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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 `AffineTransformation` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, AffineTransformation"><title>alga::linear::AffineTransformation - 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 AffineTransformation</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.Rotation">Rotation</a><a href="#associatedtype.NonUniformScaling">NonUniformScaling</a><a href="#associatedtype.Translation">Translation</a></div><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.append_rotation">append_rotation</a><a href="#tymethod.append_scaling">append_scaling</a><a href="#tymethod.append_translation">append_translation</a><a href="#tymethod.decompose">decompose</a><a href="#tymethod.prepend_rotation">prepend_rotation</a><a href="#tymethod.prepend_scaling">prepend_scaling</a><a href="#tymethod.prepend_translation">prepend_translation</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.append_rotation_wrt_point">append_rotation_wrt_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: 'AffineTransformation', 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#37-96' 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=''>AffineTransformation</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait AffineTransformation<E: <a class="trait" href="../../alga/linear/trait.EuclideanSpace.html" title="trait alga::linear::EuclideanSpa
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type <a href='#associatedtype.Rotation' class="type">Rotation</a>: <a class="trait" href="../../alga/linear/trait.Rotation.html" title="trait alga::linear::Rotation">Rotation</a><E>;
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type <a href='#associatedtype.NonUniformScaling' class="type">NonUniformScaling</a>: <a class="trait" href="../../alga/linear/trait.AffineTransformation.html" title="trait alga::linear::AffineTransformation">AffineTransformation</a><E>;
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type <a href='#associatedtype.Translation' class="type">Translation</a>: <a class="trait" href="../../alga/linear/trait.Translation.html" title="trait alga::linear::Translation">Translation</a><E>;
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fn <a href='#tymethod.decompose' class='fnname'>decompose</a>(<br> &self<br> ) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a>;
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<div class='item-spacer'></div> fn <a href='#tymethod.append_translation' class='fnname'>append_translation</a>(&self, t: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.prepend_translation' class='fnname'>prepend_translation</a>(&self, t: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.append_rotation' class='fnname'>append_rotation</a>(&self, r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.prepend_rotation' class='fnname'>prepend_rotation</a>(&self, r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.append_scaling' class='fnname'>append_scaling</a>(&self, s: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>) -> Self;
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<div class='item-spacer'></div> fn <a href='#tymethod.prepend_scaling' class='fnname'>prepend_scaling</a>(&self, s: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>) -> Self;
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fn <a href='#method.append_rotation_wrt_point' class='fnname'>append_rotation_wrt_point</a>(<br> &self, <br> r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>, <br> p: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E<br> ) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self> { ... }
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}</pre></div><div class='docblock'><p>The group of affine transformations. They are decomposable into a rotation, a non-uniform
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scaling, a second rotation, and a translation (applied in that order).</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.Rotation' class='method'><code id='Rotation.t'>type <a href='#associatedtype.Rotation' class="type">Rotation</a>: <a class="trait" href="../../alga/linear/trait.Rotation.html" title="trait alga::linear::Rotation">Rotation</a><E></code></h3><div class='docblock'><p>Type of the first rotation to be applied.</p>
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</div><h3 id='associatedtype.NonUniformScaling' class='method'><code id='NonUniformScaling.t'>type <a href='#associatedtype.NonUniformScaling' class="type">NonUniformScaling</a>: <a class="trait" href="../../alga/linear/trait.AffineTransformation.html" title="trait alga::linear::AffineTransformation">AffineTransformation</a><E></code></h3><div class='docblock'><p>Type of the non-uniform scaling to be applied.</p>
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</div><h3 id='associatedtype.Translation' class='method'><code id='Translation.t'>type <a href='#associatedtype.Translation' class="type">Translation</a>: <a class="trait" href="../../alga/linear/trait.Translation.html" title="trait alga::linear::Translation">Translation</a><E></code></h3><div class='docblock'><p>The type of the pure translation part of this affine 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.decompose' class='method'><code id='decompose.v'>fn <a href='#tymethod.decompose' class='fnname'>decompose</a>(<br> &self<br>) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a>Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>, Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></code></h3><div class='docblock'><p>Decomposes this affine transformation into a rotation followed by a non-uniform scaling,
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followed by a rotation, followed by a translation.</p>
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</div><h3 id='tymethod.append_translation' class='method'><code id='append_translation.v'>fn <a href='#tymethod.append_translation' class='fnname'>append_translation</a>(&self, t: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self</code></h3><div class='docblock'><p>Appends a translation to this similarity.</p>
