| <?php | <?php |
| /*======================================================================= | /*======================================================================= |
| // File: JPGRAPH_CONTOUR.PHP | // File: JPGRAPH_CONTOUR.PHP |
| // Description: Contour plot | // Description: Contour plot |
| // Created: 2009-03-08 | // Created: 2009-03-08 |
| // Ver: $Id: jpgraph_contour.php 1870 2009-09-29 04:24:18Z ljp $ | // Ver: $Id: jpgraph_contour.php 1870 2009-09-29 04:24:18Z ljp $ |
| // | // |
| // Copyright (c) Aditus Consulting. All rights reserved. | // Copyright (c) Aditus Consulting. All rights reserved. |
| //======================================================================== | //======================================================================== |
| */ | */ |
| require_once('jpgraph_meshinterpolate.inc.php'); | require_once('jpgraph_meshinterpolate.inc.php'); |
| define('HORIZ_EDGE',0); | define('HORIZ_EDGE',0); |
| define('VERT_EDGE',1); | define('VERT_EDGE',1); |
| /** | /** |
| * This class encapsulates the core contour plot algorithm. It will find the path | * 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 | * 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 | * data matrix models an equspaced X-Y mesh of datavalues corresponding to the Z |
| * values. | * values. |
| * | * |
| */ | */ |
| class Contour { | class Contour { |
| private $dataPoints = array(); | private $dataPoints = array(); |
| private $nbrCols=0,$nbrRows=0; | private $nbrCols=0,$nbrRows=0; |
| private $horizEdges = array(), $vertEdges=array(); | private $horizEdges = array(), $vertEdges=array(); |
| private $isobarValues = array(); | private $isobarValues = array(); |
| private $stack = null; | private $stack = null; |
| private $isobarCoord = array(); | private $isobarCoord = array(); |
| private $nbrIsobars = 10, $isobarColors = array(); | private $nbrIsobars = 10, $isobarColors = array(); |
| private $invert = true; | private $invert = true; |
| private $highcontrast = false, $highcontrastbw = false; | private $highcontrast = false, $highcontrastbw = false; |
| /** | /** |
| * Create a new contour level "algorithm machine". | * Create a new contour level "algorithm machine". |
| * @param $aMatrix The values to find the contour from | * @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 | * @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. | * 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 | * If $aIsobars is an array then this is interpretated as an array of values to be used as isobars in the |
| * contour plot. | * contour plot. |
| * @return an instance of the contour algorithm | * @return an instance of the contour algorithm |
| */ | */ |
| function __construct($aMatrix,$aIsobars=10, $aColors=null) { | function __construct($aMatrix,$aIsobars=10, $aColors=null) { |
| $this->nbrRows = count($aMatrix); | $this->nbrRows = count($aMatrix); |
| $this->nbrCols = count($aMatrix[0]); | $this->nbrCols = count($aMatrix[0]); |
| $this->dataPoints = $aMatrix; | $this->dataPoints = $aMatrix; |
| if( is_array($aIsobars) ) { | if( is_array($aIsobars) ) { |
| // use the isobar values supplied | // use the isobar values supplied |
| $this->nbrIsobars = count($aIsobars); | $this->nbrIsobars = count($aIsobars); |
| $this->isobarValues = $aIsobars; | $this->isobarValues = $aIsobars; |
| } | } |
| else { | else { |
| // Determine the isobar values automatically | // Determine the isobar values automatically |
| $this->nbrIsobars = $aIsobars; | $this->nbrIsobars = $aIsobars; |
| list($min,$max) = $this->getMinMaxVal(); | list($min,$max) = $this->getMinMaxVal(); |
| $stepSize = ($max-$min) / $aIsobars ; | $stepSize = ($max-$min) / $aIsobars ; |
| $isobar = $min+$stepSize/2; | $isobar = $min+$stepSize/2; |
| for ($i = 0; $i < $aIsobars; $i++) { | for ($i = 0; $i < $aIsobars; $i++) { |
| $this->isobarValues[$i] = $isobar; | $this->isobarValues[$i] = $isobar; |
| $isobar += $stepSize; | $isobar += $stepSize; |
| } | } |
| } | } |
