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  28  <H3><A NAME="8_1_16">8.1.16 Constructing smooth line plots with Cubic
  29   Splines</A></H3>
  30  <P> If you only have access to a few data points but still want a smooth
  31   curve between those data points JpGraph can help you achieving that by
  32   letting you construct cubic splines. If you never have heard of cubic
  33   splines before, don't worry. You only have to supply the data points
  34   you know tell JpGraph how many interpolated points in total you want in
  35   the graph. JpGraph will now take care of constructing a smooth curve
  36   between all you data points. The new, smooth, curve will be made up of
  37   exactly as many interpolated points as you have specified.</P>
  38  <P> To construct a spline you need both the X and Y coordinates for the
  39   known data points.</P>
  40  <P> You start by constructing a new <A href="">Spline</A> instance. To
  41   get access to the Spline class you must first remember to include the
  42   file &quot;jpgraph_regstat.php&quot;. You instantiate this class by calling it
  43   with your two known data arrays (X and Y) as follows.<DIV class="phpscript">
  44  <CODE><FONT color="#000000"> <FONT color="#0000BB">&nbsp;$spline&nbsp;</FONT><FONT color="#007700">
  45  =&nbsp;new&nbsp;</FONT><FONT color="#0000BB">Spline</FONT><FONT color="#007700">(</FONT><FONT
  46  color="#0000BB">$xdata</FONT><FONT color="#007700">,</FONT><FONT color="#0000BB">
  47  $ydata</FONT><FONT color="#007700">);</FONT><FONT color="#0000BB"></FONT>
  48  </FONT></CODE></DIV></P>
  49  <P>This call initializes the spline with the data points you have. These
  50   data points are also known as<I> Control points</I> for the spline.
  51   This helper class doesn't draw any line itself. Instead it is merely
  52   used to get a new (larger) data array which have all the interpolated
  53   values. You then use these new value in your plot. This way give you
  54   great flexibility in how you want to use this interpolated data.</P>
  55  <P> Continuing the above line we now use the <A href="">Spline::Get()</A>
  56   method to get an interpolated array containing a specified number of
  57   points. So for example the line<DIV class="phpscript"><CODE><FONT color="#000000">
  58   <FONT color="#0000BB">&nbsp;</FONT><FONT color="#007700">list(</FONT><FONT color="#0000BB">
  59  $sdatax</FONT><FONT color="#007700">,</FONT><FONT color="#0000BB">
  60  $sdatay</FONT><FONT color="#007700">)&nbsp;=&nbsp;</FONT><FONT color="#0000BB">
  61  $spline</FONT><FONT color="#007700">-&gt;</FONT><FONT color="#0000BB">Get</FONT><FONT
  62  color="#007700">(</FONT><FONT color="#0000BB">50</FONT><FONT color="#007700">
  63  );</FONT><FONT color="#0000BB"></FONT></FONT></CODE></DIV></P>
  64  <P>Will construct the two new data arrays '$sdatax' and '$sdatay' which
  65   contains 50 data points. These two arrays are constructed from the
  66   control point we specified when we created the '$spline' object.</P>
  67  <P> You would then use these two new data array in exactly the same way
  68   as you would form ordinary data vectors.</P>
  69  <P> The following example illustrates this<DIV class="example">
  70  <BR> <A href="exframes/frame_splineex1.html" target="blank"><IMG border="0"
  71  HEIGHT="200"  src="img/splineex1.png" WIDTH="300"></A>
  72  <BR><B>Figure 26:</B> Using spline to get a smooth curve between the
  73   control points. <A href="exframes/frame_splineex1.html" target="blank">
  74  [src]</A>&nbsp;
  75  <P></P>
  76  </DIV></P>
  77  <P> In order to make the example more interesting we actually use two
  78   plots. First a line plot to get the smooth curve and then a standard
  79   scatter plot which is used to illustrate where the control points are.</P>
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