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<article data-uid="Usage.HiMech.Topo">
<h1 id="kinematic-topology">Kinematic Topology</h1>
<p>The Kinematic Topology is composed of three elemental classes: <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong>, <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> and <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong>.</p>
<h2 id="basic-elements">Basic Elements</h2>
<h3 id="anchors-and-branches">Anchors and Branches</h3>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a></strong> object contains a cartesian coordinate. It can be a mechanical component or a flag.</p>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Branch.html">Branch</a></strong> object is a directional link between two <a class="xref" href="../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> objects. It contains the <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a></strong> object. The <a class="xref" href="../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a> object contains a coordinate <strong>transformation matrix</strong>. As shown in the following sketch:</p>
<p><img src="chainLink.png" alt="Chain Structure"></p>
<h3 id="assembly-management">Assembly Management</h3>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a></strong> (Assembly) provides organization and management of Anchors. An Assembly can contain both Anchors and other Assemblies. Key features include:</p>
<ul>
<li>Grouping related Anchors together</li>
<li>Managing coordinate transformations</li>
<li>Providing display and indexing functions</li>
<li>Supporting hierarchical structure</li>
</ul>
<h2 id="kinematic-chain-example">Kinematic Chain Example</h2>
<p>The following figure shows a kinematic chain of a non-orthogonal 5-axis machine tool:</p>
<p><img src="vmt.png" alt="VMT Structure"></p>
<p>Each <a class="xref" href="../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a> represents a component:</p>
<ul>
<li>Axis components: X, Y, Z, B, C</li>
<li>Base components: O (base1), O* (base2)</li>
<li>Tool components: S (spindle), T (tool body), T* (tool flute)</li>
<li>Workpiece: W</li>
</ul>
<p>The relative transform between two Anchors is calculated by multiplying the transform matrices along the Branch. For example, the transform matrix from W to T is:</p>
<div class="math">
\[
M_{WT} = M_{CW}^{-1} \cdot M_{YC}^{-1} \cdot M_{OY}^{-1} \cdot M_{OO^*} \cdot M_{O^*X} \cdot M_{XZ} \cdot M_{ZB} \cdot M_{BS} \cdot M_{ST}
\]</div>
<p>This matrix can be obtained using <a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html#Hi_Mech_Topo_Asmb_GetMat4d_Hi_Mech_Topo_IGetAnchor_Hi_Mech_Topo_IGetAnchor_">GetMat4d(IGetAnchor, IGetAnchor)</a>.</p>
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<article data-uid="HiMech.Overview">
<h1 id="mechanism-topology">Mechanism Topology</h1>
<p>HiAPI Mechanism Topology provides basic functionality for assembling mechanical structures and simulating their motions. It allows you to build kinematic models of milling machines and similar mechanical structures through a topology-based approach.</p>
<h2 id="core-concepts">Core Concepts</h2>
<h3 id="kinematic-topology">Kinematic Topology</h3>
<p>Kinematic Topology is the core concept of this module, which describes the motion relationships between mechanical components. With Kinematic Topology, you can:</p>
<ul>
<li>Define mechanical structures and motion relationships</li>
<li>Calculate forward and inverse kinematics</li>
<li>Display component positions and orientations</li>
<li>Conduct collision detection</li>
</ul>
<h3 id="main-modules">Main Modules</h3>
<ul>
<li><a href="Topo/index.html">Topology</a> - Kinematic topology structure, including assembly management and chain definition</li>
<li><a href="transformers/index.html">Transformers</a> - Coordinate transformation and motion transformation</li>
<li><a href="render-topology/index.html">Render Topology</a> - Rendering with topology structure and anchored display</li>
</ul>
<h2 id="api-references">API References</h2>
<ul>
<li><a class="xref" href="../../../api/Hi.Mech.Topo.html">Hi.Mech.Topo</a> - Core topology functionality</li>
<li><a class="xref" href="../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a> - Assembly-related functionality</li>
<li><a class="xref" href="../../../api/Hi.Mech.Topo.Branch.html">Branch</a> - Chain-related functionality</li>
</ul>
<h2 id="examples">Examples</h2>
<p>Please refer to the examples in each sub-section to learn how to use these features to build your applications.</p>
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<h1 id="render-topology">Render Topology</h1>
<p>Read <a href="../Topo/index.html">Kinematic Topology</a> <a href="../../rendering/index.html">Rendering</a> for the prerequisite.</p>
<p>A <a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a> is a group to render its descendent <a class="xref" href="../../../../api/Hi.Mech.Topo.Anchor.html">Anchor</a>s.</p>
<p>Several ways to render with the topology:</p>
<ul>
<li>Render by Anchoring Matrix Map</li>
<li>Render by Anchored Displayee</li>
</ul>
<h2 id="render-by-anchoring-matrix-map">Render by Anchoring Matrix Map</h2>
<h2 id="render-by-anchored-displayee">Render by Anchored Displayee</h2>
<p>Inherit <a class="xref" href="../../../../api/Hi.Mech.Topo.IAnchoredDisplayee.html">IAnchoredDisplayee</a> or apply <a class="xref" href="../../../../api/Hi.Mech.Topo.AnchoredDisplayee.html">AnchoredDisplayee</a> to <a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a>.Display().</p>
<p>Inherit <a class="xref" href="../../../../api/Hi.Mech.Topo.ITopoDisplayee.html">ITopoDisplayee</a> to manage the object with <a class="xref" href="../../../../api/Hi.Mech.Topo.Asmb.html">Asmb</a> and plural anchors .</p>
<p>The base logic is also by the anchoring matrix. Here is some class and function wrapping the logic.</p>
<p>The sample code shows the topology rendering for a <a class="xref" href="../../../../api/Hi.Milling.MillingTools.MillingTool.html">MillingTool</a> editing helper:</p>
<pre><code class="lang-csharp" name="MillingToolEditorDisplayee">using Hi.Common;
using Hi.Common.Messages;
using Hi.Disp;
using Hi.Disp.Flag;
using Hi.Geom;
using Hi.Mech.Topo;
using Hi.Milling.Cutters;
using Hi.NcMech.Holders;
using System;
using System.Collections.Generic;
namespace Hi.Milling.MillingTools
{
/// &lt;summary&gt;
/// Display host for a milling tool composed of a cutter and a holder.