| if( $aColors !== null && count($aColors) > 0 ) { | if( $aColors !== null && count($aColors) > 0 ) { |
| if( !is_array($aColors) ) { | if( !is_array($aColors) ) { |
| JpGraphError::RaiseL(28001); | JpGraphError::RaiseL(28001); |
| //'Third argument to Contour must be an array of colors.' | //'Third argument to Contour must be an array of colors.' |
| } | } |
| if( count($aColors) != count($this->isobarValues) ) { | if( count($aColors) != count($this->isobarValues) ) { |
| JpGraphError::RaiseL(28002); | JpGraphError::RaiseL(28002); |
| //'Number of colors must equal the number of isobar lines specified'; | //'Number of colors must equal the number of isobar lines specified'; |
| } | } |
| $this->isobarColors = $aColors; | $this->isobarColors = $aColors; |
| } | } |
| } | } |
| /** | /** |
| * Flip the plot around the Y-coordinate. This has the same affect as flipping the input | * Flip the plot around the Y-coordinate. This has the same affect as flipping the input |
| * data matrice | * data matrice |
| * | * |
| * @param $aFlg If true the the vertice in input data matrice position (0,0) corresponds to the top left | * @param $aFlg If true the the vertice in input data matrice position (0,0) corresponds to the top left |
| * corner of teh plot otherwise it will correspond to the bottom left corner (a horizontal flip) | * corner of teh plot otherwise it will correspond to the bottom left corner (a horizontal flip) |
| */ | */ |
| function SetInvert($aFlg=true) { | function SetInvert($aFlg=true) { |
| $this->invert = $aFlg; | $this->invert = $aFlg; |
| } | } |
| /** | /** |
| * Find the min and max values in the data matrice | * Find the min and max values in the data matrice |
| * | * |
| * @return array(min_value,max_value) | * @return array(min_value,max_value) |
| */ | */ |
| function getMinMaxVal() { | function getMinMaxVal() { |
| $min = $this->dataPoints[0][0]; | $min = $this->dataPoints[0][0]; |
| $max = $this->dataPoints[0][0]; | $max = $this->dataPoints[0][0]; |
| for ($i = 0; $i < $this->nbrRows; $i++) { | for ($i = 0; $i < $this->nbrRows; $i++) { |
| if( ($mi=min($this->dataPoints[$i])) < $min ) $min = $mi; | if( ($mi=min($this->dataPoints[$i])) < $min ) $min = $mi; |
| if( ($ma=max($this->dataPoints[$i])) > $max ) $max = $ma; | if( ($ma=max($this->dataPoints[$i])) > $max ) $max = $ma; |
| } | } |
| return array($min,$max); | return array($min,$max); |
| } | } |
| /** | /** |
| * Reset the two matrices that keeps track on where the isobars crosses the | * Reset the two matrices that keeps track on where the isobars crosses the |
| * horizontal and vertical edges | * horizontal and vertical edges |
| */ | */ |
| function resetEdgeMatrices() { | function resetEdgeMatrices() { |
| for ($k = 0; $k < 2; $k++) { | for ($k = 0; $k < 2; $k++) { |
| for ($i = 0; $i <= $this->nbrRows; $i++) { | for ($i = 0; $i <= $this->nbrRows; $i++) { |
| for ($j = 0; $j <= $this->nbrCols; $j++) { | for ($j = 0; $j <= $this->nbrCols; $j++) { |
| $this->edges[$k][$i][$j] = false; | $this->edges[$k][$i][$j] = false; |
| } | } |
| } | } |
| } | } |
| } | } |
| /** | /** |
| * Determine if the specified isobar crosses the horizontal edge specified by its row and column | * 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 $aRow Row index of edge to be checked |
| * @param $aCol Col index of edge to be checked | * @param $aCol Col index of edge to be checked |
| * @param $aIsobar Isobar value | * @param $aIsobar Isobar value |
| * @return true if the isobar is crossing this edge | * @return true if the isobar is crossing this edge |
| */ | */ |
| function isobarHCrossing($aRow,$aCol,$aIsobar) { | function isobarHCrossing($aRow,$aCol,$aIsobar) { |
| if( $aCol >= $this->nbrCols-1 ) { | if( $aCol >= $this->nbrCols-1 ) { |
| JpGraphError::RaiseL(28003,$aCol); | JpGraphError::RaiseL(28003,$aCol); |
| //'ContourPlot Internal Error: isobarHCrossing: Coloumn index too large (%d)' | //'ContourPlot Internal Error: isobarHCrossing: Coloumn index too large (%d)' |
| } | } |
| if( $aRow >= $this->nbrRows ) { | if( $aRow >= $this->nbrRows ) { |
