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<h1 id="quaternion-factory">Quaternion factory</h1>
<p>Scrawl-canvas uses quaternion objects for some of its calculations - in particular for calculating DOM element 3D rotation values. These objects are not stored in the library; rather, they are kept in a <strong>quaternion pool</strong> and pulled from it when required.</p>
<p>TODO: there’s errors in the math here! See in particular Demo <a href="../../demo/snippets-003.html">Snippets-003</a> to experiment:</p>
<ul>
<li>Pitch always appears to rotate with reference to the element. Yaw and roll, however, seem to rotate with reference to the stack frame, or the element - or possibly a combination of both - dependant on the values of the other euler attributes.</li>
<li><code>quaternionMultiply</code> is almost certainly wrong - caused by trying to convert code meant for a y-axis-upwards frame to code that works in a y-axis-downwards frame</li>
<li>The <code>setFromEuler</code> function is also (probably) wrong</li>
<li>I hate quaternions!</li>
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<h4 id="imports">Imports</h4>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">import</span> { radian, constructors } <span class="hljs-keyword">from</span> <span class="hljs-string">'../core/library.js'</span>;
<span class="hljs-keyword">import</span> { isa_quaternion, isa_number, xt, xto, Ωempty } <span class="hljs-keyword">from</span> <span class="hljs-string">'../core/utilities.js'</span>;
<span class="hljs-keyword">import</span> { requestVector, releaseVector, makeVector } <span class="hljs-keyword">from</span> <span class="hljs-string">'./vector.js'</span>;</pre></div></div>
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<h4 id="quaternion-constructor">Quaternion constructor</h4>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">const</span> <span class="hljs-title class_">Quaternion</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">items = Ωempty</span>) {
<span class="hljs-variable language_">this</span>.<span class="hljs-property">name</span> = items.<span class="hljs-property">name</span> || <span class="hljs-string">'generic'</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = items.<span class="hljs-property">n</span> || <span class="hljs-number">1</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span> = <span class="hljs-title function_">makeVector</span>();
<span class="hljs-variable language_">this</span>.<span class="hljs-title function_">set</span>(items);
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};</pre></div></div>
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<h4 id="quaternion-prototype">Quaternion prototype</h4>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">let</span> P = <span class="hljs-title class_">Quaternion</span>.<span class="hljs-property"><span class="hljs-keyword">prototype</span></span> = <span class="hljs-title class_">Object</span>.<span class="hljs-title function_">create</span>(<span class="hljs-title class_">Object</span>.<span class="hljs-property"><span class="hljs-keyword">prototype</span></span>);
P.<span class="hljs-property">type</span> = <span class="hljs-string">'Quaternion'</span>;</pre></div></div>
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<h4 id="mixins">Mixins</h4>
<p>Quaternion objects do not use mixins - they are regular Javascript objects. As such, they do not possess packet, clone or kill functionality.</p>
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<h4 id="quaternion-attributes">Quaternion attributes</h4>
<p>The <strong>name</strong>, <strong>n</strong> and <strong>v</strong> (Vector object) attributes are set in the Quaternion constructor - the Quaternion object does not have a <code>defs</code> object. The Vector attributes <strong>v.x</strong>, <strong>v.y</strong>, <strong>v.z</strong> can also be set directly.</p>
<p><strong>We strongly advise against setting Quaternion object attributes directly!</strong> Quaternions are complex beasts and their <code>n</code> and <code>v</code> attributes are linked in mysterious (and possibly debauched) ways. Set and manipulate your Quaternion object’s attributes using the functions below.</p>
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<h4 id="get-set-deltaset">Get, Set, deltaSet</h4>
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<p>Quaternion attributes can be retrieved directly - <code>myquaternion.n</code>, <code>myquaternion.v</code>. The <strong>v</strong> attribute is a Vector object, thus its attributes can be retrieved using that object’s convenience functions <code>myquaternion.v.getXYCoordinate</code> and <code>myquaternion.v.getXYZCoordinate</code> - these functions will return Arrays.</p>
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<p>The Quaternion <code>set</code> function is overloaded. It can accept the following arguments:</p>
<ul>
<li><code>set(Quaternion)</code> - a Quaternion object</li>
<li><code>set(Vector)</code> - a Vector object</li>
<li><code>set({x:Number, y:Number, z:Number})</code> - a Javascript object containing one or more attributes from: x, y, z - with values in degrees (not radians)</li>
<li><code>set({pitch:Number, yaw:Number, roll:Number})</code> - a Javascript object containing one or more attributes: <strong>pitch</strong> (for x-axis rotations); <strong>yaw</strong> (for y-axis rotations); <strong>roll</strong> (for z-axis rotations) - with values in degrees (not radians)</li>
