Line of sight

The default line of sight radius in Crawl is about 8, reduced to 6 when wielding a lantern of shadows. (Actually, it is sqrt(65), so the field at (8,1) is in sight.)

The following drawing shows fields within the default field of view with their grid distance.

       888
    777777777
   66666666666
  6555555555556
 765444444444567
 765433333334567
 765432222234567
87654321112345678
87654321@12345678
87654321112345678
 765432222234567
 765433333334567
 765444444444567
  6555555555556
   66666666666
    777777777
       888

Cartesian distance, rounded up (one quadrant).

@12345678
123456789
23345678
34455678
45556789
5666788
677788
78889
89

Modified cartesian distance (field with value 'k' is within distance sqrt(k*k+1)).

@02345678
012345678
22345678
33455678
44556788
5566778
667788
77888
88

In 0.7, the developers made an undocumented change to the LOS. Ranges are circular now, so every spell and ability that reaches a set distance got about two squares lopped off the diagonals. Stealthy characters can now reach their target in 5 squares (instead of 8) at certain angles.