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<article data-uid="Technique-AssemblyAnchors">
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<h1 id="assembly-anchors">Assembly Anchors</h1>
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<p>How the parts of a machining scene are held together. Assembly in HiNC is not a placement step but a
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statement of coincidence: two named anchors are declared equal, and everything they belong to moves
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so that they are. The buckle anchors below are the joints the machine, fixture, workpiece and tool
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are assembled at.</p>
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<p>Ordered from what an anchor is, to the two chains built out of them.</p>
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<h2 id="what-an-anchor-is">What an Anchor Is</h2>
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<p><strong>Anchors</strong> are used for assembly purposes. When anchors between geometries coincide, assembly is completed.</p>
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<p>Strictly speaking, an <strong>Anchor</strong> is not a point, but a coordinate system. For two coordinate systems to be equal, their origins must coincide and their rotation directions must be the same.</p>
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<div class="NOTE">
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<h5>Note</h5>
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<p><strong>Anchor Assembly Example</strong></p>
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<p>As shown in the figure below, there are two components, each with two anchors, {<code>AnchorA</code>,<code>AnchorB</code>} and {<code>AnchorC</code>,<code>AnchorD</code>} respectively.
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The two components are assembled by making <code>AnchorB</code> and <code>AnchorC</code> coincide.</p>
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<p><img src="assembly-anchors-img/Anchor%20for%20contact.png" alt="anc-contact"></p>
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</div>
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<h2 id="worktable-anchor-and-workpiece-anchor">Worktable Anchor and Workpiece Anchor</h2>
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<p>The machine's worktable end is the chain's <code>w</code> anchor. The fixture carries a <code>TableBuckle</code> that meets it, and a <code>WorkpieceBuckle</code> that the workpiece meets — and the workpiece's own anchor there is named <code>FixtureBuckle</code>, so this joint is made of two anchors each named after the <em>other</em> part.</p>
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<p>Only the machine-to-fixture branch carries an editable transform, which is where the fixture is placed on the table. The fixture-to-workpiece branch carries none: it is plain coincidence.</p>
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<div class="NOTE">
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<h5>Note</h5>
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<p><strong>Workpiece Fixture Assembly Example</strong></p>
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<p>Workpiece and fixture are assembled by making the fixture's <code>WorkpieceBuckle</code> and the workpiece's <code>FixtureBuckle</code> coincide.</p>
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<p><img src="assembly-anchors-img/Anchor%20for%20contact%20workpiece%20and%20fixture.png" alt=""></p>
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</div>
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<p>If no fixture is set, both fixture anchors drop out of the chain and the machine's <code>w</code> anchor meets the workpiece's <code>FixtureBuckle</code> directly, carrying the same placement transform.</p>
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<h2 id="spindle-anchor-and-cutter-anchor">Spindle Anchor and Cutter Anchor</h2>
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<p>The machine's tool end is the chain's <code>t</code> anchor, and it meets the <code>SpindleBuckle</code> of the tool as a whole. Inside that tool the holder sits between spindle and cutter: the tool's <code>SpindleBuckle</code> meets the holder's own <code>SpindleBuckle</code>, and the holder's <code>CutterBuckle</code> meets the cutter's buckle anchor (<code>Buckle</code>).</p>
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<p>If no holder is set, both holder anchors drop out and the tool's <code>SpindleBuckle</code> meets the cutter's <code>Buckle</code> directly. The machine-side joint is the same either way.</p>
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<h2 id="see-also">See Also</h2>
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<ul>
