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<?php
/*=======================================================================
// File: JPGRAPH_CONTOUR.PHP
// Description: Contour plot
// Created: 2009-03-08
// Ver: $Id: jpgraph_contour.php 1870 2009-09-29 04:24:18Z ljp $
//
// Copyright (c) Aditus Consulting. All rights reserved.
//========================================================================
*/
require_once('jpgraph_meshinterpolate.inc.php');
define('HORIZ_EDGE',0);
define('VERT_EDGE',1);
/**
* This class encapsulates the core contour plot algorithm. It will find the path
* of the specified isobars in the data matrix specified. It is assumed that the
* data matrix models an equspaced X-Y mesh of datavalues corresponding to the Z
* values.
*
*/
class Contour {
private $dataPoints = array();
private $nbrCols=0,$nbrRows=0;
private $horizEdges = array(), $vertEdges=array();
private $isobarValues = array();
private $stack = null;
private $isobarCoord = array();
private $nbrIsobars = 10, $isobarColors = array();
private $invert = true;
private $highcontrast = false, $highcontrastbw = false;
/**
* Create a new contour level "algorithm machine".
* @param $aMatrix The values to find the contour from
* @param $aIsobars Mixed. If integer it determines the number of isobars to be used. The levels are determined
* automatically as equdistance between the min and max value of the matrice.
* If $aIsobars is an array then this is interpretated as an array of values to be used as isobars in the
* contour plot.
* @return an instance of the contour algorithm
*/
function __construct($aMatrix,$aIsobars=10, $aColors=null) {
$this->nbrRows = count($aMatrix);
$this->nbrCols = count($aMatrix[0]);
$this->dataPoints = $aMatrix;
if( is_array($aIsobars) ) {
// use the isobar values supplied
$this->nbrIsobars = count($aIsobars);
$this->isobarValues = $aIsobars;
}
else {
// Determine the isobar values automatically
$this->nbrIsobars = $aIsobars;
list($min,$max) = $this->getMinMaxVal();
$stepSize = ($max-$min) / $aIsobars ;
$isobar = $min+$stepSize/2;
for ($i = 0; $i < $aIsobars; $i++) {
$this->isobarValues[$i] = $isobar;
$isobar += $stepSize;
}
}
if( $aColors !== null && count($aColors) > 0 ) {
if( !is_array($aColors) ) {
JpGraphError::RaiseL(28001);
//'Third argument to Contour must be an array of colors.'
}
if( count($aColors) != count($this->isobarValues) ) {
JpGraphError::RaiseL(28002);
//'Number of colors must equal the number of isobar lines specified';
}
$this->isobarColors = $aColors;
}
}
/**
* Flip the plot around the Y-coordinate. This has the same affect as flipping the input
* data matrice
*
* @param $aFlg If true the the vertice in input data matrice position (0,0) corresponds to the top left
* corner of teh plot otherwise it will correspond to the bottom left corner (a horizontal flip)
*/
function SetInvert($aFlg=true) {
$this->invert = $aFlg;
}
/**
* Find the min and max values in the data matrice
*
* @return array(min_value,max_value)
*/
function getMinMaxVal() {
$min = $this->dataPoints[0][0];
$max = $this->dataPoints[0][0];
for ($i = 0; $i < $this->nbrRows; $i++) {
if( ($mi=min($this->dataPoints[$i])) < $min ) $min = $mi;
if( ($ma=max($this->dataPoints[$i])) > $max ) $max = $ma;
}
return array($min,$max);
}
/**
* Reset the two matrices that keeps track on where the isobars crosses the
* horizontal and vertical edges
*/
function resetEdgeMatrices() {
for ($k = 0; $k < 2; $k++) {
for ($i = 0; $i <= $this->nbrRows; $i++) {
for ($j = 0; $j <= $this->nbrCols; $j++) {
$this->edges[$k][$i][$j] = false;
}
}
}
}
/**
* Determine if the specified isobar crosses the horizontal edge specified by its row and column
*
* @param $aRow Row index of edge to be checked
* @param $aCol Col index of edge to be checked
* @param $aIsobar Isobar value
* @return true if the isobar is crossing this edge
*/
function isobarHCrossing($aRow,$aCol,$aIsobar) {
if( $aCol >= $this->nbrCols-1 ) {
JpGraphError::RaiseL(28003,$aCol);
//'ContourPlot Internal Error: isobarHCrossing: Coloumn index too large (%d)'
}
if( $aRow >= $this->nbrRows ) {
JpGraphError::RaiseL(28004,$aRow);
//'ContourPlot Internal Error: isobarHCrossing: Row index too large (%d)'
}
$v1 = $this->dataPoints[$aRow][$aCol];
$v2 = $this->dataPoints[$aRow][$aCol+1];
return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ;
}
/**
* Determine if the specified isobar crosses the vertical edge specified by its row and column
*
* @param $aRow Row index of edge to be checked
* @param $aCol Col index of edge to be checked
* @param $aIsobar Isobar value
* @return true if the isobar is crossing this edge
*/
function isobarVCrossing($aRow,$aCol,$aIsobar) {
if( $aRow >= $this->nbrRows-1) {
JpGraphError::RaiseL(28005,$aRow);
//'isobarVCrossing: Row index too large
}
if( $aCol >= $this->nbrCols ) {
JpGraphError::RaiseL(28006,$aCol);
//'isobarVCrossing: Col index too large
}
$v1 = $this->dataPoints[$aRow][$aCol];
$v2 = $this->dataPoints[$aRow+1][$aCol];
return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ;
}
/**
* Determine all edges, horizontal and vertical that the specified isobar crosses. The crossings
* are recorded in the two edge matrices.
