PHP GD convert coordinates from Polar to Cartesian - php

Question

I want to show percentages near or over each parts of the chart.
Do I have to convert coordinates from Polar to Cartesian?
To convert polar coordinates (r, θ) to rectangular coordinates (x, y) I used the following conversion:
x = r * cos( θ )
y = r * sin( θ )
in this graph
$x = $radius * cos( $Arc ); $y = $radius * sin( $Arc );
But results doesn't match (the percentages values aren't any close to each single parts of the chart), where I go wrong?
How can I fix it?
<?php
$W = 500; $H = 500;
$Image = imagecreate($W,$H);
$colors = array();
imagecolorallocate($Image,150,150,150); // grey background
$colors[0] = imagecolorallocate($Image,255,0,0); // red
$colors[1] = imagecolorallocate($Image,100,255,10); // green
$colors[2] = imagecolorallocate($Image,0,0,255); // bleu
$colors[3] = imagecolorallocate($Image,255,255,0); // yellow
$Country = array('England', 'Northern Ireland', 'Scotland', 'Wales');
$Population = array(53012456,1810863,5295403,3063456);
$TotPopulation = array_sum($Population);
$radius = 300; $StarAngle = 0;
foreach($Population as $index => $V )
{
$Arc = (360 * $V) / $TotPopulation;
$Percentage = (100 * $V) / $TotPopulation;
imagefilledarc(
$Image,
$W / 2, $H / 2, // center x,y
$radius,
$radius,
$StarAngle,
($StarAngle + $Arc), // end arc
$colors[$index],
IMG_ARC_PIE
);
$x = $radius * cos($Arc);
$y = $radius * sin($Arc);
imagestring($Image, 15, 5, 30 + $index*15 , 'x= '.number_format($x, 2, '.', '').' y='.number_format($y, 2, '.', '').' Country='.$Country[$index].' %='. number_format($Percentage, 2, '.', '').' ' , $colors[$index]);
$StarAngle += $Arc;
imagestring($Image, 15, 5, 430 + $index*15 , 'Country='.$Country[$index].' Population= $V %='.number_format($Percentage, 2, '.', '').' ' , $colors[$index]);
}
imagestring($Image, 5, 35, 10 , 'The population of the United Kingdom year 2011' , $colors[3]);
imagepng($Image);

Answer 1

You can try the library geo-math-php
composer require rkondratuk/geo-math-php:^1
Convert coordinates polar to cartesian:
<?php
use PhpGeoMath\Model\Polar3dPoint;
$polarPoint1 = new Polar3dPoint(
40.758742779050706, -73.97855507715238, Polar3dPoint::EARTH_RADIUS_IN_METERS
);
$cartesianpoint1 = $polarPoint1->buildCartesian3DPoint();
// Result:
$cartesianpoint1->x;
$cartesianpoint1->y;
$cartesianpoint1->z;
Convert coordinates cartesian to polar:
<?php
use PhpGeoMath\Model\Cartesian3dPoint;
$x = 1001;
$y = 205;
$z = 512;
$cartesianPoint2 = new Cartesian3dPoint($x, $y, $z);
$polarPoint2 = $cartesianPoint2->buildPolar3dPoint();
// Result:
$polarPoint2->lat;
$polarPoint2->lng;
$polarPoint2->radius;