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<li><a href="topology.html">Kinematic Topology</a> — the anchor, branch and assembly classes this convention is expressed in</li>
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<li><a href="../../manual/setup/anchor.html">Anchor</a> — where these relationships are edited in the application</li>
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<li><a href="../../manual/setup/program-zero-alignment.html">Program Zero Alignment</a> — aligning the program origin onto these anchors</li>
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<article data-uid="Technique-ChainCode">
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<h1 id="machine-chain-code">Machine Chain Code</h1>
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<p>A machine tool file can carry its kinematic topology as a <strong>chain code</strong> — a short bracket notation
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||||
for the same connectivity the mechanism builder produces, meant for hand-editing the XML. It is read
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||||
and written by <a class="xref" href="../../api/Hi.Numerical.Xyzabc.CodeXyzabcChain.html">CodeXyzabcChain</a><small>(API)</small>, which builds the very
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same mechanism, so a hand-written code and a builder-drawn structure are interchangeable — with two
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exceptions on the way back: a mechanism with two components sharing one name, or with an unnamed
|
||||
component that more than one segment would have to mention, cannot be written down as code.</p>
|
||||
<p>The code carries <strong>connectivity only</strong>. Pivots, exact axis vectors, end-anchor offsets and shapes
|
||||
are properties of the mechanism, and editing the code preserves them for every component whose name
|
||||
is unchanged.</p>
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||||
<h2 id="the-notation">The Notation</h2>
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||||
<p>Each segment declares branches from left to right:</p>
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||||
<pre><code>[O][base][Z][C][w];[O][base][Y][X][B][S][t]
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||||
</code></pre>
|
||||
<ul>
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||||
<li><p><code>[A][B][C]</code> is shorthand for the branches <code>[A][B];[B][C]</code>, so a segment is just a path.</p>
|
||||
</li>
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||||
<li><p>Words are components. The <strong>same word in different segments is the same component</strong>, which is how
|
||||
segments join into one structure.</p>
|
||||
</li>
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||||
<li><p>The first word of the whole code names the ground anchor. Within a segment each branch runs from
|
||||
the word on its left to the word on its right.</p>
|
||||
</li>
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||||
<li><p>Reserved words are the topology keywords: <code>X</code>, <code>Y</code>, <code>Z</code>, <code>A</code>, <code>B</code>, <code>C</code> become motion axes, and <code>w</code>
|
||||
and <code>t</code> become the end anchors. <strong>Any other word is a plain component</strong> carried along without
|
||||
motion, such as <code>base</code> or <code>S</code> above. A code must name exactly one <code>[w]</code> and one <code>[t]</code>; the six
|
||||
axes are optional, and each may be used at most once. That uniqueness check reads the words
|
||||
without regard to letter case, so it refuses a code naming no table buckle at all — <em>the chain
|
||||
code must contain the table buckle [w]</em> — and a code letting two components claim one role —
|
||||
<em>more than one component claims the table buckle: [w], [W]</em>. A lone <code>[W]</code> satisfies it, one
|
||||
component claiming the role, and builds a component named <code>W</code>; that code is refused further
|
||||
along, by the exact-match end-anchor check below.</p>
|
||||
</li>
|
||||
<li><p><strong>Spell the keywords exactly</strong> — upper case for the axes, lower case for <code>t</code> and <code>w</code>. Everything
|
||||
downstream of the code compares them as written: axis discovery, the default collision pairs, and
|
||||
the end-anchor check a machine file is loaded through. So a mis-cased axis contributes no motion,
|
||||
and a mis-cased end anchor stops the file loading, with a message naming the near miss.</p>
|
||||
</li>
|
||||
<li><p><code>[]</code> is an anonymous component. Each occurrence is a separate one, it cannot be referred to from
|
||||
another segment, and it cannot hold a geometric shape — shapes are stored by component name.</p>
|
||||
</li>
|
||||
<li><p>Declaring the same branch twice is harmless; it states the same connection.</p>
|
