[42] | 1 | <?php |
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| 2 | /*======================================================================= |
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| 3 | // File: JPGRAPH_REGSTAT.PHP |
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| 4 | // Description: Regression and statistical analysis helper classes |
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| 5 | // Created: 2002-12-01 |
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| 6 | // Ver: $Id: jpgraph_regstat.php 1131 2009-03-11 20:08:24Z ljp $ |
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| 7 | // |
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| 8 | // Copyright (c) Asial Corporation. All rights reserved. |
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| 9 | //======================================================================== |
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| 10 | */ |
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| 11 | |
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| 12 | //------------------------------------------------------------------------ |
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| 13 | // CLASS Spline |
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| 14 | // Create a new data array from an existing data array but with more points. |
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| 15 | // The new points are interpolated using a cubic spline algorithm |
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| 16 | //------------------------------------------------------------------------ |
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| 17 | class Spline { |
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| 18 | // 3:rd degree polynom approximation |
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| 19 | |
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| 20 | private $xdata,$ydata; // Data vectors |
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| 21 | private $y2; // 2:nd derivate of ydata |
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| 22 | private $n=0; |
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| 23 | |
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| 24 | function __construct($xdata,$ydata) { |
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| 25 | $this->y2 = array(); |
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| 26 | $this->xdata = $xdata; |
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| 27 | $this->ydata = $ydata; |
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| 28 | |
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| 29 | $n = count($ydata); |
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| 30 | $this->n = $n; |
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| 31 | if( $this->n !== count($xdata) ) { |
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| 32 | JpGraphError::RaiseL(19001); |
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| 33 | //('Spline: Number of X and Y coordinates must be the same'); |
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| 34 | } |
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| 35 | |
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| 36 | // Natural spline 2:derivate == 0 at endpoints |
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| 37 | $this->y2[0] = 0.0; |
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| 38 | $this->y2[$n-1] = 0.0; |
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| 39 | $delta[0] = 0.0; |
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| 40 | |
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| 41 | // Calculate 2:nd derivate |
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| 42 | for($i=1; $i < $n-1; ++$i) { |
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| 43 | $d = ($xdata[$i+1]-$xdata[$i-1]); |
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| 44 | if( $d == 0 ) { |
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| 45 | JpGraphError::RaiseL(19002); |
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| 46 | //('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.'); |
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| 47 | } |
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| 48 | $s = ($xdata[$i]-$xdata[$i-1])/$d; |
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| 49 | $p = $s*$this->y2[$i-1]+2.0; |
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| 50 | $this->y2[$i] = ($s-1.0)/$p; |
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| 51 | $delta[$i] = ($ydata[$i+1]-$ydata[$i])/($xdata[$i+1]-$xdata[$i]) - |
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| 52 | ($ydata[$i]-$ydata[$i-1])/($xdata[$i]-$xdata[$i-1]); |
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| 53 | $delta[$i] = (6.0*$delta[$i]/($xdata[$i+1]-$xdata[$i-1])-$s*$delta[$i-1])/$p; |
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| 54 | } |
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| 55 | |
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| 56 | // Backward substitution |
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| 57 | for( $j=$n-2; $j >= 0; --$j ) { |
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| 58 | $this->y2[$j] = $this->y2[$j]*$this->y2[$j+1] + $delta[$j]; |
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| 59 | } |
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| 60 | } |
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| 61 | |
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| 62 | // Return the two new data vectors |
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| 63 | function Get($num=50) { |
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| 64 | $n = $this->n ; |
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| 65 | $step = ($this->xdata[$n-1]-$this->xdata[0]) / ($num-1); |
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| 66 | $xnew=array(); |
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| 67 | $ynew=array(); |
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| 68 | $xnew[0] = $this->xdata[0]; |
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| 69 | $ynew[0] = $this->ydata[0]; |
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| 70 | for( $j=1; $j < $num; ++$j ) { |
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| 71 | $xnew[$j] = $xnew[0]+$j*$step; |
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| 72 | $ynew[$j] = $this->Interpolate($xnew[$j]); |
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| 73 | } |
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| 74 | return array($xnew,$ynew); |
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| 75 | } |
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| 76 | |
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| 77 | // Return a single interpolated Y-value from an x value |
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| 78 | function Interpolate($xpoint) { |
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| 79 | |
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| 80 | $max = $this->n-1; |
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| 81 | $min = 0; |
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| 82 | |
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| 83 | // Binary search to find interval |
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| 84 | while( $max-$min > 1 ) { |
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| 85 | $k = ($max+$min) / 2; |
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| 86 | if( $this->xdata[$k] > $xpoint ) |
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| 87 | $max=$k; |
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| 88 | else |
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| 89 | $min=$k; |
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| 90 | } |
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| 91 | |
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| 92 | // Each interval is interpolated by a 3:degree polynom function |
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| 93 | $h = $this->xdata[$max]-$this->xdata[$min]; |
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| 94 | |
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| 95 | if( $h == 0 ) { |
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| 96 | JpGraphError::RaiseL(19002); |
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| 97 | //('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.'); |
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| 98 | } |
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| 99 | |
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| 100 | |
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| 101 | $a = ($this->xdata[$max]-$xpoint)/$h; |
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| 102 | $b = ($xpoint-$this->xdata[$min])/$h; |
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| 103 | return $a*$this->ydata[$min]+$b*$this->ydata[$max]+ |
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| 104 | (($a*$a*$a-$a)*$this->y2[$min]+($b*$b*$b-$b)*$this->y2[$max])*($h*$h)/6.0; |
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| 105 | } |
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| 106 | } |
