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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 `cgmath` crate."><meta name="keywords" content="rust, rustlang, rust-lang, cgmath"><title>cgmath - 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 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">&#9776;</div><a href='../cgmath/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><p class='location'>Crate cgmath</p><div class="sidebar-elems"><a id='all-types' href='all.html'><p>See all cgmath's items</p></a><div class="block items"><ul><li><a href="#reexports">Re-exports</a></li><li><a href="#modules">Modules</a></li><li><a href="#macros">Macros</a></li><li><a href="#structs">Structs</a></li><li><a href="#traits">Traits</a></li><li><a href="#functions">Functions</a></li></ul></div><p class='location'></p><script>window.sidebarCurrent = {name: 'cgmath', ty: 'mod', relpath: '../'};</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'>&#x2212;</span>]</a></span><a class='srclink' href='../src/cgmath/lib.rs.html#16-109' title='goto source code'>[src]</a></span><span class='in-band'>Crate <a class="mod" href=''>cgmath</a></span></h1><div class='docblock'><p>A low-dimensional linear algebra library, targeted at computer graphics.</p>
<h1 id="trait-overview" class="section-header"><a href="#trait-overview">Trait overview</a></h1>
<p>In order to make a clean, composable API, we divide operations into traits
that are roughly based on mathematical properties. The main ones that we
concern ourselves with are listed below:</p>
<ul>
<li><code>VectorSpace</code>: Specifies the main operators for vectors, quaternions, and
matrices.</li>
<li><code>MetricSpace</code>: For types that have a distance function implemented.</li>
<li><code>InnerSpace</code>: For types that have a dot (or inner) product - ie. vectors or
quaternions. This also allows for the definition of operations that are
based on the dot product, like finding the magnitude or normalizing.</li>
<li><code>EuclideanSpace</code>: Points in euclidean space, with an associated space of
displacement vectors.</li>
<li><code>Matrix</code>: Common operations for matrices of arbitrary dimensions.</li>
<li><code>SquareMatrix</code>: A special trait for matrices where the number of columns
equal the number of rows.</li>
</ul>
<p>Other traits are included for practical convenience, for example:</p>
<ul>
<li><code>Array</code>: For contiguous, indexable arrays of elements, specifically
vectors.</li>
<li><code>ElementWise</code>: For element-wise addition, subtraction, multiplication,
division, and remainder operations.</li>
</ul>
<h1 id="the-prelude" class="section-header"><a href="#the-prelude">The prelude</a></h1>
<p>Importing each trait individually can become a chore, so we provide a
<code>prelude</code> module to allow you to import the main trait all at once. For
example:</p>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="kw">use</span> <span class="ident">cgmath</span>::<span class="ident">prelude</span>::<span class="kw-2">*</span>;</pre></div>
</div><h2 id='reexports' class='section-header'><a href="#reexports">Re-exports</a></h2>
<table><tr><td><code>pub extern crate <a class="mod" href="../num_traits/index.html" title="mod num_traits">num_traits</a>;</code></td></tr></table><h2 id='modules' class='section-header'><a href="#modules">Modules</a></h2>
<table><tr class='module-item'><td><a class="mod" href="conv/index.html" title='cgmath::conv mod'>conv</a></td><td class='docblock-short'><p>Constrained conversion functions for assisting in situations where type
inference is difficult.</p>
</td></tr><tr class='module-item'><td><a class="mod" href="prelude/index.html" title='cgmath::prelude mod'>prelude</a></td><td class='docblock-short'><p>This module contains the most common traits used in <code>cgmath</code>. By
glob-importing this module, you can avoid the need to import each trait
individually, while still being selective about what types you import.</p>
</td></tr></table><h2 id='macros' class='section-header'><a href="#macros">Macros</a></h2>