||||
</li>
|
||||
<li><p>A segment with a single word just declares a component, which is how a ground anchor that only
|
||||
receives branches gets named.</p>
|
||||
</li>
|
||||
<li><p>Any number of segments is allowed, so auxiliary structures can branch off any component:</p>
|
||||
<pre><code>[O][base][Z][C][w];[O][base][Y][X][B][S][t];[base][loader][gripper]
|
||||
</code></pre>
|
||||
</li>
|
||||
</ul>
|
||||
<h2 id="direction-and-convergence">Direction and Convergence</h2>
|
||||
<p><strong>Branch direction is free.</strong> A branch authored towards the ground anchor is simply written that way,
|
||||
as in <code>[Z][O]</code>. A branch belongs to the component farther from the ground anchor, so <code>[O][Y]</code> and
|
||||
<code>[Y][O]</code> both make <code>Y</code> the axis; only the direction differs. Pointing every branch away from the
|
||||
ground anchor remains a readability convention — it makes the structure read outwards, ground → base
|
||||
→ motion axes → the <code>t</code> and <code>w</code> end anchors — but the motion, the axis keywords and the default
|
||||
collision pairs all read a branch the same way round regardless.</p>
|
||||
<p><strong>Limbs may meet again.</strong> <code>[A][B][D];[A][C][D]</code> gives <code>D</code> two incoming branches. Only one route
|
||||
through such a loop drives the motion, so use it for structure rather than for a second motion path.</p>
|
||||
<p>Axis directions follow the machine-building convention: axes between the ground anchor and <code>w</code> are
|
||||
seeded negative, the others positive.</p>
|
||||
<h2 id="see-also">See Also</h2>
|
||||
<ul>
|
||||
<li><a href="topology.html">Kinematic Topology</a> — the anchors, branches and assemblies this notation encodes</li>
|
||||
<li><a href="../../manual/setup/machine-tool.html">Machine Tool</a> — building the same structure in the mechanism builder, and the keywords both forms share</li>
|
||||
</ul>
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<article data-uid="HiMech.Overview">
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<h1 id="mechanism">Mechanism</h1>
|
||||
|
||||
<p>How a machine tool is assembled out of moving parts, and how HiAPI solves where each part ends
|
||||
up. A kinematic topology describes the motion relationships between components; from it come
|
||||
forward and inverse kinematics, component placement, and the geometry collision detection runs
|
||||
against.</p>
|
||||
<p>Ordered from the structure outwards: the topology first and the shorthand that writes it down, then
|
||||
the matrices that move it, then drawing it.</p>
|
||||
<ul>
|
||||
<li><a href="topology.html">Kinematic Topology</a> — Anchors, branches and assemblies, and how a machine chain is built out of them</li>
|
||||
<li><a href="chain-code.html">Machine Chain Code</a> — The bracket notation a machine file can carry its connectivity in, and the keyword spelling everything downstream reads it by</li>
|
||||
<li><a href="assembly-anchors.html">Assembly Anchors</a> — What an anchor is, and the buckles the machine, fixture, workpiece and tool are assembled at</li>
|
||||
<li><a href="transformers.html">Handle Transform Matrix by ITransformer</a> — The transform-matrix interface behind every joint, and the implementations covering the common cases</li>
|
||||
<li><a href="render-topology.html">Render Topology</a> — Drawing an assembly through its anchors, by anchoring matrix map or by anchored displayee</li>
|
||||
</ul>
|
||||
<h2 id="see-also">See Also</h2>
|
||||
<ul>
|
||||
<li><a href="../rendering/index.html">Rendering</a> — the engine that draws what the topology places</li>
|
||||
<li><a href="../api-foundations/index.html">API Foundations</a> — the geometry types a topology carries, and how an assembly is persisted</li>
|
||||
<li><a class="xref" href="../../api/Hi.Mech.Topo.html">Hi.Mech.Topo</a> — the generated reference for the namespace</li>
|
||||
<li><a class="xref" href="../../api/Hi.Mech.Topo.Asmb.html">Asmb</a> — assemblies</li>
|
||||
<li><a class="xref" href="../../api/Hi.Mech.Topo.Branch.html">Branch</a> — chains</li>
|
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<article data-uid="Technique-RenderTopology">
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<h1 id="render-topology">Render Topology</h1>
|
||||
|
||||
<p>Read <a class="xref" href="topology.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;
|
||||
|
||||
/// <summary>
|
||||
/// Display host for a milling tool composed of a cutter and a holder.
|
||||
/// </summary>
|
||||
public class MillingToolEditorDisplayee : ITopoDisplayee, IClearCache
|
||||
{
|
||||
/// <summary>
|
||||
/// Gets or sets the delegate that provides the <see cref="MillingTool"/> instance.
|
||||
/// </summary>
|
||||
public Func<MillingTool> MillingToolGetter { get; set; }
|
||||
/// <summary>
|
||||
/// Gets the current <see cref="MillingTool"/> instance.