| JpGraphError::RaiseL(28004,$aRow); | JpGraphError::RaiseL(28004,$aRow); |
| //'ContourPlot Internal Error: isobarHCrossing: Row index too large (%d)' | //'ContourPlot Internal Error: isobarHCrossing: Row index too large (%d)' |
| } | } |
| $v1 = $this->dataPoints[$aRow][$aCol]; | $v1 = $this->dataPoints[$aRow][$aCol]; |
| $v2 = $this->dataPoints[$aRow][$aCol+1]; | $v2 = $this->dataPoints[$aRow][$aCol+1]; |
| return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ; | return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ; |
| } | } |
| /** | /** |
| * Determine if the specified isobar crosses the vertical edge specified by its row and column | * 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 $aRow Row index of edge to be checked |
| * @param $aCol Col index of edge to be checked | * @param $aCol Col index of edge to be checked |
| * @param $aIsobar Isobar value | * @param $aIsobar Isobar value |
| * @return true if the isobar is crossing this edge | * @return true if the isobar is crossing this edge |
| */ | */ |
| function isobarVCrossing($aRow,$aCol,$aIsobar) { | function isobarVCrossing($aRow,$aCol,$aIsobar) { |
| if( $aRow >= $this->nbrRows-1) { | if( $aRow >= $this->nbrRows-1) { |
| JpGraphError::RaiseL(28005,$aRow); | JpGraphError::RaiseL(28005,$aRow); |
| //'isobarVCrossing: Row index too large | //'isobarVCrossing: Row index too large |
| } | } |
| if( $aCol >= $this->nbrCols ) { | if( $aCol >= $this->nbrCols ) { |
| JpGraphError::RaiseL(28006,$aCol); | JpGraphError::RaiseL(28006,$aCol); |
| //'isobarVCrossing: Col index too large | //'isobarVCrossing: Col index too large |
| } | } |
| $v1 = $this->dataPoints[$aRow][$aCol]; | $v1 = $this->dataPoints[$aRow][$aCol]; |
| $v2 = $this->dataPoints[$aRow+1][$aCol]; | $v2 = $this->dataPoints[$aRow+1][$aCol]; |
| return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ; | return ($aIsobar-$v1)*($aIsobar-$v2) < 0 ; |
| } | } |
| /** | /** |
| * Determine all edges, horizontal and vertical that the specified isobar crosses. The crossings | * Determine all edges, horizontal and vertical that the specified isobar crosses. The crossings |
| * are recorded in the two edge matrices. | * are recorded in the two edge matrices. |
| * | * |
| * @param $aIsobar The value of the isobar to be checked | * @param $aIsobar The value of the isobar to be checked |
| */ | */ |
| function determineIsobarEdgeCrossings($aIsobar) { | function determineIsobarEdgeCrossings($aIsobar) { |
| $ib = $this->isobarValues[$aIsobar]; | $ib = $this->isobarValues[$aIsobar]; |
| for ($i = 0; $i < $this->nbrRows-1; $i++) { | for ($i = 0; $i < $this->nbrRows-1; $i++) { |
| for ($j = 0; $j < $this->nbrCols-1; $j++) { | for ($j = 0; $j < $this->nbrCols-1; $j++) { |
| $this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($i,$j,$ib); | $this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($i,$j,$ib); |
| $this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$j,$ib); | $this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$j,$ib); |
| } | } |
| } | } |
| // We now have the bottom and rightmost edges unsearched | // We now have the bottom and rightmost edges unsearched |
| for ($i = 0; $i < $this->nbrRows-1; $i++) { | for ($i = 0; $i < $this->nbrRows-1; $i++) { |
| $this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$this->nbrCols-1,$ib); | $this->edges[VERT_EDGE][$i][$j] = $this->isobarVCrossing($i,$this->nbrCols-1,$ib); |
| } | } |
| for ($j = 0; $j < $this->nbrCols-1; $j++) { | for ($j = 0; $j < $this->nbrCols-1; $j++) { |
| $this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($this->nbrRows-1,$j,$ib); | $this->edges[HORIZ_EDGE][$i][$j] = $this->isobarHCrossing($this->nbrRows-1,$j,$ib); |
| } | } |
| } | } |
| /** | /** |
| * Return the normalized coordinates for the crossing of the specified edge with the specified | * 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 | * 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 | * on each side of the edge and the value of the isobar |
| * | * |
