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Diffstat (limited to 'src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Vector3D.java')
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diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Vector3D.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Vector3D.java new file mode 100644 index 0000000..3eaea3a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Vector3D.java @@ -0,0 +1,588 @@ +/* + * 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.exception.DimensionMismatchException; +import org.apache.commons.math3.exception.MathArithmeticException; +import org.apache.commons.math3.exception.util.LocalizedFormats; +import org.apache.commons.math3.geometry.Point; +import org.apache.commons.math3.geometry.Space; +import org.apache.commons.math3.geometry.Vector; +import org.apache.commons.math3.util.FastMath; +import org.apache.commons.math3.util.MathArrays; +import org.apache.commons.math3.util.MathUtils; + +/** + * This class implements vectors in a three-dimensional space. + * <p>Instance of this class are guaranteed to be immutable.</p> + * @since 1.2 + */ +public class Vector3D implements Serializable, Vector<Euclidean3D> { + + /** Null vector (coordinates: 0, 0, 0). */ + public static final Vector3D ZERO = new Vector3D(0, 0, 0); + + /** First canonical vector (coordinates: 1, 0, 0). */ + public static final Vector3D PLUS_I = new Vector3D(1, 0, 0); + + /** Opposite of the first canonical vector (coordinates: -1, 0, 0). */ + public static final Vector3D MINUS_I = new Vector3D(-1, 0, 0); + + /** Second canonical vector (coordinates: 0, 1, 0). */ + public static final Vector3D PLUS_J = new Vector3D(0, 1, 0); + + /** Opposite of the second canonical vector (coordinates: 0, -1, 0). */ + public static final Vector3D MINUS_J = new Vector3D(0, -1, 0); + + /** Third canonical vector (coordinates: 0, 0, 1). */ + public static final Vector3D PLUS_K = new Vector3D(0, 0, 1); + + /** Opposite of the third canonical vector (coordinates: 0, 0, -1). */ + public static final Vector3D MINUS_K = new Vector3D(0, 0, -1); + + // CHECKSTYLE: stop ConstantName + /** A vector with all coordinates set to NaN. */ + public static final Vector3D NaN = new Vector3D(Double.NaN, Double.NaN, Double.NaN); + // CHECKSTYLE: resume ConstantName + + /** A vector with all coordinates set to positive infinity. */ + public static final Vector3D POSITIVE_INFINITY = + new Vector3D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY); + + /** A vector with all coordinates set to negative infinity. */ + public static final Vector3D NEGATIVE_INFINITY = + new Vector3D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY); + + /** Serializable version identifier. */ + private static final long serialVersionUID = 1313493323784566947L; + + /** Abscissa. */ + private final double x; + + /** Ordinate. */ + private final double y; + + /** Height. */ + private final double z; + + /** Simple constructor. + * Build a vector from its coordinates + * @param x abscissa + * @param y ordinate + * @param z height + * @see #getX() + * @see #getY() + * @see #getZ() + */ + public Vector3D(double x, double y, double z) { + this.x = x; + this.y = y; + this.z = z; + } + + /** Simple constructor. + * Build a vector from its coordinates + * @param v coordinates array + * @exception DimensionMismatchException if array does not have 3 elements + * @see #toArray() + */ + public Vector3D(double[] v) throws DimensionMismatchException { + if (v.length != 3) { + throw new DimensionMismatchException(v.length, 3); + } + this.x = v[0]; + this.y = v[1]; + this.z = v[2]; + } + + /** Simple constructor. + * Build a vector from its azimuthal coordinates + * @param alpha azimuth (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 Vector3D(double alpha, double delta) { + double cosDelta = FastMath.cos(delta); + this.x = FastMath.cos(alpha) * cosDelta; + this.y = FastMath.sin(alpha) * cosDelta; + this.z = FastMath.sin(delta); + } + + /** Multiplicative constructor + * Build a vector from another one and a scale factor. + * The vector built will be a * u + * @param a scale factor + * @param u base (unscaled) vector + */ + public Vector3D(double a, Vector3D u) { + this.x = a * u.x; + this.y = a * u.y; + this.z = a * u.z; + } + + /** Linear constructor + * Build a vector