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<div class="subTitle">edu.rit.numeric</div>
<h2 title="Class CurveSmoothing" class="title">Class CurveSmoothing</h2>
</div>
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<ul class="inheritance">
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<pre>public class <span class="strong">CurveSmoothing</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">Class CurveSmoothing provides operations useful for creating smooth cubic
spline curves.
<P>
We are given a sequence of <I>n</I> coordinate values, <TT>u[0]</TT> ..
<TT>u[n-1]</TT>. These may be either the X coordinates or the Y coordinates
of a sequence of 2-D points. We wish to join successive pairs of points with
a sequence of cubic Bezier curves to create an overall cubic spline curve. We
need to know the X or Y coordinates of the two Bezier control points for each
Bezier curve. The Bezier control point coordinates are designated by
<TT>a[i]</TT> and <TT>c[i]</TT>, such that Bezier curve <I>i</I> is defined
by <TT>u[i]</TT>, <TT>a[i]</TT>, <TT>c[i]</TT>, and <TT>u[i+1]</TT> in that
order.
<P>
There are several cases:
<OL TYPE=1>
<LI>
The curve is closed (there is a Bezier curve from point <I>n</I>-1 back to
point 0). We need the <I>n</I> Bezier control points <TT>a[0]</TT> ..
<TT>a[n-1]</TT> and the <I>n</I> Bezier control points <TT>c[0]</TT> ..
<TT>c[n-1]</TT>. The first Bezier curve will be
<TT>u[0]--a[0]--c[0]--u[1]</TT>, and the last Bezier curve will be
<TT>u[n-1]--a[n-1]--c[n-1]--u[0]</TT>.
<BR>&nbsp;
<LI>
The curve is open (there is no Bezier curve from point <I>n</I>-1 back to
point 0). We need the <I>n</I>-1 Bezier control points <TT>a[0]</TT> ..
<TT>a[n-2]</TT> and the <I>n</I>-1 Bezier control points <TT>c[0]</TT> ..
<TT>c[n-2]</TT>. The first Bezier curve will be
<TT>u[0]--a[0]--c[0]--u[1]</TT>, and the last Bezier curve will be
<TT>u[n-2]--a[n-2]--c[n-2]--u[n-1]</TT>.
<P>
For the initial point <TT>u[0]</TT>, an additional condition must be
specified, either:
<OL TYPE=a>
<LI>
Zero curvature at the initial point; or
<LI>
Initial direction, specified as a straight line from a coordinate
<TT>uInitial</TT> to <TT>u[0]</TT>.
</OL>
<P>
For the final point <TT>u[n-1]</TT>, an additional condition must be
specified, either:
<OL TYPE=a>
<LI>
Zero curvature at the final point; or
<LI>
Final direction, specified as a straight line from <TT>u[n-1]</TT> to a
coordinate <TT>uFinal</TT>.
