html3dutil/Hypotrochoid.html

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<h1 id="hypotrochoid">Hypotrochoid</h1>

<p><a href="index.html">Back to documentation index.</a></p>

<p><a name="Hypotrochoid"></a>
### Hypotrochoid(outerRadius, innerRadius, distFromInnerCenter, [rotationDegrees])</p>

<p><strong>Augments:</strong> Curve</p>

<p>A curve evaluator object for a curve drawn by a circle that rolls along the inside
of another circle, whose position is fixed, with a center of (0,0).</p>

<p>The following curves can be generated with this class (in the following
descriptions, O = <code>outerRadius</code>, R means <code>innerRadius</code>,
and D = <code>distFromInnerCenter</code>).&lt;ul&gt;</p>
<li>Hypocycloid: D = R (hypotrochoid touching the fixed circle).</li>
<li>Curtate hypocycloid: D &lt; R (hypotrochoid not touching the fixed circle).</li>
<li>Prolate hypocycloid: D &gt; R (hypotrochoid crossing the fixed circle).</li>
<li>Circle: O = R\*2; the circle will have radius R - D.</li>
<li>Ellipse: O = R\*2; the ellipse (unrotated) will have width abs(R+D)\*2
and height abs(R-D)\*2.</li>
<li>Line segment with length O\*2: O = R\*2; D = R.</li>
<li>Deltoid: O = R\*3; D = R.</li>
<li>Astroid: O = R\*4; D = R.</li>
<li>N-pointed hypocycloid: O = R \* N; D = R.</li>
<p>&lt;/ul&gt;</p>

<p>This class is considered a supplementary class to the
Public Domain HTML 3D Library and is not considered part of that
library.</p>

<p>To use this class, you must include the script “extras/evaluators.js”; the
class is not included in the “h3du_min.js” file which makes up
the HTML 3D Library. Example:</p>

<pre>&lt;script type="text/javascript" src="extras/evaluators.js"&gt;&lt;/script&gt;
</pre>

<h4 id="parameters">Parameters</h4>

<ul>
  <li><code>outerRadius</code> (Type: number)<br />Radius of the circle whose position is fixed.</li>
  <li><code>innerRadius</code> (Type: number)<br />Radius of the rolling circle. A hypocycloid results when distFromInnerCenter=innerRadius.</li>
  <li><code>distFromInnerCenter</code> (Type: number)<br />Distance from the center of the rolling circle to the drawing pen.</li>
  <li><code>rotationDegrees</code> (Type: number) (optional)<br />Starting angle of the curve from the positive x-axis toward the positive y-axis, in degrees. Default is 0.</li>
</ul>

<h3 id="methods">Methods</h3>

<ul>
  <li><a href="#Hypotrochoid_arcLength">arcLength</a><br />Finds an approximate arc length (distance) between the start of this
curve and the point at the specified u-coordinate of this curve.</li>
  <li><a href="#Hypotrochoid_endPoints">endPoints</a><br />Gets the endpoints of this curve.</li>
  <li><a href="#Hypotrochoid_evaluate">evaluate</a><br />Finds the coordinates of a point on the curve from the specified u-coordinate.</li>
  <li><a href="#Hypotrochoid.rose">rose</a><br />Creates a curve evaluator object for a rose, a special
form of hypotrochoid.</li>
  <li><a href="#Hypotrochoid_scaleTo">scaleTo</a><br />Creates a modified version of this curve so that it
fits the specified radius.</li>
</ul>

<p><a name="Hypotrochoid_arcLength"></a>
### Hypotrochoid#arcLength(u)</p>

<p>Finds an approximate arc length (distance) between the start of this
curve and the point at the specified u-coordinate of this curve.</p>

<h4 id="parameters-1">Parameters</h4>

<ul>
  <li><code>u</code> (Type: number)<br />u-coordinate of a point on the curve.</li>
</ul>

<h4 id="return-value">Return Value</h4>

<p>The approximate arc length of this curve at the specified u-coordinate. (Type: Array.&lt;number&gt;)</p>

<p><a name="Hypotrochoid_endPoints"></a>
### Hypotrochoid#endPoints()</p>

<p>Gets the endpoints of this curve.
For this curve evaluator object, the curve
starts at 0 and ends at π*2.</p>

<h4 id="return-value-1">Return Value</h4>

<p>An array containing the two
endpoints of the curve. The first number is the start of the curve,
and the second number is the end of the curve. (Type: Array.&lt;number&gt;)</p>

<p><a name="Hypotrochoid_evaluate"></a>
### Hypotrochoid#evaluate(u)</p>

<p>Finds the coordinates of a point on the curve from the specified u-coordinate.</p>

<h4 id="parameters-2">Parameters</h4>

<ul>
  <li><code>u</code> (Type: number)<br />u-coordinate.</li>
</ul>

<h4 id="return-value-2">Return Value</h4>

<p>A 3-element array specifying a 3D point.
Only the x- and y-coordinates can be other than 0. (Type: Array.&lt;number&gt;)</p>

<p><a name="Hypotrochoid.rose"></a>
### (static) Hypotrochoid.rose(n, distFromInnerCenter, [rotationDegrees])</p>

<p>Creates a curve evaluator object for a rose, a special
form of hypotrochoid.</p>

<h4 id="parameters-3">Parameters</h4>

<ul>
  <li><code>n</code> (Type: number)<br />Parameter that determines the petal form of the rose. For example, the rose is symmetrical if this number is even.</li>
  <li><code>distFromInnerCenter</code> (Type: number)<br />Distance from the center of the rolling circle to the drawing pen.</li>
  <li><code>rotationDegrees</code> (Type: number) (optional)<br />Starting angle of the curve from the positive x-axis toward the positive y-axis, in degrees. Default is 0.</li>
</ul>

<h4 id="return-value-3">Return Value</h4>

<p>The resulting curve evaluator object. (Type: <a href="Hypotrochoid.html">Hypotrochoid</a>)</p>

<p><a name="Hypotrochoid_scaleTo"></a>
### Hypotrochoid#scaleTo(radius)</p>

<p>Creates a modified version of this curve so that it
fits the specified radius.</p>

<h4 id="parameters-4">Parameters</h4>

<ul>
  <li><code>radius</code> (Type: number)<br />Desired radius of the curve.</li>
</ul>

<h4 id="return-value-4">Return Value</h4>

<p>Return value. (Type: <a href="Hypotrochoid.html">Hypotrochoid</a>)</p>

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