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diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3D.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3D.java new file mode 100644 index 0000000..0bd04e5 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/FieldVector3D.java @@ -0,0 +1,1185 @@ +/* + * 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()); + } + +} |