</ul>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">set</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">obj = Ωempty</span>) {
<span class="hljs-keyword">if</span> (<span class="hljs-title function_">isa_quaternion</span>(obj)) <span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>.<span class="hljs-title function_">setFromQuaternion</span>(obj);
<span class="hljs-comment">/* if ((obj && obj.type && obj.type === 'Vector')) return this.setFromVector(obj); */</span>
<span class="hljs-keyword">if</span> (<span class="hljs-title function_">xto</span>(obj.<span class="hljs-property">pitch</span>, obj.<span class="hljs-property">yaw</span>, obj.<span class="hljs-property">roll</span>)) <span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>.<span class="hljs-title function_">setFromEuler</span>(obj);
<span class="hljs-keyword">let</span> x, y, z, n, v,
tv = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>;
v = (<span class="hljs-title function_">xt</span>(obj.<span class="hljs-property">vector</span>) || <span class="hljs-title function_">xt</span>(obj.<span class="hljs-property">v</span>)) ? (obj.<span class="hljs-property">vector</span> || obj.<span class="hljs-property">v</span>) : <span class="hljs-literal">false</span>;
n = (<span class="hljs-title function_">xt</span>(obj.<span class="hljs-property">scalar</span>) || <span class="hljs-title function_">xt</span>(obj.<span class="hljs-property">n</span>)) ? (obj.<span class="hljs-property">scalar</span> || obj.<span class="hljs-property">n</span> || <span class="hljs-number">0</span>) : <span class="hljs-literal">false</span>;
x = (v) ? (v.<span class="hljs-property">x</span> || <span class="hljs-number">0</span>) : obj.<span class="hljs-property">x</span> || <span class="hljs-literal">false</span>;
y = (v) ? (v.<span class="hljs-property">y</span> || <span class="hljs-number">0</span>) : obj.<span class="hljs-property">y</span> || <span class="hljs-literal">false</span>;
z = (v) ? (v.<span class="hljs-property">z</span> || <span class="hljs-number">0</span>) : obj.<span class="hljs-property">z</span> || <span class="hljs-literal">false</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = (<span class="hljs-title function_">isa_number</span>(n)) ? n : <span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span>;
tv.<span class="hljs-property">x</span> = (<span class="hljs-title function_">isa_number</span>(x)) ? x : tv.<span class="hljs-property">x</span>;
tv.<span class="hljs-property">y</span> = (<span class="hljs-title function_">isa_number</span>(y)) ? y : tv.<span class="hljs-property">y</span>;
tv.<span class="hljs-property">z</span> = (<span class="hljs-title function_">isa_number</span>(z)) ? z : tv.<span class="hljs-property">z</span>;
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};
P.<span class="hljs-property">setFromQuaternion</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">item</span>) {
<span class="hljs-keyword">if</span> (!<span class="hljs-title function_">isa_quaternion</span>(item)) <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">Error</span>(<span class="hljs-string">`<span class="hljs-subst">${<span class="hljs-variable language_">this</span>.name}</span> Quaternion error - setFromQuaternion() bad argument: <span class="hljs-subst">${item}</span>`</span>);
<span class="hljs-keyword">let</span> tv = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>,
iv = item.<span class="hljs-property">v</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = item.<span class="hljs-property">n</span>;
tv.<span class="hljs-property">x</span> = iv.<span class="hljs-property">x</span>;
tv.<span class="hljs-property">y</span> = iv.<span class="hljs-property">y</span>;
tv.<span class="hljs-property">z</span> = iv.<span class="hljs-property">z</span>;
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};
P.<span class="hljs-property">setFromEuler</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">items = Ωempty</span>) {
<span class="hljs-keyword">let</span> pitch, yaw, roll, c1, c2, c3, s1, s2, s3,
cos = <span class="hljs-title class_">Math</span>.<span class="hljs-property">cos</span>,
sin = <span class="hljs-title class_">Math</span>.<span class="hljs-property">sin</span>,
tv = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>;
pitch = (items.<span class="hljs-property">pitch</span> || items.<span class="hljs-property">x</span> || <span class="hljs-number">0</span>) * radian;
yaw = (items.<span class="hljs-property">yaw</span> || items.<span class="hljs-property">y</span> || <span class="hljs-number">0</span>) * radian;
roll = (items.<span class="hljs-property">roll</span> || items.<span class="hljs-property">z</span> || <span class="hljs-number">0</span>) * radian;
c1 = <span class="hljs-title function_">cos</span>( pitch / <span class="hljs-number">2</span> );
c2 = <span class="hljs-title function_">cos</span>( yaw / <span class="hljs-number">2</span> );
c3 = <span class="hljs-title function_">cos</span>( roll / <span class="hljs-number">2</span> );
s1 = <span class="hljs-title function_">sin</span>( pitch / <span class="hljs-number">2</span> );
s2 = <span class="hljs-title function_">sin</span>( yaw / <span class="hljs-number">2</span> );
s3 = <span class="hljs-title function_">sin</span>( roll / <span class="hljs-number">2</span> );
tv.<span class="hljs-property">x</span> = s1 * c2 * c3 + c1 * s2 * s3;
tv.<span class="hljs-property">y</span> = c1 * s2 * c3 + s1 * c2 * s3;
