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<title>Class PairZr | HiAPI-C# 2025 </title>
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<article data-uid="Hi.Geom.PairZr">
<h1 id="Hi_Geom_PairZr" data-uid="Hi.Geom.PairZr" class="text-break">
Class PairZr
</h1>
<div class="facts text-secondary">
<dl><dt>Namespace</dt><dd><a class="xref" href="Hi.html">Hi</a>.<a class="xref" href="Hi.Geom.html">Geom</a></dd></dl>
<dl><dt>Assembly</dt><dd>HiGeom.dll</dd></dl>
</div>
<div class="markdown summary"><p>Value pair of Z and R.</p>
</div>
<div class="markdown conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public class PairZr : IMakeXmlSource, IExpandToBox3d, IEqualityOperators&lt;PairZr, PairZr, bool&gt;, IAdditionOperators&lt;PairZr, PairZr, PairZr&gt;, ISubtractionOperators&lt;PairZr, PairZr, PairZr&gt;, IMultiplyOperators&lt;PairZr, double, PairZr&gt;, IDivisionOperators&lt;PairZr, double, PairZr&gt;, IFormattable</code></pre>
</div>
<dl class="typelist inheritance">
<dt>Inheritance</dt>
<dd>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object">object</a></div>
<div><span class="xref">PairZr</span></div>
</dd>
</dl>
<dl class="typelist implements">
<dt>Implements</dt>
<dd>
<div><a class="xref" href="Hi.Common.XmlUtils.IMakeXmlSource.html">IMakeXmlSource</a></div>
<div><a class="xref" href="Hi.Geom.IExpandToBox3d.html">IExpandToBox3d</a></div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.numerics.iequalityoperators-3">IEqualityOperators</a>&lt;<a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a>&gt;</div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.numerics.iadditionoperators-3">IAdditionOperators</a>&lt;<a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>&gt;</div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.numerics.isubtractionoperators-3">ISubtractionOperators</a>&lt;<a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>&gt;</div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.numerics.imultiplyoperators-3">IMultiplyOperators</a>&lt;<a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>&gt;</div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.numerics.idivisionoperators-3">IDivisionOperators</a>&lt;<a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>, <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a>, <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a>&gt;</div>
<div><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.iformattable">IFormattable</a></div>
</dd>
</dl>
<dl class="typelist inheritedMembers">
<dt>Inherited Members</dt>
<dd>
<div>
<a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object.equals#system-object-equals(system-object-system-object)">object.Equals(object, object)</a>
</div>
<div>
<a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object.gettype">object.GetType()</a>
</div>
<div>
<a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object.memberwiseclone">object.MemberwiseClone()</a>
</div>
<div>
<a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object.referenceequals">object.ReferenceEquals(object, object)</a>
</div>
</dd></dl>
<dl class="typelist extensionMethods">
<dt>Extension Methods</dt>
<dd>
<div>
<a class="xref" href="Hi.Common.XmlUtils.XmlUtil.html#Hi_Common_XmlUtils_XmlUtil_MakeXmlSourceFile_Hi_Common_XmlUtils_IMakeXmlSource_System_String_System_Boolean_">XmlUtil.MakeXmlSourceFile(IMakeXmlSource, string, bool)</a>
</div>
<div>
<a class="xref" href="Hi.Common.XmlUtils.XmlUtil.html#Hi_Common_XmlUtils_XmlUtil_MakeXmlSourceWithRebaseFile_Hi_Common_XmlUtils_IMakeXmlSource_System_String_System_String_System_Boolean_">XmlUtil.MakeXmlSourceWithRebaseFile(IMakeXmlSource, string, string, bool)</a>
</div>
<div>