|
||||
/// </summary>
|
||||
public MillingTool MillingTool => MillingToolGetter?.Invoke();
|
||||
|
||||
/// <summary>
|
||||
/// Gets or sets whether to show the cutter.
|
||||
/// </summary>
|
||||
public bool ShowCutter { get; set; } = true;
|
||||
/// <summary>
|
||||
/// Gets or sets whether to show the holder.
|
||||
/// </summary>
|
||||
public bool ShowHolder { get; set; } = true;
|
||||
|
||||
/// <summary>
|
||||
/// Gets the displayee for the milling cutter.
|
||||
/// </summary>
|
||||
public MillingCutterEditorDisplayee MillingCutterEditorDisplayee { get; }
|
||||
= new MillingCutterEditorDisplayee();
|
||||
/// <summary>
|
||||
/// Gets the displayee for the holder.
|
||||
/// </summary>
|
||||
public HolderEditorDisplayee HolderEditorDisplayee { get; }
|
||||
= new HolderEditorDisplayee();
|
||||
/// <inheritdoc/>
|
||||
public List<IAnchoredDisplayee> GetAnchoredDisplayeeList()
|
||||
{
|
||||
var dst = new List<IAnchoredDisplayee>();
|
||||
|
||||
var millingTool = MillingTool;
|
||||
if (millingTool == null)
|
||||
return dst;
|
||||
|
||||
if (ShowCutter)
|
||||
{
|
||||
var cutter = millingTool.Cutter;
|
||||
if (cutter is MillingCutter millingCutter)
|
||||
{
|
||||
//MessageKit.AddMessage($"MillingTool.Cutter: {MillingTool?.Cutter?.GetHashCode()}");
|
||||
MillingCutterEditorDisplayee.MillingCutterSourceFunc
|
||||
= () => 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;
|
||||
}
|
||||
/// <inheritdoc/>
|
||||
public void Display(Bind bind)
|
||||
{
|
||||
bind.PushCoveringPixelMode();
|
||||
DimensionBar.Display(bind, "mm");
|
||||
bind.ModelMatStack.Pop();
|
||||
|
||||
TopoDisplayeeUtil.Display(this, bind);
|
||||
}
|
||||
/// <inheritdoc/>
|
||||
public void ExpandToBox3d(Box3d dst)
|
||||
{
|
||||
TopoDisplayeeUtil.ExpandToBox3d(this, dst);
|
||||
}
|
||||
/// <inheritdoc/>
|
||||
public Asmb GetAsmb() => MillingTool?.Asmb;
|
||||
/// <inheritdoc/>
|
||||
public Anchor GetAnchor() => MillingTool?.GetAnchor();
|
||||
/// <inheritdoc/>
|
||||
public void ClearCache()
|
||||
{
|
||||
MillingCutterEditorDisplayee?.ClearCache();
|
||||
}
|
||||
}
|
||||
</code></pre><h2 id="see-also">See Also</h2>
|
||||
<ul>
|
||||
<li><a href="topology.html">Kinematic Topology</a> — the assembly and anchors this renders through</li>
|
||||
</ul>
|
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|
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</article>
|
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|
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|
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<a href="topology.html" name="" title="Kinematic Topology">Kinematic Topology</a>
|
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|
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|
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<a href="chain-code.html" name="" title="Machine Chain Code">Machine Chain Code</a>
|
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|
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|
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<a href="assembly-anchors.html" name="" title="Assembly Anchors">Assembly Anchors</a>
|
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|
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<a href="transformers.html" name="" title="Transformers">Transformers</a>
|
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<a href="render-topology.html" name="" title="Render Topology">Render Topology</a>
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@@ -0,0 +1,2 @@
|
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|
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{"items":[{"name":"Overview","href":"index.html","topicHref":"index.html"},{"name":"Kinematic Topology","href":"topology.html","topicHref":"topology.html"},{"name":"Machine Chain Code","href":"chain-code.html","topicHref":"chain-code.html"},{"name":"Assembly Anchors","href":"assembly-anchors.html","topicHref":"assembly-anchors.html"},{"name":"Transformers","href":"transformers.html","topicHref":"transformers.html"},{"name":"Render Topology","href":"render-topology.html","topicHref":"render-topology.html"}]}
|
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Binary file not shown.
