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<!doctype html> <html> <head> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <title>Roots — Imath Documentation</title> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" /> <link rel="stylesheet" href="../_static/bizstyle.css" type="text/css" /> <script id="documentation_options" data-url_root="../" src="../_static/documentation_options.js"></script> <script src="../_static/jquery.js"></script> <script src="../_static/underscore.js"></script> <script src="../_static/doctools.js"></script> <script async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/latest.js?config=TeX-AMS-MML_HTMLorMML"></script> <script src="../_static/bizstyle.js"></script> <link rel="index" title="Index" href="../genindex.html" /> <link rel="search" title="Search" href="../search.html" /> <link rel="next" title="Vector Functions" href="vec.html" /> <link rel="prev" title="Random Numbers" href="random.html" /> <meta name="viewport" content="width=device-width,initial-scale=1.0" /> <!--[if lt IE 9]> <script src="_static/css3-mediaqueries.js"></script> <![endif]--> </head><body> <div class="related" role="navigation" aria-label="related navigation"> <h3>Navigation</h3> <ul> <li class="right" style="margin-right: 10px"> <a href="../genindex.html" title="General Index" accesskey="I">index</a></li> <li class="right" > <a href="vec.html" title="Vector Functions" accesskey="N">next</a> \|</li> <li class="right" > <a href="random.html" title="Random Numbers" accesskey="P">previous</a> \|</li> <li class="nav-item nav-item-0"><a href="../index.html">Imath</a> »</li> <li class="nav-item nav-item-this"><a href="">Roots</a></li> </ul> </div> <div class="document"> <div class="documentwrapper"> <div class="bodywrapper"> <div class="body" role="main"> <div class="section" id="roots"> <span id="id1"></span><h1>Roots<a class="headerlink" href="#roots" title="Permalink to this headline">¶</a></h1> <p>Functions to compute roots of simple equations.</p> <div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1">#include <Imath/ImathRoots.h></span> </pre></div> </div> <dl class="cpp function"> <dt id="_CPPv4I0EN5Imath11solveLinearEi1T1TR1T"> <span id="_CPPv3I0EN5Imath11solveLinearE1T1TR1T"></span><span id="_CPPv2I0EN5Imath11solveLinearE1T1TR1T"></span>template<class <code class="sig-name descname">T</code>><br /><span class="target" id="_imath_roots_8h_1ab74b6481dec757db3aabf3afad53b42b"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveLinear</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> &<em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Permalink to this definition">¶</a><br /></dt> <dd><p>Solve for x in the linear equation: </p> <p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o"></span> <span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">0</span> </pre></div> </div> <dl class="simple"> <dt><strong>Return</strong></dt><dd><p>1 if the equation has a solution, 0 if there is no solution, and -1 if all real numbers are solutions. </p> </dd> </dl> </p> </dd></dl> <dl class="cpp function"> <dt id="_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T"> <span id="_CPPv3I0EN5Imath14solveQuadraticE1T1T1TAL2E_1T"></span><span id="_CPPv2I0EN5Imath14solveQuadraticE1T1T1TA2_1T"></span>template<class <code class="sig-name descname">T</code>><br /><span class="target" id="_imath_roots_8h_1a94c654a5ec9ce534aaf83016ba2f265a"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveQuadratic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>c</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>x</em>[2]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Permalink to this definition">¶</a><br /></dt> <dd><p>Solve for x in the quadratic equation: </p> <p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o"></span> <span class="n">x</span><span class="o"></span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o"></span> <span class="n">x</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span> </pre></div> </div> <dl class="simple"> <dt><strong>Return</strong></dt><dd><p>2 if the equation has two solutions, 1 if the equation has a single solution, 0 if there is no solution, and -1 if all real numbers are solutions. </p> </dd> </dl> </p> </dd></dl> <dl class="cpp function"> <dt id="_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T"> <span id="_CPPv3I0EN5Imath20solveNormalizedCubicE1T1T1TAL3E_1T"></span><span id="_CPPv2I0EN5Imath20solveNormalizedCubicE1T1T1TA3_1T"></span>template<class <code class="sig-name descname">T</code>><br /><span class="target" id="_imath_roots_8h_1a0266743eb556a3eb3b340d0ed9d3ded9"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveNormalizedCubic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>r</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>s</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>t</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>x</em>[3]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Permalink to this definition">¶</a><br /></dt> <dd><p>Solve for x in the normalized cubic equation: </p> <p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span><span class="o"></span><span class="n">x</span><span class="o"></span><span class="n">x</span> <span class="o">+</span> <span class="n">r</span> <span class="o"></span> <span class="n">x</span><span class="o"></span><span class="n">x</span> <span class="o">+</span> <span class="n">s</span> <span class="o"></span> <span class="n">x</span> <span class="o">+</span> <span class="n">t</span> <span class="o">==</span> <span class="mi">0</span> </pre></div> </div> The equation is solved using Cardano’s Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).</p> <p><dl class="simple"> <dt><strong>Return</strong></dt><dd><p>0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions. </p> </dd> </dl> </p> </dd></dl> <dl class="cpp function"> <dt id="_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T"> <span id="_CPPv3I0EN5Imath10solveCubicE1T1T1T1TAL3E_1T"></span><span id="_CPPv2I0EN5Imath10solveCubicE1T1T1T1TA3_1T"></span>template<class <code class="sig-name descname">T</code>><br /><span class="target" id="_imath_roots_8h_1a2a27d3e8ea4d2aadc1c506b3a3d77bf5"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveCubic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>c</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>d</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>x</em>[3]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Permalink to this definition">¶</a><br /></dt> <dd><p>Solve for x in the cubic equation: </p> <p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o"></span> <span class="n">x</span><span class="o"></span><span class="n">x</span><span class="o"></span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o"></span> <span class="n">x</span><span class="o"></span><span class="n">x</span> <span class="o">+</span> <span class="n">c</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">d</span> <span class="o">==</span> <span class="mi">0</span> </pre></div> </div> The equation is solved using Cardano’s Formula; even though only real solutions are produced, some intermediate results are complex (std::complex<T>).</p> <p><dl class="simple"> <dt><strong>Return</strong></dt><dd><p>0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions. </p> </dd> </dl> </p> </dd></dl> </div> <div class="clearer"></div> </div> </div> </div> <div class="sphinxsidebar" role="navigation" aria-label="main navigation"> <div class="sphinxsidebarwrapper"> <p class="logo"><a href="../index.html"> <img class="logo" src="../_static/imath-logo-blue.png" alt="Logo"/> 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