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<article class="content wrap" id="_content" data-uid="X10D.Math.MathUtility">
<h1 id="X10D_Math_MathUtility" data-uid="X10D.Math.MathUtility" class="text-break">Class MathUtility
</h1>
<div class="markdown level0 summary"><p>Provides static helpers methods for mathematical functions not found in the .NET <see cref="!:System.Math"></see> class.</p>
</div>
<div class="markdown level0 conceptual"></div>
<div class="inheritance">
<h5>Inheritance</h5>
<div class="level0"><span class="xref">System.Object</span></div>
<div class="level1"><span class="xref">MathUtility</span></div>
</div>
<h6><strong>Namespace</strong>: <a class="xref" href="X10D.Math.html">X10D.Math</a></h6>
<h6><strong>Assembly</strong>: X10D.dll</h6>
<h5 id="X10D_Math_MathUtility_syntax">Syntax</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static class MathUtility : object</code></pre>
</div>
<h3 id="methods">Methods
</h3>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_Bias_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.Bias(System.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_Bias_" data-uid="X10D.Math.MathUtility.Bias*"></a>
<h4 id="X10D_Math_MathUtility_Bias_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.Bias(System.Double,System.Double)">Bias(Double, Double)</h4>
<div class="markdown level1 summary"><p>Applies a simple bias function to value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double Bias(double value, double bias)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to which the bias function will be applied.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">bias</span></td>
<td><p>The bias value. Valid values range from 0-1.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The biased result.</p>
</td>
</tr>
</tbody>
</table>
<h5 id="X10D_Math_MathUtility_Bias_System_Double_System_Double__remarks">Remarks</h5>
<div class="markdown level1 remarks"><p>If <code data-dev-comment-type="paramref" class="paramref">bias</code> is less than 0.5, <code data-dev-comment-type="paramref" class="paramref">value</code> will be shifted downward; otherwise, upward.</p>
</div>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_Bias_System_Single_System_Single_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.Bias(System.Single%2CSystem.Single)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_Bias_" data-uid="X10D.Math.MathUtility.Bias*"></a>
<h4 id="X10D_Math_MathUtility_Bias_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.Bias(System.Single,System.Single)">Bias(Single, Single)</h4>
<div class="markdown level1 summary"><p>Applies a simple bias function to value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float Bias(float value, float bias)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to which the bias function will be applied.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">bias</span></td>
<td><p>The bias value. Valid values range from 0-1.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The biased result.</p>
</td>
</tr>
</tbody>
</table>
<h5 id="X10D_Math_MathUtility_Bias_System_Single_System_Single__remarks">Remarks</h5>
<div class="markdown level1 remarks"><p>If <code data-dev-comment-type="paramref" class="paramref">bias</code> is less than 0.5, <code data-dev-comment-type="paramref" class="paramref">value</code> will be shifted downward; otherwise, upward.</p>
</div>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_ExponentialDecay_System_Double_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.ExponentialDecay(System.Double%2CSystem.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_ExponentialDecay_" data-uid="X10D.Math.MathUtility.ExponentialDecay*"></a>
<h4 id="X10D_Math_MathUtility_ExponentialDecay_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.ExponentialDecay(System.Double,System.Double,System.Double)">ExponentialDecay(Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Calculates exponential decay for a value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double ExponentialDecay(double value, double alpha, double decay)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to decay.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>A factor by which to scale the decay.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">decay</span></td>
<td><p>The decay amount.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The exponentially decayed value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_ExponentialDecay_System_Single_System_Single_System_Single_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.ExponentialDecay(System.Single%2CSystem.Single%2CSystem.Single)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_ExponentialDecay_" data-uid="X10D.Math.MathUtility.ExponentialDecay*"></a>
<h4 id="X10D_Math_MathUtility_ExponentialDecay_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.ExponentialDecay(System.Single,System.Single,System.Single)">ExponentialDecay(Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Calculates exponential decay for a value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float ExponentialDecay(float value, float alpha, float decay)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to decay.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>A factor by which to scale the decay.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">decay</span></td>