|
After Width: | Height: | Size: 16 KiB |
Binary file not shown.
|
After Width: | Height: | Size: 90 KiB |
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<article data-uid="Usage.HiMech.Topo">
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<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="topology-img/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="topology-img/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>
|
||||
<h2 id="see-also">See Also</h2>
|
||||
<ul>
|
||||
<li><p><a href="chain-code.html">Machine Chain Code</a> — the bracket notation that writes this same connectivity down for hand-editing</p>
|
||||
</li>
|
||||
<li><p><a href="assembly-anchors.html">Assembly Anchors</a> — the four named buckle anchors a machining scene is assembled at</p>
|
||||
</li>
|
||||
<li><p><a href="transformers.html">Handle Transform Matrix by ITransformer</a> — what sits on each branch and moves it</p>
|
||||
</li>
|
||||
<li><p><a href="render-topology.html">Render Topology</a> — drawing an assembly through the anchors defined here</p>
|
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</li>
|
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</ul>
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<article data-uid="HiMech.Tutor.transformers">
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<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">
|
||||
\[
|
||||
M_{StaticTranslate}=
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\\\
|
||||
0 & 1 & 0 & 0 \\\\
|
||||
0 & 0 & 1 & 0 \\\\
|
||||
Trans.x & Trans.y & Trans.z & 1
|
||||
\end{bmatrix}
|
||||
\]</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">
|
||||
\[
|
||||
M_{Rotate}=
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\\\
|
||||
0 & 1 & 0 & 0 \\\\
|
||||
0 & 0 & 1 & 0 \\\\
|
||||
-Pivot.x & -Pivot.y & -Pivot.z & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\\\\
|
||||
\begin{bmatrix}
|
||||
Rot_{00}(axis,rad) & Rot_{01}(axis,rad) & Rot_{02}(axis,rad) & 0 \\\\
|
||||
Rot_{10}(axis,rad) & Rot_{11}(axis,rad) & Rot_{12}(axis,rad) & 0 \\\\
|
||||
Rot_{20}(axis,rad) & Rot_{21}(axis,rad) & Rot_{22}(axis,rad) & 0 \\\\
|
||||
0 & 0 & 0 & 1
|
||||
\end{bmatrix}
|
||||
\cdot
|
||||
\\\\
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\\\
|
||||
0 & 1 & 0 & 0 \\\\
|
||||
0 & 0 & 1 & 0 \\\\
|
||||
Pivot.x & Pivot.y & Pivot.z & 1
|
||||
\end{bmatrix}
|
||||
\]</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">
|
||||
\[
|
||||
M_{DynamicTranslate}=
|
||||
\begin{bmatrix}
|
||||
1 & 0 & 0 & 0 \\\\
|
||||
0 & 1 & 0 & 0 \\\\
|
||||
0 & 0 & 1 & 0 \\\\
|
||||
Trans.x \cdot Step & Trans.y \cdot Step & Trans.z \cdot Step & 1
|
||||
\end{bmatrix}
|
||||
\]</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>
|
||||
<h2 id="see-also">See Also</h2>
|
||||
<ul>
|
||||
<li><a href="topology.html">Kinematic Topology</a> — the anchors and branches these matrices move</li>
|
||||
<li><a href="../../anatomy/geom/transformation-geom-control.html">TransformationGeomControl</a> — the app panel that wraps a geometry in one of these transforms</li>
|
||||
</ul>
|
||||
|
||||
</article>
|
||||
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|
||||
|
||||
<div class="container-xxl search-results" id="search-results"></div>
|
||||
|
||||
<footer class="border-top text-secondary">
|
||||
<div class="container-xxl">
|
||||
<div class="flex-fill">
|
||||
<span> Copyright © 2025 <a href='https://superhightech.com.tw'>Tech Coordinate</a>. All rights reserved. <a href='https://superhightech.com.tw'>超級高科技股份有限公司</a> © 2025 版權所有 </span>
|
||||
</div>
|
||||
</div>
|
||||
</footer>
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user