tv.<span class="hljs-property">z</span> = c1 * c2 * s3 - s1 * s2 * c3;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = c1 * c2 * c3 - s1 * s2 * s3;
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};</pre></div></div>
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<h4 id="prototype-functions">Prototype functions</h4>
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<p>Set the Quaternion attributes to their default values</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">zero</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params"></span>) {
<span class="hljs-keyword">let</span> v = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = <span class="hljs-number">1</span>;
v.<span class="hljs-property">x</span> = <span class="hljs-number">0</span>;
v.<span class="hljs-property">y</span> = <span class="hljs-number">0</span>;
v.<span class="hljs-property">z</span> = <span class="hljs-number">0</span>;
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};</pre></div></div>
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<p>Get the Quaternion’s <strong>magnitude</strong> value</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">getMagnitude</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params"></span>) {
<span class="hljs-keyword">let</span> v = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>;
<span class="hljs-keyword">return</span> <span class="hljs-title class_">Math</span>.<span class="hljs-title function_">sqrt</span>((<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> * <span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span>) + (v.<span class="hljs-property">x</span> * v.<span class="hljs-property">x</span>) + (v.<span class="hljs-property">y</span> * v.<span class="hljs-property">y</span>) + (v.<span class="hljs-property">z</span> * v.<span class="hljs-property">z</span>));
};</pre></div></div>
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<p>Normalize the Quaternion</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">normalize</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params"></span>) {
<span class="hljs-keyword">let</span> mag = <span class="hljs-variable language_">this</span>.<span class="hljs-title function_">getMagnitude</span>(),
v = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>;
<span class="hljs-keyword">if</span> (!mag) <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">Error</span>(<span class="hljs-string">`<span class="hljs-subst">${<span class="hljs-variable language_">this</span>.name}</span> Quaternion error - normalize() division by zero: <span class="hljs-subst">${mag}</span>`</span>);
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> /= mag;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = (<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> > -<span class="hljs-number">0.000001</span> && <span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> < <span class="hljs-number">0.000001</span>) ? <span class="hljs-number">0</span> : <span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span>;
v.<span class="hljs-property">x</span> /= mag;
v.<span class="hljs-property">x</span> = (v.<span class="hljs-property">x</span> > -<span class="hljs-number">0.000001</span> && v.<span class="hljs-property">x</span> < <span class="hljs-number">0.000001</span>) ? <span class="hljs-number">0</span> : v.<span class="hljs-property">x</span>;
v.<span class="hljs-property">y</span> /= mag;
v.<span class="hljs-property">y</span> = (v.<span class="hljs-property">y</span> > -<span class="hljs-number">0.000001</span> && v.<span class="hljs-property">y</span> < <span class="hljs-number">0.000001</span>) ? <span class="hljs-number">0</span> : v.<span class="hljs-property">y</span>;
v.<span class="hljs-property">z</span> /= mag;
v.<span class="hljs-property">z</span> = (v.<span class="hljs-property">z</span> > -<span class="hljs-number">0.000001</span> && v.<span class="hljs-property">z</span> < <span class="hljs-number">0.000001</span>) ? <span class="hljs-number">0</span> : v.<span class="hljs-property">z</span>;
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};</pre></div></div>
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<p>Multiply the Quaternion by another Quaternion</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">quaternionMultiply</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">item</span>) {
<span class="hljs-keyword">if</span> (!<span class="hljs-title function_">isa_quaternion</span>(item)) <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">Error</span>(<span class="hljs-string">`<span class="hljs-subst">${<span class="hljs-variable language_">this</span>.name}</span> Quaternion error - quaternionMultiply() bad argument: <span class="hljs-subst">${item}</span>`</span>);
<span class="hljs-keyword">let</span> tv = <span class="hljs-variable language_">this</span>.<span class="hljs-property">v</span>,
iv = item.<span class="hljs-property">v</span>,
n1 = <span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span>,
x1 = tv.<span class="hljs-property">x</span>,
y1 = tv.<span class="hljs-property">y</span>,
z1 = tv.<span class="hljs-property">z</span>,
n2 = item.<span class="hljs-property">n</span>,
x2 = iv.<span class="hljs-property">x</span>,
y2 = iv.<span class="hljs-property">y</span>,
z2 = iv.<span class="hljs-property">z</span>;
<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span> = (n1 * n2) - (x1 * x2) - (y1 * y2) - (z1 * z2);
