArrays;
/**
* This class is a re-implementation of {@link Vector3D} using {@link RealFieldElement}.
* <p>Instance of this class are guaranteed to be immutable.</p>
* @param <T> the type of the field elements
* @since 3.2
*/
public class FieldVector3D<T extends RealFieldElement<T>> implements Serializable {
/** Serializable version identifier. */
private static final long serialVersionUID = 20130224L;
/** Abscissa. */
private final T x;
/** Ordinate. */
private final T y;
/** Height. */
private final T 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 FieldVector3D(final T x, final T y, final T 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 FieldVector3D(final T[] 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 (α) around Z
* (0 is +X, π/2 is +Y, π is -X and 3π/2 is -Y)
* @param delta elevation (δ) above (XY) plane, from -π/2 to +π/2
* @see #getAlpha()
* @see #getDelta()
*/
public FieldVector3D(final T alpha, final T delta) {
T cosDelta = delta.cos();
this.x = alpha.cos().multiply(cosDelta);
this.y = alpha.sin().multiply(cosDelta);
this.z = delta.sin();
}
/** 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 FieldVector3D(final T a, final FieldVector3D<T>u) {
this.x = a.multiply(u.x);
this.y = a.multiply(u.y);
this.z = a.multiply(u.z);
}
/** 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 FieldVector3D(final T a, final Vector3D u) {
this.x = a.multiply(u.getX());
this.y = a.multiply(u.getY());
this.z = a.multiply(u.getZ());
}
/** 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 FieldVector3D(final double a, final FieldVector3D<T> u) {
this.x = u.x.multiply(a);
this.y = u.y.multiply(a);
this.z = u.z.multiply(a);
}
/** 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 FieldVector3D(final T a1, final FieldVector3D<T> u1,
final T a2, final FieldVector3D<T> u2) {
final T prototype = a1;
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ());
}
/** 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 FieldVector3D(final T a1, final Vector3D u1,
final T a2, final Vector3D u2) {
final T prototype = a1;
this.x = prototype.linearCombination(u1.getX(), a1, u2.getX(), a2);
this.y = prototype.linearCombination(u1.getY(), a1, u2.getY(), a2);
this.z = prototype.linearCombination(u1.getZ(), a1, u2.getZ(), a2);
}
/** 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 FieldVector3D(final double a1, final FieldVector3D<T> u1,
final double a2, final FieldVector3D<T> u2) {
final T prototype = u1.getX();
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ());
}
/** 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 FieldVector3D(final T a1, final FieldVector3D<T> u1,
final T a2, final FieldVector3D<T> u2,
final T a3, final FieldVector3D<T> u3) {
final T prototype = a1;
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX(), a3, u3.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY(), a3, u3.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ(), a3, u3.getZ());
}
/** 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 FieldVector3D(final T a1, final Vector3D u1,
final T a2, final Vector3D u2,
final T a3, final Vector3D u3) {
final T prototype = a1;
this.x = prototype.linearCombination(u1.getX(), a1, u2.getX(), a2, u3.getX(), a3);
this.y = prototype.linearCombination(u1.getY(), a1, u2.getY(), a2, u3.getY(), a3);
this.z = prototype.linearCombination(u1.getZ(), a1, u2.getZ(), a2, u3.getZ(), a3);
}
/** 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 FieldVector3D(final double a1, final FieldVector3D<T> u1,
final double a2, final FieldVector3D<T> u2,
final double a3, final FieldVector3D<T> u3) {
final T prototype = u1.getX();
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX(), a3, u3.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY(), a3, u3.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ(), a3, u3.getZ());
}
/** 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 FieldVector3D(final T a1, final FieldVector3D<T> u1,
final T a2, final FieldVector3D<T> u2,
final T a3, final FieldVector3D<T> u3,
final T a4, final FieldVector3D<T> u4) {
final T prototype = a1;
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX(), a3, u3.getX(), a4, u4.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY(), a3, u3.getY(), a4, u4.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ(), a3, u3.getZ(), a4, u4.getZ());
}
/** 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 FieldVector3D(final T a1, final Vector3D u1,
final T a2, final Vector3D u2,
final T a3, final Vector3D u3,
final T a4, final Vector3D u4) {
final T prototype = a1;
this.x = prototype.linearCombination(u1.getX(), a1, u2.getX(), a2, u3.getX(), a3, u4.getX(), a4);
this.y = prototype.linearCombination(u1.getY(), a1, u2.getY(), a2, u3.getY(), a3, u4.getY(), a4);
this.z = prototype.linearCombination(u1.getZ(), a1, u2.getZ(), a2, u3.getZ(), a3, u4.getZ(), a4);
}
/** 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 FieldVector3D(final double a1, final FieldVector3D<T> u1,
final double a2, final FieldVector3D<T> u2,
final double a3, final FieldVector3D<T> u3,
final double a4, final FieldVector3D<T> u4) {
final T prototype = u1.getX();
this.x = prototype.linearCombination(a1, u1.getX(), a2, u2.getX(), a3, u3.getX(), a4, u4.getX());
this.y = prototype.linearCombination(a1, u1.getY(), a2, u2.getY(), a3, u3.getY(), a4, u4.getY());
this.z = prototype.linearCombination(a1, u1.getZ(), a2, u2.getZ(), a3, u3.getZ(), a4, u4.getZ());
}
/** Get the abscissa of the vector.