</OL>
</OL></div>
</li>
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<h3>Method Summary</h3>
<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span>Methods</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierClosed(double[], double[], double[], int, int)">computeBezierClosed</a></strong>(double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</code>
<div class="block">Compute the Bezier control point coordinates for a closed smooth curve.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double[], double[], double[], int, int)">computeBezierOpen</a></strong>(double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</code>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with zero initial curvature and zero final curvature.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double[], double, double[], double[], int, int)">computeBezierOpen</a></strong>(double[]&nbsp;u,
double&nbsp;uFinal,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</code>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with zero initial curvature and a specified final direction.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double, double[], double[], double[], int, int)">computeBezierOpen</a></strong>(double&nbsp;uInitial,
double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</code>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with a specified initial direction and zero final curvature.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double, double[], double, double[], double[], int, int)">computeBezierOpen</a></strong>(double&nbsp;uInitial,
double[]&nbsp;u,
double&nbsp;uFinal,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</code>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with a specified initial direction and a specified final direction.</div>
</td>
</tr>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h3>Method Detail</h3>
<a name="computeBezierClosed(double[], double[], double[], int, int)">
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<h4>computeBezierClosed</h4>
<pre>public static&nbsp;void&nbsp;computeBezierClosed(double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</pre>
<div class="block">Compute the Bezier control point coordinates for a closed smooth curve.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-1</TT> are
used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-1</TT> are
used.</dd><dd><code>i</code> - Index of first element used in input and output arrays.</dd><dd><code>n</code> - Number of elements used in input and output arrays. Must be
greater than or equal to 3.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>n</TT> &lt; 3.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the control points cannot be
calculated.</dd></dl>
</li>
</ul>
<a name="computeBezierOpen(double[], double[], double[], int, int)">
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<h4>computeBezierOpen</h4>
<pre>public static&nbsp;void&nbsp;computeBezierOpen(double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</pre>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with zero initial curvature and zero final curvature.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>i</code> - Index of first element used in input and output arrays.</dd><dd><code>n</code> - Number of elements used in input array; one fewer elements
used in output arrays. Must be greater than or equal to 3.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>n</TT> &lt; 3.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the control points cannot be
calculated.</dd></dl>
</li>
</ul>
<a name="computeBezierOpen(double, double[], double[], double[], int, int)">
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<h4>computeBezierOpen</h4>
<pre>public static&nbsp;void&nbsp;computeBezierOpen(double&nbsp;uInitial,
double[]&nbsp;u,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</pre>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with a specified initial direction and zero final curvature.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>uInitial</code> - Specifies initial direction as a straight line from
<TT>uInitial</TT> to <TT>u[i]</TT>.</dd><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>i</code> - Index of first element used in input and output arrays.</dd><dd><code>n</code> - Number of elements used in input array; one fewer elements
used in output arrays. Must be greater than or equal to 2.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>n</TT> &lt; 2.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the control points cannot be
calculated.</dd></dl>
</li>
</ul>
<a name="computeBezierOpen(double[], double, double[], double[], int, int)">
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</a>
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<h4>computeBezierOpen</h4>
<pre>public static&nbsp;void&nbsp;computeBezierOpen(double[]&nbsp;u,
double&nbsp;uFinal,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)</pre>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with zero initial curvature and a specified final direction.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
.. <TT>i+n-1</TT> are used.</dd><dd><code>uFinal</code> - Specifies final direction as a straight line from
<TT>u[i+n-1]</TT> to <TT>uFinal</TT>.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>i</code> - Index of first element used in input and output arrays.</dd><dd><code>n</code> - Number of elements used in input array; one fewer elements
used in output arrays. Must be greater than or equal to 2.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>n</TT> &lt; 2.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the control points cannot be
calculated.</dd></dl>
</li>
</ul>
<a name="computeBezierOpen(double, double[], double, double[], double[], int, int)">
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<h4>computeBezierOpen</h4>
<pre>public static&nbsp;void&nbsp;computeBezierOpen(double&nbsp;uInitial,
double[]&nbsp;u,
double&nbsp;uFinal,
double[]&nbsp;a,
double[]&nbsp;c,
int&nbsp;i,
int&nbsp;n)
throws <a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></pre>
<div class="block">Compute the Bezier control point coordinates for an open smooth curve
with a specified initial direction and a specified final direction.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>uInitial</code> - Specifies initial direction as a straight line from
<TT>uInitial</TT> to <TT>u[i]</TT>.</dd><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
.. <TT>i+n-1</TT> are used.</dd><dd><code>uFinal</code> - Specifies final direction as a straight line from
<TT>u[i+n-1]</TT> to <TT>uFinal</TT>.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
used.</dd><dd><code>i</code> - Index of first element used in input and output arrays.</dd><dd><code>n</code> - Number of elements used in input array; one fewer elements
used in output arrays. Must be greater than or equal to 2.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/IllegalArgumentException.html?is-external=true" title="class or interface in java.lang">IllegalArgumentException</a></code> - (unchecked exception) Thrown if <TT>n</TT> &lt; 2.</dd>
<dd><code><a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></code> - (unchecked exception) Thrown if the control points cannot be
calculated.</dd></dl>
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