Using a bounding box is a good start, but a bounding circle should be even better. A circle only needs to test one dimention:

if( $circle->distance_from_center( $x, $y ) <= $circle->radius ) {
    # Point ($x, $y) is in circle
}
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I've also found that dropping some of the calculations into C can speed it up quite a bit without being terribly complex to interface back to Perl.