Java tutorial
/* * 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()); } }