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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 `InnerSpace` trait in crate `cgmath`."><meta name="keywords" content="rust, rustlang, rust-lang, InnerSpace"><title>cgmath::InnerSpace - 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 InnerSpace</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.dot">dot</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.angle">angle</a><a href="#method.is_perpendicular">is_perpendicular</a><a href="#method.magnitude">magnitude</a><a href="#method.magnitude2">magnitude2</a><a href="#method.normalize">normalize</a><a href="#method.normalize_to">normalize_to</a><a href="#method.project_on">project_on</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='index.html'>cgmath</a></p><script>window.sidebarCurrent = {name: 'InnerSpace', 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#220-278' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='index.html'>cgmath</a>::<wbr><a class="trait" href=''>InnerSpace</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait InnerSpace: <a class="trait" href="../cgmath/prelude/trait.VectorSpace.html" title="trait cgmath::prelude::VectorSpace">VectorSpace</a> <span class="where fmt-newline">where<br> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>,<br> Self: <a class="trait" href="../cgmath/prelude/trait.MetricSpace.html" title="trait cgmath::prelude::MetricSpace">MetricSpace</a><Metric = Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>>,<br> Self: <a class="trait" href="../cgmath/trait.UlpsEq.html" title="trait cgmath::UlpsEq">UlpsEq</a><Epsilon = Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>>, </span>{
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fn <a href='#tymethod.dot' class='fnname'>dot</a>(self, other: Self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>;
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fn <a href='#method.is_perpendicular' class='fnname'>is_perpendicular</a>(self, other: Self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.magnitude2' class='fnname'>magnitude2</a>(self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.magnitude' class='fnname'>magnitude</a>(self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.angle' class='fnname'>angle</a>(self, other: Self) -> <a class="struct" href="../cgmath/struct.Rad.html" title="struct cgmath::Rad">Rad</a><Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>> { ... }
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<div class='item-spacer'></div> fn <a href='#method.normalize' class='fnname'>normalize</a>(self) -> Self { ... }
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<div class='item-spacer'></div> fn <a href='#method.normalize_to' class='fnname'>normalize_to</a>(self, magnitude: Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>) -> Self { ... }
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<div class='item-spacer'></div> fn <a href='#method.project_on' class='fnname'>project_on</a>(self, other: Self) -> Self { ... }
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}</pre></div><div class='docblock'><p>Vectors that also have a <a href="https://en.wikipedia.org/wiki/Dot_product">dot</a>
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(or <a href="https://en.wikipedia.org/wiki/Inner_product_space">inner</a>) product.</p>
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<p>The dot product allows for the definition of other useful operations, like
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finding the magnitude of a vector or normalizing it.</p>
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<p>Examples include vectors and quaternions.</p>
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</div>
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<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.dot' class='method'><code id='dot.v'>fn <a href='#tymethod.dot' class='fnname'>dot</a>(self, other: Self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a></code></h3><div class='docblock'><p>Vector dot (or inner) product.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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<h2 id='provided-methods' class='small-section-header'>Provided methods<a href='#provided-methods' class='anchor'></a></h2><div class='methods'><h3 id='method.is_perpendicular' class='method'><code id='is_perpendicular.v'>fn <a href='#method.is_perpendicular' class='fnname'>is_perpendicular</a>(self, other: Self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.bool.html">bool</a></code></h3><div class='docblock'><p>Returns <code>true</code> if the vector is perpendicular (at right angles) to the
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other vector.</p>
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</div><h3 id='method.magnitude2' class='method'><code id='magnitude2.v'>fn <a href='#method.magnitude2' class='fnname'>magnitude2</a>(self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a></code></h3><div class='docblock'><p>Returns the squared magnitude.</p>
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<p>This does not perform an expensive square root operation like in
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<code>InnerSpace::magnitude</code> method, and so can be used to compare magnitudes
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more efficiently.</p>
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</div><h3 id='method.magnitude' class='method'><code id='magnitude.v'>fn <a href='#method.magnitude' class='fnname'>magnitude</a>(self) -> Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a></code></h3><div class='docblock'><p>The distance from the tail to the tip of the vector.</p>
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</div><h3 id='method.angle' class='method'><code id='angle.v'>fn <a href='#method.angle' class='fnname'>angle</a>(self, other: Self) -> <a class="struct" href="../cgmath/struct.Rad.html" title="struct cgmath::Rad">Rad</a><Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>></code></h3><div class='docblock'><p>Returns the angle between two vectors in radians.</p>
