Destroy Them With Lazers
Perl, 301 296 282

Edit 2: Actually, competition or not, there is no reason not to golf it a little further. Test it online.

Edit: Couple of parentheses gone, simpler regex to check for non-zero integer. 

With newlines and indentation for readability:

sub i{&lt;&gt;=~/\S+/g}
@b=map[i],@r=0..&lt;&gt;-1;
print.1&lt;=&gt;(map{
    @a[1,0,2,4,3]=@a;
    @b=map{$i=$_;[map$b[$_][$i],@r]}@r;
    grep$a[3]
        &amp;&amp;($k=(($x=$_)-$a[0])/$a[3])**2&lt;=$k
        &amp;&amp;pop[sort map@{$b[$_]}[$x-!!$x,$x],
                   ($_=$a[1]+$k*$a[4]),$_-/^\d+$/]
           &gt;=$a[2]+$k*$a[5]
    ,@R=@r
}@a=map$_-shift@v,i,@u=@v=@$_),$/for([i])x&lt;&gt;


It requires 5.14 because of scalar (array reference) argument to pop.