This is just a bit of brainstorming, possibly showing my Tk mindset. I know you posed the question in terms of rigourous mathematical results, but I was thinking of using the Tk Canvas and it's overlapping tags method, to do somethink like this. Of course, you do need a Xserver going, but you also gain the benefit of being able to setup a realtime display of your point-queries. And of course, you have the problem of drawing all your states, counties and cities. 
#!/usr/bin/perl
use warnings;
use strict;
use Tk;

my $top = new MainWindow;

my $c=$top->Canvas->pack;

my $circle = $c->createOval(30,30,100,100,
               -fill => 'blue',  
               -tags =>['circle'],
               -stipple => 'gray12',
          );

my $rect1 = $c->createRectangle(10,10,44,44,
               -fill => 'green',  
               -stipple => 'gray12',
               -tags =>['rect1'],
              );


my $rect2 = $c->createRectangle(93,93,200,200,
               -fill => 'yellow',  
               -tags =>['rect2'],
               -stipple => 'gray12',
           );

my $poly1 = $c->createPolygon(0,0, 44,44, 55,55, 90,90, 200,200, 10,10
+0,0,0,
                    -fill => 'red',
            -smooth => 1,       
                    -splinesteps => 100,
            -stipple => 'gray12',
            -tags =>['poly1'],
            );

$c->Tk::bind("<Motion>", [ \&print_xy, Ev('x'), Ev('y') ]);

&print_xy($c, 42, 42);

MainLoop;

sub print_xy {
  my ($canv, $x, $y) = @_;
 print "(x,y) = ", $canv->canvasx($x), ", ", $canv->canvasy($y), "\n";
#my $x1 = $x+1;
#my $y1 = $y+1;
#it will actually use a zero size rectangle
my (@current) = $canv->find('overlapping', $x, $y, $x, $y);

foreach my $id(@current){ 
    print $canv->gettags($id),' ';
}

print "\n";

}

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I'm not really a human, but I play one on earth. Cogito ergo sum a bum

In reply to Re: Speeding up point-in-polygon by zentara
in thread Speeding up point-in-polygon by punkish

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