<a class="xref" href="Hi.Common.XmlUtils.XmlUtil.html#Hi_Common_XmlUtils_XmlUtil_SaveToByteArrayAsync_Hi_Common_XmlUtils_IMakeXmlSource_System_String_">XmlUtil.SaveToByteArrayAsync(IMakeXmlSource, string)</a>
</div>
<div>
<a class="xref" href="Hi.Geom.GeomUtil.html#Hi_Geom_GeomUtil_ExpandToBox3d_Hi_Geom_IExpandToBox3d_Hi_Geom_Mat4d_Hi_Geom_Box3d_">GeomUtil.ExpandToBox3d(IExpandToBox3d, Mat4d, Box3d)</a>
</div>
<div>
<a class="xref" href="Hi.Geom.GeomUtil.html#Hi_Geom_GeomUtil_GetBox3d_Hi_Geom_IExpandToBox3d_">GeomUtil.GetBox3d(IExpandToBox3d)</a>
</div>
<div>
<a class="xref" href="Hi.Common.DuplicateUtil.html#Hi_Common_DuplicateUtil_TryDuplicate__1___0_System_Object___">DuplicateUtil.TryDuplicate&lt;TSelf&gt;(TSelf, params object[])</a>
</div>
<div>
<a class="xref" href="Hi.Common.InvokeUtil.html#Hi_Common_InvokeUtil_SelfInvoke__1___0_System_Action___0__">InvokeUtil.SelfInvoke&lt;TSrc&gt;(TSrc, Action&lt;TSrc&gt;)</a>
</div>
<div>
<a class="xref" href="Hi.Common.InvokeUtil.html#Hi_Common_InvokeUtil_SelfInvoke__2___0_System_Func___0___1__">InvokeUtil.SelfInvoke&lt;TSrc, TDst&gt;(TSrc, Func&lt;TSrc, TDst&gt;)</a>
</div>
<div>
<a class="xref" href="Hi.Coloring.ColorUtil.html#Hi_Coloring_ColorUtil_GetGloomyColor_System_Object_System_Double_System_Double_">ColorUtil.GetGloomyColor(object, double, double)</a>
</div>
<div>
<a class="xref" href="Hi.Common.NameUtil.html#Hi_Common_NameUtil_GetSelectionName_System_Object_">NameUtil.GetSelectionName(object)</a>
</div>
<div>
<a class="xref" href="Hi.Common.StringUtil.html#Hi_Common_StringUtil_GetPropertyStringIfToStringNotOverloaded_System_Object_System_Boolean_System_Boolean_">StringUtil.GetPropertyStringIfToStringNotOverloaded(object, bool, bool)</a>
</div>
<div>
<a class="xref" href="Hi.Parallels.LockUtil.html#Hi_Parallels_LockUtil_Lock_System_Object_">LockUtil.Lock(object)</a>
</div>
</dd></dl>
<h2 class="section" id="constructors">Constructors
</h2>
<a id="Hi_Geom_PairZr__ctor_" data-uid="Hi.Geom.PairZr.#ctor*"></a>
<h3 id="Hi_Geom_PairZr__ctor" data-uid="Hi.Geom.PairZr.#ctor">
PairZr()
</h3>
<div class="markdown level1 summary"><p>Ctor.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public PairZr()</code></pre>
</div>
<a id="Hi_Geom_PairZr__ctor_" data-uid="Hi.Geom.PairZr.#ctor*"></a>
<h3 id="Hi_Geom_PairZr__ctor_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.#ctor(Hi.Geom.PairZr)">
PairZr(PairZr)
</h3>
<div class="markdown level1 summary"><p>Copy ctor.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public PairZr(PairZr src)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>src</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr__ctor_" data-uid="Hi.Geom.PairZr.#ctor*"></a>
<h3 id="Hi_Geom_PairZr__ctor_System_Double_System_Double_" data-uid="Hi.Geom.PairZr.#ctor(System.Double,System.Double)">
PairZr(double, double)
</h3>
<div class="markdown level1 summary"><p>Ctor.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public PairZr(double z, double r)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>z</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd><p>see <a class="xref" href="Hi.Geom.PairZr.html#Hi_Geom_PairZr_Z">Z</a></p>
</dd>
<dt><code>r</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd><p>see <a class="xref" href="Hi.Geom.PairZr.html#Hi_Geom_PairZr_R">R</a></p>
</dd>
</dl>
<a id="Hi_Geom_PairZr__ctor_" data-uid="Hi.Geom.PairZr.#ctor*"></a>
<h3 id="Hi_Geom_PairZr__ctor_System_String_" data-uid="Hi.Geom.PairZr.#ctor(System.String)">
PairZr(string)
</h3>
<div class="markdown level1 summary"><p>Ctor.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public PairZr(string src)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>src</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr__ctor_" data-uid="Hi.Geom.PairZr.#ctor*"></a>
