| /* |
| * 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. |
| */ |
| |
| /** |
| * This is the top-level package for Euclidean geometry components. |
| * |
| * <h2>Definition</h2> |
| * <p> |
| * Euclidean space is the space commonly thought of when people think of |
| * geometry. It corresponds with the common notion of "flat" space or the space |
| * that we usually experience in the physical world. Mathematically, Euclidean |
| * space is an <a href="https://en.wikipedia.org/wiki/Affine_space">affine |
| * space</a>, meaning that it consists of points and displacement vectors |
| * representing translations between points. Distances between points are given |
| * by the formula <code>√(A - B)<sup>2</sup></code>, which is also known |
| * as the <em>Euclidean norm</em>. |
| * </p> |
| * |
| * <h2>Points and Vectors</h2> |
| * <p> |
| * As alluded to above, points and vectors are separate, distinct entities: |
| * points represent locations in a space and vectors represent displacements. |
| * This difference is the reason that commons-geometry has separate |
| * {@link org.apache.commons.geometry.core.Point Point} and |
| * {@link org.apache.commons.geometry.core.Vector Vector} interfaces. However, |
| * in the case of Euclidean space, the data structures used for points and |
| * vectors are identical and there is overlap in the methods needed for each |
| * type. Creating separate classes for Euclidean points and vectors therefore |
| * means a large amount of very similar or exactly duplicated code in order to |
| * maintain mathematical purity. This is not desirable, so a compromise position |
| * has been taken: there is a single class for each dimension that implements |
| * both {@link org.apache.commons.geometry.core.Point Point} <em>and</em> |
| * {@link org.apache.commons.geometry.core.Vector Vector}. These classes are |
| * named <code>Vector?D</code> to reflect the fact that they support the full |
| * range of vector operations. It is up to users of the library to make the |
| * correct distinctions between instances that represent points and those that |
| * represent displacements. This approach is commonly used in other geometric |
| * libraries as well, such as the |
| * <a href="https://www.khronos.org/opengl/wiki/OpenGL_Shading_Language">OpenGL |
| * Shading Language (GLSL)</a>, <a href= |
| * "https://casual-effects.com/g3d/G3D10/G3D-base.lib/include/G3D-base/Vector3.h">G3D</a>, |
| * and <a href= |
| * "https://threejs.org/docs/index.html#api/en/math/Vector3">Three.js</a>. |
| * </p> |
| * |
| * <h2>Coordinate Systems</h2> |
| * <p> |
| * In general, geometric concepts are independent of the coordinate system |
| * used to represent them. For example, in 2-dimensional Euclidean space, the |
| * fact that two points may be subtracted to yield a displacement vector holds |
| * true regardless of whether the points are represented using Cartesian coordinates |
| * or polar coordinates. From this point of view, all coordinate systems can |
| * be considered equal. However, this library does <em>not</em> treat all systems |
| * equal. In order to keep the API lightweight and simple, all coordinates are |
| * assumed to be |
| * <a href="https://en.wikipedia.org/wiki/Cartesian_coordinate_system">Cartesian</a> |
| * unless explicitly noted otherwise. |
| * </p> |
| * |
| * @see <a href="https://en.wikipedia.org/wiki/Euclidean_space">Euclidean |
| * Space</a> |
| */ |
| package org.apache.commons.geometry.euclidean; |