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</div><h3 id='method.normalize' class='method'><code id='normalize.v'>fn <a href='#method.normalize' class='fnname'>normalize</a>(self) -> Self</code></h3><div class='docblock'><p>Returns a vector with the same direction, but with a magnitude of <code>1</code>.</p>
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</div><h3 id='method.normalize_to' class='method'><code id='normalize_to.v'>fn <a href='#method.normalize_to' class='fnname'>normalize_to</a>(self, magnitude: Self::<a class="type" href="../cgmath/prelude/trait.VectorSpace.html#associatedtype.Scalar" title="type cgmath::prelude::VectorSpace::Scalar">Scalar</a>) -> Self</code></h3><div class='docblock'><p>Returns a vector with the same direction and a given magnitude.</p>
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</div><h3 id='method.project_on' class='method'><code id='project_on.v'>fn <a href='#method.project_on' class='fnname'>project_on</a>(self, other: Self) -> Self</code></h3><div class='docblock'><p>Returns the
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<a href="https://en.wikipedia.org/wiki/Vector_projection">vector projection</a>
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of the current inner space projected onto the supplied argument.</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-InnerSpace' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> InnerSpace for <a class="struct" href="../cgmath/struct.Quaternion.html" title="struct cgmath::Quaternion">Quaternion</a><S></code><a href='#impl-InnerSpace' class='anchor'></a><a class='srclink' href='../src/cgmath/quaternion.rs.html#261-266' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.dot' class="method hidden"><code id='dot.v-1'>fn <a href='#method.dot' class='fnname'>dot</a>(self, other: <a class="struct" href="../cgmath/struct.Quaternion.html" title="struct cgmath::Quaternion">Quaternion</a><S>) -> S</code><a class='srclink' href='../src/cgmath/quaternion.rs.html#263-265' title='goto source code'>[src]</a></h4></div><h3 id='impl-InnerSpace-1' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> InnerSpace for <a class="struct" href="../cgmath/struct.Vector1.html" title="struct cgmath::Vector1">Vector1</a><S></code><a href='#impl-InnerSpace-1' class='anchor'></a><a class='srclink' href='../src/cgmath/vector.rs.html#788-793' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.dot-1' class="method hidden"><code id='dot.v-2'>fn <a href='#method.dot-1' class='fnname'>dot</a>(self, other: <a class="struct" href="../cgmath/struct.Vector1.html" title="struct cgmath::Vector1">Vector1</a><S>) -> S</code><a class='srclink' href='../src/cgmath/vector.rs.html#790-792' title='goto source code'>[src]</a></h4></div><h3 id='impl-InnerSpace-2' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> InnerSpace for <a class="struct" href="../cgmath/struct.Vector2.html" title="struct cgmath::Vector2">Vector2</a><S></code><a href='#impl-InnerSpace-2' class='anchor'></a><a class='srclink' href='../src/cgmath/vector.rs.html#795-805' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.dot-2' class="method hidden"><code id='dot.v-3'>fn <a href='#method.dot-2' class='fnname'>dot</a>(self, other: <a class="struct" href="../cgmath/struct.Vector2.html" title="struct cgmath::Vector2">Vector2</a><S>) -> S</code><a class='srclink' href='../src/cgmath/vector.rs.html#797-799' title='goto source code'>[src]</a></h4><h4 id='method.angle-1' class="method hidden"><code id='angle.v-1'>fn <a href='#method.angle-1' class='fnname'>angle</a>(self, other: <a class="struct" href="../cgmath/struct.Vector2.html" title="struct cgmath::Vector2">Vector2</a><S>) -> <a class="struct" href="../cgmath/struct.Rad.html" title="struct cgmath::Rad">Rad</a><S></code><a class='srclink' href='../src/cgmath/vector.rs.html#802-804' title='goto source code'>[src]</a></h4></div><h3 id='impl-InnerSpace-3' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> InnerSpace for <a class="struct" href="../cgmath/struct.Vector3.html" title="struct cgmath::Vector3">Vector3</a><S></code><a href='#impl-InnerSpace-3' class='anchor'></a><a class='srclink' href='../src/cgmath/vector.rs.html#807-817' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.dot-3' class="method hidden"><code id='dot.v-4'>fn <a href='#method.dot-3' class='fnname'>dot</a>(self, other: <a class="struct" href="../cgmath/struct.Vector3.html" title="struct cgmath::Vector3">Vector3</a><S>) -> S</code><a class='srclink' href='../src/cgmath/vector.rs.html#809-811' title='goto source code'>[src]</a></h4><h4 id='method.angle-2' class="method hidden"><code id='angle.v-2'>fn <a href='#method.angle-2' class='fnname'>angle</a>(self, other: <a class="struct" href="../cgmath/struct.Vector3.html" title="struct cgmath::Vector3">Vector3</a><S>) -> <a class="struct" href="../cgmath/struct.Rad.html" title="struct cgmath::Rad">Rad</a><S></code><a class='srclink' href='../src/cgmath/vector.rs.html#814-816' title='goto source code'>[src]</a></h4></div><h3 id='impl-InnerSpace-4' class='impl'><code class='in-band'>impl<S: <a class="trait" href="../cgmath/trait.BaseFloat.html" title="trait cgmath::BaseFloat">BaseFloat</a>> InnerSpace for <a class="struct" href="../cgmath/struct.Vector4.html" title="struct cgmath::Vector4">Vector4</a><S></code><a href='#impl-InnerSpace-4' class='anchor'></a><a class='srclink' href='../src/cgmath/vector.rs.html#819-824' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.dot-4' class="method hidden"><code id='dot.v-5'>fn <a href='#method.dot-4' class='fnname'>dot</a>(self, other: <a class="struct" href="../cgmath/struct.Vector4.html" title="struct cgmath::Vector4">Vector4</a><S>) -> S</code><a class='srclink' href='../src/cgmath/vector.rs.html#821-823' title='goto source code'>[src]</a></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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