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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 `Similarity` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, Similarity"><title>alga::linear::Similarity - 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='../../alga/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Trait Similarity</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.Scaling">Scaling</a></div><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.rotation">rotation</a><a href="#tymethod.scaling">scaling</a><a href="#tymethod.translation">translation</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.inverse_rotate_point">inverse_rotate_point</a><a href="#method.inverse_rotate_vector">inverse_rotate_vector</a><a href="#method.inverse_scale_point">inverse_scale_point</a><a href="#method.inverse_scale_vector">inverse_scale_vector</a><a href="#method.inverse_translate_point">inverse_translate_point</a><a href="#method.rotate_point">rotate_point</a><a href="#method.rotate_vector">rotate_vector</a><a href="#method.scale_point">scale_point</a><a href="#method.scale_vector">scale_vector</a><a href="#method.translate_point">translate_point</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='../index.html'>alga</a>::<wbr><a href='index.html'>linear</a></p><script>window.sidebarCurrent = {name: 'Similarity', 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/alga/linear/transformation.rs.html#101-184' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='../index.html'>alga</a>::<wbr><a href='index.html'>linear</a>::<wbr><a class="trait" href=''>Similarity</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Similarity<E: <a class="trait" href="../../alga/linear/trait.EuclideanSpace.html" title="trait alga::linear::EuclideanSpace">EuclideanSpace</a>>: <a class="trait" href="../../alga/linear/trait.AffineTransformation.html" title="trait alga::linear::AffineTransformation">AffineTransformation</a><E, NonUniformScaling = Self::<a class="type" href="../../alga/linear/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::Similarity::Scaling">Scaling</a>> {
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type <a href='#associatedtype.Scaling' class="type">Scaling</a>: <a class="trait" href="../../alga/linear/trait.Scaling.html" title="trait alga::linear::Scaling">Scaling</a><E>;
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fn <a href='#tymethod.translation' class='fnname'>translation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.rotation' class='fnname'>rotation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.scaling' class='fnname'>scaling</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::Similarity::Scaling">Scaling</a>;
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fn <a href='#method.translate_point' class='fnname'>translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.rotate_point' class='fnname'>rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.scale_point' class='fnname'>scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.rotate_vector' class='fnname'>rotate_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.scale_vector' class='fnname'>scale_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.inverse_translate_point' class='fnname'>inverse_translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.inverse_rotate_point' class='fnname'>inverse_rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.inverse_scale_point' class='fnname'>inverse_scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E { ... }
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<div class='item-spacer'></div> fn <a href='#method.inverse_rotate_vector' class='fnname'>inverse_rotate_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.inverse_scale_vector' class='fnname'>inverse_scale_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a> { ... }
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}</pre></div><div class='docblock'><p>Subgroups of the similarity group <code>S(n)</code>, i.e., rotations, translations, and (signed) uniform scaling.</p>
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<p>Similarities map lines to lines and preserve angles.</p>
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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.Scaling' class='method'><code id='Scaling.t'>type <a href='#associatedtype.Scaling' class="type">Scaling</a>: <a class="trait" href="../../alga/linear/trait.Scaling.html" title="trait alga::linear::Scaling">Scaling</a><E></code></h3><div class='docblock'><p>The type of the pure (uniform) scaling part of this similarity transformation.</p>
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</div></div><span class='loading-content'>Loading content...</span>
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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.translation' class='method'><code id='translation.v'>fn <a href='#tymethod.translation' class='fnname'>translation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a></code></h3><div class='docblock'><p>The pure translational component of this similarity transformation.</p>
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</div><h3 id='tymethod.rotation' class='method'><code id='rotation.v'>fn <a href='#tymethod.rotation' class='fnname'>rotation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a></code></h3><div class='docblock'><p>The pure rotational component of this similarity transformation.</p>
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</div><h3 id='tymethod.scaling' class='method'><code id='scaling.v'>fn <a href='#tymethod.scaling' class='fnname'>scaling</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::Similarity::Scaling">Scaling</a></code></h3><div class='docblock'><p>The pure scaling component of this similarity transformation.</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.translate_point' class='method'><code id='translate_point.v'>fn <a href='#method.translate_point' class='fnname'>translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation's pure translational part to a point.</p>
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</div><h3 id='method.rotate_point' class='method'><code id='rotate_point.v'>fn <a href='#method.rotate_point' class='fnname'>rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation's pure rotational part to a point.</p>
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</div><h3 id='method.scale_point' class='method'><code id='scale_point.v'>fn <a href='#method.scale_point' class='fnname'>scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation's pure scaling part to a point.</p>
