----------------------------
             [ ]
----------------------------
        [           ]
----------------------------
    [         .          ]
----------------------------
       [             ]
----------------------------
            [   ]
----------------------------

##</code><code>##

    int(X/W), int(Y/W), Z

##</code><code>##

for my $xBand (  int(($X1-$R1-$M)/$W) .. int(($X1-$R1-$M)/$W)  ) {

##</code><code>##

  for my $yBand (  int(($Y1-$R1-$M)/W) .. int(($Y1-$R1-$M)/$W)  ) {

##</code><code>##

    my $start= BuildKey( $xBand, $yBand, $Z1-$R1-$M );
    my $end=   BuildKey( $xBand, $yBand, $Z1+$R1+$M );
    ... "select * from shapes where key between $start and $end"
    my $record;
    while(  $record= Fetch( ... )   ) {
        if(  Overlap( $record, ... )  ) {
            Report( ... );
            return 1;
        }
    }
  }
}
return 0;

##</code><code>##

my @bandWidth= ( 3, 15, 0 );

sub BuildKey {
    my( $radius, $x, $y, $z )= @_;
    my $sizeRange=
        $radius <= 2 ? 0
      : $radius <= 10 ? 1
      : 2;
    my $width= $bandWidth[$sizeRange];
    if(  0 == $width  ) {
        return ConcatForKey( $sizeRange, 0, 0, 0 );
    }
    return ConcatForKey(
        $sizeRange, int($x/$width), int($y/$width), $z );
}

##</code><code>##

    real        x
    real        y
    real        z
    real        radius
    int         size
    int         xBand
    int         yBand
    index       size,xBand,yBand,z

##</code><code>##

sub BuildKey {
    my( $radius, $x, $y, $z )= @_;
    my $sizeRange=
        $radius <= 2 ? 0
      : $radius <= 10 ? 1
      : 2;
    my $width= $bandWidth[$sizeRange];
    if(  0 == $width  ) {
        return pack "c", $sizeRange;
    }
    for my $c (  $x, $y, $z  ) {
        $c= int($c/$width);
        $c ^= 0x8000_0000;
    }
    return return pack "cNNN", $sizeRange, $x, $y, $z;
}