Small algorithm for calculating coordinates on a spiral

Coordinates.php

<?php
/*
 * Calculates the coordinates from an Id. The counting starts from 0,0 and then spirals out
 * like this:
 * 
 *     +--+--+--+-->
 *     | 
 *     +  +--+--+--+
 *     |  |        |
 *     +  +  +--+  +
 *     |  |     |  |
 *     +  +--+--+  +
 *     |           |
 *     +--+--+--+--+
 * 
 * Where id 24 would be 1,2 (x = 1, y = 2)
 * Where id 18 would be -2,-1 (x = -2, y = -1)
 *
 *     21--22--23--24--15
 *     |
 *     20  7---8---9---10
 *     |   |           |
 *     19  6   1---2   11
 *     |   |       |   |
 *     18  5---4---3   12
 *     |               |
 *     17--16--15--14--13
 * 
 * This is calculated by finding the square root of the id, using that to get
 * the closest odd whole (perfect) square roots above and below it, to get the 
 * start and end points of the ring of the spiral that it is on.
 * From there the side of the ring is calculated and the position along that side.
 */
function coordinates($id) {
    if ($id == 1) {
        $x = 0;
        $y = 0;
    }
    else {
        $idSqrt = sqrt($id); //find the square root of the id
        $lowSqrt = floor($idSqrt); //round the square root down
        $highSqrt = ceil($idSqrt); //round the square root up
        if ($lowSqrt == $highSqrt) { //if they are the same it's the last position
            $lowSqrt = $lowSqrt - 2; //to calculate previous odd square root
        }
        if ($lowSqrt % 2 == 0) { //if in the second half of the ring the low root is even, need to find the previous odd because centered rings are odd number sided squares
            $lowSqrt--;
        }
        if ($highSqrt % 2 == 0) { //same but for first half and high root
            $highSqrt++;
        }
        $previousRingEnd = pow($lowSqrt, 2); //square root rounded down and then squared finds the number at the end of the previous ring
        $ringEnd = pow($highSqrt, 2); //the same but for the end of the current ring
        $ringPosition = $id - $previousRingEnd; // (15-9 = 6) taking the previous ring from the id finds the position around the current ring
        $ringTotal = $ringEnd - $previousRingEnd; // (25-9 = 16) taking the previous ring from the current finds the total count around the current ring
        $sideLengthMinusOne = $ringTotal / 4; // 16/4 = 4
        $halfSideLengthMO = $sideLengthMinusOne / 2; // 4/2 = 2
        $side = $ringPosition/$ringTotal;
        /*
         * This calculates what side it's on
         * and it's position along that side.
         * Corner positions count as being the last on the side
         * hence the minus 1 on side length, because the first
         * corner of each side counted for the previous side.
         * Corners could be calculated from either side that they
         * are a part of.
         */
        switch (true) {
            case $side <= 0.25: // right hand side
                $x = $halfSideLengthMO;
                $y = $halfSideLengthMO - $ringPosition;
                break;
            case $side <= 0.5: // bottom
                $x = $halfSideLengthMO - ($ringPosition - $sideLengthMinusOne);
                $y = -$halfSideLengthMO;
                break;
            case $side <= 0.75: // left hand side
                $x = -$halfSideLengthMO;
                $y = -$halfSideLengthMO + ($ringPosition - ($sideLengthMinusOne*2));
                break;
            case $side > 0.75: // top
                $x = -$halfSideLengthMO + ($ringPosition - ($sideLengthMinusOne*3));
                $y = $halfSideLengthMO;
                break;
        }
    }
    return compact('x','y');
}