* @return abscissa of the vector
* @see #FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
*/
public T getX() {
return x;
}
/** Get the ordinate of the vector.
* @return ordinate of the vector
* @see #FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
*/
public T getY() {
return y;
}
/** Get the height of the vector.
* @return height of the vector
* @see #FieldVector3D(RealFieldElement, RealFieldElement, RealFieldElement)
*/
public T getZ() {
return z;
}
/** Get the vector coordinates as a dimension 3 array.
* @return vector coordinates
* @see #FieldVector3D(RealFieldElement[])
*/
public T[] toArray() {
final T[] array = MathArrays.buildArray(x.getField(), 3);
array[0] = x;
array[1] = y;
array[2] = z;
return array;
}
/** Convert to a constant vector without derivatives.
* @return a constant vector
*/
public Vector3D toVector3D() {
return new Vector3D(x.getReal(), y.getReal(), z.getReal());
}
/** Get the L<sub>1</sub> norm for the vector.
* @return L<sub>1</sub> norm for the vector
*/
public T getNorm1() {
return x.abs().add(y.abs()).add(z.abs());
}
/** Get the L<sub>2</sub> norm for the vector.
* @return Euclidean norm for the vector
*/
public T getNorm() {
// there are no cancellation problems here, so we use the straightforward formula
return x.multiply(x).add(y.multiply(y)).add(z.multiply(z)).sqrt();
}
/** Get the square of the norm for the vector.
* @return square of the Euclidean norm for the vector
*/
public T getNormSq() {
// there are no cancellation problems here, so we use the straightforward formula
return x.multiply(x).add(y.multiply(y)).add(z.multiply(z));
}
/** Get the L<sub>∞</sub> norm for the vector.
* @return L<sub>∞</sub> norm for the vector
*/
public T getNormInf() {
final T xAbs = x.abs();
final T yAbs = y.abs();
final T zAbs = z.abs();
if (xAbs.getReal() <= yAbs.getReal()) {
if (yAbs.getReal() <= zAbs.getReal()) {
return zAbs;
} else {
return yAbs;
}
} else {
if (xAbs.getReal() <= zAbs.getReal()) {
return zAbs;
} else {
return xAbs;
}
}
}
/** Get the azimuth of the vector.
* @return azimuth (α) of the vector, between -π and +π
* @see #FieldVector3D(RealFieldElement, RealFieldElement)
*/
public T getAlpha() {
return y.atan2(x);
}
/** Get the elevation of the vector.
* @return elevation (δ) of the vector, between -π/2 and +π/2
* @see #FieldVector3D(RealFieldElement, RealFieldElement)
*/
public T getDelta() {
return z.divide(getNorm()).asin();
}
/** Add a vector to the instance.
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final FieldVector3D<T> v) {
return new FieldVector3D<T>(x.add(v.x), y.add(v.y), z.add(v.z));
}
/** Add a vector to the instance.
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final Vector3D v) {
return new FieldVector3D<T>(x.add(v.getX()), y.add(v.getY()), z.add(v.getZ()));
}
/** Add a scaled vector to the instance.
* @param factor scale factor to apply to v before adding it
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final T factor, final FieldVector3D<T> v) {
return new FieldVector3D<T>(x.getField().getOne(), this, factor, v);
}
/** Add a scaled vector to the instance.