<h3 id="Hi_Geom_PairZr__ctor_System_Xml_Linq_XElement_" data-uid="Hi.Geom.PairZr.#ctor(System.Xml.Linq.XElement)">
PairZr(XElement)
</h3>
<div class="markdown level1 summary"><p>Ctor.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public PairZr(XElement src)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>src</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.xml.linq.xelement">XElement</a></dt>
<dd><p>XML</p>
</dd>
</dl>
<h2 class="section" id="properties">Properties
</h2>
<a id="Hi_Geom_PairZr_R_" data-uid="Hi.Geom.PairZr.R*"></a>
<h3 id="Hi_Geom_PairZr_R" data-uid="Hi.Geom.PairZr.R">
R
</h3>
<div class="markdown level1 summary"><p>R value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public double R { get; set; }</code></pre>
</div>
<h4 class="section">Property Value</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr_XName_" data-uid="Hi.Geom.PairZr.XName*"></a>
<h3 id="Hi_Geom_PairZr_XName" data-uid="Hi.Geom.PairZr.XName">
XName
</h3>
<div class="markdown level1 summary"><p>Name for XML IO.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static string XName { get; }</code></pre>
</div>
<h4 class="section">Property Value</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr_Z_" data-uid="Hi.Geom.PairZr.Z*"></a>
<h3 id="Hi_Geom_PairZr_Z" data-uid="Hi.Geom.PairZr.Z">
Z
</h3>
<div class="markdown level1 summary"><p>Z value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public double Z { get; set; }</code></pre>
</div>
<h4 class="section">Property Value</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr_ZR_" data-uid="Hi.Geom.PairZr.ZR*"></a>
<h3 id="Hi_Geom_PairZr_ZR" data-uid="Hi.Geom.PairZr.ZR">
ZR
</h3>
<div class="markdown level1 summary"><p>(x,y)=(z,r).</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public Vec2d ZR { get; set; }</code></pre>
</div>
<h4 class="section">Property Value</h4>
<dl class="parameters">
<dt><a class="xref" href="Hi.Geom.Vec2d.html">Vec2d</a></dt>
<dd></dd>
</dl>
<h2 class="section" id="methods">Methods
</h2>
<a id="Hi_Geom_PairZr_Equals_" data-uid="Hi.Geom.PairZr.Equals*"></a>
<h3 id="Hi_Geom_PairZr_Equals_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.Equals(Hi.Geom.PairZr)">
Equals(PairZr)
</h3>
<div class="markdown level1 summary"></div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public bool Equals(PairZr other)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>other</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd></dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a></dt>
<dd></dd>
</dl>
<a id="Hi_Geom_PairZr_Equals_" data-uid="Hi.Geom.PairZr.Equals*"></a>
<h3 id="Hi_Geom_PairZr_Equals_System_Object_" data-uid="Hi.Geom.PairZr.Equals(System.Object)">
Equals(object)
</h3>
<div class="markdown level1 summary"><p>Determines whether the specified object is equal to the current object.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public override bool Equals(object obj)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>obj</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.object">object</a></dt>
<dd><p>The object to compare with the current object.</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a></dt>
<dd><p><a href="https://learn.microsoft.com/dotnet/csharp/language-reference/builtin-types/bool">true</a> if the specified object is equal to the current object; otherwise, <a href="https://learn.microsoft.com/dotnet/csharp/language-reference/builtin-types/bool">false</a>.</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_ExpandToBox3d_" data-uid="Hi.Geom.PairZr.ExpandToBox3d*"></a>
<h3 id="Hi_Geom_PairZr_ExpandToBox3d_Hi_Geom_Box3d_" data-uid="Hi.Geom.PairZr.ExpandToBox3d(Hi.Geom.Box3d)">
ExpandToBox3d(Box3d)
</h3>
<div class="markdown level1 summary"><p>Expands the destination box.
