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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 `geometry` mod in crate `nalgebra`."><meta name="keywords" content="rust, rustlang, rust-lang, geometry"><title>nalgebra::geometry - 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="http://nalgebra.org/img/favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc mod"><!--[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='../../nalgebra/index.html'><div class='logo-container'><img src='../../rust-logo.png' alt='logo'></div></a><p class='location'>Module geometry</p><div class="sidebar-elems"><div class="block items"><ul><li><a href="#structs">Structs</a></li><li><a href="#enums">Enums</a></li><li><a href="#traits">Traits</a></li><li><a href="#types">Type Definitions</a></li></ul></div><p class='location'><a href='../index.html'>nalgebra</a></p><script>window.sidebarCurrent = {name: 'geometry', ty: 'mod', 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/nalgebra/geometry/mod.rs.html#1-96' title='goto source code'>[src]</a></span><span class='in-band'>Module <a href='../index.html'>nalgebra</a>::<wbr><a class="mod" href=''>geometry</a></span></h1><div class='docblock'><p>[Reexported at the root of this crate.] Data structures for points and usual transformations
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(rotations, isometries, etc.)</p>
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</div><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
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<table><tr class='module-item'><td><a class="struct" href="struct.Isometry.html" title='nalgebra::geometry::Isometry struct'>Isometry</a></td><td class='docblock-short'><p>A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Orthographic3.html" title='nalgebra::geometry::Orthographic3 struct'>Orthographic3</a></td><td class='docblock-short'><p>A 3D orthographic projection stored as an homogeneous 4x4 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Perspective3.html" title='nalgebra::geometry::Perspective3 struct'>Perspective3</a></td><td class='docblock-short'><p>A 3D perspective projection stored as an homogeneous 4x4 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Point.html" title='nalgebra::geometry::Point struct'>Point</a></td><td class='docblock-short'><p>A point in a n-dimensional euclidean space.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Quaternion.html" title='nalgebra::geometry::Quaternion struct'>Quaternion</a></td><td class='docblock-short'><p>A quaternion. See the type alias <code>UnitQuaternion = Unit<Quaternion></code> for a quaternion
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that may be used as a rotation.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Reflection.html" title='nalgebra::geometry::Reflection struct'>Reflection</a></td><td class='docblock-short'><p>A reflection wrt. a plane.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Rotation.html" title='nalgebra::geometry::Rotation struct'>Rotation</a></td><td class='docblock-short'><p>A rotation matrix.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Similarity.html" title='nalgebra::geometry::Similarity struct'>Similarity</a></td><td class='docblock-short'><p>A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Transform.html" title='nalgebra::geometry::Transform struct'>Transform</a></td><td class='docblock-short'><p>A transformation matrix in homogeneous coordinates.</p>
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</td></tr><tr class='module-item'><td><a class="struct" href="struct.Translation.html" title='nalgebra::geometry::Translation struct'>Translation</a></td><td class='docblock-short'><p>A translation.</p>
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</td></tr></table><h2 id='enums' class='section-header'><a href="#enums">Enums</a></h2>
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<table><tr class='module-item'><td><a class="enum" href="enum.TAffine.html" title='nalgebra::geometry::TAffine enum'>TAffine</a></td><td class='docblock-short'><p>Tag representing an affine <code>Transform</code>. Its bottom-row is equal to <code>(0, 0 ... 0, 1)</code>.</p>
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</td></tr><tr class='module-item'><td><a class="enum" href="enum.TGeneral.html" title='nalgebra::geometry::TGeneral enum'>TGeneral</a></td><td class='docblock-short'><p>Tag representing the most general (not necessarily inversible) <code>Transform</code> type.</p>
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</td></tr><tr class='module-item'><td><a class="enum" href="enum.TProjective.html" title='nalgebra::geometry::TProjective enum'>TProjective</a></td><td class='docblock-short'><p>Tag representing the most general inversible <code>Transform</code> type.</p>
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</td></tr></table><h2 id='traits' class='section-header'><a href="#traits">Traits</a></h2>
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<table><tr class='module-item'><td><a class="trait" href="trait.SubTCategoryOf.html" title='nalgebra::geometry::SubTCategoryOf trait'>SubTCategoryOf</a></td><td class='docblock-short'><p>Indicates that <code>Self</code> is a more specific <code>Transform</code> category than <code>Other</code>.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.SuperTCategoryOf.html" title='nalgebra::geometry::SuperTCategoryOf trait'>SuperTCategoryOf</a></td><td class='docblock-short'><p>Indicates that <code>Self</code> is a more general <code>Transform</code> category than <code>Other</code>.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.TCategory.html" title='nalgebra::geometry::TCategory trait'>TCategory</a></td><td class='docblock-short'><p>Trait implemented by phantom types identifying the projective transformation type.</p>
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</td></tr><tr class='module-item'><td><a class="trait" href="trait.TCategoryMul.html" title='nalgebra::geometry::TCategoryMul trait'>TCategoryMul</a></td><td class='docblock-short'><p>Traits that gives the <code>Transform</code> category that is compatible with the result of the
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multiplication of transformations with categories <code>Self</code> and <code>Other</code>.</p>
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</td></tr></table><h2 id='types' class='section-header'><a href="#types">Type Definitions</a></h2>