* @param factor scale factor to apply to v before adding it
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final T factor, final Vector3D v) {
return new FieldVector3D<T>(x.add(factor.multiply(v.getX())),
y.add(factor.multiply(v.getY())),
z.add(factor.multiply(v.getZ())));
}
/** Add a scaled vector to the instance.
* @param factor scale factor to apply to v before adding it
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final double factor, final FieldVector3D<T> v) {
return new FieldVector3D<T>(1.0, this, factor, v);
}
/** Add a scaled vector to the instance.
* @param factor scale factor to apply to v before adding it
* @param v vector to add
* @return a new vector
*/
public FieldVector3D<T> add(final double factor, final Vector3D v) {
return new FieldVector3D<T>(x.add(factor * v.getX()),
y.add(factor * v.getY()),
z.add(factor * v.getZ()));
}
/** Subtract a vector from the instance.
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final FieldVector3D<T> v) {
return new FieldVector3D<T>(x.subtract(v.x), y.subtract(v.y), z.subtract(v.z));
}
/** Subtract a vector from the instance.
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final Vector3D v) {
return new FieldVector3D<T>(x.subtract(v.getX()), y.subtract(v.getY()), z.subtract(v.getZ()));
}
/** Subtract a scaled vector from the instance.
* @param factor scale factor to apply to v before subtracting it
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final T factor, final FieldVector3D<T> v) {
return new FieldVector3D<T>(x.getField().getOne(), this, factor.negate(), v);
}
/** Subtract a scaled vector from the instance.
* @param factor scale factor to apply to v before subtracting it
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final T factor, final Vector3D v) {
return new FieldVector3D<T>(x.subtract(factor.multiply(v.getX())),
y.subtract(factor.multiply(v.getY())),
z.subtract(factor.multiply(v.getZ())));
}
/** Subtract a scaled vector from the instance.
* @param factor scale factor to apply to v before subtracting it
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final double factor, final FieldVector3D<T> v) {
return new FieldVector3D<T>(1.0, this, -factor, v);
}
/** Subtract a scaled vector from the instance.
* @param factor scale factor to apply to v before subtracting it
* @param v vector to subtract
* @return a new vector
*/
public FieldVector3D<T> subtract(final double factor, final Vector3D v) {
return new FieldVector3D<T>(x.subtract(factor * v.getX()),
y.subtract(factor * v.getY()),
z.subtract(factor * v.getZ()));
}
/** Get a normalized vector aligned with the instance.
* @return a new normalized vector
* @exception MathArithmeticException if the norm is zero
*/
public FieldVector3D<T> normalize() throws MathArithmeticException {
final T s = getNorm();
if (s.getReal() == 0) {
throw new MathArithmeticException(LocalizedFormats.CANNOT_NORMALIZE_A_ZERO_NORM_VECTOR);
}
return scalarMultiply(s.reciprocal());
}
/** 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><code>
* Vector3D k = u.normalize();
* Vector3D i = k.orthogonal();
* Vector3D j = Vector3D.crossProduct(k, i);
* </code></pre></p>
* @return a new normalized vector orthogonal to the instance
* @exception MathArithmeticException if the norm of the instance is null
*/
public FieldVector3D<T> orthogonal() throws MathArithmeticException {
final double threshold = 0.6 * getNorm().getReal();
if (threshold == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_NORM);
}
if (FastMath.abs(x.getReal()) <= threshold) {
final T inverse = y.multiply(y).add(z.multiply(z)).sqrt().reciprocal();
return new FieldVector3D<T>(inverse.getField().getZero(), inverse.multiply(z), inverse.multiply(y).negate());
} else if (FastMath.abs(y.getReal()) <= threshold) {
final T inverse = x.multiply(x).add(z.multiply(z)).sqrt().reciprocal();
return new FieldVector3D<T>(inverse.multiply(z).negate(), inverse.getField().getZero(), inverse.multiply(x));
} else {
final T inverse = x.multiply(x).add(y.multiply(y)).sqrt().reciprocal();
return new FieldVector3D<T>(inverse.multiply(y), inverse.multiply(x).negate(), inverse.getField().getZero());
}
}