This function is usually used to compute the bounding box of elements.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public void ExpandToBox3d(Box3d dst)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>dst</code> <a class="xref" href="Hi.Geom.Box3d.html">Box3d</a></dt>
<dd><p>Destination box</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_GenCircle_" data-uid="Hi.Geom.PairZr.GenCircle*"></a>
<h3 id="Hi_Geom_PairZr_GenCircle_System_Int32_" data-uid="Hi.Geom.PairZr.GenCircle(System.Int32)">
GenCircle(int)
</h3>
<div class="markdown level1 summary"><p>Generates a collection of Vec3d points forming a circle at the Z coordinate with radius R.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public IEnumerable&lt;Vec3d&gt; GenCircle(int posNum)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>posNum</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.int32">int</a></dt>
<dd><p>The number of points to generate around the circle</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.collections.generic.ienumerable-1">IEnumerable</a>&lt;<a class="xref" href="Hi.Geom.Vec3d.html">Vec3d</a>&gt;</dt>
<dd><p>An enumerable collection of Vec3d points</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_GenPolarCircle_" data-uid="Hi.Geom.PairZr.GenPolarCircle*"></a>
<h3 id="Hi_Geom_PairZr_GenPolarCircle_System_Int32_" data-uid="Hi.Geom.PairZr.GenPolarCircle(System.Int32)">
GenPolarCircle(int)
</h3>
<div class="markdown level1 summary"><p>Generates a collection of Polar3d points forming a circle at the Z coordinate with radius R.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public IEnumerable&lt;Polar3d&gt; GenPolarCircle(int posNum)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>posNum</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.int32">int</a></dt>
<dd><p>The number of points to generate around the circle</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.collections.generic.ienumerable-1">IEnumerable</a>&lt;<a class="xref" href="Hi.Geom.Polar3d.html">Polar3d</a>&gt;</dt>
<dd><p>An enumerable collection of Polar3d points</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_GetHashCode_" data-uid="Hi.Geom.PairZr.GetHashCode*"></a>
<h3 id="Hi_Geom_PairZr_GetHashCode" data-uid="Hi.Geom.PairZr.GetHashCode">
GetHashCode()
</h3>
<div class="markdown level1 summary"><p>Serves as the default hash function.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public override int GetHashCode()</code></pre>
</div>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.int32">int</a></dt>
<dd><p>A hash code for the current object.</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_MakeXmlSource_" data-uid="Hi.Geom.PairZr.MakeXmlSource*"></a>
<h3 id="Hi_Geom_PairZr_MakeXmlSource_System_String_System_String_System_Boolean_" data-uid="Hi.Geom.PairZr.MakeXmlSource(System.String,System.String,System.Boolean)">
MakeXmlSource(string, string, bool)
</h3>
<div class="markdown level1 summary"><p>Creates an XML representation of the object.
This method may also generate additional resources such as related files.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public XElement MakeXmlSource(string baseDirectory, string relFile, bool exhibitionOnly)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>baseDirectory</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd><p>The base directory for resolving relative paths</p>
</dd>
<dt><code>relFile</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd><p>The relative file path for the XML source</p>
</dd>
<dt><code>exhibitionOnly</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a></dt>
<dd><p>if true, the extended file creation is suppressed.</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.xml.linq.xelement">XElement</a></dt>
<dd><p>An XML element representing the object's state</p>
</dd>
</dl>
<h4 class="section" id="Hi_Geom_PairZr_MakeXmlSource_System_String_System_String_System_Boolean__remarks">Remarks</h4>
<div class="markdown level1 remarks"><p>For the demand of easy moving source folder (especially project folder) without configuration file path corruption, the relative file path is applied.
The <code class="paramref">baseDirectory</code> is typically the folder at the nearest configuration file folder.
Since the folder can be moving with the configuration file.</p>
</div>
<a id="Hi_Geom_PairZr_ToString_" data-uid="Hi.Geom.PairZr.ToString*"></a>
<h3 id="Hi_Geom_PairZr_ToString" data-uid="Hi.Geom.PairZr.ToString">
ToString()
</h3>
<div class="markdown level1 summary"><p>Returns a string that represents the current object.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public override string ToString()</code></pre>
</div>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd><p>A string that represents the current object.</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_ToString_" data-uid="Hi.Geom.PairZr.ToString*"></a>
<h3 id="Hi_Geom_PairZr_ToString_System_String_System_IFormatProvider_" data-uid="Hi.Geom.PairZr.ToString(System.String,System.IFormatProvider)">
ToString(string, IFormatProvider)
</h3>
<div class="markdown level1 summary"><p>Returns a string representation of the PairZr formatted according to the specified format.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public string ToString(string format, IFormatProvider formatProvider)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>format</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd><p>The format to use for each component</p>
</dd>
<dt><code>formatProvider</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.iformatprovider">IFormatProvider</a></dt>
