458 lines
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458 lines
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<title>CurveSmoothing (Parallel Java 2 Library Documentation)</title>
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<div class="subTitle">edu.rit.numeric</div>
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<h2 title="Class CurveSmoothing" class="title">Class CurveSmoothing</h2>
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<div class="contentContainer">
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<ul class="inheritance">
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<li><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
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<br>
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<pre>public class <span class="strong">CurveSmoothing</span>
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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>
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<div class="block">Class CurveSmoothing provides operations useful for creating smooth cubic
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spline curves.
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<P>
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We are given a sequence of <I>n</I> coordinate values, <TT>u[0]</TT> ..
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<TT>u[n-1]</TT>. These may be either the X coordinates or the Y coordinates
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of a sequence of 2-D points. We wish to join successive pairs of points with
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a sequence of cubic Bezier curves to create an overall cubic spline curve. We
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need to know the X or Y coordinates of the two Bezier control points for each
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Bezier curve. The Bezier control point coordinates are designated by
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<TT>a[i]</TT> and <TT>c[i]</TT>, such that Bezier curve <I>i</I> is defined
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by <TT>u[i]</TT>, <TT>a[i]</TT>, <TT>c[i]</TT>, and <TT>u[i+1]</TT> in that
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order.
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<P>
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There are several cases:
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<OL TYPE=1>
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<LI>
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The curve is closed (there is a Bezier curve from point <I>n</I>-1 back to
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point 0). We need the <I>n</I> Bezier control points <TT>a[0]</TT> ..
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<TT>a[n-1]</TT> and the <I>n</I> Bezier control points <TT>c[0]</TT> ..
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<TT>c[n-1]</TT>. The first Bezier curve will be
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<TT>u[0]--a[0]--c[0]--u[1]</TT>, and the last Bezier curve will be
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<TT>u[n-1]--a[n-1]--c[n-1]--u[0]</TT>.
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<BR>
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<LI>
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The curve is open (there is no Bezier curve from point <I>n</I>-1 back to
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point 0). We need the <I>n</I>-1 Bezier control points <TT>a[0]</TT> ..
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<TT>a[n-2]</TT> and the <I>n</I>-1 Bezier control points <TT>c[0]</TT> ..
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<TT>c[n-2]</TT>. The first Bezier curve will be
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<TT>u[0]--a[0]--c[0]--u[1]</TT>, and the last Bezier curve will be
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<TT>u[n-2]--a[n-2]--c[n-2]--u[n-1]</TT>.
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<P>
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For the initial point <TT>u[0]</TT>, an additional condition must be
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specified, either:
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<OL TYPE=a>
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<LI>
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Zero curvature at the initial point; or
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<LI>
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Initial direction, specified as a straight line from a coordinate
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<TT>uInitial</TT> to <TT>u[0]</TT>.
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</OL>
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<P>
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For the final point <TT>u[n-1]</TT>, an additional condition must be
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specified, either:
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<OL TYPE=a>
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<LI>
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Zero curvature at the final point; or
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<LI>
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Final direction, specified as a straight line from <TT>u[n-1]</TT> to a
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coordinate <TT>uFinal</TT>.
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</OL>
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</OL></div>
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</li>
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</ul>
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</div>
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<!-- ========== METHOD SUMMARY =========== -->
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<h3>Method Summary</h3>
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<table class="overviewSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
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<caption><span>Methods</span><span class="tabEnd"> </span></caption>
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<tr>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<th class="colLast" scope="col">Method and Description</th>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierClosed(double[], double[], double[], int, int)">computeBezierClosed</a></strong>(double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</code>
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<div class="block">Compute the Bezier control point coordinates for a closed smooth curve.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double[], double[], double[], int, int)">computeBezierOpen</a></strong>(double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</code>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with zero initial curvature and zero final curvature.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double[], double, double[], double[], int, int)">computeBezierOpen</a></strong>(double[] u,
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double uFinal,
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double[] a,
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double[] c,
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int i,
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int n)</code>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with zero initial curvature and a specified final direction.</div>
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</td>
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</tr>
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<tr class="rowColor">
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<td class="colFirst"><code>static void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double, double[], double[], double[], int, int)">computeBezierOpen</a></strong>(double uInitial,
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double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</code>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with a specified initial direction and zero final curvature.</div>
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</td>
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</tr>
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<tr class="altColor">
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<td class="colFirst"><code>static void</code></td>
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<td class="colLast"><code><strong><a href="../../../edu/rit/numeric/CurveSmoothing.html#computeBezierOpen(double, double[], double, double[], double[], int, int)">computeBezierOpen</a></strong>(double uInitial,
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double[] u,
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double uFinal,
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double[] a,
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double[] c,
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int i,
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int n)</code>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with a specified initial direction and a specified final direction.</div>
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</td>
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</tr>
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</table>
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<h3>Methods inherited from class 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>
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<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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</ul>
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</li>
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</ul>
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</li>
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</ul>
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</div>