/** 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
* @param <T> the type of the field elements
* @return angular separation between v1 and v2
* @exception MathArithmeticException if either vector has a null norm
*/
public static <T extends RealFieldElement<T>> T angle(final FieldVector3D<T> v1, final FieldVector3D<T> v2)
throws MathArithmeticException {
final T normProduct = v1.getNorm().multiply(v2.getNorm());
if (normProduct.getReal() == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_NORM);
}
final T dot = dotProduct(v1, v2);
final double threshold = normProduct.getReal() * 0.9999;
if ((dot.getReal() < -threshold) || (dot.getReal() > threshold)) {
// the vectors are almost aligned, compute using the sine
FieldVector3D<T> v3 = crossProduct(v1, v2);
if (dot.getReal() >= 0) {
return v3.getNorm().divide(normProduct).asin();
}
return v3.getNorm().divide(normProduct).asin().subtract(FastMath.PI).negate();
}
// the vectors are sufficiently separated to use the cosine
return dot.divide(normProduct).acos();
}
/** 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
* @param <T> the type of the field elements
* @return angular separation between v1 and v2
* @exception MathArithmeticException if either vector has a null norm
*/
public static <T extends RealFieldElement<T>> T angle(final FieldVector3D<T> v1, final Vector3D v2)
throws MathArithmeticException {
final T normProduct = v1.getNorm().multiply(v2.getNorm());
if (normProduct.getReal() == 0) {
throw new MathArithmeticException(LocalizedFormats.ZERO_NORM);
}
final T dot = dotProduct(v1, v2);
final double threshold = normProduct.getReal() * 0.9999;
if ((dot.getReal() < -threshold) || (dot.getReal() > threshold)) {
// the vectors are almost aligned, compute using the sine
FieldVector3D<T> v3 = crossProduct(v1, v2);
if (dot.getReal() >= 0) {
return v3.getNorm().divide(normProduct).asin();
}
return v3.getNorm().divide(normProduct).asin().subtract(FastMath.PI).negate();
}
// the vectors are sufficiently separated to use the cosine
return dot.divide(normProduct).acos();
}
/** 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
* @param <T> the type of the field elements
* @return angular separation between v1 and v2
* @exception MathArithmeticException if either vector has a null norm
*/
public static <T extends RealFieldElement<T>> T angle(final Vector3D v1, final FieldVector3D<T> v2)
throws MathArithmeticException {
return angle(v2, v1);
}
/** Get the opposite of the instance.
* @return a new vector which is opposite to the instance
*/
public FieldVector3D<T> negate() {
return new FieldVector3D<T>(x.negate(), y.negate(), z.negate());
}
/** Multiply the instance by a scalar.
* @param a scalar
* @return a new vector
*/
public FieldVector3D<T> scalarMultiply(final T a) {
return new FieldVector3D<T>(x.multiply(a), y.multiply(a), z.multiply(a));
}
/** Multiply the instance by a scalar.
* @param a scalar
* @return a new vector
*/
public FieldVector3D<T> scalarMultiply(final double a) {
return new FieldVector3D<T>(x.multiply(a), y.multiply(a), z.multiply(a));
}
/**
* Returns true if any coordinate of this vector is NaN; false otherwise
* @return true if any coordinate of this vector is NaN; false otherwise
*/
public boolean isNaN() {
return Double.isNaN(x.getReal()) || Double.isNaN(y.getReal()) || Double.isNaN(z.getReal());
}
/**
* Returns true if any coordinate of this vector is infinite and none are NaN;
* false otherwise
* @return true if any coordinate of this vector is infinite and none are NaN;
* false otherwise
*/
public boolean isInfinite() {
return !isNaN() && (Double.isInfinite(x.getReal()) || Double.isInfinite(y.getReal()) || Double.isInfinite(z.getReal()));
}
/**
* Test for the equality of two 3D vectors.
* <p>
* If all coordinates of two 3D vectors are exactly the same, and none of their
* {@link RealFieldElement#getReal() real part} are <code>NaN</code>, the
* two 3D vectors are considered to be equal.
* </p>
* <p>
* <code>NaN</code> coordinates are considered to affect globally the vector
* and be equals to each other - i.e, if either (or all) real part of the
* coordinates of the 3D vector are <code>NaN</code>, the 3D vector is <code>NaN</code>.