tv.<span class="hljs-property">x</span> = (n1 * x2) + (x1 * n2) + (y1 * z2) - (z1 * y2);
tv.<span class="hljs-property">y</span> = (n1 * y2) + (y1 * n2) + (z1 * x2) - (x1 * z2);
tv.<span class="hljs-property">z</span> = (n1 * z2) + (z1 * n2) + (x1 * y2) - (y1 * x2);
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>;
};</pre></div></div>
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<p>Retrieve the Quaternion’s current angle (returns a Number representing degrees, not radians)</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">getAngle</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">degree</span>) {
<span class="hljs-keyword">let</span> result;
degree = (<span class="hljs-title function_">xt</span>(degree)) ? degree : <span class="hljs-literal">false</span>;
result = <span class="hljs-number">2</span> * <span class="hljs-title class_">Math</span>.<span class="hljs-title function_">acos</span>(<span class="hljs-variable language_">this</span>.<span class="hljs-property">n</span>);
<span class="hljs-keyword">if</span>(degree){
result *= (<span class="hljs-number">1</span> / radian);
}
<span class="hljs-keyword">return</span> (result > -<span class="hljs-number">0.000001</span> && result < <span class="hljs-number">0.000001</span>) ? <span class="hljs-number">0</span> : result;
};</pre></div></div>
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<p>Rotate the Quaternion using another Quaternion’s values</p>
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<div class="content"><div class='highlight'><pre>P.<span class="hljs-property">quaternionRotate</span> = <span class="hljs-keyword">function</span> (<span class="hljs-params">item</span>) {
<span class="hljs-keyword">if</span> (!<span class="hljs-title function_">isa_quaternion</span>(item)) <span class="hljs-keyword">throw</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">Error</span>(<span class="hljs-string">`<span class="hljs-subst">${<span class="hljs-variable language_">this</span>.name}</span> Quaternion error - quaternionRotate() bad argument: <span class="hljs-subst">${item}</span>`</span>);
<span class="hljs-keyword">let</span> q4 = <span class="hljs-title function_">requestQuaternion</span>(item),
q5 = <span class="hljs-title function_">requestQuaternion</span>(<span class="hljs-variable language_">this</span>);
<span class="hljs-variable language_">this</span>.<span class="hljs-title function_">setFromQuaternion</span>(q4.<span class="hljs-title function_">quaternionMultiply</span>(q5));
<span class="hljs-title function_">releaseQuaternion</span>(q4);
<span class="hljs-title function_">releaseQuaternion</span>(q5);
<span class="hljs-keyword">return</span> <span class="hljs-variable language_">this</span>
};</pre></div></div>
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<h4 id="quaternion-pool">Quaternion pool</h4>
<p>An attempt to reuse quaternions rather than constantly creating and deleting them</p>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">const</span> quaternionPool = [];</pre></div></div>
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<p><code>exported function</code> - retrieve a Quaternion from the quaternion pool</p>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">const</span> requestQuaternion = <span class="hljs-keyword">function</span> (<span class="hljs-params">items</span>) {
<span class="hljs-keyword">if</span> (!quaternionPool.<span class="hljs-property">length</span>) {
quaternionPool.<span class="hljs-title function_">push</span>(<span class="hljs-title function_">makeQuaternion</span>({
<span class="hljs-attr">name</span>: <span class="hljs-string">'pool'</span>
}));
}
<span class="hljs-keyword">let</span> q = quaternionPool.<span class="hljs-title function_">shift</span>();
q.<span class="hljs-title function_">set</span>(items);
<span class="hljs-keyword">return</span> q
};</pre></div></div>
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<p><code>exported function</code> - return a Quaternion to the quaternion pool. Failing to return Quaternion to the pool may lead to more inefficient code and possible memory leaks.</p>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">const</span> releaseQuaternion = <span class="hljs-keyword">function</span> (<span class="hljs-params">q</span>) {
<span class="hljs-keyword">if</span> (q && q.<span class="hljs-property">type</span> === <span class="hljs-string">'Quaternion'</span>) {
quaternionPool.<span class="hljs-title function_">push</span>(q.<span class="hljs-title function_">zero</span>());
}
};</pre></div></div>
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<h4 id="factory">Factory</h4>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">const</span> makeQuaternion = <span class="hljs-keyword">function</span> (<span class="hljs-params">items</span>) {
<span class="hljs-keyword">return</span> <span class="hljs-keyword">new</span> <span class="hljs-title class_">Quaternion</span>(items);
};
constructors.<span class="hljs-property">Quaternion</span> = <span class="hljs-title class_">Quaternion</span>;</pre></div></div>
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<h4 id="exports">Exports</h4>
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<div class="content"><div class='highlight'><pre><span class="hljs-keyword">export</span> {
makeQuaternion,
requestQuaternion,
releaseQuaternion,
};</pre></div></div>
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