from two other ones and corresponding scale factors. + * The vector built will be a1 * u1 + a2 * u2 + * @param a1 first scale factor + * @param u1 first base (unscaled) vector + * @param a2 second scale factor + * @param u2 second base (unscaled) vector + */ + public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2) { + this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x); + this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y); + this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z); + } + + /** Linear constructor + * Build a vector from three other ones and corresponding scale factors. + * The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + * @param a1 first scale factor + * @param u1 first base (unscaled) vector + * @param a2 second scale factor + * @param u2 second base (unscaled) vector + * @param a3 third scale factor + * @param u3 third base (unscaled) vector + */ + public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2, + double a3, Vector3D u3) { + this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x); + this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y); + this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z); + } + + /** Linear constructor + * Build a vector from four other ones and corresponding scale factors. + * The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4 + * @param a1 first scale factor + * @param u1 first base (unscaled) vector + * @param a2 second scale factor + * @param u2 second base (unscaled) vector + * @param a3 third scale factor + * @param u3 third base (unscaled) vector + * @param a4 fourth scale factor + * @param u4 fourth base (unscaled) vector + */ + public Vector3D(double a1, Vector3D u1, double a2, Vector3D u2, + double a3, Vector3D u3, double a4, Vector3D u4) { + this.x = MathArrays.linearCombination(a1, u1.x, a2, u2.x, a3, u3.x, a4, u4.x); + this.y = MathArrays.linearCombination(a1, u1.y, a2, u2.y, a3, u3.y, a4, u4.y); + this.z = MathArrays.linearCombination(a1, u1.z, a2, u2.z, a3, u3.z, a4, u4.z); + } + + /** Get the abscissa of the vector. + * @return abscissa of the vector + * @see #Vector3D(double, double, double) + */ + public double getX() { + return x; + } + + /** Get the ordinate of the vector. + * @return ordinate of the vector + * @see #Vector3D(double, double, double) + */ + public double getY() { + return y; + } + + /** Get the height of the vector. + * @return height of the vector + * @see #Vector3D(double, double, double) + */ + public double getZ() { + return z; + } + + /** Get the vector coordinates as a dimension 3 array. + * @return vector coordinates + * @see #Vector3D(double[]) + */ + public double[] toArray() { + return new double[] { x, y, z }; + } + + /** {@inheritDoc} */ + public Space getSpace() { + return Euclidean3D.getInstance(); + } + + /** {@inheritDoc} */ + public Vector3D getZero() { + return ZERO; + } + + /** {@inheritDoc} */ + public double getNorm1() { + return FastMath.abs(x) + FastMath.abs(y) + FastMath.abs(z); + } + + /** {@inheritDoc} */ + public double getNorm() { + // there are no cancellation problems here, so we use the straightforward formula + return FastMath.sqrt (x * x + y * y + z * z); + } + + /** {@inheritDoc} */ + public double getNormSq() { + // there are no cancellation problems here, so we use the straightforward formula + return x * x + y * y + z * z; + } + + /** {@inheritDoc} */ + public double getNormInf() { + return FastMath.max(FastMath.max(FastMath.abs(x), FastMath.abs(y)), FastMath.abs(z)); + } + + /** Get the azimuth of the vector. + * @return azimuth (α) of the vector, between -π and +π + * @see #Vector3D(double, double) + */ + public double getAlpha() { + return FastMath.atan2(y, x); + } + + /** Get the elevation of the vector. + * @return elevation (δ) of the vector, between -π/2 and +π/2 + * @see #Vector3D(double, double) + */ + public double getDelta() { + return FastMath.asin(z / getNorm()); + } + + /** {@inheritDoc} */ + public Vector3D add(final Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + return new Vector3D(x + v3.x, y + v3.y, z + v3.z); + } + + /** {@inheritDoc} */ + public Vector3D add(double factor, final Vector<Euclidean3D> v) { + return new Vector3D(1, this, factor, (Vector3D) v); + } + + /** {@inheritDoc} */ + public Vector3D subtract(final Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + return new Vector3D(x - v3.x, y - v3.y, z - v3.z); + } + + /** {@inheritDoc} */ + public Vector3D subtract(final double factor, final Vector<Euclidean3D> v) { + return new Vector3D(1, this, -factor, (Vector3D) v); + } + + /** {@inheritDoc} */ + public Vector3D normalize() throws MathArithmeticException { + double s = getNorm(); + if (s == 0) { + throw new MathArithmeticException(LocalizedFormats.CANNOT_NORMALIZE_A_ZERO_NORM_VECTOR); + } + return scalarMultiply(1 / s); + } + + /** Get a vector orthogonal to the instance. + * <p>There are an infinite number of normalized vectors orthogonal + * to the instance. This method picks up one of them almost + * arbitrarily. It is useful when one needs to compute a reference + * frame with one of the axes in a predefined direction. The + * following example shows how to build a frame having the k axis + * aligned with the known vector u : + * <pre><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 Vector3D orthogonal() throws MathArithmeticException { + + double threshold = 0.6 * getNorm(); + if (threshold == 0) { + throw new MathArithmeticException(LocalizedFormats.ZERO_NORM); + } + + if (FastMath.abs(x) <= threshold) { + double inverse = 1 / FastMath.sqrt(y * y + z * z); + return new Vector3D(0, inverse * z, -inverse * y); + } else if (FastMath.abs(y) <= threshold) { + double inverse = 1 / FastMath.sqrt(x * x + z * z); + return new Vector3D(-inverse * z, 0, inverse * x); + } + double inverse = 1 / FastMath.sqrt(x * x + y * y); + return new Vector3D(inverse * y, -inverse * x, 0); + + } + + /** Compute the angular separation between two vectors. + * <p>This method computes the angular separation between two + * vectors using the dot product for well separated vectors and the + * cross product for almost aligned vectors. This allows to have a + * good accuracy in all cases, even for vectors very close to each + * other.</p> + * @param v1 first vector + * @param v2 second vector + * @return angular separation between v1 and v2 + * @exception MathArithmeticException if either vector has a null norm + */ + public static double angle(Vector3D v1, Vector3D v2) throws MathArithmeticException { + + double normProduct = v1.getNorm() * v2.getNorm(); + if (normProduct == 0) { + throw new MathArithmeticException(LocalizedFormats.ZERO_NORM); + } + + double dot = v1.dotProduct(v2); + double threshold = normProduct * 0.9999; + if ((dot < -threshold) || (dot > threshold)) { + // the vectors are almost aligned, compute using the sine + Vector3D v3 = crossProduct(v1, v2); + if (dot >= 0) { + return FastMath.asin(v3.getNorm() / normProduct); + } + return FastMath.PI - FastMath.asin(v3.getNorm() / normProduct); + } + + // the vectors are sufficiently separated to use the cosine + return FastMath.acos(dot / normProduct); + + } + + /** {@inheritDoc} */ + public Vector3D negate() { + return new Vector3D(-x, -y, -z); + } + + /** {@inheritDoc} */ + public Vector3D scalarMultiply(double a) { + return new Vector3D(a * x, a * y, a * z); + } + + /** {@inheritDoc} */ + public boolean isNaN() { + return Double.isNaN(x) || Double.isNaN(y) || Double.isNaN(z); + } + + /** {@inheritDoc} */ + public boolean isInfinite() { + return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y) || Double.isInfinite(z)); + } + + /** + * Test for the equality of two 3D vectors. + * <p> + * If all coordinates of two 3D vectors are exactly the same, and none are + * <code>Double.NaN</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) coordinates of the + * 3D vector are equal to <code>Double.NaN</code>, the 3D vector is equal to + * {@link #NaN}. + * </p> + * + * @param other Object to test for equality to this + * @return true if two 3D vector objects are equal, false if + * object is null, not an instance of Vector3D, or + * not equal to this Vector3D instance + * + */ + @Override + public boolean equals(Object other) { + + if (this == other) { + return true; + } + + if (other instanceof Vector3D) { + final Vector3D rhs = (Vector3D)other; + if (rhs.isNaN()) { + return this.isNaN(); + } + + return (x == rhs.x) && (y == rhs.y) && (z == rhs.z); + } + return false; + } + + /** + * Get a hashCode for the 3D vector. + * <p> + * All NaN values have the same hash code.