| * @param $aRow Row of edge | * @param $aRow Row of edge |
| * @param $aCol Column of edge | * @param $aCol Column of edge |
| * @param $aEdgeDir Determine if this is a horizontal or vertical edge | * @param $aEdgeDir Determine if this is a horizontal or vertical edge |
| * @param $ib The isobar value | * @param $ib The isobar value |
| * @return unknown_type | * @return unknown_type |
| */ | */ |
| function getCrossingCoord($aRow,$aCol,$aEdgeDir,$aIsobarVal) { | function getCrossingCoord($aRow,$aCol,$aEdgeDir,$aIsobarVal) { |
| // In order to avoid numerical problem when two vertices are very close | // In order to avoid numerical problem when two vertices are very close |
| // we have to check and avoid dividing by close to zero denumerator. | // we have to check and avoid dividing by close to zero denumerator. |
| if( $aEdgeDir == HORIZ_EDGE ) { | if( $aEdgeDir == HORIZ_EDGE ) { |
| $d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow][$aCol+1]); | $d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow][$aCol+1]); |
| if( $d > 0.001 ) { | if( $d > 0.001 ) { |
| $xcoord = $aCol + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d; | $xcoord = $aCol + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d; |
| } | } |
| else { | else { |
| $xcoord = $aCol; | $xcoord = $aCol; |
| } | } |
| $ycoord = $aRow; | $ycoord = $aRow; |
| } | } |
| else { | else { |
| $d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow+1][$aCol]); | $d = abs($this->dataPoints[$aRow][$aCol] - $this->dataPoints[$aRow+1][$aCol]); |
| if( $d > 0.001 ) { | if( $d > 0.001 ) { |
| $ycoord = $aRow + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d; | $ycoord = $aRow + abs($aIsobarVal - $this->dataPoints[$aRow][$aCol]) / $d; |
| } | } |
| else { | else { |
| $ycoord = $aRow; | $ycoord = $aRow; |
| } | } |
| $xcoord = $aCol; | $xcoord = $aCol; |
| } | } |
| if( $this->invert ) { | if( $this->invert ) { |
| $ycoord = $this->nbrRows-1 - $ycoord; | $ycoord = $this->nbrRows-1 - $ycoord; |
| } | } |
| return array($xcoord,$ycoord); | return array($xcoord,$ycoord); |
| } | } |
| /** | /** |
| * In order to avoid all kinds of unpleasent extra checks and complex boundary | * In order to avoid all kinds of unpleasent extra checks and complex boundary |
| * controls for the degenerated case where the contour levels exactly crosses | * 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. | * 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. | * This has no visible affect but it makes the code sooooo much cleaner. |
| * | * |
| */ | */ |
| function adjustDataPointValues() { | function adjustDataPointValues() { |
| $ni = count($this->isobarValues); | $ni = count($this->isobarValues); |
| for ($k = 0; $k < $ni; $k++) { | for ($k = 0; $k < $ni; $k++) { |
| $ib = $this->isobarValues[$k]; | $ib = $this->isobarValues[$k]; |
| for ($row = 0 ; $row < $this->nbrRows-1; ++$row) { | for ($row = 0 ; $row < $this->nbrRows-1; ++$row) { |
| for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) { | for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) { |
| if( abs($this->dataPoints[$row][$col] - $ib) < 0.0001 ) { | if( abs($this->dataPoints[$row][$col] - $ib) < 0.0001 ) { |
| $this->dataPoints[$row][$col] += $this->dataPoints[$row][$col]*0.001; | $this->dataPoints[$row][$col] += $this->dataPoints[$row][$col]*0.001; |
| } | } |
| } | } |
| } | } |
| } | } |
| } | } |
| /** | /** |
| * @param $aFlg | * @param $aFlg |
| * @param $aBW | * @param $aBW |
| * @return unknown_type | * @return unknown_type |
| */ | */ |
| function UseHighContrastColor($aFlg=true,$aBW=false) { | function UseHighContrastColor($aFlg=true,$aBW=false) { |
| $this->highcontrast = $aFlg; | $this->highcontrast = $aFlg; |
| $this->highcontrastbw = $aBW; | $this->highcontrastbw = $aBW; |
| } | } |
| /** | /** |
| * Calculate suitable colors for each defined isobar | * Calculate suitable colors for each defined isobar |
| * | * |
| */ | */ |
| function CalculateColors() { | function CalculateColors() { |