* </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 FieldVector3D) {
@SuppressWarnings("unchecked")
final FieldVector3D<T> rhs = (FieldVector3D<T>) other;
if (rhs.isNaN()) {
return this.isNaN();
}
return x.equals(rhs.x) && y.equals(rhs.y) && z.equals(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 409;
}
return 311 * (107 * x.hashCode() + 83 * y.hashCode() + z.hashCode());
}
/** Compute the dot-product of the instance and another vector.
* <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)
* @param v second vector
* @return the dot product this.v
*/
public T dotProduct(final FieldVector3D<T> v) {
return x.linearCombination(x, v.x, y, v.y, z, v.z);
}
/** Compute the dot-product of the instance and another vector.
* <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)
* @param v second vector
* @return the dot product this.v
*/
public T dotProduct(final Vector3D v) {
return x.linearCombination(v.getX(), x, v.getY(), y, v.getZ(), 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 FieldVector3D<T> crossProduct(final FieldVector3D<T> v) {
return new FieldVector3D<T>(x.linearCombination(y, v.z, z.negate(), v.y),
y.linearCombination(z, v.x, x.negate(), v.z),
z.linearCombination(x, v.y, y.negate(), v.x));
}
/** 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 FieldVector3D<T> crossProduct(final Vector3D v) {
return new FieldVector3D<T>(x.linearCombination(v.getZ(), y, -v.getY(), z),
y.linearCombination(v.getX(), z, -v.getZ(), x),
z.linearCombination(v.getY(), x, -v.getX(), y));
}
/** Compute the distance between the instance and another vector according to the L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>1</sub> norm
*/
public T distance1(final FieldVector3D<T> v) {
final T dx = v.x.subtract(x).abs();
final T dy = v.y.subtract(y).abs();
final T dz = v.z.subtract(z).abs();
return dx.add(dy).add(dz);
}
/** Compute the distance between the instance and another vector according to the L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>1</sub> norm
*/
public T distance1(final Vector3D v) {
final T dx = x.subtract(v.getX()).abs();
final T dy = y.subtract(v.getY()).abs();
final T dz = z.subtract(v.getZ()).abs();
return dx.add(dy).add(dz);
}
/** Compute the distance between the instance and another vector according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNorm()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>2</sub> norm
*/
public T distance(final FieldVector3D<T> v) {
final T dx = v.x.subtract(x);
final T dy = v.y.subtract(y);
final T dz = v.z.subtract(z);
return dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz)).sqrt();
}
/** Compute the distance between the instance and another vector according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNorm()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>2</sub> norm
*/
public T distance(final Vector3D v) {
final T dx = x.subtract(v.getX());
final T dy = y.subtract(v.getY());
final T dz = z.subtract(v.getZ());
return dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz)).sqrt();
}
/** Compute the distance between the instance and another vector according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>∞</sub> norm
*/
public T distanceInf(final FieldVector3D<T> v) {
final T dx = v.x.subtract(x).abs();
final T dy = v.y.subtract(y).abs();
final T dz = v.z.subtract(z).abs();
if (dx.getReal() <= dy.getReal()) {
if (dy.getReal() <= dz.getReal()) {
return dz;
} else {
return dy;
}
} else {
if (dx.getReal() <= dz.getReal()) {
return dz;
} else {
return dx;
}
}
}
/** Compute the distance between the instance and another vector according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the distance between the instance and p according to the L<sub>∞</sub> norm
*/
public T distanceInf(final Vector3D v) {
final T dx = x.subtract(v.getX()).abs();
final T dy = y.subtract(v.getY()).abs();
final T dz = z.subtract(v.getZ()).abs();
if (dx.getReal() <= dy.getReal()) {
if (dy.getReal() <= dz.getReal()) {
return dz;
} else {
return dy;
}
} else {
if (dx.getReal() <= dz.getReal()) {
return dz;
} else {
return dx;
}
}
}
/** Compute the square of the distance between the instance and another vector.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNormSq()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the square of the distance between the instance and p
*/
public T distanceSq(final FieldVector3D<T> v) {
final T dx = v.x.subtract(x);
final T dy = v.y.subtract(y);
final T dz = v.z.subtract(z);
return dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz));
}
/** Compute the square of the distance between the instance and another vector.