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</div><h3 id='tymethod.prepend_translation' class='method'><code id='prepend_translation.v'>fn <a href='#tymethod.prepend_translation' class='fnname'>prepend_translation</a>(&self, t: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self</code></h3><div class='docblock'><p>Prepends a translation to this similarity.</p>
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</div><h3 id='tymethod.append_rotation' class='method'><code id='append_rotation.v'>fn <a href='#tymethod.append_rotation' class='fnname'>append_rotation</a>(&self, r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>) -> Self</code></h3><div class='docblock'><p>Appends a rotation to this similarity.</p>
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</div><h3 id='tymethod.prepend_rotation' class='method'><code id='prepend_rotation.v'>fn <a href='#tymethod.prepend_rotation' class='fnname'>prepend_rotation</a>(&self, r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>) -> Self</code></h3><div class='docblock'><p>Prepends a rotation to this similarity.</p>
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</div><h3 id='tymethod.append_scaling' class='method'><code id='append_scaling.v'>fn <a href='#tymethod.append_scaling' class='fnname'>append_scaling</a>(&self, s: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>) -> Self</code></h3><div class='docblock'><p>Appends a scaling factor to this similarity.</p>
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</div><h3 id='tymethod.prepend_scaling' class='method'><code id='prepend_scaling.v'>fn <a href='#tymethod.prepend_scaling' class='fnname'>prepend_scaling</a>(&self, s: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.NonUniformScaling" title="type alga::linear::AffineTransformation::NonUniformScaling">NonUniformScaling</a>) -> Self</code></h3><div class='docblock'><p>Prepends a scaling factor to this similarity.</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.append_rotation_wrt_point' class='method'><code id='append_rotation_wrt_point.v'>fn <a href='#method.append_rotation_wrt_point' class='fnname'>append_rotation_wrt_point</a>(&self, r: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>, p: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>E) -> <a class="enum" href="https://doc.rust-lang.org/nightly/core/option/enum.Option.html" title="enum core::option::Option">Option</a><Self></code></h3><div class='docblock'><p>Appends to this similarity a rotation centered at the point <code>p</code>, i.e., this point is left
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invariant.</p>
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<p>May return <code>None</code> if <code>Self</code> does not have enough translational degree of liberty to perform
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this computation.</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-AffineTransformation%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>> AffineTransformation<E> for <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code><a href='#impl-AffineTransformation%3CE%3E' class='anchor'></a><a class='srclink' href='../../src/alga/linear/id.rs.html#37-76' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='associatedtype.Rotation-1' class="type"><code id='Rotation.t-1'>type <a href='#associatedtype.Rotation-1' class="type">Rotation</a> = <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code></h4><h4 id='associatedtype.NonUniformScaling-1' class="type"><code id='NonUniformScaling.t-1'>type <a href='#associatedtype.NonUniformScaling-1' class="type">NonUniformScaling</a> = <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code></h4><h4 id='associatedtype.Translation-1' class="type"><code id='Translation.t-1'>type <a href='#associatedtype.Translation-1' class="type">Translation</a> = <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a></code></h4><h4 id='method.decompose' class="method hidden"><code id='decompose.v-1'>fn <a href='#method.decompose' class='fnname'>decompose</a>(&self) -> <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">(</a><a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a>, <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a>, <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a>, <a class="struct" href="../../alga/general/struct.Id.html" title="struct alga::general::Id">Id</a><a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.tuple.html">)</a></code><a class='srclink' href='../../src/alga/linear/id.rs.html#43-45' title='goto source code'>[src]</a></h4><h4 id='method.append_translation' class="method hidden"><code id='append_translation.v-1'>fn <a href='#method.append_translation' class='fnname'>append_translation</a>(&self, _: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self</code><a class='srclink' href='../../src/alga/linear/id.rs.html#48-50' title='goto source code'>[src]</a></h4><h4 id='method.prepend_translation' class="method hidden"><code id='prepend_translation.v-1'>fn <a href='#method.prepend_translation' class='fnname'>prepend_translation</a>(&self, _: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Translation" title="type alga::linear::AffineTransformation::Translation">Translation</a>) -> Self</code><a class='srclink' href='../../src/alga/linear/id.rs.html#53-55' title='goto source code'>[src]</a></h4><h4 id='method.append_rotation' class="method hidden"><code id='append_rotation.v-1'>fn <a href='#method.append_rotation' class='fnname'>append_rotation</a>(&self, _: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#associatedtype.Rotation" title="type alga::linear::AffineTransformation::Rotation">Rotation</a>) -> Self</code><a class='srclink' href='../../src/alga/linear/id.rs.html#58-60' title='goto source code'>[src]</a></h4><h4 id='method.prepend_rotation' class="method hidden"><code id='prepend_rotation.v-1'>fn <a href='#method.prepend_rotation' class='fnname'>prepend_rotation</a>(&self, _: &Self::<a class="type" href="../../alga/linear/trait.AffineTransformation.html#as
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