*
* @param $aIsobar The value of the isobar to be checked
*/
function determineIsobarEdgeCrossings($aIsobar) {
$ib = $this->isobarValues[$aIsobar];
for ($i = 0; $i < $this->nbrRows-1; $i++) {
for ($j = 0; $j < $this->nbrCols-1; $j++) {
$this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($i,$j,$ib);
$this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$j,$ib);
}
}
// We now have the bottom and rightmost edges unsearched
for ($i = 0; $i < $this->nbrRows-1; $i++) {
$this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$this->nbrCols-1,$ib);
}
for ($j = 0; $j < $this->nbrCols-1; $j++) {
$this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($this->nbrRows-1,$j,$ib);
}
}
/**
* Return the normalized coordinates for the crossing of the specified edge with the specified
* isobar- The crossing is simpy detrmined with a linear interpolation between the two vertices
* on each side of the edge and the value of the isobar
*
* @param $aRow Row of edge
* @param $aCol Column of edge
* @param $aEdgeDir Determine if this is a horizontal or vertical edge
* @param $ib The isobar value
* @return unknown_type
*/
function getCrossingCoord($aRow,$aCol,$aEdgeDir,$aIsobarVal) {
// In order to avoid numerical problem when two vertices are very close
// we have to check and avoid dividing by close to zero denumerator.
if( $aEdgeDir == HORIZ_EDGE ) {
$d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow][$aCol+1]);
if( $d > 0.001 ) {
$xcoord = $aCol + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d;
}
else {
$xcoord = $aCol;
}
$ycoord = $aRow;
}
else {
$d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow+1][$aCol]);
if( $d > 0.001 ) {
$ycoord = $aRow + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d;
}
else {
$ycoord = $aRow;
}
$xcoord = $aCol;
}
if( $this->invert ) {
$ycoord = $this->nbrRows-1 - $ycoord;
}
return array($xcoord,$ycoord);
}
/**
* In order to avoid all kinds of unpleasent extra checks and complex boundary
* controls for the degenerated case where the contour levels exactly crosses
* one of the vertices we add a very small delta (0.1%) to the data point value.
* This has no visible affect but it makes the code sooooo much cleaner.
*
*/
function adjustDataPointValues() {
$ni = count($this->isobarValues);
for ($k = 0; $k < $ni; $k++) {
$ib = $this->isobarValues[$k];
for ($row = 0 ; $row < $this->nbrRows-1; ++$row) {
for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) {
if( abs($this->dataPoints[$row][$col] - $ib) < 0.0001 ) {
$this->dataPoints[$row][$col] += $this->dataPoints[$row][$col]*0.001;
}
}
}
}
}
/**
* @param $aFlg
* @param $aBW
* @return unknown_type
*/
function UseHighContrastColor($aFlg=true,$aBW=false) {
$this->highcontrast = $aFlg;
$this->highcontrastbw = $aBW;
}
/**
* Calculate suitable colors for each defined isobar
*
*/
function CalculateColors() {
if ( $this->highcontrast ) {
if ( $this->highcontrastbw ) {
for ($ib = 0; $ib < $this->nbrIsobars; $ib++) {
$this->isobarColors[$ib] = 'black';
}
}
else {
// Use only blue/red scale
$step = round(255/($this->nbrIsobars-1));
for ($ib = 0; $ib < $this->nbrIsobars; $ib++) {
$this->isobarColors[$ib] = array($ib*$step, 50, 255-$ib*$step);
}
}
}
else {
$n = $this->nbrIsobars;
$v = 0; $step = 1 / ($this->nbrIsobars-1);
for ($ib = 0; $ib < $this->nbrIsobars; $ib++) {
$this->isobarColors[$ib] = RGB::GetSpectrum($v);
$v += $step;
}
}
}
/**
* This is where the main work is done. For each isobar the crossing of the edges are determined
* and then each cell is analyzed to find the 0, 2 or 4 crossings. Then the normalized coordinate
* for the crossings are determined and pushed on to the isobar stack. When the method is finished
* the $isobarCoord will hold one arrayfor each isobar where all the line segments that makes
* up the contour plot are stored.