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| 107 | |
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| 108 | //------------------------------------------------------------------------ |
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| 109 | // CLASS Bezier |
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| 110 | // Create a new data array from a number of control points |
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| 111 | //------------------------------------------------------------------------ |
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| 112 | class Bezier { |
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| 113 | /** |
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| 114 | * @author Thomas Despoix, openXtrem company |
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| 115 | * @license released under QPL |
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| 116 | * @abstract Bezier interoplated point generation, |
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| 117 | * computed from control points data sets, based on Paul Bourke algorithm : |
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| 118 | * http://local.wasp.uwa.edu.au/~pbourke/geometry/bezier/index2.html |
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| 119 | */ |
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| 120 | private $datax = array(); |
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| 121 | private $datay = array(); |
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| 122 | private $n=0; |
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| 123 | |
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| 124 | function __construct($datax, $datay, $attraction_factor = 1) { |
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| 125 | // Adding control point multiple time will raise their attraction power over the curve |
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| 126 | $this->n = count($datax); |
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| 127 | if( $this->n !== count($datay) ) { |
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| 128 | JpGraphError::RaiseL(19003); |
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| 129 | //('Bezier: Number of X and Y coordinates must be the same'); |
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| 130 | } |
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| 131 | $idx=0; |
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| 132 | foreach($datax as $datumx) { |
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| 133 | for ($i = 0; $i < $attraction_factor; $i++) { |
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| 134 | $this->datax[$idx++] = $datumx; |
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| 135 | } |
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| 136 | } |
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| 137 | $idx=0; |
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| 138 | foreach($datay as $datumy) { |
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| 139 | for ($i = 0; $i < $attraction_factor; $i++) { |
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| 140 | $this->datay[$idx++] = $datumy; |
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| 141 | } |
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| 142 | } |
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| 143 | $this->n *= $attraction_factor; |
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| 144 | } |
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| 145 | |
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| 146 | /** |
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| 147 | * Return a set of data points that specifies the bezier curve with $steps points |
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| 148 | * @param $steps Number of new points to return |
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| 149 | * @return array($datax, $datay) |
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| 150 | */ |
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| 151 | function Get($steps) { |
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| 152 | $datax = array(); |
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| 153 | $datay = array(); |
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| 154 | for ($i = 0; $i < $steps; $i++) { |
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| 155 | list($datumx, $datumy) = $this->GetPoint((double) $i / (double) $steps); |
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| 156 | $datax[$i] = $datumx; |
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| 157 | $datay[$i] = $datumy; |
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| 158 | } |
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| 159 | |
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| 160 | $datax[] = end($this->datax); |
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| 161 | $datay[] = end($this->datay); |
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| 162 | |
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| 163 | return array($datax, $datay); |
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| 164 | } |
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| 165 | |
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| 166 | /** |
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| 167 | * Return one point on the bezier curve. $mu is the position on the curve where $mu is in the |
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| 168 | * range 0 $mu < 1 where 0 is tha start point and 1 is the end point. Note that every newly computed |
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| 169 | * point depends on all the existing points |
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| 170 | * |
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| 171 | * @param $mu Position on the bezier curve |
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| 172 | * @return array($x, $y) |
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| 173 | */ |
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| 174 | function GetPoint($mu) { |
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| 175 | $n = $this->n - 1; |
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| 176 | $k = 0; |
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| 177 | $kn = 0; |
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| 178 | $nn = 0; |
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| 179 | $nkn = 0; |
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| 180 | $blend = 0.0; |
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| 181 | $newx = 0.0; |
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| 182 | $newy = 0.0; |
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| 183 | |
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| 184 | $muk = 1.0; |
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| 185 | $munk = (double) pow(1-$mu,(double) $n); |
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| 186 | |
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| 187 | for ($k = 0; $k <= $n; $k++) { |
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| 188 | $nn = $n; |
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| 189 | $kn = $k; |
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| 190 | $nkn = $n - $k; |
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| 191 | $blend = $muk * $munk; |
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| 192 | $muk *= $mu; |
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| 193 | $munk /= (1-$mu); |
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| 194 | while ($nn >= 1) { |
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| 195 | $blend *= $nn; |
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| 196 | $nn--; |
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| 197 | if ($kn > 1) { |
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| 198 | $blend /= (double) $kn; |
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| 199 | $kn--; |
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| 200 | } |
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| 201 | if ($nkn > 1) { |
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| 202 | $blend /= (double) $nkn; |
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| 203 | $nkn--; |
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| 204 | } |
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| 205 | } |
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| 206 | $newx += $this->datax[$k] * $blend; |
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| 207 | $newy += $this->datay[$k] * $blend; |
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| 208 | } |
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| 209 | |
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| 210 | return array($newx, $newy); |
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| 211 | } |
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| 212 | } |
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| 213 | |
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| 214 | // EOF |
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| 215 | ?> |
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