Java tutorial
package elements; /* * 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 peasy.org.apache.commons.math.geometry; import java.io.Serializable; /** * This class implements vectors in a three-dimensional space. * <p>Instance of this class are guaranteed to be immutable.</p> * @version $Revision: 627998 $ $Date: 2008-02-15 03:24:50 -0700 (Fri, 15 Feb 2008) $ * @since 1.2 */ public class Vector3D implements Serializable { /** First canonical vector (coordinates: 1, 0, 0). */ public static final Vector3D plusI = new Vector3D(1, 0, 0); /** Opposite of the first canonical vector (coordinates: -1, 0, 0). */ public static final Vector3D minusI = new Vector3D(-1, 0, 0); /** Second canonical vector (coordinates: 0, 1, 0). */ public static final Vector3D plusJ = new Vector3D(0, 1, 0); /** Opposite of the second canonical vector (coordinates: 0, -1, 0). */ public static final Vector3D minusJ = new Vector3D(0, -1, 0); /** Third canonical vector (coordinates: 0, 0, 1). */ public static final Vector3D plusK = new Vector3D(0, 0, 1); /** Opposite of the third canonical vector (coordinates: 0, 0, -1). */ public static final Vector3D minusK = new Vector3D(0, 0, -1); /** Null vector (coordinates: 0, 0, 0). */ public static final Vector3D zero = new Vector3D(0, 0, 0); /** Simple constructor. * Build a null vector. */ public Vector3D() { x = 0; y = 0; z = 0; } /** 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 = Math.cos(delta); this.x = Math.cos(alpha) * cosDelta; this.y = Math.sin(alpha) * cosDelta; this.z = Math.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 norm for the vector. * @return euclidian norm for the vector */ //get magnitude public double getNorm() { return Math.sqrt(x * x + y * y + z * 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 Math.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 Math.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); } public void addToThis(float x, float y, float z) { // this.x+=x; // this.y+=y; // this.z+=z; } public Vector3D div(float n) { return new Vector3D(x / n, y / n, z / n); } /** 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 new ArithmeticException("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 = 0.1 * getNorm(); if (threshold == 0) { throw new ArithmeticException("null norm"); } //if ((x >= -threshold) && (x <= threshold)) { // double inverse = 1 / Math.sqrt(y * y + z * z); // return new Vector3D(0, inverse * z, -inverse * y); // } // else if ((y >= -threshold) && (y <= threshold)) { // double inverse = 1 / Math.sqrt(x * x + z * z); // return new Vector3D(-inverse * z, 0, inverse * x); // } double inverse = 1 / Math.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 allow 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 new ArithmeticException("null 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 Math.asin(v3.getNorm() / normProduct); } return Math.PI - Math.asin(v3.getNorm() / normProduct); } // the vectors are sufficiently separated to use the cosine return Math.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); } /** 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); } /** Abscissa. */ private final double x; /** Ordinate. */ private final double y; /** Height. */ private final double z; /** Serializable version identifier */ private static final long serialVersionUID = -5721105387745193385L; }