<td><p>The decay amount.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The exponentially decayed value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_GammaToLinear_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.GammaToLinear(System.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_GammaToLinear_" data-uid="X10D.Math.MathUtility.GammaToLinear*"></a>
<h4 id="X10D_Math_MathUtility_GammaToLinear_System_Double_" data-uid="X10D.Math.MathUtility.GammaToLinear(System.Double)">GammaToLinear(Double)</h4>
<div class="markdown level1 summary"><p>Converts a gamma-encoded value to a linear value using a gamma value of <code>2.2</code>.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double GammaToLinear(double value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The gamma-encoded value to convert. Expected range is [0, 1].</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The linear value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_GammaToLinear_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.GammaToLinear(System.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_GammaToLinear_" data-uid="X10D.Math.MathUtility.GammaToLinear*"></a>
<h4 id="X10D_Math_MathUtility_GammaToLinear_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.GammaToLinear(System.Double,System.Double)">GammaToLinear(Double, Double)</h4>
<div class="markdown level1 summary"><p>Converts a gamma-encoded value to a linear value using the specified gamma value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double GammaToLinear(double value, double gamma)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The gamma-encoded value to convert. Expected range is [0, 1].</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">gamma</span></td>
<td><p>The gamma value to use for decoding.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The linear value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_GammaToLinear_System_Single_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.GammaToLinear(System.Single)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_GammaToLinear_" data-uid="X10D.Math.MathUtility.GammaToLinear*"></a>
<h4 id="X10D_Math_MathUtility_GammaToLinear_System_Single_" data-uid="X10D.Math.MathUtility.GammaToLinear(System.Single)">GammaToLinear(Single)</h4>
<div class="markdown level1 summary"><p>Converts a gamma-encoded value to a linear value using a gamma value of <code>2.2</code>.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float GammaToLinear(float value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The gamma-encoded value to convert. Expected range is [0, 1].</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The linear value.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_GammaToLinear_" data-uid="X10D.Math.MathUtility.GammaToLinear*"></a>
<h4 id="X10D_Math_MathUtility_GammaToLinear_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.GammaToLinear(System.Single,System.Single)">GammaToLinear(Single, Single)</h4>
<div class="markdown level1 summary"><p>Converts a gamma-encoded value to a linear value using the specified gamma value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float GammaToLinear(float value, float gamma)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The gamma-encoded value to convert. Expected range is [0, 1].</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">gamma</span></td>
<td><p>The gamma value to use for decoding.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The linear value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_InverseLerp_System_Double_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.InverseLerp(System.Double%2CSystem.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_InverseLerp_" data-uid="X10D.Math.MathUtility.InverseLerp*"></a>
<h4 id="X10D_Math_MathUtility_InverseLerp_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.InverseLerp(System.Double,System.Double,System.Double)">InverseLerp(Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Returns the linear interpolation inverse of a value, such that it determines where a value lies between two other
values.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double InverseLerp(double alpha, double start, double end)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The value whose lerp inverse is to be found.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">start</span></td>
<td><p>The start of the range.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">end</span></td>
<td><p>The end of the range.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>A value determined by <code>(alpha - start) / (end - start)</code>.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_InverseLerp_" data-uid="X10D.Math.MathUtility.InverseLerp*"></a>
<h4 id="X10D_Math_MathUtility_InverseLerp_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.InverseLerp(System.Single,System.Single,System.Single)">InverseLerp(Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Returns the linear interpolation inverse of a value, such that it determines where a value lies between two other
values.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float InverseLerp(float alpha, float start, float end)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The value whose lerp inverse is to be found.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">start</span></td>
<td><p>The start of the range.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">end</span></td>