| if ( $this->highcontrast ) { | if ( $this->highcontrast ) { |
| if ( $this->highcontrastbw ) { | if ( $this->highcontrastbw ) { |
| for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { | for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { |
| $this->isobarColors[$ib] = 'black'; | $this->isobarColors[$ib] = 'black'; |
| } | } |
| } | } |
| else { | else { |
| // Use only blue/red scale | // Use only blue/red scale |
| $step = round(255/($this->nbrIsobars-1)); | $step = round(255/($this->nbrIsobars-1)); |
| for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { | for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { |
| $this->isobarColors[$ib] = array($ib*$step, 50, 255-$ib*$step); | $this->isobarColors[$ib] = array($ib*$step, 50, 255-$ib*$step); |
| } | } |
| } | } |
| } | } |
| else { | else { |
| $n = $this->nbrIsobars; | $n = $this->nbrIsobars; |
| $v = 0; $step = 1 / ($this->nbrIsobars-1); | $v = 0; $step = 1 / ($this->nbrIsobars-1); |
| for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { | for ($ib = 0; $ib < $this->nbrIsobars; $ib++) { |
| $this->isobarColors[$ib] = RGB::GetSpectrum($v); | $this->isobarColors[$ib] = RGB::GetSpectrum($v); |
| $v += $step; | $v += $step; |
| } | } |
| } | } |
| } | } |
| /** | /** |
| * This is where the main work is done. For each isobar the crossing of the edges are determined | * 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 | * 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 | * 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 | * the $isobarCoord will hold one arrayfor each isobar where all the line segments that makes |
| * up the contour plot are stored. | * up the contour plot are stored. |
| * | * |
| * @return array( $isobarCoord, $isobarValues, $isobarColors ) | * @return array( $isobarCoord, $isobarValues, $isobarColors ) |
| */ | */ |
| function getIsobars() { | function getIsobars() { |
| $this->adjustDataPointValues(); | $this->adjustDataPointValues(); |
| for ($isobar = 0; $isobar < $this->nbrIsobars; $isobar++) { | for ($isobar = 0; $isobar < $this->nbrIsobars; $isobar++) { |
| $ib = $this->isobarValues[$isobar]; | $ib = $this->isobarValues[$isobar]; |
| $this->resetEdgeMatrices(); | $this->resetEdgeMatrices(); |
| $this->determineIsobarEdgeCrossings($isobar); | $this->determineIsobarEdgeCrossings($isobar); |
| $this->isobarCoord[$isobar] = array(); | $this->isobarCoord[$isobar] = array(); |
| $ncoord = 0; | $ncoord = 0; |
| for ($row = 0 ; $row < $this->nbrRows-1; ++$row) { | for ($row = 0 ; $row < $this->nbrRows-1; ++$row) { |
| for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) { | for ($col = 0 ; $col < $this->nbrCols-1; ++$col ) { |
| // Find out how many crossings around the edges | // Find out how many crossings around the edges |
| $n = 0; | $n = 0; |
| if ( $this->edges[HORIZ_EDGE][$row][$col] ) $neigh[$n++] = array($row, $col, HORIZ_EDGE); | 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 ( $this->edges[HORIZ_EDGE][$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] ) $neigh[$n++] = array($row, $col, VERT_EDGE); |
| if ( $this->edges[VERT_EDGE][$row][$col+1] ) $neigh[$n++] = array($row, $col+1,VERT_EDGE); | if ( $this->edges[VERT_EDGE][$row][$col+1] ) $neigh[$n++] = array($row, $col+1,VERT_EDGE); |
| if ( $n == 2 ) { | if ( $n == 2 ) { |
| $n1=0; $n2=1; | $n1=0; $n2=1; |
| $this->isobarCoord[$isobar][$ncoord++] = array( | $this->isobarCoord[$isobar][$ncoord++] = array( |
| $this->getCrossingCoord($neigh[$n1][0],$neigh[$n1][1],$neigh[$n1][2],$ib), | $this->getCrossingCoord($neigh[$n1][0],$neigh[$n1][1],$neigh[$n1][2],$ib), |
| $this->getCrossingCoord($neigh[$n2][0],$neigh[$n2][1],$neigh[$n2][2],$ib) ); | $this->getCrossingCoord($neigh[$n2][0],$neigh[$n2][1],$neigh[$n2][2],$ib) ); |
| } | } |
| elseif ( $n == 4 ) { | elseif ( $n == 4 ) { |
| // We must determine how to connect the edges either northwest->southeast or | // We must determine how to connect the edges either northwest->southeast or |
| // northeast->southwest. We do that by calculating the imaginary m |