I didn't have much luck with the other two functions, one of them makes circles that look like they've been printed on a dot-matrix printer. This simple function builds a border out of circles, seems to work nicely.
<?php
function imagearcunfilled($image,$x,$y,$width,$height,$border_thickness, $color) {
imagesetthickness($image, 1);
$x_radius = $width / 2;
$y_radius = $height / 2;
for ($i = 0; $i < 360; $i++) {
if (TRUE) {
$x2 = $x + cos($i) * $x_radius;
$y2 = $y + sin($i) * $y_radius;
imagefilledarc($image,$x2,$y2,$border_thickness,$border_thickness,0,360,$color,IMG_ARC_PIE);
}
}
}
?>