/// &lt;/summary&gt;
public class MillingToolEditorDisplayee : ITopoDisplayee, IClearCache
{
/// &lt;summary&gt;
/// Gets or sets the delegate that provides the &lt;see cref=&quot;MillingTool&quot;/&gt; instance.
/// &lt;/summary&gt;
public Func&lt;MillingTool&gt; MillingToolGetter { get; set; }
/// &lt;summary&gt;
/// Gets the current &lt;see cref=&quot;MillingTool&quot;/&gt; instance.
/// &lt;/summary&gt;
public MillingTool MillingTool =&gt; MillingToolGetter?.Invoke();
/// &lt;summary&gt;
/// Gets or sets whether to show the cutter.
/// &lt;/summary&gt;
public bool ShowCutter { get; set; } = true;
/// &lt;summary&gt;
/// Gets or sets whether to show the holder.
/// &lt;/summary&gt;
public bool ShowHolder { get; set; } = true;
/// &lt;summary&gt;
/// Gets the displayee for the milling cutter.
/// &lt;/summary&gt;
public MillingCutterEditorDisplayee MillingCutterEditorDisplayee { get; }
= new MillingCutterEditorDisplayee();
/// &lt;summary&gt;
/// Gets the displayee for the holder.
/// &lt;/summary&gt;
public HolderEditorDisplayee HolderEditorDisplayee { get; }
= new HolderEditorDisplayee();
/// &lt;inheritdoc/&gt;
public List&lt;IAnchoredDisplayee&gt; GetAnchoredDisplayeeList()
{
var dst = new List&lt;IAnchoredDisplayee&gt;();
var millingTool = MillingTool;
if (millingTool == null)
return dst;
if (ShowCutter)
{
var cutter = millingTool.Cutter;
if (cutter is MillingCutter millingCutter)
{
//MessageKit.AddMessage($&quot;MillingTool.Cutter: {MillingTool?.Cutter?.GetHashCode()}&quot;);
MillingCutterEditorDisplayee.MillingCutterSourceFunc
= () =&gt; MillingTool?.Cutter as MillingCutter;
dst.Add(MillingCutterEditorDisplayee);
}
else if(cutter!=null)
dst.Add(cutter);
}
if (ShowHolder)
{
HolderEditorDisplayee.Holder = millingTool.Holder;
dst.Add(HolderEditorDisplayee);
}
return dst;
}
/// &lt;inheritdoc/&gt;
public void Display(Bind bind)
{
bind.PushCoveringPixelMode();
DimensionBar.Display(bind, &quot;mm&quot;);
bind.ModelMatStack.Pop();
TopoDisplayeeUtil.Display(this, bind);
}
/// &lt;inheritdoc/&gt;
public void ExpandToBox3d(Box3d dst)
{
TopoDisplayeeUtil.ExpandToBox3d(this, dst);
}
/// &lt;inheritdoc/&gt;
public Asmb GetAsmb() =&gt; MillingTool?.Asmb;
/// &lt;inheritdoc/&gt;
public Anchor GetAnchor() =&gt; MillingTool?.GetAnchor();
/// &lt;inheritdoc/&gt;
public void ClearCache()
{
MillingCutterEditorDisplayee?.ClearCache();
}
}
}
</code></pre>
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<article data-uid="HiMech.Tutor.transformers">
<h1 id="handle-transform-matrix-by-itransformer">Handle Transform Matrix by ITransformer</h1>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a></strong> contains a transform matrix and a inverse transform matrix. The matrix is 4x4 column-major matrix, which describe the orientation or movement between 3D coordinates.</p>
<p>Several common used interface and class are implemented from <a class="xref" href="../../../../api/Hi.Mech.Topo.ITransformer.html">ITransformer</a>. The inheritance is shown:</p>
<ul>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.IStaticTransformer.html">IStaticTransformer</a>
<ul>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.NoTransform.html">NoTransform</a></li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a></li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a></li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticFreeform.html">StaticFreeform</a></li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.GeneralTransform.html">GeneralTransform</a></li>
</ul>
</li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicTransformer.html">IDynamicTransformer</a>
<ul>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a>
<ul>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicTranslation.html">DynamicTranslation</a></li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicRotation.html">DynamicRotation</a></li>