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</div><h3 id='method.rotate_vector' class='method'><code id='rotate_vector.v'>fn <a href='#method.rotate_vector' class='fnname'>rotate_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a></code></h3><div class='docblock'><p>Applies this transformation's pure rotational part to a vector.</p>
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</div><h3 id='method.scale_vector' class='method'><code id='scale_vector.v'>fn <a href='#method.scale_vector' class='fnname'>scale_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a></code></h3><div class='docblock'><p>Applies this transformation's pure scaling part to a vector.</p>
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</div><h3 id='method.inverse_translate_point' class='method'><code id='inverse_translate_point.v'>fn <a href='#method.inverse_translate_point' class='fnname'>inverse_translate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation inverse's pure translational part to a point.</p>
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</div><h3 id='method.inverse_rotate_point' class='method'><code id='inverse_rotate_point.v'>fn <a href='#method.inverse_rotate_point' class='fnname'>inverse_rotate_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation inverse's pure rotational part to a point.</p>
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</div><h3 id='method.inverse_scale_point' class='method'><code id='inverse_scale_point.v'>fn <a href='#method.inverse_scale_point' class='fnname'>inverse_scale_point</a>(&self, pt: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> E</code></h3><div class='docblock'><p>Applies this transformation inverse's pure scaling part to a point.</p>
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</div><h3 id='method.inverse_rotate_vector' class='method'><code id='inverse_rotate_vector.v'>fn <a href='#method.inverse_rotate_vector' class='fnname'>inverse_rotate_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a></code></h3><div class='docblock'><p>Applies this transformation inverse's pure rotational part to a vector.</p>
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</div><h3 id='method.inverse_scale_vector' class='method'><code id='inverse_scale_vector.v'>fn <a href='#method.inverse_scale_vector' class='fnname'>inverse_scale_vector</a>(&self, pt: &E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a></code></h3><div class='docblock'><p>Applies this transformation inverse's pure scaling part to a vector.</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-Similarity%3CE%3E' class='impl'><code class='in-band'>impl<E: <a class="trait" href="../../alga/linear/trait.EuclideanSpace.html" title="trait alga::linear::EuclideanSpace">EuclideanSpace</a>> Similarity<E> for <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code><a href='#impl-Similarity%3CE%3E' class='anchor'></a><a class='srclink' href='../../src/alga/linear/id.rs.html#78-95' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scaling-1' class="type"><code id='Scaling.t-1'>type <a href='#associatedtype.Scaling-1' class="type">Scaling</a> = <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code></h4><h4 id='method.translation' class="method hidden"><code id='translation.v-1'>fn <a href='#method.translation' class='fnname'>translation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a></code><a class='srclink' href='../../src/alga/linear/id.rs.html#82-84' title='goto source code'>[src]</a></h4><h4 id='method.rotation' class="method hidden"><code id='rotation.v-1'>fn <a href='#method.rotation' class='fnname'>rotation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a></code><a class='srclink' href='../../src/alga/linear/id.rs.html#87-89' title='goto source code'>[src]</a></h4><h4 id='method.scaling' class="method hidden"><code id='scaling.v-1'>fn <a href='#method.scaling' class='fnname'>scaling</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::Similarity::Scaling">Scaling</a></code><a class='srclink' href='../../src/alga/linear/id.rs.html#92-94' title='goto source code'>[src]</a></h4></div><h3 id='impl-Similarity%3CE%3E-1' class='impl'><code class='in-band'>impl<R, E> Similarity<E> for R <span class="where fmt-newline">where<br> R: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a> + <a class="trait" href="../../alga/general/trait.SubsetOf.html" title="trait alga::general::SubsetOf">SubsetOf</a><R>,<br> E: <a class="trait" href="../../alga/linear/trait.EuclideanSpace.html" title="trait alga::linear::EuclideanSpace">EuclideanSpace</a><RealField = R>,<br> E::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>: <a class="trait" href="../../alga/general/trait.ClosedMul.html" title="trait alga::general::ClosedMul">ClosedMul</a><R> + <a class="trait" href="../../alga/general/trait.ClosedDiv.html" title="trait alga::general::ClosedDiv">ClosedDiv</a><R> + <a class="trait" href="../../alga/general/trait.ClosedNeg.html" title="trait alga::general::ClosedNeg">ClosedNeg</a>, </span></code><a href='#impl-Similarity%3CE%3E-1' class='anchor'></a><a class='srclink' href='../../src/alga/linear/transformation.rs.html#401-420' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Scaling-2' class="type"><code id='Scaling.t-2'>type <a href='#associatedtype.Scaling-2' class="type">Scaling</a> = R</code></h4><h4 id='method.translation-1' class="method hidden"><code id='translation.v-2'>fn <a href='#method.translation-1' class='fnname'>translation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a></code><a class='srclink' href='../../src/alga/linear/transformation.rs.html#409-411' title='goto source code'>[src]</a></h4><h4 id='method.rotation-1' class="method hidden"><code id='rotation.v-2'>fn <a href='#method.rotation-1' class='fnname'>rotation</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a></code><a class='srclink' href='../../src/alga/linear/transformation.rs.html#413-415' title='goto source code'>[src]</a></h4><h4 id='method.scaling-1' class="method hidden"><code id='scaling.v-2'>fn <a href='#method.scaling-1' class='fnname'>scaling</a>(&self) -> Self::<a class="type" href="../../alga/linear/trait.Similarity.html#associatedtype.Scaling" title="type alga::linear::Similarity::Scaling">Scaling</a></code><a class='srclink' href='../../src/alga/linear/transformation.rs.html#417-419' 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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