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</a>
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<h3>Method Detail</h3>
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<a name="computeBezierClosed(double[], double[], double[], int, int)">
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<h4>computeBezierClosed</h4>
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<pre>public static void computeBezierClosed(double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</pre>
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<div class="block">Compute the Bezier control point coordinates for a closed smooth curve.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
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.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-1</TT> are
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used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-1</TT> are
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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
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greater than or equal to 3.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<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> < 3.</dd>
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<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
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calculated.</dd></dl>
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</li>
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</ul>
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<a name="computeBezierOpen(double[], double[], double[], int, int)">
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<h4>computeBezierOpen</h4>
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<pre>public static void computeBezierOpen(double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</pre>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with zero initial curvature and zero final curvature.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
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.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
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|
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
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
|
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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
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used in output arrays. Must be greater than or equal to 3.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<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> < 3.</dd>
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<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
|
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calculated.</dd></dl>
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</li>
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</ul>
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<a name="computeBezierOpen(double, double[], double[], double[], int, int)">
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</a>
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<h4>computeBezierOpen</h4>
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<pre>public static void computeBezierOpen(double uInitial,
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double[] u,
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double[] a,
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double[] c,
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int i,
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int n)</pre>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
|
|
with a specified initial direction and zero final curvature.</div>
|
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>uInitial</code> - Specifies initial direction as a straight line from
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<TT>uInitial</TT> to <TT>u[i]</TT>.</dd><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
|
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.. <TT>i+n-1</TT> are used.</dd><dd><code>a</code> - An output array of coordinates for the first Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
|
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used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
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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
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used in output arrays. Must be greater than or equal to 2.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<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> < 2.</dd>
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<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
|
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calculated.</dd></dl>
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</li>
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</ul>
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<a name="computeBezierOpen(double[], double, double[], double[], int, int)">
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<h4>computeBezierOpen</h4>
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<pre>public static void computeBezierOpen(double[] u,
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double uFinal,
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double[] a,
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double[] c,
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int i,
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int n)</pre>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
|
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with zero initial curvature and a specified final direction.</div>
|
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
|
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.. <TT>i+n-1</TT> are used.</dd><dd><code>uFinal</code> - Specifies final direction as a straight line from
|
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<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
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
|
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used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
|
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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
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used in output arrays. Must be greater than or equal to 2.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<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> < 2.</dd>
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<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
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calculated.</dd></dl>
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</li>
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</ul>
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<a name="computeBezierOpen(double, double[], double, double[], double[], int, int)">
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<!-- -->
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</a>
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<ul class="blockListLast">
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<h4>computeBezierOpen</h4>
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<pre>public static void computeBezierOpen(double uInitial,
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double[] u,
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double uFinal,
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double[] a,
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double[] c,
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int i,
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int n)
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throws <a href="../../../edu/rit/numeric/DomainException.html" title="class in edu.rit.numeric">DomainException</a></pre>
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<div class="block">Compute the Bezier control point coordinates for an open smooth curve
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with a specified initial direction and a specified final direction.</div>
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<dl><dt><span class="strong">Parameters:</span></dt><dd><code>uInitial</code> - Specifies initial direction as a straight line from
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<TT>uInitial</TT> to <TT>u[i]</TT>.</dd><dd><code>u</code> - An input array of coordinates. Elements at indexes <TT>i</TT>
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.. <TT>i+n-1</TT> are used.</dd><dd><code>uFinal</code> - Specifies final direction as a straight line from
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<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
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
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used.</dd><dd><code>c</code> - An output array of coordinates for the second Bezier control
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points. Elements at indexes <TT>i</TT> .. <TT>i+n-2</TT> are
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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
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used in output arrays. Must be greater than or equal to 2.</dd>
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<dt><span class="strong">Throws:</span></dt>
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<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> < 2.</dd>
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<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
|
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calculated.</dd></dl>
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<p class="legalCopy"><small><FONT SIZE="-2">Copyright © 2013–2016 by Alan Kaminsky. All rights reserved. Send comments to ark</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">@</FONT><FONT SIZE="1" COLOR="#FFFFFF">­</FONT><FONT SIZE="-2">cs.rit.edu.</FONT></small></p>
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