</ul>
</li>
<li><a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicFreeform.html">DynamicFreeform</a></li>
</ul>
</li>
</ul>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.IStaticTransformer.html">IStaticTransformer</a></strong> is transformer with constant matrix. <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.NoTransform.html">NoTransform</a></strong>, <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a></strong> and <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a></strong> contains transform matrix of identity, translate and rotate respectively. <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.StaticFreeform.html">StaticFreeform</a></strong> contains a arbitrary constant transform matrix.</p>
<p>The transform matrix of <a class="xref" href="../../../../api/Hi.Mech.Topo.StaticTranslation.html">StaticTranslation</a> is:</p>
<div class="math">
\[
M_{StaticTranslate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Trans.x &amp; Trans.y &amp; Trans.z &amp; 1
\end{bmatrix}
\]</div>
<p>The transform matrix of <a class="xref" href="../../../../api/Hi.Mech.Topo.StaticRotation.html">StaticRotation</a> and <a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicRotation.html">DynamicRotation</a> is:</p>
<div class="math">
\[
M_{Rotate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
-Pivot.x &amp; -Pivot.y &amp; -Pivot.z &amp; 1
\end{bmatrix}
\cdot
\\\\
\begin{bmatrix}
Rot_{00}(axis,rad) &amp; Rot_{01}(axis,rad) &amp; Rot_{02}(axis,rad) &amp; 0 \\\\
Rot_{10}(axis,rad) &amp; Rot_{11}(axis,rad) &amp; Rot_{12}(axis,rad) &amp; 0 \\\\
Rot_{20}(axis,rad) &amp; Rot_{21}(axis,rad) &amp; Rot_{22}(axis,rad) &amp; 0 \\\\
0 &amp; 0 &amp; 0 &amp; 1
\end{bmatrix}
\cdot
\\\\
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Pivot.x &amp; Pivot.y &amp; Pivot.z &amp; 1
\end{bmatrix}
\]</div>
<p>Where <a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicRotation.html#Hi_Mech_Topo_DynamicRotation_Pivot">Pivot</a> is the position of the rotation axis.</p>
<div class="TIP">
<h5>Tip</h5>
<p>Pivot is a point. However, rotation axis is a line. It means that it causes the same matrix no matter how the pivot is moving along the axis.</p>
</div>
<p><strong><a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicTransformer.html">IDynamicTransformer</a></strong> is transformer with inconstant transform matrix. <strong><a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a></strong> has a property <a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicRegular.html#Hi_Mech_Topo_IDynamicRegular_Step">Step</a>, implied that the transform matrix is one parameter driven. <a class="xref" href="../../../../api/Hi.Mech.Topo.TransformerUtil.html#Hi_Mech_Topo_TransformerUtil_GetSteps_Hi_Mech_Topo_IDynamicRegular___">GetSteps(IDynamicRegular[])</a> and <a class="xref" href="../../../../api/Hi.Mech.Topo.TransformerUtil.html#Hi_Mech_Topo_TransformerUtil_SetSteps_Hi_Mech_Topo_IDynamicRegular___System_Double___">SetSteps(IDynamicRegular[], double[])</a> provide easy handle of an array of <a class="xref" href="../../../../api/Hi.Mech.Topo.IDynamicRegular.html">IDynamicRegular</a> objects.</p>
<p>The transform matrix of <a class="xref" href="../../../../api/Hi.Mech.Topo.DynamicTranslation.html">DynamicTranslation</a> is:</p>
<div class="math">
\[
M_{DynamicTranslate}=
\begin{bmatrix}
1 &amp; 0 &amp; 0 &amp; 0 \\\\
0 &amp; 1 &amp; 0 &amp; 0 \\\\
0 &amp; 0 &amp; 1 &amp; 0 \\\\
Trans.x \cdot Step &amp; Trans.y \cdot Step &amp; Trans.z \cdot Step &amp; 1
\end{bmatrix}
\]</div>
<div class="NOTE">
<h5>Note</h5>
<p>In convention, <a class="xref" href="../../../../api/Hi.Mech.Topo.StaticTranslation.html#Hi_Mech_Topo_StaticTranslation_Trans">Trans</a> should be normalized.</p>
</div>
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