Updating a spline class on a chart so that the highest peak is a marker position - JPGraph

Question

I created a graph using Jpgraph ( http://www.jpgraph.com ).

Jpgraph has a spline class that smooths lines on a line chart. However, it does not work as I expected. As you can see, the highest peak of the line goes beyond the actual marks (red squares). Friday 10pm is 2.0, but it seems to be higher than around 6am on Friday.

Bad laptop touchpad drawn by an example of what I would expect below :)

I managed to track the class to jpgraph_regstat.php. Any idea how to make the peak center an actual mark?

//------------------------------------------------------------------------
// CLASS Spline
// Create a new data array from an existing data array but with more points.
// The new points are interpolated using a cubic spline algorithm
//------------------------------------------------------------------------
class Spline {
    // 3:rd degree polynom approximation

    private $xdata,$ydata;   // Data vectors
    private $y2;   // 2:nd derivate of ydata
    private $n=0;

    function __construct($xdata,$ydata) {
        $this->y2 = array();
        $this->xdata = $xdata;
        $this->ydata = $ydata;

        $n = count($ydata);
        $this->n = $n;
        if( $this->n !== count($xdata) ) {
            JpGraphError::RaiseL(19001);
            //('Spline: Number of X and Y coordinates must be the same');
        }

        // Natural spline 2:derivate == 0 at endpoints
        $this->y2[0]    = 0.0;
        $this->y2[$n-1] = 0.0;
        $delta[0] = 0.0;

        // Calculate 2:nd derivate
        for($i=1; $i < $n-1; ++$i) {
            $d = ($xdata[$i+1]-$xdata[$i-1]);
            if( $d == 0  ) {
                JpGraphError::RaiseL(19002);
                //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.');
            }
            $s = ($xdata[$i]-$xdata[$i-1])/$d;
            $p = $s*$this->y2[$i-1]+2.0;
            $this->y2[$i] = ($s-1.0)/$p;
            $delta[$i] = ($ydata[$i+1]-$ydata[$i])/($xdata[$i+1]-$xdata[$i]) -
            ($ydata[$i]-$ydata[$i-1])/($xdata[$i]-$xdata[$i-1]);
            $delta[$i] = (6.0*$delta[$i]/($xdata[$i+1]-$xdata[$i-1])-$s*$delta[$i-1])/$p;
        }

        // Backward substitution
        for( $j=$n-2; $j >= 0; --$j ) {
            $this->y2[$j] = $this->y2[$j]*$this->y2[$j+1] + $delta[$j];
        }
    }

    // Return the two new data vectors
    function Get($num=50) {
        $n = $this->n ;
        $step = ($this->xdata[$n-1]-$this->xdata[0]) / ($num-1);
        $xnew=array();
        $ynew=array();
        $xnew[0] = $this->xdata[0];
        $ynew[0] = $this->ydata[0];
        for( $j=1; $j < $num; ++$j ) {
            $xnew[$j] = $xnew[0]+$j*$step;
            $ynew[$j] = $this->Interpolate($xnew[$j]);
        }
        return array($xnew,$ynew);
    }

    // Return a single interpolated Y-value from an x value
    function Interpolate($xpoint) {

        $max = $this->n-1;
        $min = 0;

        // Binary search to find interval
        while( $max-$min > 1 ) {
            $k = ($max+$min) / 2;
            if( $this->xdata[$k] > $xpoint )
            $max=$k;
            else
            $min=$k;
        }

        // Each interval is interpolated by a 3:degree polynom function
        $h = $this->xdata[$max]-$this->xdata[$min];

        if( $h == 0  ) {
            JpGraphError::RaiseL(19002);
            //('Invalid input data for spline. Two or more consecutive input X-values are equal. Each input X-value must differ since from a mathematical point of view it must be a one-to-one mapping, i.e. each X-value must correspond to exactly one Y-value.');
        }


        $a = ($this->xdata[$max]-$xpoint)/$h;
        $b = ($xpoint-$this->xdata[$min])/$h;
        return $a*$this->ydata[$min]+$b*$this->ydata[$max]+
        (($a*$a*$a-$a)*$this->y2[$min]+($b*$b*$b-$b)*$this->y2[$max])*($h*$h)/6.0;
    }
}

(http://jpgraph.net/download/manuals/chunkhtml/example_src/splineex1.html)

Answer 1

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