</p> + * + * @return a hash code value for this object + */ + @Override + public int hashCode() { + if (isNaN()) { + return 642; + } + return 643 * (164 * MathUtils.hash(x) + 3 * MathUtils.hash(y) + MathUtils.hash(z)); + } + + /** {@inheritDoc} + * <p> + * The implementation uses specific multiplication and addition + * algorithms to preserve accuracy and reduce cancellation effects. + * It should be very accurate even for nearly orthogonal vectors. + * </p> + * @see MathArrays#linearCombination(double, double, double, double, double, double) + */ + public double dotProduct(final Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + return MathArrays.linearCombination(x, v3.x, y, v3.y, z, v3.z); + } + + /** Compute the cross-product of the instance with another vector. + * @param v other vector + * @return the cross product this ^ v as a new Vector3D + */ + public Vector3D crossProduct(final Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + return new Vector3D(MathArrays.linearCombination(y, v3.z, -z, v3.y), + MathArrays.linearCombination(z, v3.x, -x, v3.z), + MathArrays.linearCombination(x, v3.y, -y, v3.x)); + } + + /** {@inheritDoc} */ + public double distance1(Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + final double dx = FastMath.abs(v3.x - x); + final double dy = FastMath.abs(v3.y - y); + final double dz = FastMath.abs(v3.z - z); + return dx + dy + dz; + } + + /** {@inheritDoc} */ + public double distance(Vector<Euclidean3D> v) { + return distance((Point<Euclidean3D>) v); + } + + /** {@inheritDoc} */ + public double distance(Point<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + final double dx = v3.x - x; + final double dy = v3.y - y; + final double dz = v3.z - z; + return FastMath.sqrt(dx * dx + dy * dy + dz * dz); + } + + /** {@inheritDoc} */ + public double distanceInf(Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + final double dx = FastMath.abs(v3.x - x); + final double dy = FastMath.abs(v3.y - y); + final double dz = FastMath.abs(v3.z - z); + return FastMath.max(FastMath.max(dx, dy), dz); + } + + /** {@inheritDoc} */ + public double distanceSq(Vector<Euclidean3D> v) { + final Vector3D v3 = (Vector3D) v; + final double dx = v3.x - x; + final double dy = v3.y - y; + final double dz = v3.z - z; + return dx * dx + dy * dy + dz * dz; + } + + /** Compute the dot-product of two vectors. + * @param v1 first vector + * @param v2 second vector + * @return the dot product v1.v2 + */ + public static double dotProduct(Vector3D v1, Vector3D v2) { + return v1.dotProduct(v2); + } + + /** Compute the cross-product of two vectors. + * @param v1 first vector + * @param v2 second vector + * @return the cross product v1 ^ v2 as a new Vector + */ + public static Vector3D crossProduct(final Vector3D v1, final Vector3D v2) { + return v1.crossProduct(v2); + } + + /** Compute the distance between two vectors according to the L<sub>1</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 + * @return the distance between v1 and v2 according to the L<sub>1</sub> norm + */ + public static double distance1(Vector3D v1, Vector3D v2) { + return v1.distance1(v2); + } + + /** Compute the distance between two vectors according to the L<sub>2</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 + * @return the distance between v1 and v2 according to the L<sub>2</sub> norm + */ + public static double distance(Vector3D v1, Vector3D v2) { + return v1.distance(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 + * @return the distance between v1 and v2 according to the L<sub>∞</sub> norm + */ + public static double distanceInf(Vector3D v1, Vector3D v2) { + return v1.distanceInf(v2); + } + + /** Compute the square of the distance between two vectors. + * <p>Calling this method is equivalent to calling: + * <code>v1.subtract(v2).getNormSq()</code> except that no intermediate + * vector is built</p> + * @param v1 first vector + * @param v2 second vector + * @return the square of the distance between v1 and v2 + */ + public static double distanceSq(Vector3D v1, Vector3D v2) { + return v1.distanceSq(v2); + } + + /** Get a string representation of this vector. + * @return a string representation of this vector + */ + @Override + public String toString() { + return Vector3DFormat.getInstance().format(this); + } + + /** {@inheritDoc} */ + public String toString(final NumberFormat format) { + return new Vector3DFormat(format).format(this); + } + +} |