<?php

class Plot 

{

  private $aCoords;

  function __construct(&$aCoords) 

  {

    $this->aCoords = &$aCoords;

  }

  public function drawLine($vImage, $vColor, $iPosX = 0, $imaxX = false) 

  {

    $maxX = $imaxX;

    if ($imaxX === false) $maxX = imagesx($vImage);

    reset($this->aCoords);

    list($iPrevX, $iPrevY) = each($this->aCoords);

    while (list ($x, $y) = each($this->aCoords)) 

    {

      $laCouleur = null;

      if (!is_array($vColor)) $laCouleur = $vColor;

      else

      {

        $s = count($vColor) - 1;

        $laCouleur = $vColor[$s]->color;

        $pct = $x / $maxX;

        while(($s>0)&&($pct < $vColor[$s]->pct))

        {

          $s -= 1;

          $laCouleur = $vColor[$s]->color;

        }

      }

      imageline($vImage, round($iPrevX), round($iPrevY), round($x), round($y), $laCouleur);

      $iPrevX = $x;

      $iPrevY = $y;

    }

  }

  public function drawDots($vImage, $vColor, $iPosX = 0, $iPosY = false, $iDotSize = 1) {

    if ($iPosY === false)

      $iPosY = imagesy($vImage);

    $vBorderColor = imagecolorallocate($vImage, 0, 0, 0);

    foreach ($this->aCoords as $x => $y) {

      imagefilledellipse($vImage, $iPosX + round($x), $iPosY - round($y), $iDotSize, $iDotSize, $vColor);

      imageellipse($vImage, $iPosX + round($x), $iPosY - round($y), $iDotSize, $iDotSize, $vBorderColor);

    }

  }

  public function drawAxis($vImage, $vColor, $iPosX = 0, $iPosY = false) {

    if ($iPosY === false) $iPosY = imagesy($vImage);

    $vImageWidth = imagesx($vImage);

    imageline($vImage, $iPosX, $iPosY, $iPosX, 0, $vColor);

    imageline($vImage, $iPosX, $iPosY, $vImageWidth, $iPosY, $vColor);

    imagefilledpolygon($vImage, array($iPosX, 0, $iPosX - 3, 5, $iPosX + 3, 5), 3, $vColor);

    imagefilledpolygon($vImage, array($vImageWidth, $iPosY, $vImageWidth - 5, $iPosY - 3, $vImageWidth - 5, $iPosY + 3), 3, $vColor);

  }

}

class CubicSplines 

{

  protected $aCoords;

  protected $aCrdX;

  protected $aCrdY;

  protected $aSplines = array();

  protected $iMinX;

  protected $iMaxX;

  protected $iStep;

  protected function prepareCoords(&$aCoords, $iStep, $iMinX = -1, $iMaxX = -1) {

    $this->aCrdX = array();

    $this->aCrdY = array();

    $this->aCoords = array();

    ksort($aCoords);

    foreach ($aCoords as $x => $y) {

      $this->aCrdX[] = $x;

      $this->aCrdY[] = $y;

    }

    $this->iMinX = $iMinX;

    $this->iMaxX = $iMaxX;

    if ($this->iMinX == -1)

      $this->iMinX = min($this->aCrdX);

    if ($this->iMaxX == -1)

      $this->iMaxX = max($this->aCrdX);

    $this->iStep = $iStep;

  }

  public function setInitCoords(&$aCoords, $iStep = 1, $iMinX = -1, $iMaxX = -1) {

    $this->aSplines = array();

    if (count($aCoords) < 4) {

      return false;

    }

    $this->prepareCoords($aCoords, $iStep, $iMinX, $iMaxX);

    $this->buildSpline($this->aCrdX, $this->aCrdY, count($this->aCrdX));

  }

  public function processCoords() {

    for ($x = $this->iMinX; $x <= $this->iMaxX; $x += $this->iStep) {

      $this->aCoords[$x] = $this->funcInterp($x);

    }

    return $this->aCoords;

  }

  private function buildSpline($x, $y, $n) {

    for ($i = 0; $i < $n; ++$i) {

      $this->aSplines[$i]['x'] = $x[$i];

      $this->aSplines[$i]['a'] = $y[$i];

    }

    $this->aSplines[0]['c'] = $this->aSplines[$n - 1]['c'] = 0;

    $alpha[0] = $beta[0] = 0;

    for ($i = 1; $i < $n - 1; ++$i) {

      $h_i = $x[$i] - $x[$i - 1];

      $h_i1 = $x[$i + 1] - $x[$i];

      $A = $h_i;

      $C = 2.0 * ($h_i + $h_i1);

      $B = $h_i1;

      $F = 6.0 * (($y[$i + 1] - $y[$i]) / $h_i1 - ($y[$i] - $y[$i - 1]) / $h_i);

      $z = ($A * $alpha[$i - 1] + $C);

      $alpha[$i] = - $B / $z;

      $beta[$i] = ($F - $A * $beta[$i - 1]) / $z;

    }

    for ($i = $n - 2; $i > 0; --$i) {

      $this->aSplines[$i]['c'] = $alpha[$i] * $this->aSplines[$i + 1]['c'] + $beta[$i];

    }

    for ($i = $n - 1; $i > 0; --$i) {

      $h_i = $x[$i] - $x[$i - 1];

      $this->aSplines[$i]['d'] = ($this->aSplines[$i]['c'] - $this->aSplines[$i - 1]['c']) / $h_i;

      $this->aSplines[$i]['b'] = $h_i * (2.0 * $this->aSplines[$i]['c'] + $this->aSplines[$i - 1]['c']) / 6.0 + ($y[$i] - $y[$i - 1]) / $h_i;

    }

  }

  private function funcInterp($x) {

    $n = count($this->aSplines);

    if ($x <= $this->aSplines[0]['x'])  {

      $s = $this->aSplines[1];

    } else {

      if ($x >= $this->aSplines[$n - 1]['x']) {

        $s = $this->aSplines[$n - 1];

      } else {

        $i = 0;

        $j = $n - 1;

        while ($i + 1 < $j) {

          $k = $i + ($j - $i) / 2;

          if ($x <= $this->aSplines[$k]['x']) {

            $j = $k;

          } else {

            $i = $k;

          }

        }

        $s = $this->aSplines[$j];

      }

    }

    $dx = ($x - $s['x']);

    return $s['a'] + ($s['b'] + ($s['c'] / 2.0 + $s['d'] * $dx / 6.0) * $dx) * $dx;

  }

}

?>