*
* @return array( $isobarCoord, $isobarValues, $isobarColors )
*/
function getIsobars() {
$this->adjustDataPointValues();
for ($isobar = 0; $isobar < $this->nbrIsobars; $isobar++) {
$ib = $this->isobarValues[$isobar];
$this->resetEdgeMatrices();
$this->determineIsobarEdgeCrossings($isobar);
$this->isobarCoord[$isobar] = array();
$ncoord = 0;
for ($row = 0 ; $row < $this->nbrRows-1; ++$row) {
for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) {
// Find out how many crossings around the edges
$n = 0;
if ( $this->edges[HORIZ_EDGE][$row][$col] ) $neigh[$n++] = array($row, $col, HORIZ_EDGE);
if ( $this->edges[HORIZ_EDGE][$row+1][$col] ) $neigh[$n++] = array($row+1,$col, HORIZ_EDGE);
if ( $this->edges[VERT_EDGE][$row][$col] ) $neigh[$n++] = array($row, $col, VERT_EDGE);
if ( $this->edges[VERT_EDGE][$row][$col+1] ) $neigh[$n++] = array($row, $col+1,VERT_EDGE);
if ( $n == 2 ) {
$n1=0; $n2=1;
$this->isobarCoord[$isobar][$ncoord++] = array(
$this->getCrossingCoord($neigh[$n1][0],$neigh[$n1][1],$neigh[$n1][2],$ib),
$this->getCrossingCoord($neigh[$n2][0],$neigh[$n2][1],$neigh[$n2][2],$ib) );
}
elseif ( $n == 4 ) {
// We must determine how to connect the edges either northwest->southeast or
// northeast->southwest. We do that by calculating the imaginary middle value of
// the cell by averaging the for corners. This will compared with the value of the
// top left corner will help determine the orientation of the ridge/creek
$midval = ($this->dataPoints[$row][$col]+$this->dataPoints[$row][$col+1]+$this->dataPoints[$row+1][$col]+$this->dataPoints[$row+1][$col+1])/4;
$v = $this->dataPoints[$row][$col];
if( $midval == $ib ) {
// Orientation "+"
$n1=0; $n2=1; $n3=2; $n4=3;
} elseif ( ($midval > $ib && $v > $ib) || ($midval < $ib && $v < $ib) ) {
// Orientation of ridge/valley = "\"
$n1=0; $n2=3; $n3=2; $n4=1;
} elseif ( ($midval > $ib && $v < $ib) || ($midval < $ib && $v > $ib) ) {
// Orientation of ridge/valley = "/"
$n1=0; $n2=2; $n3=3; $n4=1;
}
$this->isobarCoord[$isobar][$ncoord++] = array(
$this->getCrossingCoord($neigh[$n1][0],$neigh[$n1][1],$neigh[$n1][2],$ib),
$this->getCrossingCoord($neigh[$n2][0],$neigh[$n2][1],$neigh[$n2][2],$ib) );
$this->isobarCoord[$isobar][$ncoord++] = array(
$this->getCrossingCoord($neigh[$n3][0],$neigh[$n3][1],$neigh[$n3][2],$ib),
$this->getCrossingCoord($neigh[$n4][0],$neigh[$n4][1],$neigh[$n4][2],$ib) );
}
}
}
}
if( count($this->isobarColors) == 0 ) {
// No manually specified colors. Calculate them automatically.
$this->CalculateColors();
}
return array( $this->isobarCoord, $this->isobarValues, $this->isobarColors );
}
}
/**
* This class represent a plotting of a contour outline of data given as a X-Y matrice
*
*/
class ContourPlot extends Plot {
private $contour, $contourCoord, $contourVal, $contourColor;
private $nbrCountours = 0 ;
private $dataMatrix = array();
private $invertLegend = false;
private $interpFactor = 1;
private $flipData = false;
private $isobar = 10;
private $showLegend = false;
private $highcontrast = false, $highcontrastbw = false;
private $manualIsobarColors = array();
/**
* Construct a contour plotting algorithm. The end result of the algorithm is a sequence of
* line segments for each isobar given as two vertices.
*
* @param $aDataMatrix The Z-data to be used
* @param $aIsobar A mixed variable, if it is an integer then this specified the number of isobars to use.
* The values of the isobars are automatically detrmined to be equ-spaced between the min/max value of the
* data. If it is an array then it explicetely gives the isobar values
* @param $aInvert By default the matrice with row index 0 corresponds to Y-value 0, i.e. in the bottom of
* the plot. If this argument is true then the row with the highest index in the matrice corresponds to
* Y-value 0. In affect flipping the matrice around an imaginary horizontal axis.