<dd><p>The format provider to use</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.string">string</a></dt>
<dd><p>A formatted string representation of the PairZr</p>
</dd>
</dl>
<h2 class="section" id="operators">Operators
</h2>
<a id="Hi_Geom_PairZr_op_Addition_" data-uid="Hi.Geom.PairZr.op_Addition*"></a>
<h3 id="Hi_Geom_PairZr_op_Addition_Hi_Geom_PairZr_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.op_Addition(Hi.Geom.PairZr,Hi.Geom.PairZr)">
operator +(PairZr, PairZr)
</h3>
<div class="markdown level1 summary"><p>Addition operator that adds two PairZr instances.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static PairZr operator +(PairZr left, PairZr right)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>left</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The left operand</p>
</dd>
<dt><code>right</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The right operand</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>A new PairZr instance with the sum of Z and R values</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_op_Division_" data-uid="Hi.Geom.PairZr.op_Division*"></a>
<h3 id="Hi_Geom_PairZr_op_Division_Hi_Geom_PairZr_System_Double_" data-uid="Hi.Geom.PairZr.op_Division(Hi.Geom.PairZr,System.Double)">
operator /(PairZr, double)
</h3>
<div class="markdown level1 summary"><p>Division operator that divides a PairZr instance by a scalar value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static PairZr operator /(PairZr left, double right)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>left</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The PairZr instance</p>
</dd>
<dt><code>right</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd><p>The scalar value</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>A new PairZr instance with Z and R values divided by the scalar</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_op_Equality_" data-uid="Hi.Geom.PairZr.op_Equality*"></a>
<h3 id="Hi_Geom_PairZr_op_Equality_Hi_Geom_PairZr_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.op_Equality(Hi.Geom.PairZr,Hi.Geom.PairZr)">
operator ==(PairZr, PairZr)
</h3>
<div class="markdown level1 summary"><p>Equality operator that compares two PairZr instances.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static bool operator ==(PairZr left, PairZr right)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>left</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The left operand</p>
</dd>
<dt><code>right</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The right operand</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a></dt>
<dd><p>True if both instances are equal; otherwise, false</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_op_Inequality_" data-uid="Hi.Geom.PairZr.op_Inequality*"></a>
<h3 id="Hi_Geom_PairZr_op_Inequality_Hi_Geom_PairZr_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.op_Inequality(Hi.Geom.PairZr,Hi.Geom.PairZr)">
operator !=(PairZr, PairZr)
</h3>
<div class="markdown level1 summary"><p>Inequality operator that compares two PairZr instances.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static bool operator !=(PairZr left, PairZr right)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>left</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The left operand</p>
</dd>
<dt><code>right</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The right operand</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="https://learn.microsoft.com/dotnet/api/system.boolean">bool</a></dt>
<dd><p>True if the instances are not equal; otherwise, false</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_op_Multiply_" data-uid="Hi.Geom.PairZr.op_Multiply*"></a>
<h3 id="Hi_Geom_PairZr_op_Multiply_Hi_Geom_PairZr_System_Double_" data-uid="Hi.Geom.PairZr.op_Multiply(Hi.Geom.PairZr,System.Double)">
operator *(PairZr, double)
</h3>
<div class="markdown level1 summary"><p>Multiplication operator that multiplies a PairZr instance by a scalar value.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static PairZr operator *(PairZr left, double right)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>left</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The PairZr instance</p>
</dd>
<dt><code>right</code> <a class="xref" href="https://learn.microsoft.com/dotnet/api/system.double">double</a></dt>
<dd><p>The scalar value</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>A new PairZr instance with Z and R values multiplied by the scalar</p>
</dd>
</dl>
<a id="Hi_Geom_PairZr_op_Subtraction_" data-uid="Hi.Geom.PairZr.op_Subtraction*"></a>
<h3 id="Hi_Geom_PairZr_op_Subtraction_Hi_Geom_PairZr_Hi_Geom_PairZr_" data-uid="Hi.Geom.PairZr.op_Subtraction(Hi.Geom.PairZr,Hi.Geom.PairZr)">
operator -(PairZr, PairZr)
</h3>
<div class="markdown level1 summary"><p>Subtraction operator that subtracts one PairZr instance from another.</p>
</div>
<div class="markdown level1 conceptual"></div>
<div class="codewrapper">
<pre><code class="lang-csharp hljs">public static PairZr operator -(PairZr a, PairZr b)</code></pre>
</div>
<h4 class="section">Parameters</h4>
<dl class="parameters">
<dt><code>a</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The left operand</p>
</dd>
<dt><code>b</code> <a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>The right operand to subtract</p>
</dd>
</dl>
<h4 class="section">Returns</h4>
<dl class="parameters">
<dt><a class="xref" href="Hi.Geom.PairZr.html">PairZr</a></dt>
<dd><p>A new PairZr instance with the difference of Z and R values</p>
</dd>
</dl>
</article>
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