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<table><tr class='module-item'><td><a class="type" href="type.Affine2.html" title='nalgebra::geometry::Affine2 type'>Affine2</a></td><td class='docblock-short'><p>A 2D affine transformation. Stored as an homogeneous 3x3 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Affine3.html" title='nalgebra::geometry::Affine3 type'>Affine3</a></td><td class='docblock-short'><p>A 3D affine transformation. Stored as an homogeneous 4x4 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Isometry2.html" title='nalgebra::geometry::Isometry2 type'>Isometry2</a></td><td class='docblock-short'><p>A 2-dimensional direct isometry using a unit complex number for its rotational part. Also known as a rigid-body motion, or as an element of SE(2).</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Isometry3.html" title='nalgebra::geometry::Isometry3 type'>Isometry3</a></td><td class='docblock-short'><p>A 3-dimensional direct isometry using a unit quaternion for its rotational part. Also known as a rigid-body motion, or as an element of SE(3).</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.IsometryMatrix2.html" title='nalgebra::geometry::IsometryMatrix2 type'>IsometryMatrix2</a></td><td class='docblock-short'><p>A 2-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(2).</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.IsometryMatrix3.html" title='nalgebra::geometry::IsometryMatrix3 type'>IsometryMatrix3</a></td><td class='docblock-short'><p>A 3-dimensional direct isometry using a rotation matrix for its rotational part. Also known as a rigid-body motion, or as an element of SE(3).</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point1.html" title='nalgebra::geometry::Point1 type'>Point1</a></td><td class='docblock-short'><p>A statically sized 1-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point2.html" title='nalgebra::geometry::Point2 type'>Point2</a></td><td class='docblock-short'><p>A statically sized 2-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point3.html" title='nalgebra::geometry::Point3 type'>Point3</a></td><td class='docblock-short'><p>A statically sized 3-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point4.html" title='nalgebra::geometry::Point4 type'>Point4</a></td><td class='docblock-short'><p>A statically sized 4-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point5.html" title='nalgebra::geometry::Point5 type'>Point5</a></td><td class='docblock-short'><p>A statically sized 5-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Point6.html" title='nalgebra::geometry::Point6 type'>Point6</a></td><td class='docblock-short'><p>A statically sized 6-dimensional column point.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Projective2.html" title='nalgebra::geometry::Projective2 type'>Projective2</a></td><td class='docblock-short'><p>An invertible 2D general transformation. Stored as an homogeneous 3x3 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Projective3.html" title='nalgebra::geometry::Projective3 type'>Projective3</a></td><td class='docblock-short'><p>An invertible 3D general transformation. Stored as an homogeneous 4x4 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Rotation2.html" title='nalgebra::geometry::Rotation2 type'>Rotation2</a></td><td class='docblock-short'><p>A 2-dimensional rotation matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Rotation3.html" title='nalgebra::geometry::Rotation3 type'>Rotation3</a></td><td class='docblock-short'><p>A 3-dimensional rotation matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Similarity2.html" title='nalgebra::geometry::Similarity2 type'>Similarity2</a></td><td class='docblock-short'><p>A 2-dimensional similarity.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Similarity3.html" title='nalgebra::geometry::Similarity3 type'>Similarity3</a></td><td class='docblock-short'><p>A 3-dimensional similarity.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.SimilarityMatrix2.html" title='nalgebra::geometry::SimilarityMatrix2 type'>SimilarityMatrix2</a></td><td class='docblock-short'><p>A 2-dimensional similarity using a rotation matrix for its rotation part.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.SimilarityMatrix3.html" title='nalgebra::geometry::SimilarityMatrix3 type'>SimilarityMatrix3</a></td><td class='docblock-short'><p>A 3-dimensional similarity using a rotation matrix for its rotation part.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Transform2.html" title='nalgebra::geometry::Transform2 type'>Transform2</a></td><td class='docblock-short'><p>A 2D general transformation that may not be invertible. Stored as an homogeneous 3x3 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Transform3.html" title='nalgebra::geometry::Transform3 type'>Transform3</a></td><td class='docblock-short'><p>A 3D general transformation that may not be inversible. Stored as an homogeneous 4x4 matrix.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation1.html" title='nalgebra::geometry::Translation1 type'>Translation1</a></td><td class='docblock-short'><p>A 1-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation2.html" title='nalgebra::geometry::Translation2 type'>Translation2</a></td><td class='docblock-short'><p>A 2-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation3.html" title='nalgebra::geometry::Translation3 type'>Translation3</a></td><td class='docblock-short'><p>A 3-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation4.html" title='nalgebra::geometry::Translation4 type'>Translation4</a></td><td class='docblock-short'><p>A 4-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation5.html" title='nalgebra::geometry::Translation5 type'>Translation5</a></td><td class='docblock-short'><p>A 5-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.Translation6.html" title='nalgebra::geometry::Translation6 type'>Translation6</a></td><td class='docblock-short'><p>A 6-dimensional translation.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.UnitComplex.html" title='nalgebra::geometry::UnitComplex type'>UnitComplex</a></td><td class='docblock-short'><p>A complex number with a norm equal to 1.</p>
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</td></tr><tr class='module-item'><td><a class="type" href="type.UnitQuaternion.html" title='nalgebra::geometry::UnitQuaternion type'>UnitQuaternion</a></td><td class='docblock-short'><p>A unit quaternions. May be used to represent a rotation.</p>
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