* <p>Calling this method is equivalent to calling:
* <code>q.subtract(p).getNormSq()</code> except that no intermediate
* vector is built</p>
* @param v second vector
* @return the square of the distance between the instance and p
*/
public T distanceSq(final Vector3D v) {
final T dx = x.subtract(v.getX());
final T dy = y.subtract(v.getY());
final T dz = z.subtract(v.getZ());
return dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz));
}
/** Compute the dot-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the dot product v1.v2
*/
public static <T extends RealFieldElement<T>> T dotProduct(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.dotProduct(v2);
}
/** Compute the dot-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the dot product v1.v2
*/
public static <T extends RealFieldElement<T>> T dotProduct(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.dotProduct(v2);
}
/** Compute the dot-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the dot product v1.v2
*/
public static <T extends RealFieldElement<T>> T dotProduct(final Vector3D v1,
final FieldVector3D<T> v2) {
return v2.dotProduct(v1);
}
/** Compute the cross-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the cross product v1 ^ v2 as a new Vector
*/
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.crossProduct(v2);
}
/** Compute the cross-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the cross product v1 ^ v2 as a new Vector
*/
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.crossProduct(v2);
}
/** Compute the cross-product of two vectors.
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the cross product v1 ^ v2 as a new Vector
*/
public static <T extends RealFieldElement<T>> FieldVector3D<T> crossProduct(final Vector3D v1,
final FieldVector3D<T> v2) {
return new FieldVector3D<T>(v2.x.linearCombination(v1.getY(), v2.z, -v1.getZ(), v2.y),
v2.y.linearCombination(v1.getZ(), v2.x, -v1.getX(), v2.z),
v2.z.linearCombination(v1.getX(), v2.y, -v1.getY(), v2.x));
}
/** Compute the distance between two vectors according to the L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>1</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance1(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.distance1(v2);
}
/** Compute the distance between two vectors according to the L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>1</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance1(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.distance1(v2);
}
/** Compute the distance between two vectors according to the L<sub>1</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm1()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>1</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance1(final Vector3D v1,
final FieldVector3D<T> v2) {
return v2.distance1(v1);
}
/** Compute the distance between two vectors according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>2</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.distance(v2);
}
/** Compute the distance between two vectors according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>2</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.distance(v2);
}
/** Compute the distance between two vectors according to the L<sub>2</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNorm()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>2</sub> norm
*/
public static <T extends RealFieldElement<T>> T distance(final Vector3D v1,
final FieldVector3D<T> v2) {
return v2.distance(v1);
}
/** Compute the distance between two vectors according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>∞</sub> norm
*/
public static <T extends RealFieldElement<T>> T distanceInf(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.distanceInf(v2);
}
/** Compute the distance between two vectors according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>∞</sub> norm
*/
public static <T extends RealFieldElement<T>> T distanceInf(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.distanceInf(v2);
}
/** Compute the distance between two vectors according to the L<sub>∞</sub> norm.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormInf()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the distance between v1 and v2 according to the L<sub>∞</sub> norm
*/
public static <T extends RealFieldElement<T>> T distanceInf(final Vector3D v1,
final FieldVector3D<T> v2) {
return v2.distanceInf(v1);
}
/** Compute the square of the distance between two vectors.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormSq()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the square of the distance between v1 and v2
*/
public static <T extends RealFieldElement<T>> T distanceSq(final FieldVector3D<T> v1,
final FieldVector3D<T> v2) {
return v1.distanceSq(v2);
}
/** Compute the square of the distance between two vectors.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormSq()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the square of the distance between v1 and v2
*/
public static <T extends RealFieldElement<T>> T distanceSq(final FieldVector3D<T> v1,
final Vector3D v2) {
return v1.distanceSq(v2);
}
/** Compute the square of the distance between two vectors.
* <p>Calling this method is equivalent to calling:
* <code>v1.subtract(v2).getNormSq()</code> except that no intermediate
* vector is built</p>
* @param v1 first vector
* @param v2 second vector
* @param <T> the type of the field elements
* @return the square of the distance between v1 and v2
*/
public static <T extends RealFieldElement<T>> T distanceSq(final Vector3D v1,
final FieldVector3D<T> v2) {
return v2.distanceSq(v1);
}
/** Get a string representation of this vector.
* @return a string representation of this vector
*/
@Override
public String toString() {
return Vector3DFormat.getInstance().format(toVector3D());
}
/** Get a string representation of this vector.
* @param format the custom format for components
* @return a string representation of this vector
*/
public String toString(final NumberFormat format) {
return new Vector3DFormat(format).format(toVector3D());
}
}