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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 `EuclideanSpace` trait in crate `alga`."><meta name="keywords" content="rust, rustlang, rust-lang, EuclideanSpace"><title>alga::linear::EuclideanSpace - 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 EuclideanSpace</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.Coordinates">Coordinates</a><a href="#associatedtype.RealField">RealField</a></div><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.origin">origin</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.coordinates">coordinates</a><a href="#method.distance">distance</a><a href="#method.distance_squared">distance_squared</a><a href="#method.from_coordinates">from_coordinates</a><a href="#method.scale_by">scale_by</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: 'EuclideanSpace', 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/vector.rs.html#156-224' 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=''>EuclideanSpace</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait EuclideanSpace: <a class="trait" href="../../alga/linear/trait.AffineSpace.html" title="trait alga::linear::AffineSpace">AffineSpace</a><Translation = Self::<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><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="../../alga/general/trait.ClosedDiv.html" title="trait alga::general::ClosedDiv">ClosedDiv</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a><Output = Self> {
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type <a href='#associatedtype.Coordinates' class="type">Coordinates</a>: <a class="trait" href="../../alga/linear/trait.FiniteDimInnerSpace.html" title="trait alga::linear::FiniteDimInnerSpace">FiniteDimInnerSpace</a><RealField = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, ComplexField = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a><Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>>;
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type <a href='#associatedtype.RealField' class="type">RealField</a>: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a>;
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fn <a href='#tymethod.origin' class='fnname'>origin</a>() -> Self;
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fn <a href='#method.scale_by' class='fnname'>scale_by</a>(&self, s: Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>) -> Self { ... }
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<div class='item-spacer'></div> fn <a href='#method.coordinates' class='fnname'>coordinates</a>(&self) -> Self::<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.from_coordinates' class='fnname'>from_coordinates</a>(coords: Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> Self { ... }
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<div class='item-spacer'></div> fn <a href='#method.distance_squared' class='fnname'>distance_squared</a>(&self, b: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a> { ... }
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<div class='item-spacer'></div> fn <a href='#method.distance' class='fnname'>distance</a>(&self, b: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a> { ... }
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}</pre></div><div class='docblock'><p>The finite-dimensional affine space based on the field of reals.</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.Coordinates' class='method'><code id='Coordinates.t'>type <a href='#associatedtype.Coordinates' class="type">Coordinates</a>: <a class="trait" href="../../alga/linear/trait.FiniteDimInnerSpace.html" title="trait alga::linear::FiniteDimInnerSpace">FiniteDimInnerSpace</a><RealField = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, ComplexField = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Add.html" title="trait core::ops::arith::Add">Add</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.AddAssign.html" title="trait core::ops::arith::AddAssign">AddAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Sub.html" title="trait core::ops::arith::Sub">Sub</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.SubAssign.html" title="trait core::ops::arith::SubAssign">SubAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Mul.html" title="trait core::ops::arith::Mul">Mul</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.MulAssign.html" title="trait core::ops::arith::MulAssign">MulAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Div.html" title="trait core::ops::arith::Div">Div</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>, Output = Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.DivAssign.html" title="trait core::ops::arith::DivAssign">DivAssign</a><Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>> + <a class="trait" href="https://doc.rust-lang.org/nightly/core/ops/arith/trait.Neg.html" title="trait core::ops::arith::Neg">Neg</a><Output = Self::<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>The underlying finite vector space.</p>
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</div><h3 id='associatedtype.RealField' class='method'><code id='RealField.t'>type <a href='#associatedtype.RealField' class="type">RealField</a>: <a class="trait" href="../../alga/general/trait.RealField.html" title="trait alga::general::RealField">RealField</a></code></h3><div class='docblock'><p>The underlying reals.</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.origin' class='method'><code id='origin.v'>fn <a href='#tymethod.origin' class='fnname'>origin</a>() -> Self</code></h3><div class='docblock'><p>The preferred origin of this euclidean space.</p>
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<p>Theoretically, an euclidean space has no clearly defined origin. Though it is almost always
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useful to have some reference point to express all the others as translations of it.</p>
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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.scale_by' class='method'><code id='scale_by.v'>fn <a href='#method.scale_by' class='fnname'>scale_by</a>(&self, s: Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a>) -> Self</code></h3><div class='docblock'><p>Multiplies the distance of this point to <code>Self::origin()</code> by <code>s</code>.</p>
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<p>Same as self * s.</p>
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</div><h3 id='method.coordinates' class='method'><code id='coordinates.v'>fn <a href='#method.coordinates' class='fnname'>coordinates</a>(&self) -> Self::<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>The coordinates of this point, i.e., the translation from the origin.</p>
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</div><h3 id='method.from_coordinates' class='method'><code id='from_coordinates.v'>fn <a href='#method.from_coordinates' class='fnname'>from_coordinates</a>(coords: Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.Coordinates" title="type alga::linear::EuclideanSpace::Coordinates">Coordinates</a>) -> Self</code></h3><div class='docblock'><p>Builds a point from its coordinates relative to the origin.</p>
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</div><h3 id='method.distance_squared' class='method'><code id='distance_squared.v'>fn <a href='#method.distance_squared' class='fnname'>distance_squared</a>(&self, b: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a></code></h3><div class='docblock'><p>The distance between two points.</p>
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</div><h3 id='method.distance' class='method'><code id='distance.v'>fn <a href='#method.distance' class='fnname'>distance</a>(&self, b: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.reference.html">&</a>Self) -> Self::<a class="type" href="../../alga/linear/trait.EuclideanSpace.html#associatedtype.RealField" title="type alga::linear::EuclideanSpace::RealField">RealField</a></code></h3><div class='docblock'><p>The distance between two points.</p>
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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'></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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