<table><tr class='module-item'><td><a class="macro" href="macro.abs_diff_eq.html" title='cgmath::abs_diff_eq macro'>abs_diff_eq</a></td><td class='docblock-short'><p>Approximate equality of using the absolute difference.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.abs_diff_ne.html" title='cgmath::abs_diff_ne macro'>abs_diff_ne</a></td><td class='docblock-short'><p>Approximate inequality of using the absolute difference.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_abs_diff_eq.html" title='cgmath::assert_abs_diff_eq macro'>assert_abs_diff_eq</a></td><td class='docblock-short'><p>An assertion that delegates to <code>abs_diff_eq!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_abs_diff_ne.html" title='cgmath::assert_abs_diff_ne macro'>assert_abs_diff_ne</a></td><td class='docblock-short'><p>An assertion that delegates to <code>abs_diff_ne!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_relative_eq.html" title='cgmath::assert_relative_eq macro'>assert_relative_eq</a></td><td class='docblock-short'><p>An assertion that delegates to <code>relative_eq!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_relative_ne.html" title='cgmath::assert_relative_ne macro'>assert_relative_ne</a></td><td class='docblock-short'><p>An assertion that delegates to <code>relative_ne!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_ulps_eq.html" title='cgmath::assert_ulps_eq macro'>assert_ulps_eq</a></td><td class='docblock-short'><p>An assertion that delegates to <code>ulps_eq!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.assert_ulps_ne.html" title='cgmath::assert_ulps_ne macro'>assert_ulps_ne</a></td><td class='docblock-short'><p>An assertion that delegates to <code>ulps_ne!</code>, and panics with a helpful error on failure.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.relative_eq.html" title='cgmath::relative_eq macro'>relative_eq</a></td><td class='docblock-short'><p>Approximate equality using both the absolute difference and relative based comparisons.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.relative_ne.html" title='cgmath::relative_ne macro'>relative_ne</a></td><td class='docblock-short'><p>Approximate inequality using both the absolute difference and relative based comparisons.</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.ulps_eq.html" title='cgmath::ulps_eq macro'>ulps_eq</a></td><td class='docblock-short'><p>Approximate equality using both the absolute difference and ULPs (Units in Last Place).</p>
</td></tr><tr class='module-item'><td><a class="macro" href="macro.ulps_ne.html" title='cgmath::ulps_ne macro'>ulps_ne</a></td><td class='docblock-short'><p>Approximate inequality using both the absolute difference and ULPs (Units in Last Place).</p>
</td></tr></table><h2 id='structs' class='section-header'><a href="#structs">Structs</a></h2>
<table><tr class='module-item'><td><a class="struct" href="struct.AbsDiff.html" title='cgmath::AbsDiff struct'>AbsDiff</a></td><td class='docblock-short'><p>The requisite parameters for testing for approximate equality using a
absolute difference based comparison.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Basis2.html" title='cgmath::Basis2 struct'>Basis2</a></td><td class='docblock-short'><p>A two-dimensional rotation matrix.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Basis3.html" title='cgmath::Basis3 struct'>Basis3</a></td><td class='docblock-short'><p>A three-dimensional rotation matrix.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Decomposed.html" title='cgmath::Decomposed struct'>Decomposed</a></td><td class='docblock-short'><p>A generic transformation consisting of a rotation,
displacement vector and scale amount.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Deg.html" title='cgmath::Deg struct'>Deg</a></td><td class='docblock-short'><p>An angle, in degrees.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Euler.html" title='cgmath::Euler struct'>Euler</a></td><td class='docblock-short'><p>A set of <a href="https://en.wikipedia.org/wiki/Euler_angles">Euler angles</a> representing a rotation in three-dimensional space.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Matrix2.html" title='cgmath::Matrix2 struct'>Matrix2</a></td><td class='docblock-short'><p>A 2 x 2, column major matrix</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Matrix3.html" title='cgmath::Matrix3 struct'>Matrix3</a></td><td class='docblock-short'><p>A 3 x 3, column major matrix</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Matrix4.html" title='cgmath::Matrix4 struct'>Matrix4</a></td><td class='docblock-short'><p>A 4 x 4, column major matrix</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Ortho.html" title='cgmath::Ortho struct'>Ortho</a></td><td class='docblock-short'><p>An orthographic projection with arbitrary left/right/bottom/top distances</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Perspective.html" title='cgmath::Perspective struct'>Perspective</a></td><td class='docblock-short'><p>A perspective projection with arbitrary left/right/bottom/top distances</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.PerspectiveFov.html" title='cgmath::PerspectiveFov struct'>PerspectiveFov</a></td><td class='docblock-short'><p>A perspective projection based on a vertical field-of-view angle.