<td><p>The end of the range.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>A value determined by <code>(alpha - start) / (end - start)</code>.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_Lerp_" data-uid="X10D.Math.MathUtility.Lerp*"></a>
<h4 id="X10D_Math_MathUtility_Lerp_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.Lerp(System.Double,System.Double,System.Double)">Lerp(Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Linearly interpolates from one value to a target using a specified alpha.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double Lerp(double value, double target, double alpha)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The interpolation source.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">target</span></td>
<td><p>The interpolation target.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The interpolation alpha.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The interpolation result as determined by <code>(1 - alpha) * value + alpha * target</code>.</p>
</td>
</tr>
</tbody>
</table>
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<h4 id="X10D_Math_MathUtility_Lerp_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.Lerp(System.Single,System.Single,System.Single)">Lerp(Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Linearly interpolates from one value to a target using a specified alpha.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float Lerp(float value, float target, float alpha)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The interpolation source.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">target</span></td>
<td><p>The interpolation target.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The interpolation alpha.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The interpolation result as determined by <code>(1 - alpha) * value + alpha * target</code>.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_LinearToGamma_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.LinearToGamma(System.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_LinearToGamma_" data-uid="X10D.Math.MathUtility.LinearToGamma*"></a>
<h4 id="X10D_Math_MathUtility_LinearToGamma_System_Double_" data-uid="X10D.Math.MathUtility.LinearToGamma(System.Double)">LinearToGamma(Double)</h4>
<div class="markdown level1 summary"><p>Converts a linear value to a gamma-encoded value using a gamma value of <code>2.2</code>.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double LinearToGamma(double value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The linear value to convert. Expected range is [0, 1].</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The gamma-encoded value.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_LinearToGamma_" data-uid="X10D.Math.MathUtility.LinearToGamma*"></a>
<h4 id="X10D_Math_MathUtility_LinearToGamma_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.LinearToGamma(System.Double,System.Double)">LinearToGamma(Double, Double)</h4>
<div class="markdown level1 summary"><p>Converts a linear value to a gamma-encoded value using the specified gamma value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double LinearToGamma(double value, double gamma)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The linear value to convert. Expected range is [0, 1].</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">gamma</span></td>
<td><p>The gamma value to use for encoding.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The gamma-encoded value.</p>
</td>
</tr>
</tbody>
</table>
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<h4 id="X10D_Math_MathUtility_LinearToGamma_System_Single_" data-uid="X10D.Math.MathUtility.LinearToGamma(System.Single)">LinearToGamma(Single)</h4>
<div class="markdown level1 summary"><p>Converts a linear value to a gamma-encoded value using a gamma value of <code>2.2</code>.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float LinearToGamma(float value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The linear value to convert. Expected range is [0, 1].</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The gamma-encoded value.</p>
</td>
</tr>
</tbody>
</table>
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<h4 id="X10D_Math_MathUtility_LinearToGamma_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.LinearToGamma(System.Single,System.Single)">LinearToGamma(Single, Single)</h4>
<div class="markdown level1 summary"><p>Converts a linear value to a gamma-encoded value using the specified gamma value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float LinearToGamma(float value, float gamma)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The linear value to convert. Expected range is [0, 1].</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">gamma</span></td>
<td><p>The gamma value to use for encoding.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The gamma-encoded value.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_Pulse_" data-uid="X10D.Math.MathUtility.Pulse*"></a>
<h4 id="X10D_Math_MathUtility_Pulse_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.Pulse(System.Double,System.Double,System.Double)">Pulse(Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Returns the pulse wave for a given value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double Pulse(double value, double lowerBound, double upperBound)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to calculate.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">lowerBound</span></td>
