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<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="API documentation for the Rust `VectorSpace` trait in crate `cgmath`."><meta name="keywords" content="rust, rustlang, rust-lang, VectorSpace"><title>cgmath::prelude::VectorSpace - Rust</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><script src="../../storage.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="../../favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">☰</div><a href='../../cgmath/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait VectorSpace</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#associated-types">Associated Types</a><div class="sidebar-links"><a href="#associatedtype.Scalar">Scalar</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>cgmath</a>::<wbr><a href='index.html'>prelude</a></p><script>window.sidebarCurrent = {name: 'VectorSpace', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>−</span>]</a></span><a class='srclink' href='../../src/cgmath/structure.rs.html#164-179' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>cgmath</a>::<wbr><a href='index.html'>prelude</a>::<wbr><a class="trait" href=''>VectorSpace</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait VectorSpace: <a class="trait" href="https://doc.rust-lang.org/nightly/core/marker/trait.Copy.html" title="trait core::marker::Copy">Copy</a> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/clone/trait.Clone.html" title="trait core::clone::Clone">Clone</a> <span class="where fmt-newline">where<br> Self: <a class="trait" href="../../cgmath/prelude/trait.Zero.html" title="trait cgmath::prelude::Zero">Zero</a>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><Self, Output = Self>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a><Self, Output = Self>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/iter/traits/accum/trait.Sum.html" title="trait core::iter::traits::accum::Sum">Sum</a><Self>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self::<a class="type" href="../../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>, Output = Self>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a><Self::<a class="type" href="../../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>, Output = Self>,<br> Self: <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Rem.html" title="trait core::ops::arith::Rem">Rem</a><Self::<a class="type" href="../../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>, Output = Self>, </span>{
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type <a href='#associatedtype.Scalar' class="type">Scalar</a>: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a>;
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}</pre></div><div class='docblock'><p>Vectors that can be <a href="http://mathworld.wolfram.com/VectorAddition.html">added</a>
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together and <a href="https://en.wikipedia.org/wiki/Scalar_multiplication">multiplied</a>
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by scalars.</p>
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<p>Examples include vectors, matrices, and quaternions.</p>
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<h1 id="required-operators" class="section-header"><a href="#required-operators">Required operators</a></h1><h2 id="vector-addition" class="section-header"><a href="#vector-addition">Vector addition</a></h2>
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<p>Vectors can be added, subtracted, or negated via the following traits:</p>
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<ul>
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<li><code>Add<Output = Self></code></li>
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<li><code>Sub<Output = Self></code></li>
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<li><code>Neg<Output = Self></code></li>
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</ul>
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<div class="example-wrap"><pre class="rust rust-example-rendered">
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<span class="kw">use</span> <span class="ident">cgmath</span>::<span class="ident">Vector3</span>;
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<span class="kw">let</span> <span class="ident">velocity0</span> <span class="op">=</span> <span class="ident">Vector3</span>::<span class="ident">new</span>(<span class="number">1</span>, <span class="number">2</span>, <span class="number">0</span>);
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<span class="kw">let</span> <span class="ident">velocity1</span> <span class="op">=</span> <span class="ident">Vector3</span>::<span class="ident">new</span>(<span class="number">1</span>, <span class="number">1</span>, <span class="number">0</span>);
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<span class="kw">let</span> <span class="ident">total_velocity</span> <span class="op">=</span> <span class="ident">velocity0</span> <span class="op">+</span> <span class="ident">velocity1</span>;
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<span class="kw">let</span> <span class="ident">velocity_diff</span> <span class="op">=</span> <span class="ident">velocity1</span> <span class="op">-</span> <span class="ident">velocity0</span>;
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<span class="kw">let</span> <span class="ident">reversed_velocity0</span> <span class="op">=</span> <span class="op">-</span><span class="ident">velocity0</span>;</pre></div>
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<p>Vector spaces are also required to implement the additive identity trait,
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<code>Zero</code>. Adding this to another vector should have no effect:</p>
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<div class="example-wrap"><pre class="rust rust-example-rendered">
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<span class="kw">use</span> <span class="ident">cgmath</span>::<span class="ident">prelude</span>::<span class="kw-2">*</span>;
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<span class="kw">use</span> <span class="ident">cgmath</span>::<span class="ident">Vector2</span>;
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<span class="kw">let</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">Vector2</span>::<span class="ident">new</span>(<span class="number">1</span>, <span class="number">2</span>);
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<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">v</span> <span class="op">+</span> <span class="ident">Vector2</span>::<span class="ident">zero</span>(), <span class="ident">v</span>);</pre></div>