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Point1.html" title='cgmath::Point1 struct'>Point1</a></td><td class='docblock-short'><p>A point in 1-dimensional space.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Point2.html" title='cgmath::Point2 struct'>Point2</a></td><td class='docblock-short'><p>A point in 2-dimensional space.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Point3.html" title='cgmath::Point3 struct'>Point3</a></td><td class='docblock-short'><p>A point in 3-dimensional space.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Quaternion.html" title='cgmath::Quaternion struct'>Quaternion</a></td><td class='docblock-short'><p>A <a href="https://en.wikipedia.org/wiki/Quaternion">quaternion</a> in scalar/vector
form.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Rad.html" title='cgmath::Rad struct'>Rad</a></td><td class='docblock-short'><p>An angle, in radians.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Relative.html" title='cgmath::Relative struct'>Relative</a></td><td class='docblock-short'><p>The requisite parameters for testing for approximate equality using a
relative based comparison.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Ulps.html" title='cgmath::Ulps struct'>Ulps</a></td><td class='docblock-short'><p>The requisite parameters for testing for approximate equality using an ULPs
based comparison.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Vector1.html" title='cgmath::Vector1 struct'>Vector1</a></td><td class='docblock-short'><p>A 1-dimensional vector.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Vector2.html" title='cgmath::Vector2 struct'>Vector2</a></td><td class='docblock-short'><p>A 2-dimensional vector.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Vector3.html" title='cgmath::Vector3 struct'>Vector3</a></td><td class='docblock-short'><p>A 3-dimensional vector.</p>
</td></tr><tr class='module-item'><td><a class="struct" href="struct.Vector4.html" title='cgmath::Vector4 struct'>Vector4</a></td><td class='docblock-short'><p>A 4-dimensional vector.</p>
</td></tr></table><h2 id='traits' class='section-header'><a href="#traits">Traits</a></h2>
<table><tr class='module-item'><td><a class="trait" href="trait.AbsDiffEq.html" title='cgmath::AbsDiffEq trait'>AbsDiffEq</a></td><td class='docblock-short'><p>Equality that is defined using the absolute difference of two numbers.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Angle.html" title='cgmath::Angle trait'>Angle</a></td><td class='docblock-short'><p>Angles and their associated trigonometric functions.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Array.html" title='cgmath::Array trait'>Array</a></td><td class='docblock-short'><p>An array containing elements of type <code>Element</code></p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.BaseFloat.html" title='cgmath::BaseFloat trait'>BaseFloat</a></td><td class='docblock-short'><p>Base floating point types</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.BaseNum.html" title='cgmath::BaseNum trait'>BaseNum</a></td><td class='docblock-short'><p>Base numeric types with partial ordering</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Bounded.html" title='cgmath::Bounded trait'>Bounded</a></td><td class='docblock-short'><p>Numbers which have upper and lower bounds</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.ElementWise.html" title='cgmath::ElementWise trait'>ElementWise</a></td><td class='docblock-short'><p>Element-wise arithmetic operations. These are supplied for pragmatic
reasons, but will usually fall outside of traditional algebraic properties.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.EuclideanSpace.html" title='cgmath::EuclideanSpace trait'>EuclideanSpace</a></td><td class='docblock-short'><p>Points in a <a href="https://en.wikipedia.org/wiki/Euclidean_space">Euclidean space</a>
with an associated space of displacement vectors.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.InnerSpace.html" title='cgmath::InnerSpace trait'>InnerSpace</a></td><td class='docblock-short'><p>Vectors that also have a <a href="https://en.wikipedia.org/wiki/Dot_product">dot</a>