* @param $aHighContrast Use high contrast colors (blue/red:ish)
* @param $aHighContrastBW Use only black colors for contours
* @return an instance of the contour plot algorithm
*/
function __construct($aDataMatrix, $aIsobar=10, $aFactor=1, $aInvert=false, $aIsobarColors=array()) {
$this->dataMatrix = $aDataMatrix;
$this->flipData = $aInvert;
$this->isobar = $aIsobar;
$this->interpFactor = $aFactor;
if ( $this->interpFactor > 1 ) {
if( $this->interpFactor > 5 ) {
JpGraphError::RaiseL(28007);// ContourPlot interpolation factor is too large (>5)
}
$ip = new MeshInterpolate();
$this->dataMatrix = $ip->Linear($this->dataMatrix, $this->interpFactor);
}
$this->contour = new Contour($this->dataMatrix,$this->isobar,$aIsobarColors);
if( is_array($aIsobar) )
$this->nbrContours = count($aIsobar);
else
$this->nbrContours = $aIsobar;
}
/**
* Flipe the data around the center
*
* @param $aFlg
*
*/
function SetInvert($aFlg=true) {
$this->flipData = $aFlg;
}
/**
* Set the colors for the isobar lines
*
* @param $aColorArray
*
*/
function SetIsobarColors($aColorArray) {
$this->manualIsobarColors = $aColorArray;
}
/**
* Show the legend
*
* @param $aFlg true if the legend should be shown
*
*/
function ShowLegend($aFlg=true) {
$this->showLegend = $aFlg;
}
/**
* @param $aFlg true if the legend should start with the lowest isobar on top
* @return unknown_type
*/
function Invertlegend($aFlg=true) {
$this->invertLegend = $aFlg;
}
/* Internal method. Give the min value to be used for the scaling
*
*/
function Min() {
return array(0,0);
}
/* Internal method. Give the max value to be used for the scaling
*
*/
function Max() {
return array(count($this->dataMatrix[0])-1,count($this->dataMatrix)-1);
}
/**
* Internal ramewrok method to setup the legend to be used for this plot.
* @param $aGraph The parent graph class
*/
function Legend($aGraph) {
if( ! $this->showLegend )
return;
if( $this->invertLegend ) {
for ($i = 0; $i < $this->nbrContours; $i++) {
$aGraph->legend->Add(sprintf('%.1f',$this->contourVal[$i]), $this->contourColor[$i]);
}
}
else {
for ($i = $this->nbrContours-1; $i >= 0 ; $i--) {
$aGraph->legend->Add(sprintf('%.1f',$this->contourVal[$i]), $this->contourColor[$i]);
}
}
}
/**
* Framework function which gets called before the Stroke() method is called
*
* @see Plot#PreScaleSetup($aGraph)
*
*/
function PreScaleSetup($aGraph) {
$xn = count($this->dataMatrix[0])-1;
$yn = count($this->dataMatrix)-1;
$aGraph->xaxis->scale->Update($aGraph->img,0,$xn);
$aGraph->yaxis->scale->Update($aGraph->img,0,$yn);
$this->contour->SetInvert($this->flipData);
list($this->contourCoord,$this->contourVal,$this->contourColor) = $this->contour->getIsobars();
}
/**
* Use high contrast color schema
*
* @param $aFlg True, to use high contrast color
* @param $aBW True, Use only black and white color schema
*/
function UseHighContrastColor($aFlg=true,$aBW=false) {
$this->highcontrast = $aFlg;
$this->highcontrastbw = $aBW;
$this->contour->UseHighContrastColor($this->highcontrast,$this->highcontrastbw);
}
/**
* Internal method. Stroke the contour plot to the graph
*
* @param $img Image handler
* @param $xscale Instance of the xscale to use
* @param $yscale Instance of the yscale to use
*/
function Stroke($img,$xscale,$yscale) {
if( count($this->manualIsobarColors) > 0 ) {
$this->contourColor = $this->manualIsobarColors;
if( count($this->manualIsobarColors) != $this->nbrContours ) {
JpGraphError::RaiseL(28002);
}
}
$img->SetLineWeight($this->line_weight);
for ($c = 0; $c < $this->nbrContours; $c++) {
$img->SetColor( $this->contourColor[$c] );
$n = count($this->contourCoord[$c]);
$i = 0;
while ( $i < $n ) {
list($x1,$y1) = $this->contourCoord[$c][$i][0];
$x1t = $xscale->Translate($x1);
$y1t = $yscale->Translate($y1);
list($x2,$y2) = $this->contourCoord[$c][$i++][1];
$x2t = $xscale->Translate($x2);
$y2t = $yscale->Translate($y2);
$img->Line($x1t,$y1t,$x2t,$y2t);
}
}
}
}
// EOF
?>
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