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.math.geometry; import java.io.Serializable; import org.apache.commons.math.MathRuntimeException; import org.apache.commons.math.exception.util.LocalizedFormats; import org.apache.commons.math.util.MathUtils; import org.apache.commons.math.util.FastMath; /** * This class implements vectors in a three-dimensional space. * <p>Instance of this class are guaranteed to be immutable.</p> * @version $Revision: 990655 $ $Date: 2010-08-29 23:49:40 +0200 (dim. 29 aot 2010) $ * @since 1.2 */ public class Vector3D implements Serializable { /** 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); /** Default format. */ private static final Vector3DFormat DEFAULT_FORMAT = Vector3DFormat.getInstance(); /** Serializable version identifier. */ private static final long serialVersionUID = 5133268763396045979L; /** 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 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 = a1 * u1.x + a2 * u2.x; this.y = a1 * u1.y + a2 * u2.y; this.z = 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 = a1 * u1.x + a2 * u2.x + a3 * u3.x; this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y; this.z = 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 = a1 * u1.x + a2 * u2.x + a3 * u3.x + a4 * u4.x; this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y + a4 * u4.y; this.z = 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 L<sub>1</sub> norm for the vector. * @return L<sub>1</sub> norm for the vector */ public double getNorm1() { return FastMath.abs(x) + FastMath.abs(y) + FastMath.abs(z); } /** Get the L<sub>2</sub> norm for the vector. * @return euclidian norm for the vector */ public double getNorm() { return FastMath.sqrt(x * x + y * y + z * z); } /** Get the square of the norm for the vector. * @return square of the euclidian norm for the vector */ public double getNormSq() { return x * x + y * y + z * z; } /** Get the L<sub>∞</sub> norm for the vector. * @return L<sub>∞</sub> norm for the vector */ 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()); } /** Add a vector to the instance. * @param v vector to add * @return a new vector */ public Vector3D add(Vector3D v) { return new Vector3D(x + v.x, y + v.y, z + v.z); } /** 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 Vector3D add(double factor, Vector3D v) { return new Vector3D(x + factor * v.x, y + factor * v.y, z + factor * v.z); } /** Subtract a vector from the instance. * @param v vector to subtract * @return a new vector */ public Vector3D subtract(Vector3D v) { return new Vector3D(x - v.x, y - v.y, z - v.z); } /** 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 Vector3D subtract(double factor, Vector3D v) { return new Vector3D(x - factor * v.x, y - factor * v.y, z - factor * v.z); } /** Get a normalized vector aligned with the instance. * @return a new normalized vector * @exception ArithmeticException if the norm is zero */ public Vector3D normalize() { double s = getNorm(); if (s == 0) { throw MathRuntimeException .createArithmeticException(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 ArithmeticException if the norm of the instance is null */ public Vector3D orthogonal() { double threshold = 0.6 * getNorm(); if (threshold == 0) { throw MathRuntimeException.createArithmeticException(LocalizedFormats.ZERO_NORM); } if ((x >= -threshold) && (x <= threshold)) { double inverse = 1 / FastMath.sqrt(y * y + z * z); return new Vector3D(0, inverse * z, -inverse * y); } else if ((y >= -threshold) && (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 ArithmeticException if either vector has a null norm */ public static double angle(Vector3D v1, Vector3D v2) { double normProduct = v1.getNorm() * v2.getNorm(); if (normProduct == 0) { throw MathRuntimeException.createArithmeticException(LocalizedFormats.ZERO_NORM); } double dot = dotProduct(v1, 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); } /** Get the opposite of the instance. * @return a new vector which is opposite to the instance */ public Vector3D negate() { return new Vector3D(-x, -y, -z); } /** Multiply the instance by a scalar * @param a scalar * @return a new vector */ public Vector3D scalarMultiply(double a) { return new Vector3D(a * x, a * y, a * z); } /** * 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) || Double.isNaN(y) || Double.isNaN(z); } /** * 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) || 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 8; } return 31 * (23 * MathUtils.hash(x) + 19 * MathUtils.hash(y) + MathUtils.hash(z)); } /** 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.x * v2.x + v1.y * v2.y + v1.z * v2.z; } /** 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(Vector3D v1, Vector3D v2) { return new Vector3D(v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x * v2.y - v1.y * 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 * @return the distance between v1 and v2 according to the L<sub>1</sub> norm */ public static double distance1(Vector3D v1, Vector3D v2) { final double dx = FastMath.abs(v2.x - v1.x); final double dy = FastMath.abs(v2.y - v1.y); final double dz = FastMath.abs(v2.z - v1.z); return dx + dy + dz; } /** 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) { final double dx = v2.x - v1.x; final double dy = v2.y - v1.y; final double dz = v2.z - v1.z; return FastMath.sqrt(dx * dx + dy * dy + dz * dz); } /** 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) { final double dx = FastMath.abs(v2.x - v1.x); final double dy = FastMath.abs(v2.y - v1.y); final double dz = FastMath.abs(v2.z - v1.z); return FastMath.max(FastMath.max(dx, dy), dz); } /** 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) { final double dx = v2.x - v1.x; final double dy = v2.y - v1.y; final double dz = v2.z - v1.z; return dx * dx + dy * dy + dz * dz; } /** Get a string representation of this vector. * @return a string representation of this vector */ @Override public String toString() { return DEFAULT_FORMAT.format(this); } }