(or <a href="https://en.wikipedia.org/wiki/Inner_product_space">inner</a>) product.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Matrix.html" title='cgmath::Matrix trait'>Matrix</a></td><td class='docblock-short'><p>A column-major matrix of arbitrary dimensions.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.MetricSpace.html" title='cgmath::MetricSpace trait'>MetricSpace</a></td><td class='docblock-short'><p>A type with a distance function between values.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.One.html" title='cgmath::One trait'>One</a></td><td class='docblock-short'><p>Defines a multiplicative identity element for <code>Self</code>.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.RelativeEq.html" title='cgmath::RelativeEq trait'>RelativeEq</a></td><td class='docblock-short'><p>Equality comparisons between two numbers using both the absolute difference and
relative based comparisons.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Rotation.html" title='cgmath::Rotation trait'>Rotation</a></td><td class='docblock-short'><p>A trait for a generic rotation. A rotation is a transformation that
creates a circular motion, and preserves at least one point in the space.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Rotation2.html" title='cgmath::Rotation2 trait'>Rotation2</a></td><td class='docblock-short'><p>A two-dimensional rotation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Rotation3.html" title='cgmath::Rotation3 trait'>Rotation3</a></td><td class='docblock-short'><p>A three-dimensional rotation.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.SquareMatrix.html" title='cgmath::SquareMatrix trait'>SquareMatrix</a></td><td class='docblock-short'><p>A column-major major matrix where the rows and column vectors are of the same dimensions.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Transform.html" title='cgmath::Transform trait'>Transform</a></td><td class='docblock-short'><p>A trait representing an <a href="https://en.wikipedia.org/wiki/Affine_transformation">affine
transformation</a> that
can be applied to points or vectors. An affine transformation is one which</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Transform2.html" title='cgmath::Transform2 trait'>Transform2</a></td><td class='docblock-short'></td></tr><tr class='module-item'><td><a class="trait" href="trait.Transform3.html" title='cgmath::Transform3 trait'>Transform3</a></td><td class='docblock-short'></td></tr><tr class='module-item'><td><a class="trait" href="trait.UlpsEq.html" title='cgmath::UlpsEq trait'>UlpsEq</a></td><td class='docblock-short'><p>Equality comparisons between two numbers using both the absolute difference and ULPs
(Units in Last Place) based comparisons.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.VectorSpace.html" title='cgmath::VectorSpace trait'>VectorSpace</a></td><td class='docblock-short'><p>Vectors that can be <a href="http://mathworld.wolfram.com/VectorAddition.html">added</a>
together and <a href="https://en.wikipedia.org/wiki/Scalar_multiplication">multiplied</a>
by scalars.</p>
</td></tr><tr class='module-item'><td><a class="trait" href="trait.Zero.html" title='cgmath::Zero trait'>Zero</a></td><td class='docblock-short'><p>Defines an additive identity element for <code>Self</code>.</p>
</td></tr></table><h2 id='functions' class='section-header'><a href="#functions">Functions</a></h2>
<table><tr class='module-item'><td><a class="fn" href="fn.dot.html" title='cgmath::dot fn'>dot</a></td><td class='docblock-short'><p>Dot product of two vectors.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.frustum.html" title='cgmath::frustum fn'>frustum</a></td><td class='docblock-short'><p>Create a perspective matrix from a view frustum.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.ortho.html" title='cgmath::ortho fn'>ortho</a></td><td class='docblock-short'><p>Create an orthographic projection matrix.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.perspective.html" title='cgmath::perspective fn'>perspective</a></td><td class='docblock-short'><p>Create a perspective projection matrix.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.vec1.html" title='cgmath::vec1 fn'>vec1</a></td><td class='docblock-short'><p>The short constructor.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.vec2.html" title='cgmath::vec2 fn'>vec2</a></td><td class='docblock-short'><p>The short constructor.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.vec3.html" title='cgmath::vec3 fn'>vec3</a></td><td class='docblock-short'><p>The short constructor.</p>
</td></tr><tr class='module-item'><td><a class="fn" href="fn.vec4.html" title='cgmath::vec4 fn'>vec4</a></td><td class='docblock-short'><p>The short constructor.</p>
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