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<HTML>
<HEAD>
<TITLE>SPLINTERP function</TITLE>
</HEAD>
<BODY bgcolor="#FFFFFF" fgcolor="#000000">
<P><font size="+3" color="green"><B>SPLINTERP function</B></font></P>
<P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%"><CODE>
mout = SPLINTERP(x,y,n)</CODE>
</TD></TR>
</table></p>
<p>
The <CODE>SPLINTERP</CODE> function interpolates the data contained in vector <CODE>x</CODE>,
the independent variable, and vector <CODE>y</CODE>, the dependent variable. There are no
restrictions on <CODE>x</CODE>, it doesn't even need to be increasing. The number of interpolant
locations is given in scalar <CODE>n</CODE>, which must be greater than <code>1</code>. The output
of the <CODE>SPLINTERP</CODE> function is a matrix with <CODE>n</CODE> rows and <code>2</code>
columns. The first column will contain the output locations and the second column the
interpolated values.</p>
<P>
<font size="+1" color="green"><B>Method</B></font></P>
<p>
The points are first parameterized in terms of normalized arc length. The normalized length of
<CODE>x</CODE> is the real length divided by the range of <CODE>x</CODE>, that is, the maximum
value minus the minimum value. The arclength at a point is approximated by the sum of the lengths
of straight line segments connecting all points up to that point. A spline under tension is
calculated for <CODE>x</CODE> versus arc length and <CODE>y</CODE> versus arc length. The
<CODE>x</CODE> and <CODE>y</CODE> values are interpolated separately and then combined to
form the output interpolant.</p>
<P>
<font size="+1" color="green"><B>Tension</B></font></P>
<p>
The interpolant is calculated by the method of cubic splines under tension. The tension factor
corresponds to the <i>curviness</i>, and must be greater than zero. If it is close to zero, each
interpolated function is almost a cubic spline and the resulting curve is quite <i>loose</i>.
If the tension is large, then the resultant is almost linear. The tension used is the current value
of <CODE><a href="../../../Characteristics/GeneralGraph/tension/tension.htm">TENSION</a></CODE>,
which may be changed with the <CODE><font color="blue">
<a href="../../../SetCommand/setcommand.htm">SET TENSION</a></font></CODE> command.</P>
<P>
<a href="fc.htm"><img align=middle border="0" src="../../../shadow_left.gif">
<font size="+1" color="olive">Fritch-Carlson interpolation</font></a><br />
<a href="bivinterp.htm"><img align=middle border="0" src="../../../shadow_right.gif">
<font size="+1" color="olive">2D interpolation</font></a>
</P>
</BODY>
</HTML>
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