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<h2 id="scalar-multiplication" class="section-header"><a href="#scalar-multiplication">Scalar multiplication</a></h2>
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<p>Vectors can be multiplied or divided by their associated scalars via the
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following traits:</p>
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<ul>
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<li><code>Mul<Self::Scalar, Output = Self></code></li>
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<li><code>Div<Self::Scalar, Output = Self></code></li>
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<li><code>Rem<Self::Scalar, Output = Self></code></li>
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</ul>
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<div class="example-wrap"><pre class="rust rust-example-rendered">
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<span class="kw">use</span> <span class="ident">cgmath</span>::<span class="ident">Vector2</span>;
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<span class="kw">let</span> <span class="ident">translation</span> <span class="op">=</span> <span class="ident">Vector2</span>::<span class="ident">new</span>(<span class="number">3.0</span>, <span class="number">4.0</span>);
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<span class="kw">let</span> <span class="ident">scale_factor</span> <span class="op">=</span> <span class="number">2.0</span>;
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<span class="kw">let</span> <span class="ident">upscaled_translation</span> <span class="op">=</span> <span class="ident">translation</span> <span class="op">*</span> <span class="ident">scale_factor</span>;
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<span class="kw">let</span> <span class="ident">downscaled_translation</span> <span class="op">=</span> <span class="ident">translation</span> <span class="op">/</span> <span class="ident">scale_factor</span>;</pre></div>
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</div>
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<h2 id='associated-types' class='small-section-header'>Associated Types<a href='#associated-types' class='anchor'></a></h2><div class='methods'><h3 id='associatedtype.Scalar' class='method'><code id='Scalar.t'>type <a href='#associatedtype.Scalar' class="type">Scalar</a>: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a></code></h3><div class='docblock'><p>The associated scalar.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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<h2 id='implementors' class='small-section-header'>Implementors<a href='#implementors' class='anchor'></a></h2><div class='item-list' id='implementors-list'><h3 id='impl-VectorSpace' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Matrix2.html" title="struct cgmath::Matrix2">Matrix2</a><S></code><a href='#impl-VectorSpace' class='anchor'></a><a class='srclink' href='../../src/cgmath/matrix.rs.html#434-436' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-1' class="type"><code id='Scalar.t-1'>type <a href='#associatedtype.Scalar-1' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-1' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Matrix3.html" title="struct cgmath::Matrix3">Matrix3</a><S></code><a href='#impl-VectorSpace-1' class='anchor'></a><a class='srclink' href='../../src/cgmath/matrix.rs.html#438-440' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-2' class="type"><code id='Scalar.t-2'>type <a href='#associatedtype.Scalar-2' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-2' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Matrix4.html" title="struct cgmath::Matrix4">Matrix4</a><S></code><a href='#impl-VectorSpace-2' class='anchor'></a><a class='srclink' href='../../src/cgmath/matrix.rs.html#442-444' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-3' class="type"><code id='Scalar.t-3'>type <a href='#associatedtype.Scalar-3' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-3' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Quaternion.html" title="struct cgmath::Quaternion">Quaternion</a><S></code><a href='#impl-VectorSpace-3' class='anchor'></a><a class='srclink' href='../../src/cgmath/quaternion.rs.html#225-227' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-4' class="type"><code id='Scalar.t-4'>type <a href='#associatedtype.Scalar-4' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-4' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Vector1.html" title="struct cgmath::Vector1">Vector1</a><S></code><a href='#impl-VectorSpace-4' class='anchor'></a><a class='srclink' href='../../src/cgmath/vector.rs.html#194-196' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-5' class="type"><code id='Scalar.t-5'>type <a href='#associatedtype.Scalar-5' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-5' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Vector2.html" title="struct cgmath::Vector2">Vector2</a><S></code><a href='#impl-VectorSpace-5' class='anchor'></a><a class='srclink' href='../../src/cgmath/vector.rs.html#194-196' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-6' class="type"><code id='Scalar.t-6'>type <a href='#associatedtype.Scalar-6' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-6' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Vector3.html" title="struct cgmath::Vector3">Vector3</a><S></code><a href='#impl-VectorSpace-6' class='anchor'></a><a class='srclink' href='../../src/cgmath/vector.rs.html#194-196' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-7' class="type"><code id='Scalar.t-7'>type <a href='#associatedtype.Scalar-7' class="type">Scalar</a> = S</code></h4></div><h3 id='impl-VectorSpace-7' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../../cgmath/trait.BaseNum.html" title="trait cgmath::BaseNum">BaseNum</a>> VectorSpace for <a class="struct" href="../../cgmath/struct.Vector4.html" title="struct cgmath::Vector4">Vector4</a><S></code><a href='#impl-VectorSpace-7' class='anchor'></a><a class='srclink' href='../../src/cgmath/vector.rs.html#194-196' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scalar-8' class="type"><code id='Scalar.t-8'>type <a href='#associatedtype.Scalar-8' class="type">Scalar</a> = S</code></h4></div></div><span class='loading-content'>Loading content...</span><script type="text/javascript">window.inlined_types=new Set([]);</script><script type="text/javascript" async
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src="../../implementors/cgmath/prelude/trait.VectorSpace.js">
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