<td><p>The inclusive lower bound of the pulse.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">upperBound</span></td>
<td><p>The inclusive upper bound of the pulse.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>1 if <code data-dev-comment-type="paramref" class="paramref">value</code> lies between <code data-dev-comment-type="paramref" class="paramref">lowerBound</code> and <code data-dev-comment-type="paramref" class="paramref">upperBound</code>;
otherwise, 0.</p>
</td>
</tr>
</tbody>
</table>
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<a id="X10D_Math_MathUtility_Pulse_" data-uid="X10D.Math.MathUtility.Pulse*"></a>
<h4 id="X10D_Math_MathUtility_Pulse_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.Pulse(System.Single,System.Single,System.Single)">Pulse(Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Returns the pulse wave for a given value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float Pulse(float value, float lowerBound, float upperBound)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to calculate.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">lowerBound</span></td>
<td><p>The inclusive lower bound of the pulse.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">upperBound</span></td>
<td><p>The inclusive upper bound of the pulse.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>1 if <code data-dev-comment-type="paramref" class="paramref">value</code> lies between <code data-dev-comment-type="paramref" class="paramref">lowerBound</code> and <code data-dev-comment-type="paramref" class="paramref">upperBound</code>;
otherwise, 0.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_Sawtooth_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.Sawtooth(System.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_Sawtooth_" data-uid="X10D.Math.MathUtility.Sawtooth*"></a>
<h4 id="X10D_Math_MathUtility_Sawtooth_System_Double_" data-uid="X10D.Math.MathUtility.Sawtooth(System.Double)">Sawtooth(Double)</h4>
<div class="markdown level1 summary"><p>Returns the incremental sawtooth wave of a given value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double Sawtooth(double value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to calculate.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The sawtooth wave of the given value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_Sawtooth_System_Single_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.Sawtooth(System.Single)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_Sawtooth_" data-uid="X10D.Math.MathUtility.Sawtooth*"></a>
<h4 id="X10D_Math_MathUtility_Sawtooth_System_Single_" data-uid="X10D.Math.MathUtility.Sawtooth(System.Single)">Sawtooth(Single)</h4>
<div class="markdown level1 summary"><p>Returns the incremental sawtooth wave of a given value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float Sawtooth(float value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to calculate.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The sawtooth wave of the given value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_ScaleRange_System_Double_System_Double_System_Double_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.ScaleRange(System.Double%2CSystem.Double%2CSystem.Double%2CSystem.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<a id="X10D_Math_MathUtility_ScaleRange_" data-uid="X10D.Math.MathUtility.ScaleRange*"></a>
<h4 id="X10D_Math_MathUtility_ScaleRange_System_Double_System_Double_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.ScaleRange(System.Double,System.Double,System.Double,System.Double,System.Double)">ScaleRange(Double, Double, Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Converts a value from being a percentage of one range, to being the same percentage in a new range.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double ScaleRange(double value, double oldMin, double oldMax, double newMin, double newMax)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to convert.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">oldMin</span></td>
<td><p>The old minimum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">oldMax</span></td>
<td><p>The old maximum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">newMin</span></td>
<td><p>The new minimum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">newMax</span></td>
<td><p>The new maximum value.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The scaled value.</p>
</td>
</tr>
</tbody>
</table>
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<h4 id="X10D_Math_MathUtility_ScaleRange_System_Single_System_Single_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.ScaleRange(System.Single,System.Single,System.Single,System.Single,System.Single)">ScaleRange(Single, Single, Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Converts a value from being a percentage of one range, to being the same percentage in a new range.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float ScaleRange(float value, float oldMin, float oldMax, float newMin, float newMax)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The value to convert.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">oldMin</span></td>
<td><p>The old minimum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">oldMax</span></td>
<td><p>The old maximum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">newMin</span></td>
<td><p>The new minimum value.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">newMax</span></td>
<td><p>The new maximum value.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The scaled value.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_Sigmoid_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.Sigmoid(System.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<h4 id="X10D_Math_MathUtility_Sigmoid_System_Double_" data-uid="X10D.Math.MathUtility.Sigmoid(System.Double)">Sigmoid(Double)</h4>
<div class="markdown level1 summary"><p>Calculates the sigmoid function for the given input value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double Sigmoid(double value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The input value for which to calculate the sigmoid function.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The result of applying the sigmoid function to the input value.</p>
</td>
</tr>
</tbody>
</table>
<h5 id="X10D_Math_MathUtility_Sigmoid_System_Double__remarks">Remarks</h5>
<div class="markdown level1 remarks"><p>The sigmoid function is a commonly used activation function in artificial neural networks and logistic regression. It
maps any real-valued number to a value between 0 and 1.</p>
</div>
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<h4 id="X10D_Math_MathUtility_Sigmoid_System_Single_" data-uid="X10D.Math.MathUtility.Sigmoid(System.Single)">Sigmoid(Single)</h4>
<div class="markdown level1 summary"><p>Calculates the sigmoid function for the given input value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float Sigmoid(float value)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The input value for which to calculate the sigmoid function.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The result of applying the sigmoid function to the input value.</p>
</td>
</tr>
</tbody>
</table>
<h5 id="X10D_Math_MathUtility_Sigmoid_System_Single__remarks">Remarks</h5>
<div class="markdown level1 remarks"><p>The sigmoid function is a commonly used activation function in artificial neural networks and logistic regression. It
maps any real-valued number to a value between 0 and 1.</p>
</div>
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<a href="https://github.com/oliverbooth/X10D/new/main/apiSpec/new?filename=X10D_Math_MathUtility_SmoothStep_System_Double_System_Double_System_Double_.md&amp;value=---%0Auid%3A%20X10D.Math.MathUtility.SmoothStep(System.Double%2CSystem.Double%2CSystem.Double)%0Asummary%3A%20'*You%20can%20override%20summary%20for%20the%20API%20here%20using%20*MARKDOWN*%20syntax'%0A---%0A%0A*Please%20type%20below%20more%20information%20about%20this%20API%3A*%0A%0A">Improve this Doc</a>
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<h4 id="X10D_Math_MathUtility_SmoothStep_System_Double_System_Double_System_Double_" data-uid="X10D.Math.MathUtility.SmoothStep(System.Double,System.Double,System.Double)">SmoothStep(Double, Double, Double)</h4>
<div class="markdown level1 summary"><p>Performs smooth Hermite interpolation from one value to a target using a specified alpha.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static double SmoothStep(double value, double target, double alpha)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">value</span></td>
<td><p>The interpolation source.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">target</span></td>
<td><p>The interpolation target.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Double</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The interpolation alpha.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Double</span></td>
<td><p>The interpolation result.</p>
</td>
</tr>
</tbody>
</table>
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<a href="https://github.com/oliverbooth/X10D/blob/main/X10D/src/Math/MathUtility.cs/#L202">View Source</a>
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<a id="X10D_Math_MathUtility_SmoothStep_" data-uid="X10D.Math.MathUtility.SmoothStep*"></a>
<h4 id="X10D_Math_MathUtility_SmoothStep_System_Single_System_Single_System_Single_" data-uid="X10D.Math.MathUtility.SmoothStep(System.Single,System.Single,System.Single)">SmoothStep(Single, Single, Single)</h4>
<div class="markdown level1 summary"><p>Performs smooth Hermite interpolation from one value to a target using a specified alpha.</p>
</div>
<div class="markdown level1 conceptual"></div>
<h5 class="decalaration">Declaration</h5>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static float SmoothStep(float value, float target, float alpha)</code></pre>
</div>
<h5 class="parameters">Parameters</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Name</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">value</span></td>
<td><p>The interpolation source.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">target</span></td>
<td><p>The interpolation target.</p>
</td>
</tr>
<tr>
<td><span class="xref">System.Single</span></td>
<td><span class="parametername">alpha</span></td>
<td><p>The interpolation alpha.</p>
</td>
</tr>
</tbody>
</table>
<h5 class="returns">Returns</h5>
<table class="table table-bordered table-striped table-condensed">
<thead>
<tr>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr>
<td><span class="xref">System.Single</span></td>
<td><p>The interpolation result.</p>
</td>
</tr>
</tbody>
</table>
</article>
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